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tomekkorbak

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[ "BH 27-08-2012 – Open Wide for the Camera!", "\n\nTo start with Sasha seemed to be enjoying herself – stripped totally naked, clover clamped nipples, legs spread and suspended, and her hands tied too. ", "But her contentment didn’t last long, and soon she was asking to be let go. ", "Yeah right…Not! ", "We decided to up the ante by ballgagging her, and taping a vibrator to her beautiful pussy… Enjoy the views of this bondage sex kitten!!" ]

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[ "Tidally-locked planets – planets with one side perpetually facing their star while the other remains shrouded in darkness – tend to be warmer on one side than the other. ", "The presence of an atmosphere can help distribute the heat across the planet, equalizing the temperatures. ", "But tidal locking could result in wide climate variations, a result that could threaten the evolution of life on the surface of these planets.", "\n\nTidal locking depends on the planet’s mass and its distance from its star. ", "For planets orbiting M-stars, which are slightly smaller than our Sun, the region where planets become tidally locked overlaps with the habitable zone, where water can remain as a liquid on a planet’s surface.", "\n\nIn the solar system, the Moon is tidally locked in orbit around Earth.", "\n\nAccording to new research published in the December edition of the Astrophysical Journal, strong heating of a planet at a single point can change or even control how much weathering occurs on the planet, which can lead to significant and even unstable climate changes. ", "These dramatic climate effects could make planets that otherwise have the potential for life to instead be uninhabitable.", "\n\nWhatever the weather\n\nWhen rocks and minerals are exposed to the air, they react to the gases within it.", "\n\nAs the rocks erode, a fresh face comes into contact with the air, allowing even more gas to be converted. ", "If the erosion process keeps pace with the output of fresh gas into the atmosphere – say, from volcanic eruptions – the climate remains stable.", "\n\nOn tidally-locked planets, a single region is consistently close to the star. ", "Known as the substellar point, this region receives more direct sunlight, and thus more heat. ", "The recent paper proposes that such constant attention could affect weathering, and thus could influence the climate of the atmosphere.", "\n\nThe process, referred to as enhanced substellar weathering instability (ESWI), is based on the fact that the influx of heat would cause an increase of weathering at the substellar point.", "\n\nThe higher temperatures can also result in stronger rainfall, which go on to affect weathering.", "\n\n\"The harder it rains, the more it erodes,\" said principal investigator Edwin Kite, of the University of California at Berkeley.", "\n\nMore rain means an abundance of fresh rock to react with the atmosphere, removing more of its components.", "\n\nSimilarly, if the substellar point cools for any reason, the weathering process slows. ", "Less rock is available to chemically react, and the atmospheric gas builds up. ", "Volcanism could put more material into the atmosphere than the rocks can absorb — and since volcanoes on Earth release greenhouse gases like sulfur dioxide and carbon dioxide, presumably a runaway greenhouse effect could take flight, leading to additional heating.", "\n\nAll of this happens because the heat is focused on a single region that is constantly closest to its star.", "\n\n\"What controls the weathering rate of the planet is just that patch,\" Kite said.", "\n\nOn Earth, carbon dioxide from the air reacts with calcium silicate, creating calcium carbonate and silicone dioxide. ", "The process removes carbon dioxide from the air and controls the greenhouse effect.", "\n\n\"Weathering regulates the climate on Earth on long time scales, and makes sure it doesn’t get too hot or too cold,\" explained Dorian Abbot, of the University of Chicago. ", "Abbot studies climate dynamics on Earth and on extrasolar planets.", "\n\nThe same thing could happen on other planets, but if the conditions are right – or wrong – the results could be more detrimental.", "\n\n\"We sometimes see catastrophic exits from the habitable zone,\" Kite said.", "\n\nFor instance, a habitable planet could find itself moving to a Venus-like situation, with clouds of gas significantly increasing the surface temperature to points where water would boil off.", "\n\nOr it could simply boast wide swings over its lifetime, significant shifts from cold to hot and back again. ", "Such fluctuations could mean trouble for life trying to evolve on a planet.", "\n\n\"It has taken a very long time for life to develop complexity on Earth,\" Kite said.", "\n\nHe explained that a number of key steps were required to get life to the point as we know it today.", "\n\n\"It would require a long period of habitability on a planet to allow these different steps to take place,\" he said.", "\n\n\"It’s not enough just to rain on a planet for ten thousand years and expect interesting things to happen.\"", "\n\nAbbot agreed.", "\n\n\"Climate instabilities are not good for the life we usually think about.\"", "\n\nCatastrophic changes – rare or common?", "\n\nHow many planets could find their atmosphere destabilized by tidal locking?", "\n\nTo narrow that down, one must first look at how frequently tidally-locked planets might exist.", "\n\nFor M stars, \"We would expect that a lot of the planets in the habitable zone would be tidally locked,\" Abbot said.", "\n\nFor ESWI to occur, certain conditions must be met on these planets.", "\n\nThe substellar point, closest to the star, cannot be underwater. ", "Land is required for the strongly temperature-dependant weathering.", "\n\nSimilarly, the gas that is absorbed by weathering must be the prevalent gas in the atmosphere.", "\n\nKite notes that, even if Earth were moved to another star and became tidally locked, it would not be in danger. ", "Though weathering on Earth consumes carbon dioxide, nitrogen makes up most of the atmosphere.", "\n\nSuch results are not just limited to planets that can only reveal a single face to their star.", "\n\nAccording to Kite, \"All that’s really important to get this process going is a large day/night temperature contrast.\"", "\n\nAs an example, the team worked with Itay Halevy, of the Weizmann Institute of Science, to consider a Martian mystery. ", "Mars is not tidally locked but has wide temperature variations across a Martian day. ", "The red planet lost its atmosphere long ago, and scientists are still trying to determine exactly how that happened.", "\n\nKite thinks ESWI could be a potential contributor.", "\n\n\"It’s an open question whether enough weathering occurred over its geological history to draw down a significant amount of carbon dioxide,\" he said.", "\n\nBut he was clear that such conditions shouldn’t stop astronomers from studying planets that fall in the danger zone. ", "These bodies could still have the potential to be habitable.", "\n\n\"Ultimately, only observing can tell.\"" ]

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[ "Many biological tissues are renewed via small numbers of stem cells, which divide to produce a steady stream of differentiated cells and balance homeostatic cell loss. ", "Although novel experimental approaches in the past decade have produced key insights into the number, identity, and (often stochastic) dynamics of stem cells in multiple organs, an outstanding question remains as to whether stem cell potential is a cell-intrinsic, \"inherited\" property or, rather, an extrinsic, context-dependent state emerging from the collective dynamics of a tissue and cues from local \"niches,\" or microenvironments ([@r1][@r2][@r3][@r4][@r5][@r6][@r7]--[@r8]). ", "Although recent experiments have provided evidence for the latter in settings such as the growing mammary gland ([@r9]), adult interfollicular epidermis ([@r10], [@r11]), spermatogenesis ([@r12]), or the intestinal epithelium ([@r13]), a more global theoretical framework allowing one to quantitatively interpret these findings is still lacking.", "\n\nThe case of the intestinal crypt serves as a paradigmatic example of the dynamics of tissue renewal and is one of the fastest in mammals ([@r13]). ", "The intestinal crypt consists of a small invagination in the intestine where the epithelial cells populating the intestinal walls are constantly produced. ", "The very bottom of the crypt hosts a small number of proliferative, Lgr5+ stem cells ([@r14]) that divide and push the cells located above them to the transit amplification (TA) region, where cells lose self-renewal potential. ", "Cells are eventually shed in the villus a few days later, constituting a permanent \"conveyor-belt\" dynamics. ", "Lineage-tracing approaches, which irreversibly label a cell and its progeny ([@r3]), have been used to ask which cell type will give rise to lineages that renew the whole tissue and have revealed that all Lgr5+ cells can stochastically compete in an equipotent manner on the long-term ([@r15][@r16][@r17]--[@r18]), but still display positional-dependent short-term biases for survival ([@r13]). ", "Interestingly, similar conclusions have been reached in pubertal mammary gland development ([@r9]), where branching morphogenesis occurs through the proliferation of the cells in the terminal end buds of the ducts ([@r19]), the region where the mammary stem cells (MaSCs) reside ([@r9], [@r20]). ", "In both cases, intravital imaging revealed random cellular motions, enabling cells to move against the cellular flow/drift defined by the conveyor-belt dynamics. ", "Moreover, in the intestine, tissue damage, or genetic ablation of all Lgr5+ stem cells, caused Lgr5-- cells to recolonize the crypts and re-express Lgr5 to function as stem cells ([@r13]), arguing for extensive reversibility and flexibility in the system ([@r21]). ", "In addition, Lgr5-- and Lgr5+ cells of the fetal gut were also shown to nearly equally contribute to intestinal morphogenesis ([@r22]). ", "Altogether, this supports proposals that the definition of stem cell potential should evolve to emphasize, instead of molecular markers, the functional ability of cells to renew over the long-term ([@r23], [@r24]).", "\n\nHowever, this definition raises a number of outstanding conceptual problems: What, then, defines the number of functional stem cells in a tissue? ", "How can short-term biases be reconciled with long-term equipotency? ", "Is there a sharp distinction between stem and nonstem cells, or is there instead a continuum of stem cell potential together with flexible transitions between states? ", "Qualitatively, it is clear that fluctuations and positional exchanges are needed to prevent a single cell in the most favorable position to be the unique \"functional\" stem cell (defined as cells whose lineage colonizes a tissue compartment on the long-term). ", "Incorporating these features in a dynamical model of stem cell growth and replacement, able to make predictions, e.g., on the probability of lineage perpetuation, would represent an important step toward the understanding of how stem cells operate in the process of tissue growth and renewal.", "\n\nIn this paper, we develop a reaction--diffusion formalism for stem cell renewal in the presence of noise and local niches, taking into account local tissue geometry, as well as cell division and random cell movements ([Fig. ", "1 *A*--*C*](#fig01){ref-type=\"fig\"}). ", "Importantly, within this purely extrinsic and dynamical approach, which does not need to posit any intrinsic \"stem cell identity,\" a well-defined number of functional stem cells emerges, which only depends on the geometry and a balance between the noisiness of cell movements and division rates advecting cells away from niche regions. ", "This model also predicts that stem cell potential should decay continuously as a function of distance from the niche, with a \"universal\" Gaussian functional dependence. ", "We test this prediction against published live-imaging datasets for the homeostatic intestinal crypt ([@r13]) and during the branching of embryonic kidney explants ([@r25]) and find a good quantitative agreement for the full survival probability of cells, depending on their initial position relative to the niche. ", "Furthermore, we use our theoretical results to extract the amplitude of the random positional fluctuations in the developing mammary gland using static lineage-tracking experiments ([@r9]). ", "This enables us to predict the number of functional stem cells for this system, finding values consistent with previously reported estimates.", "\n\n{ref-type=\"disp-formula\"}. *", "F*, *Inset* shows the plot of best fit for the variance of the numerical distributions (black crosses) against the analytical model prediction $\\sim \\sqrt{k_{r}/k_{d}}$ (orange solid line).](pnas.1921205117fig01){#fig01}\n\nDynamics of Tissue Renewal and Development {#s1}\n==========================================\n\nTo develop the model, we first considered the simplest situation of a one-dimensional column of cells, with a rigid boundary condition at the base (mimicking, for instance, the bottom of the crypt), so that each cell division produces a pushing force upward transmitted to the cells above (or, in the case of growing mammary gland or kidney, driving ductal elongation). ", "This model is motivated by its simplicity, as it is able to qualitatively derive the essential traits of the complex dynamics studied here. ", "As we shall see, further refinements, aimed at making predictions for real systems, considered more realistic geometries. ", "From this simple dynamics, we defined the number of functional stem cells as the typical number of cells that have a nonnegligible probability to produce long-term progenies (without \"losing\" the competition against other cells). ", "If the dynamics was fully devoid of noise (a simple conveyor belt) and all cell divisions were symmetric, then one of the bottom-most cells would always win the competition. ", "In the case of a one-dimensional array of cells, this problem is trivial. ", "If one considers a cylindric geometry, there would be a single row of functional stem cells, which is the limiting case of the model described in ref. [", "@r16] of symmetric and stochastic one-dimensional, neutral competition along a ring of equipotent cells. ", "However, live-imaging studies show that, in multiple settings, including mammary gland ([@r9]), kidney morphogenesis ([@r25], [@r26]), and intestinal crypts ([@r13]), there is widespread rearrangement of cells through stochastic cell movements ([@r27]). ", "Intuitively, such rearrangements are expected to increase the number of \"functional\" stem cells, as rearrangements allow cells away from the niche to relocate to favorable positions, and would thus provide a biophysical mechanism for setting the number of stem cells assumed in models such as that developed in ref. [", "@r16].", "\n\nThe simplest abstraction of the system is a one-dimensional column of $N$ cells. ", "Each cell divides at constant rate $k_{d}$. In one dimension, we assumed a rigid boundary at the bottom so that cell proliferation generated a net flow of cells along the positive axis, i.e., advection away from the niche. ", "In addition, the position of the cells can fluctuate stochastically at rate $k_{r}$ (either via local cell--cell rearrangements, or more global movements of cells relative to the niche; [*SI Appendix*, sections S1A and S4](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)), allowing cells far away from the niche to reposition, despite the overall flow.", "\n\nAt $t = 0$, each cell is characterized by its starting position $n$ (distance from the niche) and will give rise in time to a lineage denoted $c_{n}$, which can span the entire tissue. ", "However, as soon as a cell reaches the position $N$, it disappears from the system, resulting after a sufficiently large time period in a single surviving lineage. ", "This competitive dynamics can be metaphorically understood as a conveyor belt with random fluctuations in the cell positions, sketched in [Fig. ", "1 *A*--*C*](#fig01){ref-type=\"fig\"}. ", "This is why we call it *stochastic conveyor belt* (SCB) dynamics and use it to model tissue renewal (e.g., intestinal crypt homeostasis) or organ growth (e.g., kidney and mammary gland morphogenesis). ", "The only difference between these two general cases is a change of reference frame ([*SI Appendix*, section S1 and Fig. ", "S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)). ", "In [Fig. ", "1*D*](#fig01){ref-type=\"fig\"}, we show an example of a typical run of the simulated SCB dynamics in one dimension, until monoclonality is achieved (see also [*SI Appendix*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental), [Movies S1--S3](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) and [section S5A](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details).", "\n\nTo make quantitative predictions from the dynamics outlined above, we start by following the prevalence of a single lineage. ", "Here, the action of the other lineages can be imposed as an average drift force that depends on the position of each cell of the lineage we follow. ", "The equation accounting for the time evolution of the prevalence of lineage $c_{n}$, to be referred to as $\\rho_{n}\\left( {z,t} \\right)$, in the continuum limit is:$$\\frac{\\partial\\rho_{n}}{\\partial t} = - k_{d}\\frac{\\partial}{\\partial z}\\left( {z\\rho_{n}} \\right) + \\frac{k_{r}}{2}\\frac{\\partial^{2}\\rho_{n}}{\\partial z^{2}} + k_{d}\\rho_{n}.$$We refer to this reaction--diffusion equation ([@r28], [@r29]) as the SCB equations (see [*SI Appendix*, section S1B](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details). ", "The first term on the right-hand side is a drift term, accounting for the average push-up movement at position $z$ due to random cellular proliferation at rate $k_{d}$ at lower levels, $\\sim k_{d}z$. The second term is a diffusive term ([@r30], [@r31]), accounting for the random reallocations of cells, occurring at rate $k_{r}$. The third term is a proliferative term, accounting for the exponential proliferation of each cell of the lineage under study, at rate $k_{d}$.\n\nConsidering initial conditions $t_{0} = 0$, $\\rho_{n}\\left( {z,0} \\right)$, a Gaussian centered on $n$ with $\\sigma^{2} = 1/2$ (a density representing a single cell at position $n$), and natural boundary conditions, the solution of [Eq. **", "1**](#eq1){ref-type=\"disp-formula\"} can be approximated by (see [*SI Appendix*, section S1B](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details):$$\\rho_{n}\\left( {z,t} \\right) \\approx \\sqrt{\\frac{k_{d}}{2\\pi k_{r}}}\\exp\\left\\{ {- \\frac{k_{d}}{2k_{r}}\\left( \\frac{z - ne^{k_{d}t}}{e^{k_{d}t}} \\right)^{2}} \\right\\}.$$Next, we sought to relate this lineage prevalence to the experimentally relevant quantity of long-term lineage survival; in other words, how likely is it for a cell starting at a given position $n$ to take over the entire crypt? ", "Although lineage fixation is a concept that only makes sense in the discrete description, we observed that lineage prevalence converges asymptotically toward a simple scaling form $\\rho_{n}\\left( \\infty \\right)$:$$\\rho_{n}\\left( \\infty \\right) \\equiv \\lim\\limits_{t\\rightarrow\\infty}\\rho_{n}\\left( {z,t} \\right),$$which is a constant that does not depend on position $z$ or time $t$, but only on the starting position of the lineage. ", "This argues that, on the long-term, lineages starting at different positions $n$ and $n\\prime$ have well-defined relative prevalence, leading to the natural assumption that the long-term lineage-survival probability of lineage $c_{n}$ is proportional to this asymptotic lineage prevalence. ", "This means that the probability of lineage survival, $p\\left( c_{n} \\right)$, can be expressed as:$$p\\left( c_{n} \\right) \\approx \\frac{\\rho_{n}\\left( \\infty \\right)}{\\sum_{j}\\rho_{j}\\left( \\infty \\right)} \\propto \\exp\\left\\{ {- \\frac{k_{d}}{2k_{r}}n^{2}} \\right\\}.$$The above equation, which is a central result of the study, defines the probability that a cell starting at position $n$ will \"win the competition\" and colonize the whole one-dimensional system (see [*SI Appendix*, section S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details).", "\n\nDespite the approximations outlined above, stochastic numerical simulations of the model system show excellent agreement with [Eq. **", "4**](#eq4){ref-type=\"disp-formula\"} ([Fig. ", "1 *E* and *F*](#fig01){ref-type=\"fig\"}). ", "We also note that, although we have assumed here that positional rearrangements occur between two cells, more complex sources of positional noise $k_{r}$ can be considered (which can be mechanistically dependent or independent on $k_{d}$) and lead to the same qualitative results. ", "These include, for instance, postmitotic dispersal, as seen during the branching morphogenesis of the kidney uteric bud ([@r26]) and where daughter cells can travel long distances outside the epithelium postdivision, or correlated \"tectonic\" movements of the epithelium, where cells could collectively reposition relative to the niche, as proposed during mammary or gut morphogenesis ([@r9], [@r22]) (see [*SI Appendix*, section S4](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details).", "\n\nFunctional Stem Cell Numbers and Dynamics in the SCB {#s2}\n====================================================\n\nThe prediction for the probability of long-term lineage survival under the SCB dynamics is surprisingly simple, decaying as a Gaussian distribution as a function of position away the niche, with a length scale that is simply the amplitude of the stochastic fluctuations divided by the proliferation rate, $\\sim \\sqrt{k_{r}/k_{d}}$ ([Eq. **", "4**](#eq4){ref-type=\"disp-formula\"}). ", "Intuitively, cells close to the origin have the highest chance to win and survive, whereas this probability drops abruptly for cells starting the competition further away, i.e., around $N_{s}$ cell diameters away from the base, with:$$N_{s}^{1D} = 1 + \\sqrt{\\frac{k_{r}}{k_{d}}}.$$Note that the first term satisfies the boundary condition that, in the case $k_{r} = 0$, the system has a single functional stem cell (located at the base) in one dimension. [", "Eq. **", "5**](#eq5){ref-type=\"disp-formula\"} thus implies that multiple rows of cells possess long-term self-renewal potential (as assessed, for example, in a lineage-tracing assay), emerging through their collective dynamics, and with a number that depends only on the ratio of the division to rearrangement rates (respectively \\[resp.\\], $k_{d}$ and $k_{r}$). ", "Although [Eq. **", "5**](#eq5){ref-type=\"disp-formula\"} is the outcome of a one-dimensional approximation, we show that it holds and can be generalized in more complex geometries ([*SI Appendix*, section S3](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)). ", "In particular, in a cylindrical two-dimensional geometry, we show that the functional stem cell number would simply be the same number $N_{s}^{1D}$ of cell rows (arising from the SCB dynamics) multiplied by the number of cells per row (fixed by the geometry of the tissue). ", "Moreover, the above result can be generalized, giving an estimate of $N_{s}$ for general geometries (see [*SI Appendix*, Eq. **", "26**](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental), where we give the general expression for $N_{s}$ in arbitrary organ geometries). ", "This general result will be at the basis of the forthcoming sections, when dealing to more realistic geometries to explore the dynamics of the organs under study. ", "Importantly, our framework generalizes the work of ref. [", "@r16], as we do not fix the stem cell number $N_{s}$ explicitly, which, rather, emerges from an interplay between geometry and SCB dynamics, together with the competitive dynamics being qualitatively different in the flow direction ([*SI Appendix*, section S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)).", "\n\nWe now turn to experimental data to test whether the proposed dynamics can help predict the number of functional stem cells in several organs, as well as the evolution of the survival probability with the starting position of a clone. ", "Although the division rate $k_{d}$ is well known in most systems considered, the stochastic movement rate $k_{r}$ is harder to estimate and can potentially vary widely, from rather small in intestinal crypts ([@r13]) to large in mammary and kidney tips, with extensive clonal fragmentation and random cell movements ([@r9], [@r25]).", "\n\nPredictions on Clonal Dynamics and Survival. {#", "s3}\n--------------------------------------------\n\nIntravital live imaging provides an ideal platform to test the model, as it provides both knowledge of the starting position of a given cell, as well as its clonal time evolution (whereas classical lineage tracing relies on clonal ensembles obtained from fixed samples). ", "In small intestinal crypts, different Lgr5+ cells have been predicted to have very different lineage-survival potential on the short-term, depending on their position within the stem cell niche, resulting in an effective number of stem cells smaller than the number of Lgr5+ cells ([@r13], [@r32]). ", "We thus reanalyzed quantitatively this dataset by plotting the survival probability of a clone as a function of its starting position $n$ ([Fig. ", "2](#fig02){ref-type=\"fig\"}) after a given time period assumed to be large enough for [Eq. **", "4**](#eq4){ref-type=\"disp-formula\"} to hold. ", "We then compared this to a two-dimensional stochastic simulation of the model (see [*SI Appendix*, section 5](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details). ", "Importantly, we found a good qualitative and quantitative agreement between model and data, with the survival probability decaying smoothly with the starting position ([Fig. ", "2*B*](#fig02){ref-type=\"fig\"}). ", "The only parameter here was $k_{r}/k_{d} \\approx 1$, which fits well with short-term live-imaging experiments and the idea of cell division promoting rearrangements ([@r13]).", "\n\n![(*", "A*) Schema of the self-renewal of the crypt epithelia, showing the origin of the coordinate system at the bottom of the system. (*", "B*) The probability (prob) that a given lineage remains within the system as a function of the starting position after a time lapse against the predictions of the conveyor belt dynamics for the crypt. ", "Data corresponding to the probability that a lineage remains in the system for the small intestinal crypt, reported in Ritsma et al. ([", "@r13]), depending on its starting position. ", "The orange line represents the prediction of the SCB dynamics, fitting well the data for $k_{r}/k_{d} \\approx 1$. Shaded areas represent the CI (one SD) of the prediction.](pnas.1921205117fig02){#fig02}\n\nTo back these simulations with an analytical prediction on stem cell numbers, the details of tissue geometry must be taken into account (with the number of cells per row $i$ needing to be estimated and the number of rows participating in the competition arising as an emergent property from the one-dimensional model). ", "A good approximation is based on that fact that the crypt can be abstracted as a hemispherical monolayer with radius $R$ (measured in units of cell diameter) coupled to a cylindrical region (see [*SI Appendix*, Figs. ", "S1, S3, and S4 and section S3](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details), so that one can get the number of stem cells, $N_{s}^{2D}$, as:$$N_{s}^{2D} \\approx 2\\pi R^{2}\\left\\lbrack {1 - \\cos\\left\\{ {\\frac{1}{R}\\left( {1 + \\sqrt{\\frac{\\pi}{2}\\frac{k_{r}}{k_{d}}}} \\right)} \\right\\}} \\right\\rbrack.$$With $k_{r}/k_{d} \\approx 1$ as above, and estimating $R \\approx 2$ for the radius, our simple theory then predicts that the number of functional stem cells should be $N^{2D} \\approx 11$, which agrees well with measurements of ref. [", "@r13], as well as inferred numbers from continuous clonal labeling experiments ([@r32]). ", "This is expected, as our model reduces to the one-dimensional ring model of ref. [", "@r16] for low $k_{r}/k_{d}$.\n\nWe then sought to test the model further using a published dataset on embryonic kidney branching in explants ([@r25]). ", "This has been recently noted to be a highly stochastic process, with neighboring cells at the start of the tracing ending up either surviving long-term in tips or being expelled to ducts. ", "Moreover, ref. [", "@r25] observed extensive random cell intercalations, in addition to the described mitotic dispersal ([@r26]), where cells extrude from the epithelium postdivision and reinsert at a distance of $d_{c}$ cell diameters away. ", "Importantly, these processes can still be captured as an effective diffusion coefficient $k_{r}$ in our framework (see [*SI Appendix*, section S4](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details). ", "Specifically, knowing that the fluctuations may occur at each duplication, and that they imply a displacement up to $d_{c} \\approx 2 - 4$ cell lengths, we can estimate that $k_{r}/k_{d} \\approx d_{c}^{2}\\quad$ at the minimum (i.e., discounting other fluctuations). ", "Note that the conveyor-belt dynamics applies exactly for tip elongation as in crypt: The only difference is that the reference frame from which the dynamics is observed changes (see [*SI Appendix*, section S1 and Fig. ", "S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details).", "\n\nThe above observation argues again that noise will play a key role in kidney-tip cell dynamics. ", "Strikingly, extracting from ref. [", "@r25] the probability of survival as a function of distance from the edge of a tip, we found that the two-dimensional simulations of our model provided again an excellent prediction for the full probability distribution ([Fig. ", "3](#fig03){ref-type=\"fig\"}), with cells much further away (compared to the intestinal crypt) having a nonnegligible probability to go back and contribute. ", "Again, the only fit parameter was the ratio $k_{r}/k_{d} = 16$, which agrees well with our estimate of the noise arising from mitotic dispersal. ", "Taking into account the full two-dimensional geometry as above, and estimating in this case a tip radius of $R = 3 - 5$ cells, this predicts $N_{s} \\approx 90 \\pm 10$, which could be tested in clonal lineage-tracing experiments.", "\n\n![(*", "A*) Schema of the kidney tip during development. ", "The conveyor-belt dynamics holds; the only difference is the reference frame: Whereas in the stem cell replacement model of the intestinal crypt, the reference frame is the bottom of the gland, in the kidney and mammary gland, the reference frame is taken from the newly created ducts. (*", "B*) The probability (prob) that a given clonal remains within the system as a function of the starting position of the mother cell after a given time against the predictions of the conveyor-belt model dynamics. ", "Black circles represent real data points, obtained by counting the amount of cells of a given lineage remaining in the system \\[from Riccio et al. ([", "@r25])\\]. ", "We observe that the distribution is much broader, fitting well to the theory for a ratio $k_{r}/k_{d} \\approx 16$ in kidney, over an order of magnitude larger than in intestinal crypt. ", "The shaded area represents the CI (one SD) of the prediction.](pnas.1921205117fig03){#fig03}\n\nThese two examples show that the same model of SCB dynamics and its prediction of the master curve for the survival probability of clones can be used in different organs to understand their stem cell dynamics and that ratios of relocation to advection $k_{r}/k_{d}$ can be widely different, even in systems with similar division rates $k_{d}$.\n\nNumber of Functional Stem Cells in the Developing Mammary Gland. {#", "s4}\n----------------------------------------------------------------\n\nNext, we sought to test the suitability of the SCB dynamics to model stem cell dynamics of mammary gland morphogenesis, where extensive cell movements have been reported within tips via intravital live imaging ([@r9]), with rapid rearrangements occurring on time scales of a few hours ([Fig. ", "4](#fig04){ref-type=\"fig\"} and [*SI Appendix*, Fig. ", "S6*A*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)). ", "In this case, however, tips cannot be followed for long enough for survival probabilities to be directly measured as in [Figs. ", "2](#fig02){ref-type=\"fig\"} and [3](#fig03){ref-type=\"fig\"} for intestine and kidney, respectively. ", "However, extensive clonal dispersion has been observed in quantitative clonal lineage-tracing experiments during pubertal growth ([@r9], [@r33]), and we therefore sought to infer the value of noise from these experiments ([*SI Appendix*, Fig. ", "S6*B*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)).", "\n\n for details), showing a good fit from $k_{r}/k_{d} \\approx 3$ for both time points. ", "Error bars represent mean and SD. ", "Scale bars represent 100 $\\mu$m (*B*) and 10 $\\mu$m (*C*). ", "Min, minimum.](pnas.1921205117fig04){#fig04}\n\nTurning back to published lineage-tracing datasets, where single MaSCs are labeled at the beginning of puberty (3 wk of age) and traced until either 5 or 8 wk of age, clones in tips displayed extensive fragmentation, which is expected to be directly related to the ratio $k_{r}/k_{d}$ ([Fig. ", "4 *C* and *D*](#fig04){ref-type=\"fig\"} and [*SI Appendix*, Fig. ", "S6 *B*--*D*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)). ", "We thus ran as above two-dimensional simulations of our SCB dynamics (see [*SI Appendix*, section S5](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details), using measured values of the tip width and length to set the geometry. ", "As a metric for clonal dispersion, we then computationally measured for each labeled cell the distance to its closest clonal neighbor: For a fully cohesive clone, all cells should be touching, and the distance to the closest neighbor should be always one cell diameter. ", "Increasing the value of $k_{r}/k_{d}$ robustly increased the closest neighbor distance. ", "We then performed the same measurements in the experimental dataset, both for the 5- and 8-wk time points ([Fig. ", "4 *C* and *D*](#fig04){ref-type=\"fig\"}) and also for luminal and basal cell types separately, given the dominant unipotency of these cell populations in pubertal development ([@r9], [@r33][@r34]--[@r35]). ", "We found highly consistent results in all four cases (average closest distance of around 1.85 cell diameter), which allowed us to infer a ratio of (see [*SI Appendix*, section S5 and Fig. ", "S6](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details):$$k_{r}/k_{d} \\approx 2 - 5,$$in mammary gland, emphasizing the importance of considering stochasticity in the conveyor-belt picture. ", "Indeed, we found that, with this fitting parameter, the model reproduced well the probability distribution of closest distances, both at the 5- and 8-wk time points ([Fig. ", "4 *C* and *D*](#fig04){ref-type=\"fig\"}).", "\n\nIn addition to this value, we must again pay attention to the geometry of the mammary tip, with basal cells forming a two-dimensional monolayer (similar to the previous cases), while luminal cells form multiple layers in three dimensions within the tip. ", "Assuming that the intercalation between cells occurs mainly at the same layer, the system of luminal cells in the tip of the mammary gland can be abstracted as $R - 1$ successive hemispherical two-dimensional layers. ", "Let us emphasize the dependence of $N^{2D}$, as defined by [Eq. **", "6**](#eq6){ref-type=\"disp-formula\"}, on $R$, writing $N_{s}^{2D} \\equiv N_{s}^{2D}\\left( R \\right)$. In that case, the amount of luminal stem cells can be inferred as:$$N_{s}^{3D} = \\sum\\limits_{R\\prime < R}N_{s}^{2D}\\left( {R\\prime} \\right).$$Taking the fitted range of $k_{r}/k_{d} \\in \\left( 2,5 \\right)$, together with an estimation of the radius of $R = 5 \\pm 2$, [Eq. **", "8**](#eq8){ref-type=\"disp-formula\"} then predicts that a number of luminal stem cells per tip of $N_{s}^{3D} = 170 \\pm 110$, in good quantitative agreement with experimental estimates from lineage tracing of $N_{s}^{\\exp} = 172 \\pm 102$ (mean $\\pm$ SD) ([@r9]). ", "For basal cells, using the same parameters for a two-dimensional monolayer, [Eq. **", "6**](#eq6){ref-type=\"disp-formula\"} predicts that $N_{s}^{2D} = 37 \\pm 11$, against empirical observations reporting an amount of basal stem cells of at least 15 ([@r33]), and $N_{s}^{\\exp} = 93 \\pm 76$ (mean $\\pm$ SD) ([@r9]). ", "Although the prediction thus falls in the correct range, the underestimation of basal stem cell number may be due to the highly anisotropic geometry of basal stem cells.", "\n\nDiscussion {#s5}\n==========\n\nThe main objective of this study was to provide insights to the question of whether stem cell function is a cell-intrinsic, inherited property, or rather an extrinsic, context-dependent notion emerging from the collective dynamics of a tissue ([@r2], [@r3], [@r7], [@r8]). ", "To that end, we took a complementary standpoint to the one based on the classification of molecular markers and their potential functional role, adopting a purely dynamical/geometrical descriptions of niches. ", "Combining the two would be a logical extension for future work. ", "We analyzed stem cell lineage survival as a purely dynamical process of competition for finite niche space, taking into account the presence of stochastic cell rearrangements, cell proliferation, and tissue geometry. ", "This gives rise to a complex reaction--diffusion process that can be abstracted as an SCB. ", "We show that survival probability as a function of starting position away from the most favorable position adopts a simple universal Gaussian shape, so that a well-defined number of functional stem cells (i.e., cells which have a nonnegligible probability of surviving long-term) arises in the theory, set by tissue geometry and the ratio between random reallocation and cell proliferation rates, $k_{r}/k_{d}$. We applied this theory to recent live-imaging data tracing stem cell survival as a function of position in the homeostatic intestinal crypt and kidney morphogenesis and found good quantitative agreement. ", "We also used the model to infer values of $k_{r}/k_{d}$ from fixed lineage-tracing experiments in mammary-gland morphogenesis and showed that this inference allows us to predict the typical number of stem cells in this system. ", "Interestingly, the ratio of noise to advection $k_{r}/k_{d}$ appeared to be an order of magnitude larger in kidney development as compared to the intestinal crypt (with the mammary gland being intermediate), which explained well the widely different number of functional stem cells observed in each.", "\n\nAlthough we have sketched here the simplest source of noise in cellular movements (random exchange of position in cell neighbors), our results are highly robust to different types of microscopic mechanisms and should thus be seen as representative of a general class of models for stem cell dynamics with advection and noise. ", "In mammary-gland and kidney morphogenesis, direct cell--cell rearrangements are observed ([@r9], [@r25]), while kidney also displays mitotic dispersal ([@r26]), where noise arises from the randomness of cell reinsertion in the layer after division. ", "Furthermore, on short time scales, directed cellular movements have been observed in kidney-tip morphogenesis, with Ret and Etv4 mutant clones being statistically overtaken by wild-type cells, leading to the proposal that Ret/Etv4 were involved in directional movement toward tips ([@r25]). ", "However, tips maintain heterogeneity in Ret expression through branching, arguing that cells must shuttle between high-Ret and low-Ret states ([@r25]), which would effectively contribute to movement stochasticity on long time scales. ", "Finally, \"tectonic\" movements, which collectively reposition cells toward/away from niches, can also be captured in the model ([*SI Appendix*, Fig. ", "S5](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental)). ", "These are particularly relevant in developmental settings, such as gut morphogenesis, where the global shape of the epithelium changes, displacing collectively cells from villus to crypt regions ([@r22]), or upon tip-splitting during branching morphogenesis ([@r9]). ", "Active migration, as observed in adult intestinal homeostasis ([@r36]), could also contribute to such collective random repositioning events. ", "In the future, it would be interesting to further understand quantitatively random cell rearrangements $k_{r}$ and how they could be modulated by parameters such as tissue density, aspect ratio, active cell migration, or division rates (see [*SI Appendix*, section S3C](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental) for details). ", "Mechanical models of cell motility upon rheological transitions ([@r37][@r38]--[@r39]) or of rearrangements and junctional remodeling upon cell divisions ([@r40], [@r41]) in densely packed tissues could also help to understand quantitatively what sets $k_{r}$ in each system.", "\n\nThe proposed framework can, in principle, be applied to any tissue dynamics in which niche signals and/or cellular proliferation is localized, leading to directional flows ([@r42], [@r43]). ", "On the other hand, substantial extension of the model would be necessary in the context of an \"open niche,\" such as spermatogenesis ([@r44]) or skin homeostasis ([@r11]), where renewing cells form a two-dimensional layer of neutrally competing progenitors, thus with little in-plane cellular flows. ", "Finally, the theory could be extended to cases of nonneutral growth. ", "Live imaging of skin-tumor growth, for instance, is consistent with very low values of $k_{r}/k_{d}$ ([@r45]), as little to no clonal dispersion is observed, which would tend to favor deterministic growth in our model. ", "Nevertheless, this does not occur, as tumor cells trigger higher proliferation rates of normal cells ([@r45]), resulting in complex geometrical changes and encapsulation of the malignant clone. ", "Incorporating these types of complex signaling and geometric feedbacks between multiple cell populations ([@r46][@r47]--[@r48]) in our model would thus have particular relevance to understand the dynamics of tumor initiation ([@r49], [@r50]). ", "Our approach must be taken as part of a more general enterprise, namely, understanding the role of both intrinsic cues and complex collective dynamics in defining the functional stem cells.", "\n\nMaterials and Methods {#s6}\n=====================\n\nAdditional information on the theoretical, computational, and experimental methods used can be found in [*SI Appendix*, *SI Materials and Methods*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental). ", "In brief, all mice for mammary-gland experiments were females from a mixed background, housed under standard laboratory conditions. ", "All experiments were performed in accordance with the Animal Welfare Committee (Instantie voor Dierenwelzijn) of the Royal Netherlands Academy of Arts and Sciences (Hubrecht Institute). ", "Clonal dispersion in the developing mammary tips was measured in whole-mount glands from R26-CreERT2;R26-Confetti mice, traced from 3 wk of age and killed at midpuberty (5 wk) or at the end of puberty (8 wk). ", "The length and the width of the tips were measured, and the coordinates of each labeled confetti cell in the tip were determined, to calculate the distance between each cell and their closest neighbor. ", "Raw data used to generate [Fig. ", "4](#fig04){ref-type=\"fig\"} can be found in [*SI Appendix*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental), [Dataset S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental).", "\n\nSupplementary Material\n======================\n\nWe thank all members of the E.H., B.D.S., and J.v.", "R. groups for stimulating discussions. ", "This project was supported by the European Research Council (648804 to J.v.", "R. and 851288 to E.H.). ", "It has also received support from the CancerGenomics.nl (Netherlands Organization for Scientific Research) program (J.v.", "R.) and the Doctor Josef Steiner Foundation (J.v.", "R). ", "B.D.S. was supported by Royal Society E. P. Abraham Research Professorship RP/R1/180165 and Wellcome Trust Grant 098357/Z/12/Z.\n\nThe authors declare no competing interest.", "\n\nThis article is a PNAS Direct Submission.", "\n\nThis article contains supporting information online at <https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1921205117/-/DCSupplemental>.", "\n\n[^1]: Edited by Elaine Fuchs, Rockefeller University, New York, NY, and approved June 1, 2020 (received for review December 10, 2019)\n\n[^2]: Author contributions: B.C.-M., B.D.S., J.v.", "R., and E.H. designed research; B.C.-M., C.L.G.J.S., K.K., S.I.J.E., and E.H. performed research; C.L.G.J.S., S.I.J.E., and J.v.", "R. contributed new reagents/analytic tools; B.C.-M. and C.L.G.J.S. analyzed data; and B.C.-M. and E.H. wrote the paper.", "\n\n[^3]: ^1^B.C.-M. and C.L.G.J.S. contributed equally to this work.", "\n" ]

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[ "RATIONALE: Controlled mechanical ventilation is used to deliver lung-protective ventilation in patients with acute respiratory distress syndrome. ", "Despite recognized benefits, such as preserved diaphragm activity, partial support ventilation modes may be incompatible with lung-protective ventilation due to high Vt and high transpulmonary pressure. ", "As an alternative to high-dose sedatives and controlled mechanical ventilation, pharmacologically induced neuromechanical uncoupling of the diaphragm should facilitate lung-protective ventilation under partial support modes.", "\n\nMETHODS: In a proof-of-concept study, we enrolled 10 patients with lung injury and a Vt greater than 8 ml/kg under pressure support ventilation (PSV) and under sedation. ", "After baseline measurements, rocuronium administration was titrated to a target Vt of 6 ml/kg during neurally adjusted ventilatory assist (NAVA). ", "Thereafter, patients were ventilated in PSV and NAVA under continuous rocuronium infusion for 2 hours. ", "Respiratory parameters, hemodynamic parameters, and blood gas values were measured.", "\n\nRATIONALE: Respiratory syncytial virus (RSV) is the leading cause of acute lower respiratory tract infections and hospitalizations in infants worldwide. ", "Known risk factors, however, incompletely explain the variability of RSV disease severity, especially among healthy children. ", "We postulate that the severity of RSV infection is influenced by modulation of the host immune response by the local bacterial ecosystem.", "\n\nOBJECTIVES: To assess whether specific nasopharyngeal microbiota (clusters) are associated with distinct host transcriptome profiles and disease severity in children less than 2 years of age with RSV infection.", "\n\nMETHODS: We characterized the nasopharyngeal microbiota profiles of young children with mild and severe RSV disease and healthy children by 16S-rRNA sequencing. ", "In parallel, using multivariable models, we analyzed whole-blood transcriptome profiles to study the relationship between microbial community composition, the RSV-induced host transcriptional response, and clinical disease severity.", "\n\nMEASUREMENTS AND MAIN RESULTS: We identified five nasopharyngeal microbiota clusters characterized by enrichment of either Haemophilus influenzae, Streptococcus, Corynebacterium, Moraxella, or Staphylococcus aureus. ", "RSV infection and RSV hospitalization were positively associated with H. influenzae and Streptococcus and negatively associated with S. aureus abundance, independent of age. ", "Children with RSV showed overexpression of IFN-related genes, independent of the microbiota cluster. ", "In addition, transcriptome profiles of children with RSV infection and H. influenzae- and Streptococcus-dominated microbiota were characterized by greater overexpression of genes linked to Toll-like receptor and by neutrophil and macrophage activation and signaling.", "\n\nRATIONALE: Vitamin D and its metabolites have potent immunomodulatory effects in vitro, including up-regulation of cathelicidin, a critical antimicrobial protein.", "\n\nOBJECTIVES: We investigated whether administration of 1,25-dihydroxyvitamin D (calcitriol) to critically ill patients with sepsis would have beneficial effects on markers of innate immunity, inflammation, and kidney injury.", "\n\nCONCLUSIONS: Calcitriol administration did not increase plasma cathelicidin protein levels in critically ill patients with sepsis and had mixed effects on other immunomodulatory markers. ", "Additional phase II trials investigating the dose and timing of calcitriol as a therapeutic agent in specific sepsis phenotypes may be warranted. ", "Clinical trial registered with clinicaltrials.gov (NCT 01689441)." ]

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[ "I'll check into it for you, thanks for the heads up....." ]

[ 0 ]

[ "Polycarbonates are well known, commercially important materials which are produced in large quantities. ", "Such polymers are typically prepared by reacting a carbonate precursor with a dihydric phenol to provide a linear polymer consisting of units of the dihydric phenol linked to one another through carbonate linkages. ", "These polymers have outstanding mechanical, thermal, and optical properties such as high tensile strength, optical clarity (transparency), thermal and dimensional stability and impact strength.", "\nThese aromatic polycarbonates differ from most thermoplastic polymers in their melt rheology behavior. ", "Most thermoplastic polymers exhibit non-Newtonian flow characteristics over essentially all melt processing conditions. ", "Newtonian flow is defined as the type of flow occurring in a liquid system where the rate of shear is directly proportional to the shearing force. ", "However, in contrast to most thermoplastic polymers, polycarbonates prepared from dihydric phenols exhibit Newtonian flow at normal processing temperatures and shear rates below 300 reciprocal seconds.", "\nTwo other characteristics of molten thermoplastic polymers are considered to be significant for molding operations: melt elasticity and melt strength. ", "Melt elasticity is the recovery of the elastic energy stored within the melt from distortion or orientation of the molecules by shearing stresses. ", "Melt strength may be simply described as the tenacity of a molten strand and indicates the ability of the melt to support a stress. ", "Both of these characteristics are important in extrusion blow molding, particularly in fabrication by extrusion blow molding. ", "Non-Newtonian flow characteristics tend to impart melt elasticity and melt strength to polymers thus allowing their use in blow molding fabrication. ", "In the usual blow molding operation, a tube of a molten thermoplastic is extruded vertically downward into a mold, followed by the introduction of a gas, such as air, into the tube thus forcing the molten plastic to conform to the shape of the mold. ", "The length of the tube and the quantity of material forming the tube are limiting factors in determining the size and wall thickness of the object that can be molded by this process. ", "The fluidity of the melt obtained from bisphenol-A polycarbonate, or the lack of melt strength as well as the paucity of extrudate swelling, serve to limit blow molding applications to relatively small, thin walled parts. ", "Temperatures must generally be carefully controlled to prevent the extruded tube from falling away before it attains the desired length and the mold is closed around it for blowing. ", "Consequently, the Newtonian behavior of polycarbonate resin melts has severely restricted their use in the production of large hollow bodies by conventional extrusion blow molding operations as well as the production of various other shapes by profile extrusion methods.", "\nThermoplastic randomly branched polycarbonates exhibit unique properties of non-Newtonian flow, melt elasticity and melt strength which permit them to be used to obtain such articles as bottles which were not heretofore easily or readily produced with linear polycarbonates. ", "The thermoplastic randomly branched polycarbonates can be prepared by reacting a tetraphenolic compound with a dihydric phenol and a carbonate precursor." ]

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[ "Coffee with co-workers: role of caffeine on evaluations of the self and others in group settings.", "\nThis research explores the effect of consuming a moderate amount of commercially available caffeinated coffee on an individual's self-evaluated participation in a group activity and subsequent evaluations of the experience. ", "Across two studies, results show that consuming a moderate amount of caffeinated coffee prior to indulging in a group activity enhances an individual's task-relevant participation in the group activity. ", "In addition, subjective evaluations of the participation of other group members and oneself are also positively influenced. ", "Finally, the positive impact of consuming a moderate amount of caffeinated coffee on the evaluation of participation of other group members and oneself is moderated by a sense of an increased level of alertness." ]

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[ "Intake of energy, nutrients and food items in an urban elderly population.", "\nThis study is part of a transcultural investigation under the auspices of the International Union of Nutritional Sciences, where dietary habits are studied with similar methodology in different populations throughout the world. ", "The present paper describes and evaluates the intake of energy and nutrients, and food habits in an urban elderly population in Sweden, in relation to existing standards. ", "The study population comprised 66 males and 122 females, aged 70 years and over (average 78 years) living in the city of Gothenburg. ", "Energy intake was on average 11.5 MJ in males and 9.9 MJ in females. ", "Nutrient intakes were on average above recommendations, and neither intake nor food choice seemed to change much with increasing age. ", "A validation by a 4-day record and 24-hour urinary nitrogen determination was performed in a subsample, and indicated a probable systematic overestimation of at least 10% for protein consumed. ", "The data from this study support the view that people 70 years of age and older in Sweden are generally healthy, active and have good food habits. ", "This population, however, was not a representative sample. ", "They were all living in a well defined area, with a stable social situation, and belonged generally to middle class. ", "With this background the nutrient data seem reasonable. ", "As long as elderly people stay healthy and do not have other serious risk factors, they seem to keep good food habits and nutritional status up into their eighties and nineties." ]

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[ "Where the best is yet to be….", "\n\nLocation\n\nThe Apison, Ooltewah & Collegedale area has consistently maintained its position as one of the strongest growth areas in residential real estate in our region.", "\n\nPrairie Pass is ideally situated just inside Apison on East Brainerd Road. ", "An easy commute to the Volkswagen site, downtown Chattanooga or nearby Cleveland. ", "The community is within walking distance of the new Apison Elementary School (Grades Pre Kindergarten – Fifth.) ", "The community is also zoned for the highly regarded East Hamilton Middle/High School.", "\n\nMinutes from the major residential thoroughfare of Ooltewah/Ringgold Road, the community has easy access to Hamilton Place, restaurants, entertainment and healthcare. ", "The Super Bi-Lo grocery is located only minutes away on Ooltewah/Ringgold Road.", "\n\nBut it is the natural beauty, peaceful setting and simplistically elegant architecture and home designs that make Prairie Pass the perfect location." ]

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[ "Vinay Gupta is a man with a novel approach to disaster relief and emergency shelters.", "\n\nThe Red Cross is interested. ", "FEMA is interested.", "\n\nDoes OpenSource architecture and peer-to-peer emergency response hold the key to effectively meeting people’s needs in a disaster?", "\n\nIn an interview with TreeHugger, OpenSource designer Vinay Gupta had this to say:\n\n“The idea that the U.S. might have to handle a city worth of refugees very suddenly shouldn’t be a strange thing to anybody who’s aware of the fact that there is some risk of terrorism on a mass scale. ", "An organization like FEMA really has the responsibility to be able to evacuate a city worth of Americans in 24 hours if they have to be able to do so. ", "That capability had not been developed so it couldn’t be deployed.”", "\n\nImplementing Gupta’s emergency response plan and simple disaster shelters could develop that capability, working with FEMA, the Red Cross, and other local aid organizations.", "\n\nLooking at the events surrounding the Katrina disaster, I’d say we really need to have a plan that works next time. ", "The Hexayurt sounds like a phenomenal answer for sheltering displaced people, quickly. ", "It’s a public domain project, OpenSource and ready to be taken to the next level.", "\n\nA hexayurt is a 166 square foot “microbuilding” assembled from one to\n\ntwo dozen 4′ x 8′ panels. ", "These panels are typically off-the-shelf\n\npolyisocyanurate building insulation boards, as commonly found at Home\n\nDepot and other building supply outlets for around $15 ea. ", "Harsher\n\nclimates and longer term use requirements can be met by custom runs of\n\nthis material. ", "The building geometry is extremely simple: the roof is\n\nmade from half-panels, and the walls are made from full panels – an\n\nentire building requires only six straight cross-panel diagonal cuts. ", "There\n\nare no framing timbers or other structural components. ", "The pieces are\n\nthen joined using an off-the-shelf 6″ wide 600lb breaking strain\n\nindustrial box closure tape or a custom adhesive. ", "The entire process –\n\nfrom panels in a truck to a finished building – takes about two hours the\n\nfirst time and more like one hour with an experienced team of five or six.", "\n\nThe design is in the public domain so can be used by anybody.", "\n\nThe Hexayurt (about $200 to build) is only one piece of the puzzle in coping with the emergency needs of displaced people. ", "The rest of the infrastructure (sanitation, power, heat, communications) comes next.", "\n\nTake 100,000 hexayurts and an open field. ", "Ship no infrastructure and you have an immediate problem: open sewers contaminating any local water supplies you have. ", "People start dying in groups within days. – ", "Vinay Gupta\n\nThat infrastructure could cost as little as $100 per unit. ", "With composting (or even bucket) toilets, a shared solar power source with rechargers for batteries, solar water pasteurizers, solar hot water, and wood gasification stoves for heating, the temporary shelter becomes less of a hardship and more of a home base for the families.", "\n\nThis PDF shows the details of the Hexayurt Infrastructure system: TIDES – Infrastructure\n\nDownload this PDF for a closer look at Hexayurts for disaster relief: Pentagon Presentation\n\nPeer-to-Peer Emergency Response – Disastr\n\nDisastr is a simple, clear, logical proposal for evacuating whole cities in the event of terrorism or natural catastrophe. ", "It is a last ditch sheltering solution for hundreds of thousands to tens of millions. ", "We may never need this plan, but if we do, it may save lives one day. ", "It relies on peer-to-peer disaster relief and commercial supply chains to provide housing, and the power of the network to coordinate relief efforts. ", "There is an opportunity for a major tech company (Amazon, Google, Yahoo etc.) ", "to provide this service using their redundant computer clusters. ", "Disastr has no official status, but has been positively reviewed by the American Red Cross and FEMA.", "\n\nNetworked Domestic Disaster Response is a low cost approach to handling millions or tens of millions of domestic refugees in the event of a natural disaster, epidemic, industrial accident, WMD or other event.", "\n\nRead the plan, Hexayurt mass evacuation, at Appropedia. ", "Add to it.", "\n\nBuild your own Hexayurt.", "\n\nThe plans are in the public domain, and available free: Hexayurt schematics\n\nLearn how to build a Hexayurt for Burning Man.", "\n\nVote for the Hexayurt in Google’s Project 10 to the 100th.", "\n\nCheck out The Open Toolbox:\n\nThe Open Toolbox is a consulting group that utilizes the power of open source to create solutions that build life-embracing communities at all levels of economic welfare and risk exposure. ", "Life-embracing communities are equipped to take care of their citizens during normal economic situations, economic hardship, and crisis and/or disaster conditions. ", "In life-embracing communities, resilience in times of crisis is built on a foundation of stability, integrity and forward planning at all levels.", "\n\nVisit the Open Architecture Network:\n\nOne billion people live in abject poverty. ", "Four billion live in fragile but growing economies. ", "One in seven people live in slum settlements. ", "By 2020 it will be one in three. ", "We don’t need to choose between architecture or revolution. ", "What we need is an architectural revolution. ", "The U.N. Millennium Development Goals aim to “achieve improvement in the lives of 100 million slum dwellers by the year 2015.” ", "Reaching this goal will require a profoundly new approach to improving the built environment. ", "The Open Architecture Network aims to be just such a catalyst for change.", "\n\nJoin the Open Sustainability Network: Global Swadeshi\n\nIf you have skills to share in any of these areas, please join up with one of these groups and jump in! ", "It’s going to take all of us to solve our issues." ]

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[ "Hannah Storm’s Stylish, Sophisticated, and Comfortable Home\n\nHannah Storm: SportsCenter anchor, former heavy-metal disc jockey, Art Deco fan. ", "Sometimes the most innocent of questions can lead to the most spectacular answers. ", "In the case of Hannah Storm, what made all the difference in her domestic life was a simple question that she posed to Karen Miller, a Houston decorator she met through a friend: “Can you come look at my bookshelves?”", "\n\nSince that fateful meeting a couple of years ago, the house that Hannah shares with her husband, NBC sportscaster Dan Hicks, and their three daughters in suburban Connecticut has been utterly but discreetly transformed. ", "Though its exterior has the same humble good looks it has maintained for more than a hundred years—the clapboard former farmhouse was built in 1850 and has had only a few alterations in the intervening century—the interiors are sexy, sophisticated rooms whose Art Deco furnishings and modern paintings and sculpture come as a bit of a surprise when visitors step through the paneled front door.", "\n\n“We looked at huge modern homes with big rooms and all sorts of conveniences, but they all felt impersonal,” says Hannah, who began her career as a heavy-metal disc jockey in Texas and eventually became a major presence at NBC and ESPN as a pioneering woman sports reporter (as well as a host of CBS’s Early Show for five years). “", "But when I walked into this house, it had an emotional pull. ", "It was charming and welcoming.”", "\n\nHer visceral reaction shocked her as much as her husband; she likes sleek modern furniture while Dan, who was raised in Arizona, leans toward the lively rusticity of the American Southwest and Latin America. “", "We are more funky in our tastes rather than super-traditional,” Hannah explains, adding that she and her husband have amassed a wide-ranging array of art that includes a cache of crosses and Madonnas that Hannah, who is Catholic, has picked up on visits to Mexico and Greece, where she covered the Olympics. ", "The couple also came equipped with an eclectic array of furniture, much of it generously overscaled. ", "The Connecticut farmhouse, however, is cozy, with small rooms, eight-foot ceilings, and a long, narrow footprint. ", "And the smallest of the already small bedrooms, which is used as a nursery, is little more than a glorified closet.", "\n\n“Obviously, nothing we had worked,” Hannah explains. ", "When Karen Miller entered the picture, though, a decorative focus was quickly found. ", "Though the rooms of the house provided a challenge of scale, Miller suggested that the simple, straightforward architecture would work beautifully with simple-in-silhouette but rich-in-finishes treasures made in France during the 1920s and 1930s. ", "A surprising choice, it was a style that addressed Hannah’s interest in giving the rooms an unfussy formality and an elegant rigor that would hold their own in the company of the couple’s growing collection of modern art, such as a pair of paintings in the living room by the American master Robert Motherwell. “", "This is the kind of stuff that’s totally in line with our personalities,” Hannah says, “and Art Deco totally flies with an old country house, believe it or not.”", "\n\nContributing to the sense of grandeur as much as the Art Deco furniture (some of it antique pieces, others custom-made) is the house’s surprisingly luxurious color scheme: taupe walls, cream ceilings, woodwork subtly supercharged with dashes of shining black lacquer, and upholstery whose tones range from bronze to mulberry. ", "The floors, once farm-style golden, are now ebony dark, as are the staircase’s treads, balusters, and railing. ", "And there are touches of glam glitter, too, like the extravagant 1930s Venetian-style French mirror that hangs in one corner of the living room. ", "The mirror is paired with a custom-made black lacquer cabinet.", "\n\nEspecially eye-catching is the big chunk of pyrite, a mineral more commonly known as fool’s gold, which sits in splendor above the new stone fireplace. “", "It’s supposed to be the biggest piece of pyrite to come out of Peru in years,” says Miller, noting that similarly sparkling minerals—geodes, rock crystal, quartz—were often incorporated into Art Deco interiors by designers like Jean-Michel Frank and tastemakers like Coco Chanel. ", "More important to Miller was the pyrite’s site-perfect scale. “", "There isn’t much clearance between the fireplace and the ceiling,” she says, “so a standard painting wouldn’t fit.”", "\n\nSmall-scale houses often present space challenges, and the Storm-Hicks place is no exception. ", "Upstairs, for instance, the ceiling of the master bedroom has a steep angle that corresponds to the contours of the roof. ", "The result, Miller says, is that the second-floor “windows are squatty, practically dormer size.” ", "Her solution to a problem another designer might have solved through demolition? ", "Make the master bedroom window seem larger by mounting the valance onto the ceiling and installing floor-length curtains to give it a bit of fool-the-eye height.", "\n\nIt’s a house that’s glamorous, yes, but surprisingly unstuffy. “", "We entertain a lot, and I wanted people not to feel afraid of sitting down to eat with a plate of food in their laps,” Hannah says, adding that a usual weekend involves cocktails on the veranda and watching kids go crazy in the yard before sitting down to dinner. “", "We really use every room in the house.”", "\n\nThe home’s living room has modern appeal, its graphic sofa soothed by “Wheeling Neutral” wall paint from Benjamin Moore. ", "A pair of paintings by the American master Robert Motherwell hang above the living room sofa.", "\n\nSunlight floods the white kitchen, creating a cheerful space for cooking and dining. ", "Wicker barstools line the spacious center island; green and yellow tiles on the backsplash compliment the warm woods throughout the rest of the main floor." ]

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[ "# This file is distributed under the same license as the Django package.", "\n#\n# Translators:\n# Carles Barrobés <[email protected]>, 2012.", "\n# Jannis Leidel <[email protected]>, 2011.", "\nmsgid \"\"\nmsgstr \"\"\n\"Project-Id-Version: Django\\n\"\n\"Report-Msgid-Bugs-To: \\n\"\n\"POT-Creation-Date: 2012-10-22 09:28+0200\\n\"\n\"PO-Revision-Date: 2012-10-22 08:46+0000\\n\"\n\"Last-Translator: Carles Barrobés <[email protected]>\\n\"\n\"Language-Team: Catalan (http://www.transifex.com/projects/p/django/language/\"\n\"ca/)\\n\"\n\"MIME-Version: 1.0\\n\"\n\"Content-Type: text/plain; charset=UTF-8\\n\"\n\"Content-Transfer-Encoding: 8bit\\n\"\n\"Language: ca\\n\"\n\"Plural-Forms: nplurals=2; plural=(n !", "= 1);\\n\"\n\n#: views.py:58 views.py:60 views.py:62\nmsgid \"tag:\"\nmsgstr \"etiqueta:\"\n\n#: views.py:93 views.py:95 views.py:97\nmsgid \"filter:\"\nmsgstr \"filtre:\"\n\n#: views.py:156 views.py:158 views.py:160\nmsgid \"view:\"\nmsgstr \"vista:\"\n\n#: views.py:188\n#, python-format\nmsgid \"App %r not found\"\nmsgstr \"No s'ha pogut trobar l'aplicació %r\"\n\n#: views.py:195\n#, python-format\nmsgid \"Model %(model_name)r not found in app %(app_label)r\"\nmsgstr \"El model %(model_name)r no s'ha trobat a l'aplicació %(app_label)r\"\n\n#: views.py:207\n#, python-format\nmsgid \"the related `%(app_label)s.%(data_type)s` object\"\nmsgstr \"l'objecte relacionat `%(app_label)s.%(data_type)s`\"\n\n#: views.py:207 views.py:226 views.py:231 views.py:245 views.py:259\n#: views.py:264\nmsgid \"model:\"\nmsgstr \"model:\"\n\n#: views.py:222 views.py:254\n#, python-format\nmsgid \"related `%(app_label)s.%(object_name)s` objects\"\nmsgstr \"objectes relacionats `%(app_label)s.%(object_name)s`\"\n\n#: views.py:226 views.py:259\n#, python-format\nmsgid \"all %s\"\nmsgstr \"tots %s\"\n\n#: views.py:231 views.py:264\n#, python-format\nmsgid \"number of %s\"\nmsgstr \"nombre de %s\"\n\n#: views.py:269\n#, python-format\nmsgid \"Fields on %s objects\"\nmsgstr \"Camps en objectes %s\"\n\n#: views.py:361\n#, python-format\nmsgid \"%s does not appear to be a urlpattern object\"\nmsgstr \"%s no sembla ser un objecte 'urlpattern'\"\n\n#: templates/admin_doc/bookmarklets.html:6 templates/admin_doc/index.html:6\n#: templates/admin_doc/missing_docutils.html:6\n#: templates/admin_doc/model_detail.html:14\n#: templates/admin_doc/model_index.html:8\n#: templates/admin_doc/template_detail.html:6\n#: templates/admin_doc/template_filter_index.html:7\n#: templates/admin_doc/template_tag_index.html:7\n#: templates/admin_doc/view_detail.html:6\n#: templates/admin_doc/view_index.html:7\nmsgid \"Home\"\nmsgstr \"Inici\"\n\n#: templates/admin_doc/bookmarklets.html:7 templates/admin_doc/index.html:7\n#: templates/admin_doc/missing_docutils.html:7\n#: templates/admin_doc/model_detail.html:15\n#: templates/admin_doc/model_index.html:9\n#: templates/admin_doc/template_detail.html:7\n#: templates/admin_doc/template_filter_index.html:8\n#: templates/admin_doc/template_tag_index.html:8\n#: templates/admin_doc/view_detail.html:7\n#: templates/admin_doc/view_index.html:8\nmsgid \"Documentation\"\nmsgstr \"Documentació\"\n\n#: templates/admin_doc/bookmarklets.html:8\nmsgid \"Bookmarklets\"\nmsgstr \"'Bookmarklets'\"\n\n#: templates/admin_doc/bookmarklets.html:11\nmsgid \"Documentation bookmarklets\"\nmsgstr \"'Bookmarklets' de documentació\"\n\n#: templates/admin_doc/bookmarklets.html:15\nmsgid \"\"\n\"\\n\"\n\"<p class=\\\"help\\\">To install bookmarklets, drag the link to your bookmarks\\n\"\n\"toolbar, or right-click the link and add it to your bookmarks. ", "Now you can\\n\"\n\"select the bookmarklet from any page in the site. ", " Note that some of these\\n\"\n\"bookmarklets require you to be viewing the site from a computer designated\\n\"\n\"as \\\"internal\\\" (talk to your system administrator if you aren't sure if\\n\"\n\"your computer is \\\"internal\\\").</p>\\n\"\nmsgstr \"\"\n\"\\n\"\n\"<p class=\\\"help\\\">Per tal d'instal·lar 'bookmarklets', arrosegueu l'enllaç\\n\"\n\"a la vostra barra de marcadors, o feu click amb el botó dret a l'enllaç i\\n\"\n\"afegiu-lo als marcadors.\\n\"\n\"Ara podeu escollir el 'bookmarklet' des de qualsevol pàgina del lloc.\\n\"\n\"Observeu que per a alguns d'aquests 'bookmarklets' cal que estigueu veient\\n\"\n\"el lloc des d'un ordinador designat com a \\\"intern\\\" (parleu\\n\"\n\"amb el vostre administrador de sistemes si no esteu segurs si el vostre \"\n\"ordinador és \\\"intern\\\").</p>\\n\"\n\n#: templates/admin_doc/bookmarklets.html:25\nmsgid \"Documentation for this page\"\nmsgstr \"Documentació d'aquesta pàgina\"\n\n#: templates/admin_doc/bookmarklets.html:26\nmsgid \"\"\n\"Jumps you from any page to the documentation for the view that generates \"\n\"that page.\"", "\nmsgstr \"\"\n\"Us porta des de qualsevol pàgina a la documentació de la vista que la genera.\"", "\n\n#: templates/admin_doc/bookmarklets.html:28\nmsgid \"Show object ID\"\nmsgstr \"Mostra l'ID de l'objecte\"\n\n#: templates/admin_doc/bookmarklets.html:29\nmsgid \"\"\n\"Shows the content-type and unique ID for pages that represent a single \"\n\"object.\"", "\nmsgstr \"\"\n\"Mostra el 'content-type' (tipus de contingut) i l'ID inequívoc de les \"\n\"pàgines que representen un únic objecte.\"", "\n\n#: templates/admin_doc/bookmarklets.html:31\nmsgid \"Edit this object (current window)\"\nmsgstr \"Editar aquest objecte (finestra actual)\"\n\n#: templates/admin_doc/bookmarklets.html:32\nmsgid \"Jumps to the admin page for pages that represent a single object.\"", "\nmsgstr \"\"\n\"El porta a la pàgina d'administració de pàgines que representen un únic \"\n\"objecte.\"", "\n\n#: templates/admin_doc/bookmarklets.html:34\nmsgid \"Edit this object (new window)\"\nmsgstr \"Editar aquest objecte (nova finestra)\"\n\n#: templates/admin_doc/bookmarklets.html:35\nmsgid \"As above, but opens the admin page in a new window.\"", "\nmsgstr \"Com abans, però obre la pàgina d'administració en una nova finestra.\"", "\n\n#: templates/admin_doc/model_detail.html:16\n#: templates/admin_doc/model_index.html:10\nmsgid \"Models\"\nmsgstr \"Models\"\n\n#: templates/admin_doc/template_detail.html:8\nmsgid \"Templates\"\nmsgstr \"Plantilles\"\n\n#: templates/admin_doc/template_filter_index.html:9\nmsgid \"Filters\"\nmsgstr \"Filtres\"\n\n#: templates/admin_doc/template_tag_index.html:9\nmsgid \"Tags\"\nmsgstr \"Etiquetes\"\n\n#: templates/admin_doc/view_detail.html:8\n#: templates/admin_doc/view_index.html:9\nmsgid \"Views\"\nmsgstr \"Vistes\"\n\n#: tests/__init__.py:23\nmsgid \"Boolean (Either True or False)\"\nmsgstr \"Booleà (Cert o Fals)\"\n\n#: tests/__init__.py:33\n#, python-format\nmsgid \"Field of type: %(field_type)s\"\nmsgstr \"Camp del tipus: %(field_type)s\"\n" ]

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[ "Q:\n\nFitNesse: Test that an element is not in a list?", "\n\nI'm using FitSharp to test an application and have a question related to testing contents of lists. ", "Testing that an element is present in a list is simple to do using, for example, a SubsetFixture and could be written as this:\n| Check that element is in list |\n| 5 |\n\nBut is there a way to write a fixture that tests if an element is not in a list?", "\n| Check that element is not in list |\n| 5 |\n\nI want the last table to pass only if 5 is not in the processed list.", "\n\nA:\n\nThe closest you can come with any kind of list fixture would be to use a array or set fixture and to list ALL of the items you DO expect. ", "There is no \"not one of these\" list fixtures.", "\nI would recommend you just do a do fixture in one like like:\n|check|that element | 5 | is in the list | False |\n\nor you could use a column fixture to get the feel for a set fixture\n| Check that element is not in list |\n| element | exists? ", "|\n| 5 | false |\n\n" ]

[ 0, 0.00980392156862745, 0.004032258064516129, 0, 0, 0, 0, 0 ]

[ "Diurnal variation of mood and neuropsychological function in major depression with melancholia.", "\n20 DSM-III-R melancholics with clinically evident diurnal symptoms and 20 controls were assessed with a battery of neuropsychological tests, a test of maximum voluntary hand-grip, and neuroendocrine measures of hypothalamic-pituitary-adrenal axis function morning and evening in a 24-h period, using a balanced design. ", "The morning pattern of neuropsychological impairment in the melancholics was comprehensive, affecting attention and concentration/working memory, episodic memory, reaction time and, strikingly, the speed of simultaneous match to sample, which was performed more slowly than the version of the task delayed to 0 or 4 s. The melancholics were significantly weaker than controls, on a measure of maximal voluntary contraction. ", "Significantly improved neuropsychological function was seen in the melancholic patients in the evening, in line with diurnal improvement in mood; there was also a large increase in strength. ", "Slowing on the digit symbol substitution test, the simultaneous match to sample task, total errors on the match to sample and hand-grip remained impaired in the evening compared to controls; other neuropsychological measures were no longer statistically different from control values which were often worsened. ", "Neuroendocrine measures showed significantly raised levels of cortisol and ACTH morning and evening in the melancholics. ", "Morning cortisol in the melancholics correlated with the diurnal improvement in neuropsychological functioning. ", "The results have implications for the timing of neuropsychological assessment in major depression. ", "Indices of neuropsychological and motor function may be as reliable quantitative estimates of illness severity as subjective estimates of mood." ]

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[ "Pokemon is too commercial now I liked when it was just an anime\n\n16,504 shares" ]

[ 0.01282051282051282 ]

[ "module Foreman::Controller::Parameters::Operatingsystem\n extend ActiveSupport::Concern\n include Foreman::Controller::Parameters::OsDefaultTemplate\n include Foreman::Controller::Parameters::Parameter\n\n class_methods do\n def operatingsystem_params_filter\n Foreman::ParameterFilter.new(::Operatingsystem).tap do |filter|\n filter.permit :description,\n :family,\n :major,\n :minor,\n :name,\n :password_hash,\n :release_name,\n :to_label,\n :architectures => [:id, :name], :architecture_ids => [], :architecture_names => [],\n :medium_ids => [], :medium_names => [],\n :os_default_templates_attributes => [os_default_template_params_filter],\n :os_parameters_attributes => [parameter_params_filter(OsParameter)],\n :provisioning_templates => [], :provisioning_template_names => [], :provisioning_template_ids => [],\n :ptable_ids => [], :ptable_names => []\n end\n end\n end\n\n def operatingsystem_params\n self.class.operatingsystem_params_filter.filter_params(params, parameter_filter_context)\n end\nend\n" ]

[ 0.00176522506619594 ]

[ " factors of 13721.", "\n13721\nList the prime factors of 1312.", "\n2, 41\nWhat are the prime factors of 1613?", "\n1613\nWhat are the prime factors of 9222?", "\n2, 3, 29, 53\nWhat are the prime factors of 132495?", "\n3, 5, 11, 73\nWhat are the prime factors of 274?", "\n2, 137\nWhat are the prime factors of 9585?", "\n3, 5, 71\nWhat are the prime factors of 20660?", "\n2, 5, 1033\nList the prime factors of 26562.", "\n2, 3, 19, 233\nWhat are the prime factors of 560?", "\n2, 5, 7\nList the prime factors of 1565.", "\n5, 313\nList the prime factors of 12948.", "\n2, 3, 13, 83\nWhat are the prime factors of 34387?", "\n137, 251\nList the prime factors of 7338.", "\n2, 3, 1223\nList the prime factors of 300.", "\n2, 3, 5\nWhat are the prime factors of 70212?", "\n2, 3, 5851\nList the prime factors of 32052.", "\n2, 3, 2671\nWhat are the prime factors of 2261?", "\n7, 17, 19\nWhat are the prime factors of 36708?", "\n2, 3, 7, 19, 23\nList the prime factors of 1079.", "\n13, 83\nList the prime factors of 2064.", "\n2, 3, 43\nList the prime factors of 8311.", "\n8311\nWhat are the prime factors of 119241?", "\n3, 13249\nList the prime factors of 621.", "\n3, 23\nWhat are the prime factors of 6928?", "\n2, 433\nList the prime factors of 28445.", "\n5, 5689\nList the prime factors of 4563.", "\n3, 13\nWhat are the prime factors of 4014?", "\n2, 3, 223\nList the prime factors of 42266.", "\n2, 7, 3019\nWhat are the prime factors of 4053?", "\n3, 7, 193\nWhat are the prime factors of 977?", "\n977\nWhat are the prime factors of 7555?", "\n5, 1511\nList the prime factors of 16177.", "\n7, 2311\nWhat are the prime factors of 124492?", "\n2, 31123\nList the prime factors of 7506.", "\n2, 3, 139\nWhat are the prime factors of 2874?", "\n2, 3, 479\nWhat are the prime factors of 1852?", "\n2, 463\nWhat are the prime factors of 1841?", "\n7, 263\nList the prime factors of 179.", "\n179\nList the prime factors of 41467.", "\n41467\nWhat are the prime factors of 31648?", "\n2, 23, 43\nList the prime factors of 4079.", "\n4079\nList the prime factors of 1582.", "\n2, 7, 113\nList the prime factors of 3527.", "\n3527\nWhat are the prime factors of 2863?", "\n7, 409\nWhat are the prime factors of 171?", "\n3, 19\nList the prime factors of 7013.", "\n7013\nList the prime factors of 661.", "\n661\nWhat are the prime factors of 1933?", "\n1933\nWhat are the prime factors of 64241?", "\n227, 283\nList the prime factors of 9428.", "\n2, 2357\nWhat are the prime factors of 537?", "\n3, 179\nList the prime factors of 865.", "\n5, 173\nWhat are the prime factors of 163787?", "\n13, 43, 293\nWhat are the prime factors of 2979?", "\n3, 331\nWhat are the prime factors of 1110?", "\n2, 3, 5, 37\nList the prime factors of 108800.", "\n2, 5, 17\nWhat are the prime factors of 1640?", "\n2, 5, 41\nList the prime factors of 5345.", "\n5, 1069\nList the prime factors of 114.", "\n2, 3, 19\nWhat are the prime factors of 1749?", "\n3, 11, 53\nWhat are the prime factors of 78274?", "\n2, 7, 5591\nList the prime factors of 31094.", "\n2, 7, 2221\nList the prime factors of 9567.", "\n3, 1063\nWhat are the prime factors of 5124?", "\n2, 3, 7, 61\nList the prime factors of 718.", "\n2, 359\nList the prime factors of 335.", "\n5, 67\nList the prime factors of 15368.", "\n2, 17, 113\nList the prime factors of 292.", "\n2, 73\nList the prime factors of 19357.", "\n13, 1489\nList the prime factors of 4524.", "\n2, 3, 13, 29\nWhat are the prime factors of 41613?", "\n3, 11, 13, 97\nList the prime factors of 43110.", "\n2, 3, 5, 479\nList the prime factors of 13889.", "\n17, 19, 43\nList the prime factors of 35801.", "\n35801\nWhat are the prime factors of 924?", "\n2, 3, 7, 11\nWhat are the prime factors of 8419?", "\n8419\nWhat are the prime factors of 67006?", "\n2, 33503\nList the prime factors of 4798.", "\n2, 2399\nWhat are the prime factors of 646?", "\n2, 17, 19\nWhat are the prime factors of 2051?", "\n7, 293\nList the prime factors of 11290.", "\n2, 5, 1129\nWhat are the prime factors of 27953?", "\n27953\nList the prime factors of 679.", "\n7, 97\nWhat are the prime factors of 2183?", "\n37, 59\nList the prime factors of 1338.", "\n2, 3, 223\nList the prime factors of 92.", "\n2, 23\nWhat are the prime factors of 263?", "\n263\nWhat are the prime factors of 28694?", "\n2, 14347\nWhat are the prime factors of 50938?", "\n2, 25469\nList the prime factors of 1407.", "\n3, 7, 67\nList the prime factors of 12812.", "\n2, 3203\nList the prime factors of 871.", "\n13, 67\nWhat are the prime factors of 145943?", "\n7, 20849\nWhat are the prime factors of 10705?", "\n5, 2141\nList the prime factors of 342.", "\n2, 3, 19\nWhat are the prime factors of 264?", "\n2, 3, 11\nWhat are the prime factors of 1335?", "\n3, 5, 89\nList the prime factors of 12364.", "\n2, 11, 281\nList the prime factors of 33.", "\n3, 11\nWhat are the prime factors of 826?", "\n2, 7, 59\nWhat are the prime factors of 2278?", "\n2, 17, 67\nList the prime factors of 2741.", "\n2741\nWhat are the prime factors of 3420?", "\n2, 3, 5, 19\nList the prime factors of 347.", "\n347\nWhat are the prime factors of 4335?", "\n3, 5, 17\nWhat are the prime factors of 20571?", "\n3, 6857\nList the prime factors of 13322.", "\n2, 6661\nList the prime factors of 3136.", "\n2, 7\nList the prime factors of 3200.", "\n2, 5\nWhat are the prime factors of 42618?", "\n2, 3, 7103\nList the prime factors of 284.", "\n2, 71\nWhat are the prime factors of 1009?", "\n1009\nList the prime factors of 1292.", "\n2, 17, 19\nList the prime factors of 2002.", "\n2, 7, 11, 13\nWhat are the prime factors of 1871?", "\n1871\nWhat are the prime factors of 16?", "\n2\nWhat are the prime factors of 7138?", "\n2, 43, 83\nWhat are the prime factors of 16517?", "\n83, 199\nWhat are the prime factors of 192907?", "\n11, 13, 19, 71\nWhat are the prime factors of 5416?", "\n2, 677\nList the prime factors of 14934.", "\n2, 3, 19, 131\nWhat are the prime factors of 38157?", "\n3, 7, 23, 79\nWhat are the prime factors of 24936?", "\n2, 3, 1039\nWhat are the prime factors of 25577?", "\n25577\nWhat are the prime factors of 49470?", "\n2, 3, 5, 17, 97\nWhat are the prime factors of 25618?", "\n2, 12809\nWhat are the prime factors of 8948?", "\n2, 2237\nWhat are the prime factors of 4857?", "\n3, 1619\nWhat are the prime factors of 65023?", "\n7, 1327\nList the prime factors of 20072.", "\n2, 13, 193\nWhat are the prime factors of 875?", "\n5, 7\nWhat are the prime factors of 5346?", "\n2, 3, 11\nWhat are the prime factors of 55449?", "\n3, 61, 101\nList the prime factors of 42638.", "\n2, 21319\nList the prime factors of 100034.", "\n2, 11, 4547\nWhat are the prime factors of 3872?", "\n2, 11\nList the prime factors of 3815.", "\n5, 7, 109\nList the prime factors of 976.", "\n2, 61\nWhat are the prime factors of 2022?", "\n2, 3, 337\nWhat are the prime factors of 3519?", "\n3, 17, 23\nList the prime factors of 23281.", "\n31, 751\nList the prime factors of 501.", "\n3, 167\nList the prime factors of 2915.", "\n5, 11, 53\nWhat are the prime factors of 18631?", "\n31, 601\nList the prime factors of 426.", "\n2, 3, 71\nWhat are the prime factors of 159?", "\n3, 53\nWhat are the prime factors of 5012?", "\n2, 7, 179\nWhat are the prime factors of 97?", "\n97\nWhat are the prime factors of 54396?", "\n2, 3, 1511\nWhat are the prime factors of 4629?", "\n3, 1543\nList the prime factors of 7068.", "\n2, 3, 19, 31\nWhat are the prime factors of 6707?", "\n19, 353\nWhat are the prime factors of 507?", "\n3, 13\nList the prime factors of 82.", "\n2, 41\nList the prime factors of 2982.", "\n2, 3, 7, 71\nList the prime factors of 273.", "\n3, 7, 13\nWhat are the prime factors of 1340?", "\n2, 5, 67\nList the prime factors of 40893.", "\n3, 43, 317\nWhat are the prime factors of 1096?", "\n2, 137\nWhat are the prime factors of 42155?", "\n5, 8431\nList the prime factors of 98364.", "\n2, 3, 7, 1171\nList the prime factors of 3289.", "\n11, 13, 23\nList the prime factors of 658.", "\n2, 7, 47\nWhat are the prime factors of 536?", "\n2, 67\nWhat are the prime factors of 1046?", "\n2, 523\nWhat are the prime factors of 516?", "\n2, 3, 43\nList the prime factors of 10765.", "\n5, 2153\nWhat are the prime factors of 48973?", "\n48973\nList the prime factors of 52196.", "\n2, 13049\nWhat are the prime factors of 33866?", "\n2, 7, 41, 59\nList the prime factors of 1958.", "\n2, 11, 89\nList the prime factors of 7710.", "\n2, 3, 5, 257\nList the prime factors of 2385.", "\n3, 5, 53\nList the prime factors of 13252.", "\n2, 3313\nList the prime factors of 4100.", "\n2, 5, 41\nList the prime factors of 4292.", "\n2, 29, 37\nWhat are the prime factors of 1318?", "\n2, 659\nWhat are the prime factors of 2478?", "\n2, 3, 7, 59\nWhat are the prime factors of 1187?", "\n1187\nList the prime factors of 26057.", "\n71, 367\nList the prime factors of 30761.", "\n19, 1619\nWhat are the prime factors of 19715?", "\n5, 3943\nWhat are the prime factors of 12510?", "\n2, 3, 5, 139\nList the prime factors of 14496.", "\n2, 3, 151\nList the prime factors of 64944.", "\n2, 3, 11, 41\nWhat are the prime factors of 595?", "\n5, 7, 17\nWhat are the prime factors of 109713?", "\n3, 36571\nWhat are the prime factors of 14337?", "\n3, 59\nWhat are the prime factors of 9083?", "\n31, 293\nList the prime factors of 776.", "\n2, 97\nW" ]

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[ "Plutonium in the Ozyorsk population.", "\nResults of the long-term autopsy studies on plutonium body burden in the population of Ozyorsk situated in the vicinity of the radiochemical plant of the Mayak Production Association (Russia) have been presented. ", "The data were obtained from radiochemical analysis of the soft tissue and bone samples collected at the autopsy of 239 non-occupational individuals for the period 1975-2003. ", "The dynamics of plutonium accumulation in the Ozyorsk population is associated with the environmental contamination due to radioactive releases from the Mayak Production Association. ", "Plutonium body burden and its distribution between the respiratory tract and extrapulmonary organs depend on the residence time of individuals in the city. ", "Since the early 1950s, plutonium body burden in the Ozyorsk population was linearly increasing at the almost constant rate of accumulation and amounted to 5.8 Bq at 35 y after the beginning of residence in the city that was several tens of times higher than background levels of fallout plutonium. ", "Distribution of plutonium in the body was also studied in Ozyorsk population. ", "Plutonium deposition fraction in the respiratory tract did not exceed 11% of the body burden in individuals with short residence times (1-9 y) and is halved for increasing residence times more than 10 y. The average skeleton:liver ratio was 65:20 = 3.25." ]

[ 0, 0.004672897196261682, 0, 0.00546448087431694, 0, 0, 0.01282051282051282, 0 ]

[ "PET and PET/CT with radiolabeled choline in prostate cancer: a critical reappraisal of 20 years of clinical studies.", "\nWe here aim to provide a comprehensive and critical review of the literature concerning the clinical applications of positron emission tomography/computed tomography (PET/CT) with radiolabeled choline in patients with prostate cancer (PCa). ", "We will initially briefly summarize the historical context that brought to the synthesis of [11C]choline, which occurred exactly 20 years ago. ", "We have arbitrarily grouped the clinical studies in three different periods, according to the year in which they were published and according to their relation with their applications in urology, radiotherapy and oncology. ", "Studies at initial staging and, more extensively, studies in patients with biochemical failure, as well as factors predicting positive PET/CT will be reviewed. ", "The capability of PET/CT with radiolabeled choline to provide prognostic information on PCa-specific survival will also be examined. ", "The last sections will be devoted to the use of radiolabeled choline for monitoring the response to androgen deprivation therapy, radiotherapy, and chemotherapy. ", "The accuracy and the limits of the technique will be discussed according to the information available from standard validation processes, including biopsy or histology. ", "The clinical impact of the technique will be discussed on the basis of changes induced in the management of patients and in the evaluation of the response to therapy. ", "Current indications to PET/CT, as officially endorsed by guidelines, or as routinely performed in the clinical practice will be illustrated. ", "Emphasis will be made on methodological factors that might have influenced the results of the studies or their interpretation. ", "Finally, we will briefly highlight the potential role of positron emission tomography/magnetic resonance and of new radiotracers for PCa imaging." ]

[ 0.017241379310344827, 0.004132231404958678, 0, 0, 0.00625, 0.007518796992481203, 0, 0, 0, 0.0070921985815602835, 0, 0 ]

[ "2019 Kate Sheppard Cup\n\nThe 2019 Kate Sheppard Cup is New Zealand's women's 25th annual knockout football competition. ", "This is the second year that the competition is known by the Kate Sheppard Cup, or New Zealand Football Foundation Kate Sheppard Cup for sponsorship purposes, after previously been known as the Women's Knockout Cup since its establishment.", "\n\nThe 2019 competition has three rounds before quarter-finals, semi-finals, and a final. ", "Competition will run in three regions (northern, central/capital, southern) until the quarter-finals, from which stage the draw will be open. ", "In all, 40 teams entered the competition.", "\n\nThe 2019 final\nThe 2019 final saw Eastern Suburbs win their first Kate Sheppard Cup as well as completing a league-cup double after earlier winning the Northern Region Football League's premier women's division. ", "The final was played at North Harbour Stadium before the men's Chatham Cup final. ", "This was Eastern Suburbs's third finals appearance, having lost twice previously in 2005 and 2017. ", "It was also Coastal Spirit third appearance however while they lost in their first appearance in 2011, they had won the cup before in 2013 in a final that was played at home in Christchurch.", "\n\nAn early goal to Suburbs inside the first five minutes to Hannah Pilley was quickly followed up by Tayla O'Brien in the ninth. ", "Pilley got her second in the 25th minute and by that stage Suburbs was controlling the game. ", "O'Brien got her second in the 35th minute which saw Suburbs go into the half up four nil. ", "Suburbs controlled the second half and while they had a few more chances they also kept Coastal scoreless, leaving the final score the half time score. ", "Tayla O’Brien was jointly awarded the Maia Jackman trophy for the most valuable player with Suburbs fullback Erinna Wong.", "\n\nResults\n\nRound 1\nAll matches will be played on the weekend of 11–12 May 2019.", "\n\nCentral/Capital Region\n\nMainland Region\n\nSouthern Region\n\nAll teams listed below received byes to the second round.", "\nNorthern Region: Hibiscus Coast, Forrest Hill Milford United, Glenfield Rovers, Waitemata, Warkworth, Three Kings United, Central United, Ellerslie, Eastern Suburbs, Western Springs, Bucklands Beach, Papakura City, Onehunga Sports, Waiuku, Claudelands Rovers, Hamilton Wanderers.", "\nCentral/Capital Region: Palmerston North Marist, Wairarapa United, Seatoun, Western Suburbs, Wellington United.", "\nMainland Region: Nelson Suburbs.", "\nSouthern Region: Dunedin Technical, Green Island.", "\n\nRound 2\nAll matches were played on Queen's Birthday weekend 31 May - 3 June 2019.", "\n\nNorthern Region\n\nCentral/Capital Region\n\nMainland Region\n\nSouthern Region\n\n* Match defaulted by Warkworth.", "\n\nRound 3\nAll matches were played on the weekend 15–16 June 2019.", "\n\nNorthern Region\n\nCentral/Capital Region\n\nMainland\n\nSouthern Region\n\nQuarter-finals\nAll matches were played on the weekend 6–7 July 2019.", "\n\nNorthern Region\n\nCentral/Capital Region\n\nMainland/Southern Region\n\nSemi-finals\nMatches were played on the weekend 24–25 August 2019.", "\n\nFinal\nThe final was played on the 8 September 2019.", "\n\nReferences\n\nExternal links\nWomen's knockout cup section on the New Zealand Football website\n\nCategory:Women's Knockout Cup\nWomen's Knockout Cup\nWomen's Knockout Cup\nNew Zealand, Kate Sheppard Cup\nNew Zealand, Kate Sheppard Cup\nKate Sheppard Cup" ]

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[ "Image copyright Getty Images Image caption 10-year-old Barron (left) is Donald Trump's youngest son\n\nA Saturday Night Live writer has been suspended after posting a tweet mocking US President Donald Trump's son Barron, US media reports say.", "\n\nThey quote a person familiar with SNL's plans as saying Katie Rich was suspended indefinitely. ", "The programme's network, NBC, is yet to comment.", "\n\nOn Friday, Ms Rich posted a now-deleted tweet, saying \"Barron will be this country's first home-school shooter\".", "\n\nAn avalanche of criticism on social media followed.", "\n\nMs Rich later deleted her tweet, suspending her Twitter account.", "\n\nHowever, on Monday she was back online to issue an apology.", "\n\nImage copyright Twitter\n\nOne Facebook post in reaction to her previous tweet has been shared nearly three million times.", "\n\nThe post read: \"NO child deserves to be talked to in such a manner... He is a child, he is to be respected and he is off limits\".", "\n\nChelsea Clinton, a former first child, joined the support for Barron.", "\n\nImage copyright Twitter\n\nSNL has made a number of shows in recent months, parodying President Trump.", "\n\nMr Trump, who took office on 20 January, has described the programme as \"not funny\" and with \"terrible\" cast." ]

[ 0.016666666666666666, 0.020618556701030927, 0.020833333333333332, 0.008771929824561403, 0, 0, 0, 0, 0, 0.028169014084507043, 0.029411764705882353, 0.009009009009009009 ]

[ "The politics behind the Diversity Visa Program\n\nThe Moslem who ran down people in Manhattan this week came to American from Uzbekistan in 2010 through the Diversity Visa Lottery Program, a program that selects up to 50,000 foreigners annually from countries that have sent fewer than 50,000 people to the U.S. in the past five years.", "\n\nIt’s part of the 1990 Immigration Act passed with bi-partisan support and signed into law by globalist George H.W. Bush. ", "The program was ostensibly designed to allow into the U.S. more Irish immigrants as a sort of reparation for the anti-Irish bias contained in the 1965 Immigration Act.", "\n\nSayfullo Saipov, who on Tuesday drove a rented truck onto a New York bike path, killing eight people and injuring 13, is the second (at least) murderer allowed into the U.S. via the Diversity Visa lottery system. ", "In 2002 an Egyptian terrorist killed two people in Los Angeles. ", "He was allowed in the U.S. because his wife had been granted a Diversity Visa.", "\n\nLeftist politicians are defending the program. ", "Of course, leftist politicians from both major parties are always promoting diversity as if it’s a way to create a better society. ", "But diversity is a code word for anti-white, anti-Christian and anti-liberty.", "\n\nPrograms promoting diversity are designed to create minorities that can be manipulated and agitated to contribute to the power and collectivism of government. ", "One can always identify minority special interests simply because they welcome government intervention and intrusion (socialism) as a net for perceived social inequality, poverty and underachievement. ", "Guilt manipulation and all manner of charades are used to force social and economic equality where none is earned. ", "Manipulating minorities who are naturally drawn to socialism is a basic political strategy to justify government politics and plunder.", "\n\nMass immigration is part of the globalist agenda for world fascism and is phase two of the free trade movement, the first phase of which exported American manufacturing jobs and companies to Third World nations. ", "By this method the globalists circumvent the American political process (another notorious Council on Foreign Relation “end run around national sovereignty,” as Richard Gardner described it), for certainly very few Americans would vote to revolutionize the white middle class population base and to create an Aztlan or New Africa nation that looks and acts nothing like themselves. ", "It’s one of the list of things I wrote in September 2004 that all governments want/need to use to destroy liberty and enslave their populations.", "\n\nThe principle of government is that political power is maximized by forcibly leveling every individual to the same status of conformity, collectivism, ecumenicalism and serfdom. ", "The truth goes deeper. ", "Because of perceived social, cultural, racial and psychic inferiority, minorities desire to parasite on government force and socialism to subvert those they envy and wish to imitate.", "\n\nIt would never succeed except for the very sophisticated propaganda of altruism. ", "Altruism has a double meaning. ", "To the unsuspecting public, it appears good; hence the creation of the term, “diversity” and its use as a purported means to advancing American society. ", "But it is hypocrisy with a hidden agenda to cover evil. ", "It is the philosophical basis of democracy and benevolent totalitarianism.", "\n\nAltruism cleverly hides the depravity of human nature. ", "It makes evil appear good and good appear evil. ", "See no evil, hear no evil, do no evil permeates the propaganda. ", "It conceals the political agenda, promotes ignorance, creates a state of mind of dependence on government and quashes every form of individualism, independence and creative thinking.", "\n\nThe globalists’ plan to import great masses of Third World peoples to take American jobs at starvation wages and thus finish off the middle class once and for all has been ongoing for decades and supported by both parties. ", "As the Democrats discovered, and as George W. Bush’s establishment branch of the Republicans seeks to take advantage of, Third Worlders make a wonderful voter base for the expansion of national collectivism, a wonderful new crop of potential unionists and a pool of potential slave wage workers for the crony corporations. ", "And those on the Diversity Visa Program are automatically registered for the entire spectrum of U.S. welfare upon arrival.", "\n\nAnd there is more to it. ", "All governments need crisis, no matter how much lip service they give to “peace.” ", "Crisis is a well-known Machiavellian strategy to gain and solidify political power and persuade public opinion.", "\n\nCrisis provides the stage where governments can control all sides. ", "At least they can arrange events to “naturally” unfold.", "\n\nGovernments must have scapegoats and phony enemies. ", "The people must have perceived threats to their security, and so naturally government is there to “protect.” ", "Governments must have enemies to the extent that they finance them, as the U.S. government and its allies did with al-Qaida, and have been doing with ISIS. ", "There can be no military budgets without perceived enemies." ]

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[ "Tracheostomy or endotracheal tubes are often placed in severely injured or ill patients to assist them in breathing. ", "In many instances, a ventilator is connected to the tube to provide controlled ventilation.", "\nPatients with tracheostomy tubes and ventilator circuitry are many times severely compromised and ill due to associated complications. ", "Existing in these patients are various complications from tube movement, circuitry weight and accidental circuitry disconnections. ", "These complications can create discomfort, skin, stoma and tracheal irritation, skin, stoma and tracheal malacia, leading to potential infections and surgical intervention, brain injury or death. ", "The unintended pressure from the weighty and moving circuitry may result in tubing disconnection, Stoma site damage and posterior wall tracheal damage from improper tube positioning.", "\nTracheostomy and endotracheal tubes were customarily supported in place by a thin cotton tape extending about the neck or head of a patient. ", "The cotton tape was typically tied to slotted flanges on either side of the tube to secure it in place. ", "This method for securing a tracheostomy or endotracheal tube has many drawbacks. ", "The cotton tape had to be threaded through and knotted to each flange or separate pieces had to be threaded through the flanges and then tied to each other to secure the tube. ", "There was no convenient means for securing and/or adjusting the cotton tape to ensure a proper fit. ", "This could result in a poorly secured or mislocated tracheostomy tube, contributing to the potential for injury of the soft tissues surrounding the stoma of a tracheostomy.", "\nThe cotton tape utilized to secure the tube also has a tendency to stretch more at the edges than at the center as it is being installed, and the tying process further distorts the tape. ", "This results in an uneven force distribution across the width of the tape causing patient discomfort and possible skin irritation. ", "This condition is evidenced by the typical curl at the edges of the cotton tape.", "\nBecause of the degree of intensive care required in using tracheostomy or endotracheal tubes and their accompanied tubing and circuitry, ease in maintaining the tracheostomy tube through adjustment or replacement of the retention means is also a prime concern. ", "Not only must the retention means be easy to install and adjust, but asepsis concerns make it desirable that the retention means be low cost, soft fabric, skin friendly and therefore disposable.", "\nU.S. Pat. ", "No. ", "4,313,437 to Martin, issued Feb. 2, 1982, and U.S. Pat. ", "No. ", "4,331,144 to\nWapner, issued May 25, 1982 have attempted to address some of these problems. ", "Both show the use of a padded foam neck band and VELCRO™ fastening means. ", "These provide easier installation, replacement and adjustment as well as more even force distribution and patient comfort. ", "Although the tube retainer disclosed by Martin does provide for some expansion or contraction once installed, it has limited adjustability and several sizes are required for different size patients.", "\nThe support provided by Wapner involves a more complex structure. ", "It utilizes two straps, one of which has an elastic webbing portion. ", "This is to allow the attendant applying the band to select a comfortable pressure for securing the band to the patient. ", "Because of its more complex structure, this support band is more costly to manufacture.", "\nU.S. Pat. ", "No. ", "5,101,822 (Kimmel), issued Apr. 7, 1992, also attempts to address these problems. ", "Kimmel discloses a two-piece collar system which appears complex and requires the alignment of snaps on the two collar pieces and threading tapes from one collar piece through loops in the other for installation. ", "This more complex structure could increase the cost of the device making disposable usage cost prohibitive.", "\nU.S. Pat. ", "No. ", "5,357,952 (Schuster), issued Oct. 25, 1994 addresses these problems by disclosing a collar with a complex buckle and long securement strap to retain circuitry. ", "However, the buckle system is found to be difficult to engage and the hard , hook material used on the long strap may potentially lead to skin irritation and skin breakdown issues as well as difficulty in application of securement strap.", "\nNone of these devices provide a means for positively retaining a ventilator tube connection to the tracheostomy tube in an uncomplicated method without risking skin irritation and infection risks." ]

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[ "One of the key silhouettes of the season, our Simone patterned shirt dress is adorned with delicate botanical prints and embroidered trims. ", "This button-up style has a flattering v-shaped neckline and three-quarter length sleeves, and is cinched at the waist with a self-tie sash.", "\n\nSophisticated in its simplicity, Three Dot's chic Lbd is tailored in a casual shirting silhouette. ", "The sleeveless design makes this piece ideal for layering--style it with trending bombers, sleek moto jackets and more." ]

[ 0.007142857142857143, 0, 0.009900990099009901, 0 ]

[ "On the day in which fallen Peace Corps volunteer Nick Castle would have celebrated his 28th birthday, legislation has been introduced in the United States Senate to address a series of issues related to the health and safety of Volunteers.", "\n\nThe Nick Castle Peace Corps Reform Act of 2018 (S. 2286) was introduced Wednesday, January 10th by Senator Bob Corker (R-TN), Chairman of the Senate Foreign Relations Committee. ", "Other lead sponsors include Senators Johnny Isakson (R-GA), Dianne Feinstein (D-CA) and Chris Coons (D-DE).", "\n\nNick Castle died while serving in China in 2013. ", "A November 2014 report on the death by the Peace Corps Office of Inspector General cited poor judgement and misdiagnosis by the Peace Corps Medical Officer, as well as \"cascading failures and delays in treatment.\"", "\n\nAbout the Legislation\n\nProvisions in the Corker legislation would ensure that \"the Peace Corps maintains well-qualified and capable medical officers and support staff for overseas Peace Corps posts and that the Director reviews and evaluates the performance of such staff and implements outstanding recommendations by the Inspector General to improve associated systems and programs.\"", "\n\nAnother key provision would allow Peace Corps to be fully involved in the diagnosis, treatment and support of returning Volunteers with service related illness or injuries for a four-month period following their completion of service. ", "Currently, volunteers who come home with service-related health issues are swiftly referred to the U.S. Department of Labor (DoL) for benefits provided under the Federal Employees Compensation Act (FECA).", "\n\nAlong with requiring public disclosure of volunteer satisfaction surveys and other reporting requirements, the legislation would also promote further reforms and extend key initiatives pertaining to sexual assault and other acts of violence against volunteers. ", "This includes a re-authorization of the Peace Corps Office of Victim Advocacy and the agency's Sexual Assault Advisory Council.", "\n\nClick here for a copy of the legislation.", "\n\nClick here for Senator Corker's press release.", "\n\nHouse Legislation\n\nMeanwhile, Peace Corps health legislation in the House of Representatives (H.R. 2259) introduced last May by Congressman Ted Poe (R-TX) and returned Peace Corps Volunteer Joseph Kennedy III (D-MA) has a bi-partisan list of nearly 50 co-sponsors.", "\n\nAlong with the most provisions outlined above, the House legislation also includes an important proposal for volunteers who served their country but came home with service-related injuries or illness that rendered them temporarily or permanently disabled. ", "The legislation proposes raising the worker's compensation payments for these individuals. ", "This has been a priority issue of the affiliate group Health Justice for Peace Corps Volunteers, which has led efforts and worked tirelessly for years on efforts to provide relief for those in our community who struggle most in the aftermath of their service. ", "However, questions have arisen about the ability to sustain this provision in accordance with House rules on entitlement spending.", "\n\nForward Motion\n\n\"While the content and presentation of the Senate and House Peace Corps health bills have significant differences, we are grateful that Senator Corker, Congressman Poe and other lead sponsors have introduced legislation to keep us moving forward,\" said NPCA President and CEO Glenn Blumhorst. \"", "Taken together, both bills contain improvements, reforms and re-authorizations that are important to various members of our community. ", "We look forward to continued progress with Senate and House sponsors, and urge them to work collaboratively so we can come away with the best possible legislation to support our Volunteers and respect their sacrifices in serving our country.\"", "\n\nTake Action\n\nCall your Senators and ask them to support and advance S. 2286, Peace Corps health legislation introduced by Senator Corker.", "\n\nIf your Congressman/woman has not yet co-sponsored H.R. 2259, take action here." ]

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[ "// Copyright 2018 The Chromium Authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style license that can be\n// found in the LICENSE file.", "\n\n#ifndef CEF_LIBCEF_BROWSER_EXTENSIONS_EXTENSIONS_BROWSER_API_PROVIDER_H_\n#define CEF_LIBCEF_BROWSER_EXTENSIONS_EXTENSIONS_BROWSER_API_PROVIDER_H_\n\n#include \"base/macros.h\"\n#include \"extensions/browser/extensions_browser_api_provider.h\"\n\nnamespace extensions {\n\nclass CefExtensionsBrowserAPIProvider : public ExtensionsBrowserAPIProvider {\n public:\n CefExtensionsBrowserAPIProvider();\n ~CefExtensionsBrowserAPIProvider() override;\n\n void RegisterExtensionFunctions(ExtensionFunctionRegistry* registry) override;\n\n private:\n DISALLOW_COPY_AND_ASSIGN(CefExtensionsBrowserAPIProvider);\n};\n\n} // namespace extensions\n\n#endif // CEF_LIBCEF_BROWSER_EXTENSIONS_EXTENSIONS_BROWSER_API_PROVIDER_H_\n" ]

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[ "Sulfhydryl compounds, a class of radioprotectors, were originally developed to protect against nitrogen mustard gas. ", "Therefore, those compounds may be useful in protecting against chemotherapeutic drugs whose action is mainly alkylation. ", "The purpose of this work is to study the ability of WR 2721 and other radioprotectors to protect critical normal tissues against damage from chemotherapeutic agents." ]

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[ "Call Us For A FREE Quote 713-412-0900 Visit Our Office Furniture Showroom Located at 10704 Telge Rd, Houston, TX 77095. ", "Visit Our Office Furniture Showroom Located at 10704 Telge Rd, Houston, TX 77095.", "\n\nModern Office Cubicles\n\nThink you know everything there is to know about cubicles? ", "Think again. ", "Celebrating its 50th anniversary this year, the cubicle was an innovative concept when it first debuted in 1965, and has continued to evolve ever since. ", "Today’s modern cubicles offer advanced functionality and a breadth and depth of features which give new meaning to the phrase, “outside the box.” ", "Read on to learn more about what you can expect from today’s modern cubicles, as well as how to choose the best fit for your employee needs and office space.", "\n\nFrom Humble Origins…\n\nCubicles were the brainchild of leading furniture design company Herman Miller’s research team, spearheaded by Robert Probst. ", "At the time, most office workers sat at open desks with a complete lack of privacy and storage. ", "While carrel tables were standard operating procedure in environments like libraries, these privacy-enhancing designs had yet to penetrate the office until Probst came along and forever changed the landscape of the American workplace.", "\n\nContrary to common misconception, original cubicle designs were more than mere partitions. ", "They also integrated functional elements, such as vertical storage, display boards, and even standing desk elements.", "\n\nWhile many of these features continue to serve contemporary office workers, they’ve since been joined by many other innovative elements.", "\n\n…To Modern Office Cubicles\n\nThe world is a more knowledgeable place today than it was 50, 25 or even 10 years ago, and cubicles help transform this knowledge into more productive workplace solutions.", "\n\nOne change characterizing modern office cubicles in the era of collaboration? ", "Set-ups that allow privacy while also encouraging teamwork and communication between employees. ", "Some cubicles even offer space for meetings! ", "And while smaller cubicles are still ideal for certain workplaces, such as call centers, today’s larger “executive” style cubicles can also support the work of upper level employees.", "\n\nMobile also continues to guide changes to workflow, and contemporary cubicles nod at the need for both wired and wireless connectivity for everything from phones and tablets to laptops.", "\n\nAnd don’t forget that the science of ergonomics has made huge strides in recent years. ", "From built-in task lighting which spares eyes and prevents headaches to awareness and acknowledgement of the importance of a healthy “reach zone,” today’s cubicles not only help employees work smarter, but also healthier. ", "This isn’t just good news for employees, but also for employers battling high healthcare costs and worker’s compensation claims.", "\n\nIt’s not just about functionality, however. ", "A welcoming and aesthetically appealing office invites employees, clients and other visitors to gather. ", "Different colors, fabrics and design elements ensure a look that coordinates with your overall scheme.", "\n\nSpace Planning Success\n\nBut finding the right cubicle is only part of the equation. ", "Another equally important factor? ", "An efficient and effective office set-up.", "\n\nA professional space planner can mean the difference between wasted space and unnecessary downtime and a smooth seamless workflow. ", "Companies like Cubiture don’t just sell cubicles, but also offer the means to organize your office to its optimal functionality.", "\n\nToday’s office cubicles don’t merely offer privacy, but also the exciting opportunity for employers to leverage technology into better productivity. ", "Just as the newest generation of workers offer new skills and capabilities, so have the newest generation of cubicles evolved to meet them." ]

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[ "In a general floating caliper disc brake device, a caliper arranged astride a disc rotor is supported on a mounting bracket. ", "Further, a pair of slide pins is provided to the caliper, and fitting holes to which the pair of slide pins is slidably fitted are provided to the mounting bracket. ", "Accordingly, the slide pins slide along the fitting holes so that the caliper is movable in a rotational axis direction of a wheel. ", "In addition, an inner pad (friction pad) is movably supported on one side of the caliper, and an outer pad (friction pad) is fixed on the other side thereof. ", "Moreover, a piston and a cylinder are provided to the caliper so as to press the inner pad on one side against the disc rotor (bring the inner pad into press contact with the disc rotor).", "\nIn such a floating caliper disc brake device, when a driver steps on a brake pedal, the piston supported on the cylinder advances in accordance with a leg power thus generated so that the inner pad is pressed against the disc rotor (the inner pad is brought into press contact with the disc rotor). ", "Further, the caliper moves in the rotational axis direction of the wheel due to a reaction force generated through the advance of the piston so that the outer pad is pressed against the disc rotor (the outer pad is brought into press contact with the disc rotor). ", "Accordingly, the inner pad and the outer pad can squeeze the disc rotor, and can therefore apply a braking force to the wheel via the disc rotor rotating integrally with the wheel.", "\nBy the way, the piston provided to the caliper is movably supported on the cylinder that is formed in the caliper, and is retained by a piston seal in a fluid tight manner. ", "When a hydraulic fluid (brake fluid) is supplied at the time of braking to a hydraulic pressure chamber that is formed in the cylinder, the piston advances while deforming the piston seal, and when the hydraulic pressure is released (removed) from the hydraulic pressure chamber, the piston retreats toward the hydraulic pressure chamber due to a restoring force of the deformed piston seal. ", "However, when the leg power of the driver applied to the brake pedal is excessively large, for example, along with the increase in hydraulic pressure in the hydraulic pressure chamber, the piston is pushed toward the disc rotor to a higher extent than in a predetermined setting. ", "Hence, a relative movement occurs between the piston and the piston seal, which may hinder the piston from retreating sufficiently due to the restoring force of the piston seal. ", "In this case, there may occur such a phenomenon that the inner pad or the outer pad is continuously held in contact with the disc rotor, that is, a so-called drag phenomenon. ", "Further, when the drag phenomenon occurs as described above, there may occur so-called knockback, in which the inner pad or the outer pad is knocked by the rotating disc rotor and therefore the piston is pushed backward.", "\nTo address those problems, for example, a disc brake device disclosed in JP 07-253128 A, a disc brake caliper disclosed in JP 05-65929 A, a disc brake device disclosed in JP 2009-156292 A, and a floating disc brake disclosed in JP 2009-185976 A have been known conventionally." ]

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[ "Q:\n\nJAX-RS: Multiple paths\n\nIs it possible to do something like that?", "\nimport javax.ws.rs.", "GET;\nimport javax.ws.rs.", "Path;\n\npublic class xxx\n{\n @GET\n @Path(value = \"path1\")\n public Response m1()\n {\n ...\n }\n\n @GET\n @Path(value = \"path2\")\n public Response m2()\n {\n ...\n }\n}\n\nI'm using RESTEasy.", "\n\nA:\n\n@Path(\"/{a:path1|path2}\")\n\nFrom resteasy docs:\nhttp://docs.jboss.org/resteasy/docs/1.0.2.GA/userguide/html_single/index.html#_Path_and_regular_expression_mappings\n\nA:\n\nyes you can do that although you will have to rename your methods so that their signature is different.", "\nUpdate: Check Dieter Cailliau's answer, @Path(\"/{a:path1|path2}\") is probably what you want...\npublic class BlahResource{\n @GET\n @Path(\"path1\")\n public Response m1(){\n return Response.ok(\"blah\").build();\n }\n\n @GET\n @Path(\"path2\")\n public Response m2(){\n return this.m1();\n}\n\nyou can check JSR-311's API and it's reference implementation named \"jersey\" there:\nJSR311 API \nJersey \n\nA:\n\nSome extra details about Path annotation...\nAs a previous responses state, regular expressions to be used with in the annotated path declaration mapping:\n{\" variable-name [ \":\" regular-expression ] \"} \n\nYou can declare multiple paths, but there is also a path hierarchy that was not immediately obvious to me whereby the class annotated path prefixes the following method path annotations. ", "One might write the following class for a concise multiple path option which could be useful for resource versioning perhaps.", "\n@Path(\"/{a:v1|v2}\")\n@Produces(\"text/*\")\npublic class BlahResource {\n\n @GET\n @Path(\"/blah\")\n public Response m1() {\n return Response.ok(\"blah\").build();\n }\n}\n\nPlease note the fact that the class \"BlahResource\" has been declared with the path \"/v1\" or \"/v2\" making the resource accessible as:\n$ curl localhost:8080/v1/blah\nblah\n\nand also\n$ curl localhost:8080/v2/blah\nblah\n\n" ]

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[ "App Store Preview\n\nEarthChat\n17+\n\nThe universal translator\n\niPhone Screenshots\n\nDescription\n\nEarthChat is an instant messaging and social media app that offers real-time translation in over 100 languages.", "\n\nEarthChat was created with the goal to bring the world closer together by eliminating the language barrier. ", "We hope this will spark new conversations, friendships, and an overall better understanding of people.", "\n\nHow does it work? ", "It’s incredibly simple, the translations occur automatically; you don’t have to do anything. ", "You will see everything in English, or whatever language you are most comfortable with, as will any other user.", "\n\nFor example, if a user’s native tongue is Spanish, they will set their language settings to “Spanish,” and any conversation they have will be translated into Spanish. ", "They can have a natural conversation with someone who speaks Russian, and their phone will have the dialogue in Spanish, and the Russian user will see the discussion in Russian.", "\n\nYou can keep up with your friends across the globe or just down the street with the EarthChat social media feed. ", "Don’t let the language barrier stop you!", "\n\nWhat's New\n\nVersion History\n\n2.5\n\nMay 16, 2018\n\nA few minor upgrades.", "\n\n2.4\n\nMay 14, 2018\n\nBigger stickers and other fun enhancements.", "\n\n2.3\n\nMay 9, 2018\n\nFixed some minor bugs\n\n2.2\n\nMay 4, 2018\n\nOver 100 new languages added!", "\n\n2.1\n\nMay 2, 2018\n\nBug fixes\n\n1\n\nFeb 28, 2018\n\nMay 16, 2018\n\nVersion 2.5\n\nA few minor upgrades.", "\n\nRatings and Reviews\n\nWorks well for chatting with people in different languages\n\nMay 14, 2018\n\nDeePeaG\n\nI had an amazing conversation with an Italian woman. ", "She was typing in Italian and I was typing in English. ", "Very cool!", "\n\nWorks well for chatting with people in different languages\n\nMay 14, 2018\n\nDeePeaG\n\nI had an amazing conversation with an Italian woman. ", "She was typing in Italian and I was typing in English. ", "Very cool!" ]

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[ "Search This Blog\n\nContact the Blog\n\nJoin me on the forum below as I am on the staff as Samuria 24/7/365 worldwide support\nall FREE\n\n&nbsp\n\n'\n\nMonday, 11 February 2013\n\nCheshire Police say ‘speak out’ this Valentines!", "\n\nDo not suffer in silence this Valentine’s Day − that is the message that Cheshire Police want to give out.", "\n\nCheshire Police’s ‘speak out, don’t be silent’ campaign seeks to encourage victims to speak out. ", "Officers receive specialist training in investigating this type of crime. ", "They work closely alongside a number of voluntary organisations and council departments within the local community to tackle the issue and to provide a life line to the victim and places of safety if needed.", "\n\nValentine’s Day should be a day filled with romance − with ‘loved up’ couples showing their affection for each other on this special day. ", "At this time of year, the message to speak out is particularly pertinent as many celebrate their love for each other whilst undertones of domestic abuse can be prevalent through other times of the year in a relationship. ", "Domestic abuse is not just confined to women - many men and women continue to endure domestic abuse and sexual violence for the sake of keeping their relationship together at these times.", "\n\nNo one should have to put up with emotional, physical or sexual abuse by their partner. ", "Being abused can often result in low self esteem for the victim, particularly if the abuse continues over a sustained period which can feel isolating if there is nowhere else to turn. ", "A feeling of desperation can result because in some cases their partner may have pressured them into severing ties with their family and friends making it difficult for them to confide in someone close.", "\n\nDetective Chief Inspector Nigel Wenham, who leads the Strategic Public Protection Unit with Cheshire Constabulary, said: \"We hope that by raising awareness of the issue and reinforcing our commitment to victims of abuse that it will encourage more victims to come forward. ", "Domestic abuse is an issue that Cheshire Police takes extremely seriously and is not acceptable under any circumstances. ", "We are committed to taking action to bring offenders to justice and holding them to account for their behaviour. ", "We urge anyone who is a victim, male or female, of any type of domestic abuse to come forward and report it. ", "Every report will be treated confidentially.\"", "\n\nDomestic abuse will not be tolerated and subjecting others to acts of violence - often resulting in injury, so the message to all abusers is to think about the consequences of your actions." ]

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[ "Daisy Miller by Henry James (Tor Classics)\n\nTor Classics are affordably-priced editions designed to attract the young reader. ", "Original dynamic cover art enthusiastically represents the excitement of each story. ", "Appropriate \"reader friendly\" type sizes have been chosen for each title—offering clear, accurate, and readable text. ", "All editions are complete and unabridged.", "\n\nAmerican teenager Daisy miller was on a holiday--and Europe might never recover. ", "From Switzerland to Rome, she caused scandals everywhere: because Daisy Miller did whatever she wanted, with whomever she wanted, whenever she chose. ", "And she truly didn't care what society thought.", "\n\nBut Winterbourne, a dignified, proper, upper-crust young man, was utterly fascinated by her. ", "To the horror of his relatives and friends, Winterbourne helplessly followed Daisy across a continent. ", "Even though Daisy was too much woman for WInterbourne to every understand...\n\nAnd even though Daisy Miller might be a danger to herself.", "\n\nAt the publisher's request, this title is being sold without Digital Rights Management software (DRM) applied.", "\n\nColm Tóibín was born in Ireland in 1955. ", "He is the author of six novels including The Blackwater Lightship; The Master, winner of a Los Angeles Times Book Prize; and Brooklyn, winner of a Costa Book Award. ", "Twice short-listed for the Man Booker Prize, Colm Tóibín is the Leonard Milberg Lecturer in Irish Studies at Princeton University and lives in Dublin and New York." ]

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[ "Les Vraies Housewives\n\nLes Vraies Housewives (translated The Real Housewives and abbreviated LVH) was a French reality television series that aired on NT1 on March 18, 2013 until April 1, 2013. ", "Developed as international installment of the Real Housewives franchise, it aired only one season and documented the personal and professional lives of several French women residing in Beverly Hills, California.", "\n\nOverview and casting\n\nThe series premiered on March 18, 2013 with a cast of five women; Soumaya Akaaboune, Christina Amrani, Karine Kaplan, Christine Snider-Decroix, and Natalie Wizman. ", "\nDuring its airing, the French press was very critical of the programme and referred to the series as a \"mirror of stupidity.\"", "\n\nThe series was not subsequently renewed and remained a one season series.", "\n\nTaglines\nChristina: \"I'm not the richest, but I intend to become.\"", "\nChristine: \"Luxury is great but money does not always bring happiness!\"", "\nKarine: \"You're either gonna love me or hate me!\"", "\nNatalie: \"In life, I can be sweet, but annoy me and the claws come out, rawr!\"", "\nSoumaya: \"I don't like staying in the shadows.\"", "\n\nReferences\n\nExternal links\n \n\nCategory:2010s French television series\nCategory:2013 French television series debuts\nCategory:2013 French television series endings\nCategory:French-language television programs\nCategory:Television shows set in Beverly Hills, California\nCategory:The Real Housewives" ]

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[ "Q:\n\nNot receiving GET response from Express server\n\nWhen I send a GET req from my client to my Express server it sends the data to the client but I get an XMLHttpRequest ready state of 1 and a status of 0 and it never logs the response text.", "\nClient:\nreq.onreadystatechange = function() {\n console.log(this.readyState);\n if (this.readyState == 4 && this.status == 200) {\n console.log(this.responseText);\n }\n};\nreq.open('GET', url + 'users', true);\nreq.send();\n\nServer: \napp.get('/users', function(req, res) {\n res.send(users);\n});\n\nIf anyone can tell me why I can't receive the array of users on client side and how to fix it. ", "That would be great.", "\n\nA:\n\nFirst I would use fetch javascript because it looks more natural.", "\n/* on server */\napp.get('/users', function(req, res) {\n res.send(users);\n});\n\n/* on client */\nfetch('/users').then(async (response) => {\n if (response.status === 200) {\n console.log(await response.text());\n // do you receive something ?", "\n }\n else {\n throw new Error('something unexpected occurred');\n }\n}.catch(err => { console.err(err) })\n\nIf you don't receive anything, then you should check if your front page is served from the same data-providing server because when you call for /users the browser is prepending the host to the path. ", "So if both your client page and your back server is not running on the same host it will fail.", "\n\n" ]

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[ "Conquer (album)\n\nConquer is the sixth studio album by the band Soulfly. ", "It saw official release on July 23, 2008, in Australia, although the album had leaked early onto file-sharing networks. ", "It was released on July 29, 2008 in Canada and the United States and debuted at #66 on the U.S. Billboard 200 — Soulfly's highest Billboard peak since their 2002 release, 3.", "\n\nProduction and release\nThe album was tracked by Tim C. Lau in late 2007 at The Porch Recording Studio in Orlando Florida and mixed by Andy Sneap in early 2008. ", "In promotion for the album, Max Cavalera stated that he had been heavily influenced by Bolt Thrower, Napalm Death and Slayer in writing for this album, which he declared would make Dark Ages sound like a pop album.", "\n\nA bonus edition of the album was released containing three bonus tracks and a DVD. ", "The DVD features a full live concert from Warsaw, Poland and the music video for \"Innerspirit\" from the previous album, Dark Ages.", "\n\nThe album sold over 8,400 copies in the U.S. during the first week of its release.", "\n\nSongs\n\"Unleash\" was the album's first single with the accompanying music video directed by Robert Sexton. ", "This song and its video features Dave Peters of Throwdown. ", "The second single released was Blood Fire War Hate, the first track of the album, featuring Morbid Angel vocalist David Vincent. \"", "Touching the Void\" is heavily influenced by Black Sabbath as it contains doom and sludgy riffs, with outro recorded by French dub artist Fedaya Pacha. \"", "Warmageddon\" explores war and Armageddon, hence its portmanteau.", "\n\nCritical reception\nConquer has thus far garnered positive reviews from most media outlets and review websites. ", "Chad Bower of About.com calls it \"outstanding\", with \"great musicianship and songwriting\" and \"new styles, sounds and experiments, which also hit the mark.\" ", "Nikos Patelis of Metal Invader notes the \"hardcore beatings, extreme thrash speeds and many implements of weird sounds that have nothing to do with metal\" and deems the album \"dark as hell\". ", "In comparison to Cavalera Conspiracy's debut earlier this year, Dominic Hemy of Planet Loud considers Conquer \"tighter, heavier, more diverse, more original, and far more engaging than Inflikted\".", "\n\nTrack listing\n\nBonus DVD listing\nLive in Warsaw, Poland\n\"Prophecy\"\n\"Downstroy\"\n\"Seek 'n' Strike\"\n\"No Hope = No Fear\"\n\"Jumpdafuckup/Bring It\"\n\"Living Sacrifice\"\n\"Mars\"\n\"Brasil\"\n\"No\"\n\"L.O.T.M.\"\n\"Porrada\"\n\"Drums\"\n\"Moses\"\n\"Frontlines\"\n\"Back to the Primitive\"\n\"Eye for an Eye\"\n\nMusic Video\n\"Innerspirit\"\n\nPersonnel \n\nSoulfly\n Max Cavalera – lead vocals, 4-string guitar, berimbau, sitar\n Marc Rizzo – guitar, flamenco guitar\n Bobby Burns – bass guitar\n Joe Nunez – drums, percussion\nAdditional musicians\n David Vincent – additional vocals on \"Blood Fire War Hate\"\n Dave Peters – additional vocals on \"Unleash\"\n Fedayi Pacha – duduk, percussion on \"Touching the Void\", dub outro on \"For Those About to Rot\"\n Jean-Pol Dub - didgeridoo on \"Touching the Void\"\n Tim Lau - drum programming\n\nProduction\n Max Cavalera - production\n Tim Laud productions - engineering, recording\n Tim Lau - digital editing\n Andy Sneap - mixing\n Ted Jensen - mastering\n Monte Conner - A&R\n Logan Mader - mixing on \"The Beautiful People\"\nManagement\n Gloria Cavalera - management\n Christina Stajanovic - assistant\n Bryan Roberts - assistant\nArtwork\nAndroid Jones - artwork\nMax Cavalera - art direction\nCharles Dooher - art direction\n Mr. Scott Disign inc. - ", "design\n Eddie Malluk - band photography\n Leo Zuletta - Soulfly logo\n\nChart positions\nAlbum\n\nReferences\n\nCategory:2008 albums\nCategory:Soulfly albums\nCategory:Albums produced by Max Cavalera\nCategory:Roadrunner Records albums" ]

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[ "Vesicular sequestration limits the buildup of toxic products of enzymatic and spontaneous oxidation of catecholamines. ", "A vesicular storage defect therefore could play a pathogenic role in the death of catecholaminergic neurons in a variety of neurodegenerative diseases. ", "In putamen, deficient vesicular storage is revealed in vivo by accelerated loss of 18F-DOPA-derived radioactivity and post-mortem by decreased tissue dopamine (DA):DOPA ratios; in myocardium in vivo by accelerated loss of 18F-DA-derived radioactivity and post-mortem by increased 3,4-dihydroxyphenylglycol:norepinephrine (DHPG:NE) ratios; and in sympathetic noradrenergic nerves overall in vivo by increased plasma F-dihydroxyphenylacetic acid (F-DOPAC):DHPG ratios. ", "We retrospectively analyzed data from 20 conditions with decreased or intact catecholaminergic innervation, involving different etiologies, pathogenetic mechanisms, and lesion locations. ", "All conditions involving parkinsonism had accelerated loss of putamen 18F-DOPA-derived radioactivity; in those with post-mortem data there were also decreased putamen DA:DOPA ratios. ", "All conditions involving cardiac sympathetic denervation had accelerated loss of myocardial 18F-DA-derived radioactivity; in those with post-mortem data there were increased myocardial DHPG:NE ratios. ", "All conditions involving localized loss of catecholaminergic innervation had evidence of decreased vesicular storage specifically in the denervated regions. ", "Thus, across neurodegenerative diseases, loss of catecholaminergic neurons seems to be associated with decreased vesicular storage in the residual neurons. (", "Goldstein DS, Holmes C, Mash D, Sidransky E, Stefani A, Kopin IJ, Sharabi Y. Deficient vesicular storage: A common theme in catecholaminergic neurodegeneration. ", "Parkinsonism Relat Disord 2015;21:1013-1022.) ", "PD with orthostatic hypotension (PD+OH) can be difficult to distinguish clinically from parkinsonian form of MSA (MSA-P). ", "Cardiac sympathetic neuroimaging by 18F-DAPET scanning efficiently separates these diseases, but this testing is not generally available. ", "We assessed whether plasma biomarkers of a vesicular storage defect can separate PD+OH from MSA-P. After F-DA injection, augmented production of F-dihydroxyphenylacetic acid (F-DOPAC) indicates decreased vesicular storage, and we predicted that arterial plasma F-DOPAC would be elevated in PD+OH but not in MSA-P. We measured plasma F-DOPAC after 18F-DA administration in patients with PD+OH or MSA-P and in healthy control subjects. ", "Peak F-DOPAC:DHPG was calculated, to adjust for effects of denervation on F-DOPAC production. ", "All MSA-P patients had peak F-DOPAC:DHPG <60, in contrast with 9 of 12 PD+OH patients (p<0.0001). ", "Adjustment of peak F-DOPAC for DHPG increased test sensitivity from 58% to 81% at similar high specificity. ", "Thus, after F-DA injection plasma peak F-DOPAC:DHPG distinguishes PD+OH from MSA-P (Goldstein DS, Kopin IJ, Sharabi Y, Holmes C. Plasma biomarkers of decreased vesicular storage distinguish Parkinson disease with orthostatic hypotension from the Parkinsonian form of multiple system atrophy. ", "Clin Auton Res 2015;25:61-67). ", "About 1/3 of PD patients, most MSA patients, and all PAF patients have neurogenic orthostatic hypotension (OH). ", "In a prospective cohort study we compared long-term survival in these synucleinopathies. ", "We found that survival depends on the particular disease, with the risk of death greater in MSA than in PD+OH and in PD+OH than in PD without OH or in PAF. ", "The analysis also demonstrated differential survivals based on 18F-DOPA putamen and 18F-DA cardiac neuroimaging data alone, regardless of the clinical diagnosis (Goldstein DS, Holmes C, Sharabi Y, Wu T. Long-term survival in synucleinopathies: A prospective cohort study of Parkinson disease, multiple system atrophy, and pure autonomic failure. ", "Neurology 2015 (in press)). ", "We recently published post-mortem neurochemical evidence for decreased putamen aldehyde dehydrogenase (ALDH) activity in both PD and MSA (Cook GA, Sullivan P, Holmes C, Goldstein DS. ", "Cardiac sympathetic denervation without Lewy bodies in a case of multiple system atrophy. ", "Park Rel Dis 2014;20:926-928; Goldstein DS, Sullivan P, Holmes C, Kopin IJ, Sharabi Y, Mash DC. ", "Decreased vesicular storage and aldehyde dehydrogenase in multiple system atrophy. ", "Park Rel Dis 2015;21:567-572). ", "We have sought an in vivo biomarker of central ALDH activity. ", "Decreased ALDH activity should increase CSF levels of indices of DA auto-oxidation with respect to indices of DA enzymatic oxidation. ", "We published previously that PD and MSA involve decreased CSF levels of DOPAC, the main deaminated metabolite of DA. ", "To assess DA auto-oxidation we developed and applied an assay method for measuring cysteinyl-DA (Cys-DA) simultaneously with DOPAC. ", "Preliminarily, CSF Cys-DA:DOPAC is about twice as high in PD and MSA as in controls. ", "Elevated CSF Cys-DA:DOPAC may provide an in vivo biomarker of decreased central ALDH activity in parkinsonian disorders. ", "In a collaborative study with Dr. Alessandro Stefani (University of Tor Vergata, Rome, Italy) we have assayed catechols in CSF from patients with PD, progressive supranuclear palsy (PSP), Alzheimers disease (AD), and controls. ", "Preliminarily, we have found decreased CSF DOPAC in PD and PSP and not in AD, replicating and extending on our previous report based on patients referred to the NIH. ", "In parkinsonian disorders low CSF DOPAC seems to provide a biomarker of central dopaminergic deficiency regardless of the particular pathogenetic mechanism. ", "We are using 11C-methylreboxetine (11C-MRB), a positron-emitting ligand for the cell membrane norepinephrine transporter (NET), as a biomarker to visualize sites of noradrenergic innervation by PET scanning. ", "A potential limitation of 11C-MRB PET scanning is non-specific binding of the tracer. ", "To assess non-specific binding, we are examining effects of NET blockade by desipramine on cardiac 11C-MRB-derived radioactivity and are studying patients who are status post cardiac transplantation and therefore have denervated hearts. ", "In the NINDS PDRisk study (NIH Clinical Protocol 09-N-0010) we are following people with multiple PD risk factors (family history, loss of sense of smell, dream enactment behavior, orthostatic hypotension) to determine whether biomarkers of catecholamine deficiency predict later development of PD. ", "The biomarkers we are focusing on are CSF DOPAC, the putamen:occipital cortex (PUT:OCC) ratio of 18F-DOPA-derived radioactivity assessed by brain PET scanning, and the interventricular septal myocardial concentration of 18F-DA-derived radioactivity assessed by thoracic PET scanning. ", "As of this report, 131,084 people have visited the protocol-specific PDRisk website, 3,030 have entered their risk factor data, 371 have been flagged as eligible at the website, and 78 have come to the NIH Clinical Center and have been accrued. ", "Of the 78 accrued at risk participants, 35 have had confirmation of all their risk factors. ", "Of the 35, 3 already had PD at the time of screening and were not studied further, and 32 screened participants have been invited back for inpatient biomarkers testing. ", "Of the 32, 29 have had data obtained for all three biomarkers. ", "Of the 29, 16 (55%) have had at least one positive biomarker, and of these 4 (25%) so far have developed PD (Lewy body dementia in 1 patient). ", "None of the 13 accrued subjects with confirmed risk factors but without positive biomarkers has developed PD. ", "Under NIH Clinical Protocol 03-N-0004 we are obtaining skin biopsy specimens from patients with different forms of alpha-synucleinopathy. ", "In collaboration with extramural Associate Investigators we are testing whether alpha-synuclein, tyrosine hydroxylase, or DA-beta-hydroxylase immunostaining provides pathophysiologically relevant biomarkers." ]

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[ "The Best Air Conditioning Companies For Optimum Home Comfort\n\nAn air conditioner is probably one of most expensive purchases that you make for your home. ", "If you have an idea how the air conditioners work, you must know that the day of installation is the most crucial time in the life span of an air conditioner. ", "Apart from this, it is also important to ensure that the company from where you buy the system is reliable enough. ", "While you visit a store for purchasing an ac machine, you can easily be confused seeing so many models under the same roof. ", "It is therefore important to know what basic things to check while making choosing the perfect air conditioner for your home.", "\n\nTime has gone when air conditioners use to be a part of luxury. ", "Rapidly increasing global warming has made this machine a very important part and parcel in our lives. ", "More importantly in the hot and dry climate of the Middle Eastern Asian countries, demand of the air conditioners never goes down throughout the year. ", "Air conditioners are available at more lucrative prices when compared to other countries, where ac machines are still considered luxurious possessions.", "\n\nHowever, the most important factor you need to decide while buying an ac is the size of the room. ", "Generally a 10ftx 10ft room requires an ac of 2ton. ", "You can consider buying a lesser one if your room is small. ", "Alternatively, you can opt for the central air conditioners too, when budget is not a constraint. ", "Many confuse whether the domestic central air conditioners are as good as normal ac machines, but they actually are. ", "As a matter of fact, the central air conditioners are best for hot and dry climate of the Middle East. ", "Hence, decide this aspect well before you choose one.", "\n\nAnother important factor while you set out for purchasing an ac machine is the brand you have your mind. ", "More than a handful of ac manufacturers have their dealers in the Middle Eastern countries. ", "Quite naturally, not all of these companies have the same level of reputation in the market. ", "Moreover, they heavily differ in their performance qualities. ", "If you are not that updated on all the technical specifications of the air conditioners, others can easily misguide you. ", "To avoid the same, you must grow knowledge on particular details of the leading air conditioner dealers at your locale.", "\n\nThe best way to earn knowledge on the air conditioners is to read the online specifications of each of brand. ", "Most of the air conditioning companies have their reviews online, from where you can know in detail about the product. ", "A thorough knowledge will of course help you making the right selection from a vast array of products, which all seem to best apparently. ", "Unlike the commercial and industrial air conditioners, you may not require an installation team for a domestic ac. ", "Nevertheless, you would require one or two installation expert so that the installation is done perfectly. ", "Remember, that the performance and durability of an ac machines highly depends on the perfect installation of the machine." ]

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[ "Imaging of neuroinflammation in parkinsonian syndromes with positron emission tomography.", "\nMicroglial activation is a key aspect of the neuroinflammatory process in neurodegenerative disorders including idiopathic and atypical parkinsonian disorders. ", "Using positron emission tomography, it has become possible to image this phenomenon in vivo and over the last years patterns of microglia activation corresponding well known distribution of neuropathologic changes in these disorders have successfully been demonstrated using this technique. ", "It has also been possible to measure the effects of interventions aimed at suppressing microglia activation as part interventional trials. ", "Current research aims at evaluating positron emission tomography tracers for microglial activation with more favorable properties than the prototypical [(11)C]-(R)-PK11195, as well as developing tracers targeting additional parameters of the neuroinflammatory process like astroglial function or the cannabinoid receptor type 2." ]

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[ "Ly49D-mediated ITAM signaling in immature thymocytes impairs development by bypassing the pre-TCR checkpoint.", "\nActivating and inhibitory NK receptors regulate the development and effector functions of NK cells via their ITAM and ITIM motifs, which recruit protein tyrosine kinases and phosphatases, respectively. ", "In the T cell lineage, inhibitory Ly49 receptors are expressed by a subset of activated T cells and by CD1d-restricted NKT cells, but virtually no expression of activating Ly49 receptors is observed. ", "Using mice transgenic for the activating receptor Ly49D and its associated ITAM signaling DAP12 chain, we show in this article that Ly49D-mediated ITAM signaling in immature thymocytes impairs development due to a block in maturation from the double negative (DN) to double positive (DP) stages. ", "A large proportion of Ly49D/DAP12 transgenic thymocytes were able to bypass the pre-TCR checkpoint at the DN3 stage, leading to the appearance of unusual populations of DN4 and DP cells that lacked expression of intracellular (ic) TCRβ-chain. ", "High levels of CD5 were expressed on ic TCRβ(-) DN and DP thymocytes from Ly49D/DAP12 transgenic mice, further suggesting that Ly49D-mediated ITAM signaling mimics physiological ITAM signaling via the pre-TCR. ", "We also observed unusual ic TCRβ(-) single positive thymocytes with an immature CD24(high) phenotype that were not found in the periphery. ", "Importantly, thymocyte development was completely rescued by expression of an Ly49A transgene in Ly49D/DAP12 transgenic mice, indicating that Ly49A-mediated ITIM signaling can fully counteract ITAM signaling via Ly49D/DAP12. ", "Collectively, our data indicate that inappropriate ITAM signaling by activating NK receptors on immature thymocytes can subvert T cell development by bypassing the pre-TCR checkpoint." ]

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[ "Q:\n\nHow can I change the text using JavaScript\n\n<div class=\"basePrice\">$99.99</div>\n\nI want to change the value $99.99 using JavaScript.", "\nI tried using getElementByClass but it didn't produce the results that I was hoping to get.", "\n\nA:\n\ndocument.getElementsByClass returns a NodeList, which is kind of like an array.", "\nYou have to specify which element (there's only one here, so I'm assuming the first) you're looking for, and then you can use .textContent to change the text of the node.", "\ndocument.getElementsByClassName(\"basePrice\")[0].textContent = \"$49.99\";\n\ndocument.getElementsByClassName(\"basePrice\")[0].textContent = \"$49.99\";\n<div class=\"basePrice\">$99.99</div>\n\n" ]

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[ "The campaign is co-ordinated annually by the national road safety and sustainable transport charity Brake.", "\n\nAs the charity launched its campaign today (Monday, November 20) it has revealed new figures showing that more than one in five (22 per cent) patients admitted to trauma centres in the East Midlands region were involved in road crashes in 2016.", "\n\nIts new figures show that nationally road crashes were the second largest cause of trauma centre admissions last year.", "\n\nAn additional analysis of more than 75,000 road crash trauma patients in the last decade show that young people (aged 16-25) accounted for more than one in five (21 per cent) admissions – the largest affected age group.", "\n\nGovernment statistics show that speeding was a factor in almost a quarter (22 per cent) of fatal crashes on roads in Britain last year.", "\n\nThis year’s Road Safety Week is urging drivers to slow down to cut the number of crashes fatalities and serious injury collision on roads.", "\n\nJason Wakeford, director of campaigns for Brake, said: “Not only do needless road collisions cause untold suffering but they also place an enormous strain on the NHS and other public services.", "Speeding is a factor in many deadly crashes and remains a major problem.", "\n\n“Driving is unpredictable and if something unexpected happens on the road ahead, such as a child stepping out from between parked cars, it’s a driver’s speed that determines whether they can stop in time and, if they can’t, how hard they will hit.", "\n\n“Brake is also calling for a default 20mph limit in all built-up areas, increased enforcement and ‘Intelligent Speed Adaptation’, which helps drivers stay within the limit, to be fitted as standard to new vehicles.”" ]

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[ "Introduction {#s1}\n============\n\nSatellite cells are mononucleated muscle precursor cells which play critical roles in the growth, maintenance and repair of skeletal muscle [@pone.0058554-Seale1]. ", "In mouse models of muscle atrophy (i.e., aging, myopathy, or muscle denervation) the number and activity of satellite cells are reduced suggesting that satellite cell dysfunction contributes to the development of muscle atrophy [@pone.0058554-Mitchell1], [@pone.0058554-Jejurikar1]. ", "In a mouse model of chronic kidney disease (CKD), we found impaired satellite cell proliferation and differentiation which delayed muscle regeneration and decreased muscle mass [@pone.0058554-Zhang1]. ", "These reports suggest that functional satellite cells are required to maintain muscle mass in catabolic conditions.", "\n\nCatabolic conditions are often associated with elevated glucocorticoid (GC) production [@pone.0058554-Hasselgren1], [@pone.0058554-Lang1]. ", "This is relevant because an excess of GC can contribute to muscle wasting [@pone.0058554-Hasselgren1]--[@pone.0058554-Sandri1]. ", "Whether GCs contribute to muscle mass loss by impairing satellite cell function is unknown. ", "But, it is reported that dexamethasone, a potent synthetic member of the glucocorticoid class of steroid drugs, inhibits myoblast proliferation and differentiation and decreases myogenic gene expression [@pone.0058554-tePas1]. ", "However, the signaling pathways by which GCs lead to decreased myogenic gene expression are not clear. ", "One possibility is that GCs increase myostatin secretion [@pone.0058554-Gilson1], [@pone.0058554-Ma1]. ", "This is relevant because myostatin expression is increased in muscles of rodents developing muscle atrophy and can negatively regulate satellite cell activation and self-renewal [@pone.0058554-Lalani1]--[@pone.0058554-McCroskery1]. ", "In the current study, we tested the hypothesis that GCs cause muscle loss by triggering myostatin expression with impaired satellite cell function. ", "The mechanism by which myostatin suppresses satellite cell activation is unknown but one candidate is activation of Smad3 signaling [@pone.0058554-Liu1], [@pone.0058554-Liu2]. ", "Another candidate pathway involves Akirin1, because suppressive subtraction hybridization analyses identified that Akirin1 is specifically regulated by myostatin [@pone.0058554-Marshall1].", "\n\nAkirins are 20--25 kDa nuclear proteins that regulate gene expression in processes such as innate immune response or carcinogenesis [@pone.0058554-Komiya1]. ", "They interact with cofactors to either promote or repress mRNA transcription including 14-3-3 proteins [@pone.0058554-Komiya1] or the basic helix-loop-helix transcription factor, Twist [@pone.0058554-Nowak1]. ", "In the present studies, we found that GCs suppress satellite cell activation *in vivo* and *in vitro* and we uncovered that the mechanism involves an upregulation of myostatin and downregulation of Akirin1 which leads to inhibition of MyoD.\n\nMaterials and Methods {#s2}\n=====================\n\nReagents and Antibodies {#s2a}\n-----------------------\n\nAntibodies against p-Akt (Ser473) (Cell Signaling Technology, Beverly, MA), the glucocorticoid receptor (GR) (Santa Cruz Biotechnology, Santa Cruz, CA), MyoD (Vector Laboratories, Burlingame, CA), eMyHC and myogenin (Developmental Studies Hybridoma Bank, University of Iowa, Iowa City, IA), Akirin1 (Sigma-Aldrich, St. Louis, MO), myostatin (Abcam, Cambridge, MA), and Atrogin-1 and MuRF-1 (ECM Bioscience; Versailles, KY) were used according to the companies' protocols. ", "The anti-Ki67-Alexa Fluor® 555 antibody was from BD Bioscience (San Jose, CA). ", "Cardiotoxin (CTX) and dexamethasone (Dex) were from Sigma-Aldrich and the anti-myostatin peptibody (myostatin inhibitor) was from Amgen (Amgen, Thousand Oaks, CA, USA) [@pone.0058554-Zhang2].", "\n\nAnimal Experiments {#s2b}\n------------------\n\nAll animal experiments and procedures were approved by the Baylor College of Medicine Institutional Animal Care and Use Committee. ", "C57/BL6 mice (Jackson Lab, Bar Harbor, ME, 10 to 12 weeks) were intraperitoneally injected with Dex (5 mg/kg) twice a day for 14 days [@pone.0058554-May1], [@pone.0058554-Hu1]. ", "The anti-myostatin peptibody (5 mg/kg, IC50 ∼1.2 nM) [@pone.0058554-Zhang2] was injected subcutaneously every other day into one of a pair of Dex-injected mice; the other Dex-treated mice was injected with an equal volume of PBS (Control). ", "The mice were pair-fed and body weights were assessed daily. ", "Gastrocnemius, tibialis anterior (TA), soleus and extensor digitorum longus (EDL) muscles were removed and weighed at the time of mice sacrifice.", "\n\nTransgenic mice bearing MyoD-Cre were a gift from Dr David J. Goldhamer (U. Connecticut, Storrs, CT) [@pone.0058554-Chen1]. ", "MyoD-Cre mice were crossed with floxed-GR transgenic mice [@pone.0058554-Hu1] to create glucocorticoid receptor knockout mice (GRKO).", "\n\nMuscle Injury and Regeneration Model {#s2c}\n------------------------------------\n\nNormally satellite cells are quiescent, but they are activated by stress (including weight bearing, trauma or injury) to proliferate, differentiate and fuse into multinucleated myofibers [@pone.0058554-Buckingham1]. ", "We injured TA muscle with cardiotoxin (CTX) in order to study satellite cell function in muscle [@pone.0058554-Zhang1], [@pone.0058554-Musaro1], [@pone.0058554-Pelosi1]. ", "For example, one TA muscle of each mouse was injected with 80 µl of 10 µM CTX; the contralateral TA muscle was injected with an equal volume of PBS (control). ", "Mice were sacrificed at different times after injury and both TA muscles were collected and either embedded with a medium consisting of polyethylene glycol and polyvinyl alcohol and frozen in dry-ice chilled isopentane for histological analysis or muscles were stored in liquid nitrogen until protein or RNA was isolated. ", "Myogenic markers of satellite cells in injured muscles were examined by immunostaining, RT-PCR or western blotting.", "\n\nSatellite Cell Isolation, Proliferation and Differentiation Assay {#s2d}\n-----------------------------------------------------------------\n\nSatellite cell isolation and identification were performed as described [@pone.0058554-Zhang1]. ", "Briefly, skeletal muscles were digested with 0.2% Collagenase Type II (Worthington Biochemical, Lakewood, NJ) in DMEM plus 1% penicillin/streptomycin at 37°C for 30 minutes. ", "The mixture was passed through a 100 µm filter and then subjected to Percoll gradient centrifugation. ", "Satellite cells were obtained from the interface between 40% and 70% of Percoll and immunostained with anti-Pax-7; \\>95% of cells were Pax-7 positive [@pone.0058554-Zhang1]. ", "RNA and protein were isolated from satellite cells or the cells were cultured on Matrigel-coated plates (BD Bioscience, San Jose, CA) in growth media (DMEM with 20% FBS, 1% penicillin/streptomycin, 40 µg/ml gentamicin and 2% chicken embryo extract). ", "Satellite cell proliferation was assessed by co-immunostaining of anti-Pax-7 with anti-Ki67. ", "The average percentage of the number of Pax7 and Ki67 dual positive cells to total Pax7 positive cells in 10 areas was designated as the proliferation rate.", "\n\nSome of the satellite cells were converted into myotubes by incubation in differentiation media (DMEM plus 2% horse serum, 1% penicillin/streptomycin) for 4 days. ", "Myotubes were fixed in 2% paraformaldehyde for 10 min before they were immunostained for anti-eMyHC. ", "The differentiation index was calculated as the sum of nuclei within myotubes that stained positively for eMyHC plus the number of eMyHC positive, mononucleated cells divided by the total number of nuclei [@pone.0058554-Wang1].", "\n\nSatellite cells also were transducted with shRNA-myostatin or shRNA-control lentivirus. ", "The shRNA-myostatin lentiviral particles contain 3 target-specific constructs that encode 19--25 nt shRNA designed to knock down myostatin expression; shRNA-control lentivirus contain a shRNA construct encoding a scrambled sequence that will not lead to the specific degradation of any known cellular mRNA. ", "Lentiviral particles of shRNA-myostatin or shRNA-control were from Santa Cruz Technology. ", "Freshly isolated satellite cells were plated into 12 wells plates and incubated in growth media for 3 days to allow cell attachment, then satellite cells were transducted with 20 µl of 1×10^6^ infectious units of virus (IFU) of shRNA-myostatin or shRNA-control with 8 µg/ml polybrane. ", "These cells were then treated with Dex or recombinant myostatin and co-immunostained with Pax7 and Ki67 to evaluate satellite cell proliferation. ", "Other cells transducted with shRNA lentivirus were differentiated into myotubes and immunostained with eMyHC to evaluate satellite cell differentiation in the presence of GC or myostatin.", "\n\nRT-PCR Analysis {#s2e}\n---------------\n\nRT-PCR was performed as described [@pone.0058554-Zhang1], [@pone.0058554-Zhang3] with relative gene expression calculated from cycle threshold (Ct) values using GAPDH or 18S as an internal control (relative expression = 2^(sample\\ Ct\\ −\\ GAPDH\\ Ct)^). ", "Primers and their sequences are listed in [Table 1](#pone-0058554-t001){ref-type=\"table\"}.", "\n\n10.1371/journal.pone.0058554.t001\n\n###### RT-PCR primer sequences.", "\n\n![](", "pone.0058554.t001){#pone-0058554-t001-1}\n\n mRNA Forward Reverse\n ----------- -------------------------------- --------------------------------\n Myf5 5′-ATCTGGCTTCTCTCTCTCCAGTTG-3′ 5′-TTAGGCCCTCCTGGAAGAAGTCAT-3′\n Akirin1 5′-GCAGAACAGTATGAATCG-3′ 5′-AGGCTTCAGGATACATAG-3′\n Myostatin 5′-TGGCATTACTCAAAAGCAAAAAG-3′ 5′-CATCAATACTCTGCCAAATACCA-3′\n Myogenin 5′-ACAGCATCACGGTGGAGGATATGT-3′ 5′-CCCTGCTACAGAAGTGATGGCTTT-3′\n MyoD 5′-ACGACTGCTTTCTTCACCACTCCT-3′ 5′-TCGTCTTAACTTTCTGCCACTCCG-3′\n GAPDH 5′-ACCACCATGGAGAAGGCCGG-3′ 5′-CTCAGTGTAGCCCAAGATGC-3′\n 18S 5′-GAAACGGCTACCACATCCAAGG-3′ 5′-GTCCCTCTTAATCATGGCCTCAG-3′\n\nImmunohistochemical Analyses {#s2f}\n----------------------------\n\nSerial, transverse cryo-sections (8 µm thick) of TA muscles were air-dried and fixed in cold acetone or 4% paraformaldehyde for 10 min. ", "before staining with hematoxylin and eosin (H&E). ", "Tissue sections were immunostained for eMyHC to evaluate new-myofiber formation. ", "To calculate the cross-sectional areas of individual myofibers, TA muscles were first immunostained with anti-laminin to define the basement membrane. ", "Fiber sizes were measured using Nikon NIS-Elements Br 3.0 software (Melville, NY). ", "The distribution of myofibers was expressed as the percentage of myofibers within a designated size range divided by the total number of myofibers. ", "The measurement was made by observers masked to the treatment.", "\n\nCell Transfection {#s2g}\n-----------------\n\nC2C12 myoblasts were transfected with plasmids expressing Akirin1 or cDNA3 using Amaxa Nucleofector technology (Lonza, Allendale, NJ). ", "Cells were collected by centrifugation at 450 g for 5 minutes at room temperature and 1×10^6^ cells were re-suspended in 100 µl of Basic Nucleofector reagent. ", "The cell suspension mixed with 2 µg plasmid was transfected by electroporation. ", "Transfection success was \\>90% with this method. ", "The electro-transfected cells were transferred to a 6 well plate and allowed to grow or differentiate. ", "Following treatment with Dex (10 µM), the proliferation or differentiation rates were evaluated from Ki67 or eMyHC immunostaining, respectively.", "\n\nEstablishing Stable Clones with shRNA-myostatin {#s2h}\n-----------------------------------------------\n\nshRNA-myostatin and shRNA-control lentiviral particles were bought from Santa Cruz Technology. ", "C2C12 myoblasts were grown in a 12-well plate with DMEM plus 10% FBS for 24 h before viral infection (approximately 50% confluent on the day of infection). ", "The cell culture media was changed to new DMEM plus 10% FBS, 8 µg/ml polybrene and 1×10^6^ infectious units of virus. ", "After 24 h, the media was changed to DMEM plus 10% FBS for another 24 h. The cells were split in a 1 to 5 concentration and replated in different concentrations of puromycin (2, 5 or 10 µg/ml); 5 ug/ml puromycin achieved the best selection. ", "The selected clone by knocked down of myostatin was evaluated by western blot and RT-PCR.", "\n\nStatistical Analysis {#s2i}\n--------------------\n\nValues are presented as mean ± SEM. ", "Data were compared across different treatment and time points using two-way ANOVA. ", "Student's ***t***-test was performed with statistical significance (p\\<0.05). ", "A minimum of three replicates were performed for each experimental condition.", "\n\nResults {#s3}\n=======\n\nDex Suppresses Satellite Cell Function in vitro {#s3a}\n-----------------------------------------------\n\nConsistent with others, we found that high doses of Dex (5 mg/kg) induced a significant decrease in body and muscle weights *vs.* results in untreated, control mice ([Table 2](#pone-0058554-t002){ref-type=\"table\"}) [@pone.0058554-Roy1]--[@pone.0058554-May2]. ", "There also was activation of the ubiquitin-proteasome system as evidenced by increased expression of E3 ubiquitin ligases, Atrogin-1 or MuRF-1 in muscles ([Fig. ", "1A](#pone-0058554-g001){ref-type=\"fig\"}). ", "Dex-induced loss of muscle weight was further demonstrated by the finding that the distribution of myofibers in TA muscles of Dex-treated mice was shifted to the left (smaller direction) ([Fig. ", "1B](#pone-0058554-g001){ref-type=\"fig\"}).", "\n\n{#pone-0058554-g001}\n\n10.1371/journal.pone.0058554.t002\n\n###### Dex treatemnt decreases body and muscle weight in mice.", "\n\n![](", "pone.0058554.t002){#pone-0058554-t002-2}\n\n BW (g) Gastr. (", "mg) TA(mg) Soleus(mg) EDL(mg)\n -------- ----------- ------------- ------------ ------------ -----------\n Ctrl 26±0.56 132.66±1.48 47.23±0.98 9.14±0.47 9.32±0.35\n Dex 22.3±0.86 113.66±1.79 40±0.59 7.34±0.90 8.17±0.45\n t-test 0.016 0.017 0.006 0.132 0.009\n\n12 week-old male mice (C57/BL6) were injected with Dex (5 mg/kg twice a day) for 14 days, n = 5 mice in each groups.", "\n\nRegarding the mechanism for loss of muscle mass, we have found that chronic kidney disease (CKD) induces satellite cell dysfunction which contribute to loss of muscle mass [@pone.0058554-Zhang1]. ", "To examine this mechanism in Dex-treated C57/BL6 mice, we isolated satellite cells and measured their functions (proliferation and differentiation) following Dex treatment. ", "First, we confirmed there are glucocorticoid receptors (GR) in satellite cells by co-immunostaining the cells with anti-GR and anti-Pax7. ", "We found that satellite cells from wild type mice express GR but that the GR was absent in satellite cells isolated from muscles of glucocorticoid receptor knockout mice (GRKO, [Fig. ", "2A](#pone-0058554-g002){ref-type=\"fig\"}). ", "We then incubated satellite cells isolated from muscles of WT mice with or without 10 µM Dex for 24 h and co-immunostained them with anti-Ki67 (a proliferation marker) and anti-Pax7 (a satellite cell marker): Dex significantly decreased Ki67 positive cells ([Fig. ", "2B](#pone-0058554-g002){ref-type=\"fig\"}), suggesting that Dex suppressed satellite cell proliferation. ", "Satellite cells incubated in differentiation media (DMEM plus 2% horse serum) with or without 10 µM Dex for 4 days were immunostained for eMyHC and as with proliferation, Dex-decreased satellite cell differentiation *vs.* results in non-Dex-treated satellite cells ([Fig. ", "2C](#pone-0058554-g002){ref-type=\"fig\"}).", "\n\n{#pone-0058554-g002}\n\nDex Suppresses Satellite Cell Function in vivo {#s3b}\n----------------------------------------------\n\nTo examine whether Dex causes satellite cell dysfunction *in vivo*, we used a standard model of muscle injury by CTX injection, because it activates satellite cells to proliferate, differentiate and develop into myofibers [@pone.0058554-Collins1]. ", "12 week-old C57/BL6 mice were treated with Dex for 2 days before TA muscle were injured with CTX for 1.5 days. ", "Cryo-cross-sections of injured TA muscles were co-immunostained with anti-Pax7 and Ki-67. ", "We found significantly fewer Pax7 and Ki-67 dual positive cells in injured muscle of Dex treated mice *vs.* in injured muscle of control mice ([Fig. ", "3A](#pone-0058554-g003){ref-type=\"fig\"}). ", "At different time points following muscle injury, the mRNA expression of myogenic genes including Myf-5, MyoD and myogenin were significantly lower in muscles of Dex-treated mice *vs.* values in muscles of non-Dex-treated control mice ([Fig. ", "3B](#pone-0058554-g003){ref-type=\"fig\"}). ", "We also examined formation of new myofibers (indicated by myofibers with central nuclei) to evaluate whether the inhibition of myogenic genes by Dex was correlated with diminished satellite cell differentiation into muscle fibers. ", "At 5 or 7 days after injury, muscle sections from Dex-treated mice had more space among newly generated myofibers and these new myofibers were smaller *vs.* results from injured muscle of control mice ([Fig. ", "3C](#pone-0058554-g003){ref-type=\"fig\"}). ", "At 7 days following injury, the size distribution of newly formed myofibers in muscles of Dex-treated mice was shifted to left (smaller myofiber direction) *vs.* the values in control mice ([Fig. ", "3C](#pone-0058554-g003){ref-type=\"fig\"}). ", "These data demonstrate that Dex causes loss of body and muscle weight in mice and suppresses satellite cell activation while impairing the regeneration of injured muscles ([Fig. ", "1](#pone-0058554-g001){ref-type=\"fig\"}, [2](#pone-0058554-g002){ref-type=\"fig\"}&[3](#pone-0058554-g003){ref-type=\"fig\"}).", "\n\n{#pone-0058554-g003}\n\nDex Induces Myostatin Expression to Suppress Satellite Cell Activation {#s3c}\n----------------------------------------------------------------------\n\nBecause there are no glucocorticoid response elements in the promoter region of atrogenes or myogenic genes, GCs must cause loss of muscle weight by an indirect mechanism [@pone.0058554-Gilson1], [@pone.0058554-Ma1]. ", "GCs can induce myostatin expression, we examined whether Dex stimulation of myostatin suppresses satellite cell function. ", "We examined this hypothesis in satellite cells isolated from muscles of WT mice and found that Dex did stimulate myostatin mRNA and protein expression in satellite cells ([Fig. ", "4A&B](#pone-0058554-g004){ref-type=\"fig\"}). ", "In addition, satellite cells treated with Dex had decreased proliferation ([Fig. ", "2B](#pone-0058554-g002){ref-type=\"fig\"}) and inhibition of myostatin in Dex-treated satellite cells with the anti-myostatin peptibody (Myo-inh) significantly increased Ki67 expression *vs.* responses to Dex treatment only ([Fig. ", "2B](#pone-0058554-g002){ref-type=\"fig\"}). ", "Besides improving satellite cell proliferation, inhibition of myostatin also increased satellite cell differentiation despite Dex treatment ([Fig. ", "2C](#pone-0058554-g002){ref-type=\"fig\"}). ", "These results provide a potential mechanism for the catabolic effect of GC, Dex stimulates myostatin which suppresses satellite cell function. ", "To further support this conclusion, we transducted isolated satellite cells with shRNA control or shRNA-myostatin lentivirus; myostatin knockdown was confirmed by western blot (data not shown). ", "These cells were then treated with Dex for 24 h, and the fixed cells were co-immunostained with anti-Pax7 and Ki-67. ", "The results indicate that knockdown of myostatin blocks Dex-suppressed satellite cell proliferation ([Fig. ", "4C](#pone-0058554-g004){ref-type=\"fig\"}). ", "Lentivirus transducted satellite cells were cultured with 2% horse serum to induce differentiation and treated with Dex for 96 h; knockdown of myostatin abolished Dex suppression of satellite cell differentiation ([Fig. ", "4D](#pone-0058554-g004){ref-type=\"fig\"}). ", "To confirm the specificity of myostatin knockdown with myostatin shRNA, we treated lentivirus transducted satellite cells with recombinant myostatin and found that myostatin reversed the effects of shRNA-myostatin on satellite cell proliferation and differentiation ([Fig. ", "4C&D](#pone-0058554-g004){ref-type=\"fig\"}).", "\n\n{#pone-0058554-g004}\n\nBoth Dex and Myostatin can Inhibit Akirin1 Expression in Satellite Cells {#s3d}\n------------------------------------------------------------------------\n\nAlthough our results indicate that myostatin suppresses satellite cell proliferation and differentiation ([Fig. ", "4](#pone-0058554-g004){ref-type=\"fig\"}), the mechanism underlying this response is not clear. ", "Akirin1 is a target of myostatin and when satellite cells were treated with increasing concentrations of Dex, there was a dose-dependent increase in myostatin along with a decrease in both the mRNA and protein expression of Akrin1 ([Fig. ", "5A&B](#pone-0058554-g005){ref-type=\"fig\"}, [Fig. ", "4A&B](#pone-0058554-g004){ref-type=\"fig\"}) [@pone.0058554-Marshall1]. ", "Moreover, when recombinant myostatin was added to satellite cells, Akirin1 mRNA and protein levels decreased in a dose-dependent manner ([Fig. ", "5](#pone-0058554-g005){ref-type=\"fig\"} C&D).", "\n\n{#pone-0058554-g005}\n\nNext, we tested the hypothesis that the inhibition of Akirin1 by Dex is mediated by myostatin. ", "Myostatin was knocked down in myoblasts using a shRNA-myostatin lentivirus. ", "Control and myostatin knockdown cells were treated with 10 µM Dex for 24 h. In control cells, Dex increased myostatin and decreased Akirin1 protein expression (compare lane 1 with lane 3 in [Fig. ", "5E](#pone-0058554-g005){ref-type=\"fig\"}). ", "In contrast, in cells in which myostatin was knocked down, Dex treated cells had higher expression of Akirin1. ", "Myostatin knockdown also significantly increased cell proliferation and differentiation even when Dex was present ([Fig. ", "4C&D](#pone-0058554-g004){ref-type=\"fig\"}). ", "The results indicate that Dex suppresses satellite cell activation by upregulating myostatin leading to inhibition of Akirin1 expression.", "\n\nTo document that Dex suppresses satellite cell function by inhibiting Akirin1 expression, we overexpressed Akirin1 in myoblasts; cDNA3 was transfected as control. ", "Akirin1 expression increased the levels of MyoD and myogenin even when cells were treated with Dex ([Fig. ", "6A](#pone-0058554-g006){ref-type=\"fig\"}). ", "Increased Akirin1 expression also improved the proliferation and differentiation of myoblasts despite treatment with Dex ([Fig. ", "6](#pone-0058554-g006){ref-type=\"fig\"} B&C).", "\n\n{#pone-0058554-g006}\n\nDex causes Loss of Muscle Mass and Satellite Cell Dysfunction via Myostatin in Mice {#s3e}\n-----------------------------------------------------------------------------------\n\nWe tested our hypothesis *in vivo* by treating mice with Dex. ", "From 2 to 9 days, myostatin expression increased in muscles of mice treated with Dex ([Fig. ", "7A](#pone-0058554-g007){ref-type=\"fig\"}). ", "At 14 days of Dex treatment, myostatin expression persisted and was associated with reduced levels of p-Akt and the satellite cell proliferation marker MyoD in muscles ([Fig. ", "7B](#pone-0058554-g007){ref-type=\"fig\"}). ", "To determine if Dex impairs the abilities of satellite cells to repair injured muscle, we treated mice with Dex for 5 days and then injected CTX to induce TA muscle damage. ", "Unexpectedly, injury decreased myostatin mRNA but was still significantly higher in muscles of Dex-treated mice *vs.* non-Dex-treated mice in both injured and non-injured muscles ([Fig. ", "7C](#pone-0058554-g007){ref-type=\"fig\"}).", "\n\n{#pone-0058554-g007}\n\nSince myostatin negatively influenced satellite cell functions in cultured cells ([Fig. ", "4](#pone-0058554-g004){ref-type=\"fig\"}), we tested the hypothesis that inhibition of myostatin in Dex-treated mice would increase satellite cell activity and improve muscle regeneration after injury. ", "We injected anti-myostatin peptibody (6.25 mg/kg) every other day into mice because this dose can effectively block myostatin expression and block CKD-induced muscle wasting [@pone.0058554-Zhang2]. ", "Mice received Dex plus PBS or Dex plus the anti-myostatin peptibody and TA muscles were injured for 4 days, cross-sections of injured muscles were immunostained with the satellite cell myogenic marker, anti-myogenin; number of myogenin positive cells was significantly higher in injured muscles of mice treated with Dex plus the myostatin inhibitor *vs.* values in mice that were treated with Dex plus PBS ([Fig. ", "7D](#pone-0058554-g007){ref-type=\"fig\"}). ", "Myogenin positive cells were not found in non-injured muscles (data not shown). ", "We also evaluated satellite cell differentiation plus formation of new myofibers by immunostaining cross sections of injured TA muscles with eMyHC. ", "At 3 days after injury, no new myofibers were present in mice treated with Dex plus the myostatin inhibitor or with Dex plus PBS. ", "After 5 days of injury, the inhibition of myostatin in Dex-treated mice resulted in more newly formed myofibers (eMyHC positive cells) *vs.* results in mice treated with Dex plus PBS; this response was more pronounced at day 7 after injury ([Fig. ", "7E](#pone-0058554-g007){ref-type=\"fig\"}). ", "Sections of muscle immunostained with laminin and DAPI at 7 days after injury found increased numbers and sizes of myofibers with central nuclei in mice treated with Dex plus the anti-myostatin peptibody ([Fig. ", "7F](#pone-0058554-g007){ref-type=\"fig\"}). ", "At 14 days after injury, the distribution of myofiber sizes was shifted to the right (larger) in Dex plus anti-myostatin peptibody-treated mice *vs.* Dex-PBS-treated mice ([Fig. ", "7G](#pone-0058554-g007){ref-type=\"fig\"}). ", "Inhibition of myostatin in Dex-treated mice also led to increased body and muscle weights and myofiber sizes ([Fig. ", "S1](#pone.0058554.s001){ref-type=\"supplementary-material\"} A, B&C). ", "The increase in body and muscle weight was accompanied by a decrease in the expression of the E3 ubiquitin ligases Atrogin-1 and MuRF-1 ([Fig. ", "S1D](#pone.0058554.s001){ref-type=\"supplementary-material\"}). ", "Taken together, the results suggest that blocking myostatin *in vivo* abrogates the inhibited satellite cell activation that is induced by Dex. ", "The result is improved muscle regeneration and growth.", "\n\nIn Activated Satellite Cells Dex Decreases Akirin1 Expression by a Myostatin Pathway {#s3f}\n------------------------------------------------------------------------------------\n\nWe evaluated Akirin1 expression in muscles of mice that had been treated with Dex. ", "In injured muscle of non-Dex-treated, control mice, both the mRNA and protein expressions of Akirin1 increased while in injured muscles of Dex-treated mice, Akirin1 expression was significantly lower *vs.* values in non-Dex-treated mice ([Fig. ", "8](#pone-0058554-g008){ref-type=\"fig\"} A&B). ", "Finally, we injected PBS or the myostatin inhibitor into Dex-treated mice with injured TA muscles. ", "In injured muscles of mice treated with Dex plus the myostatin inhibitor, Akirin1 levels were significantly higher *vs.* values in mice treated with Dex plus PBS ([Fig. ", "8](#pone-0058554-g008){ref-type=\"fig\"} C) suggesting that Dex decreases Akirin1 in satellite cells by a myostatin-mediated mechanism.", "\n\n{#pone-0058554-g008}\n\nDiscussion {#s4}\n==========\n\nThere have been reports exploring how GCs cause muscle wasting. ", "First, GCs stimulate protein degradation in the ubiquitin proteasome systems by leading to an increase in the expression of muscle-specific E3 ubiquitin ligases, Atrogin-1/MAFbx and MuRF-1. ", "In this case, however, the expression of atrophy-related genes are not directly regulated by GCs because there are no glucocorticoid response element binding sites in the promoter region of atrogenes [@pone.0058554-Sandri1], [@pone.0058554-Lecker1]. ", "Second, physiologic levels of GCs were shown to stimulate an interaction between the activated GC receptor and p85 of PI3K/Akt in muscle. ", "The interaction stimulates protein breakdown in muscle by inhibiting Akt phosphorylation [@pone.0058554-Hu1]. ", "In the present studies, we uncovered a third mechanism, namely that GCs impair satellite cell functions in muscle. ", "The mechanism for this response is that GCs suppress satellite cell activation by inhibiting the expression of Akirin1, a gene associated with satellite cell activation. ", "GC induces inhibition of Akirin1 by stimulating myostatin. ", "Specifically, we have shown that GCs stimulate myostatin expression in isolated satellite cells and in muscles of mice. ", "But, when myostatin was inhibited by anti-myostatin peptibody or by treating myoblast with shRNA-myostatin, the response to GCs that inhibits Akrin1 expression is blocked. ", "We also show that an increase in Akrin1 potentiates myoblast proliferation and differentiation when GCs are present. ", "Thus, GCs suppress the ability of satellite cell to counteract muscle growth.", "\n\nHow do GCs affect satellite cell function? ", "Dex suppresses satellite cell proliferation and differentiation both *in vitro* ([Fig. ", "2](#pone-0058554-g002){ref-type=\"fig\"}) and in muscles of satellite cells activated by injury ([Fig. ", "3](#pone-0058554-g003){ref-type=\"fig\"}). ", "The signaling pathway by which an increase in GCs causes satellite cell dysfunction involves an increase in myostatin expression. ", "The myostatin activation can be linked to putative glucocorticoid response elements (GREs) in the myostatin promoter and our finding that Dex up-regulates myostatin mRNA and its protein in cultured satellite cells ([Fig. ", "4](#pone-0058554-g004){ref-type=\"fig\"}) [@pone.0058554-Artaza1], [@pone.0058554-Ma2]. ", "An increase in myostatin is relevant because it is expressed in satellite cells and reportedly regulate satellite cell quiescence and self-renewal [@pone.0058554-McCroskery1]. ", "Indeed, we found that in mice treated with Dex, there was increased myostatin expression in muscle associated with satellite cell dysfunction ([Fig. ", "7](#pone-0058554-g007){ref-type=\"fig\"} A&B). ", "Proof of the myostatin role was obtained by inhibiting it. ", "When myostatin was blocked, satellite cell functions improved and the number of activated satellite cells in injured muscles increased ([Fig. ", "7D](#pone-0058554-g007){ref-type=\"fig\"}). ", "Thus, GC induces myostatin expression in satellite cells leading to inhibition of satellite cell activity ([Fig. ", "7](#pone-0058554-g007){ref-type=\"fig\"}).", "\n\nBesides confirming that myostatin adversely affects satellite cell activity [@pone.0058554-McCroskery1], [@pone.0058554-Langley1]--[@pone.0058554-McCroskery2], we uncovered another major mediator of satellite cell response to GC stimulation. ", "Specifically, we found that Akirin1 counteracts the GC-induced suppression of satellite cells; it improves the functions of satellite cells including an increase in the expression of MyoD and myogenin ([Fig. ", "6](#pone-0058554-g006){ref-type=\"fig\"}). ", "The changes in satellite cell function stimulated by Akirin1 are complicated because Akirin1is a target of myostatin. ", "For example, the level of Akirin1 increases in muscles of myostatin KO mice and it is also increased in activated satellite cells and in injured muscles ([Fig. ", "8](#pone-0058554-g008){ref-type=\"fig\"}) [@pone.0058554-Marshall1], [@pone.0058554-Salerno1]. ", "We probed these results further by treating satellite cells with recombinant myostatin; there was a decrease in Akirin1 mRNA and expression of its protein ([Fig. ", "5C&D](#pone-0058554-g005){ref-type=\"fig\"}). ", "These results explain how inhibition of myostatin led to an increase in Akirin1 expression in muscles of mice or in satellite cells leading to improved muscle regeneration ([Fig. ", "7](#pone-0058554-g007){ref-type=\"fig\"}) and muscle growth ([Fig. ", "S1](#pone.0058554.s001){ref-type=\"supplementary-material\"}). ", "In addition, we showed that knock down of myostatin increased Akirin1 expression and enhanced myoblast or satellite cell proliferation and differentiation even in the presence of Dex ([Fig. ", "5](#pone-0058554-g005){ref-type=\"fig\"} E, 4 C&D). ", "Contrariwise, over-expression of Akirin1 in muscle cells increased the expression of myogenic genes, MyoD and myogenin even when Dex was present ([Fig. ", "6](#pone-0058554-g006){ref-type=\"fig\"}). ", "The results suggest that Akirin1 functions upstream of MyoD. This is relevant because MyoD, like Twist, is a basic Helix-loop-Helix (bHLH) transcription factor and reportedly, Akirin1 interacts with Twist in a chromatin remodeling complex which promotes gene expression during embryogenesis [@pone.0058554-Nowak1]. ", "Combining these results, we conclude that Akirin1 regulates MyoD to influence satellite cell function and we plan to explore this proposal in future studies.", "\n\nRegarding to responses to injury, we found that myostatin expression decreased in injured muscles of control mice while the expression of satellite cell myogenic genes increased ([Fig. ", "7C](#pone-0058554-g007){ref-type=\"fig\"}). ", "These results are consistent with those of Cornelison et al, who concluded that myostatin was significantly down-regulated in activated satellite cells; they suggest that an increase in myostatin could be involved in maintaining satellite cell quiescent [@pone.0058554-Cornelison1]. ", "In agreement with that conclusion, we found that Dex increased myostatin expression in both injured and non-injured muscles ([Fig. ", "7A&C](#pone-0058554-g007){ref-type=\"fig\"}) and that inhibition of myostatin stimulated satellite cell function to prevent Dex-induced loss of body and muscle weight ([Fig. ", "S1](#pone.0058554.s001){ref-type=\"supplementary-material\"} & [Fig. ", "7E&F](#pone-0058554-g007){ref-type=\"fig\"}).", "\n\nInflammation and myofiber necrosis occurs after muscle injury and these responses are associated with secretion of cytokines and growth factors that can influence satellite cell activation [@pone.0058554-Zhang4]. ", "In our results, Dex decreased mRNA levels of several cytokines and chemokines in injured muscles ([Fig. ", "S2](#pone.0058554.s002){ref-type=\"supplementary-material\"}). ", "Potentially, decreases in the expression of genes could contribute to inadequate muscle regeneration responses in Dex-treated mice. ", "Indeed, Salerno et al reported that Akirin1 is expressed in macrophages and participates in chemotaxis of both macrophages and myoblasts into injured muscle [@pone.0058554-Salerno1]. ", "Our finding that Dex suppresses Akirin1 expression in satellite cells as well as injured muscle could extend the proposal about changes in chemotoxins; specifically reduction in Akirin1 could reduce macrophage infiltration into injured muscles, thereby reducing the release of cytokines, chemokines and growth factors. ", "These are prominent features of muscle repair and could impair or suppress satellite cell activation. ", "Dex affects these factors will be explored in the future.", "\n\nIn summary, we have defined a new mechanism for GC-induced loss of muscle mass. ", "The results add insights into the regulation of satellite cell function. ", "Specifically, GCs suppress satellite cell function by upregulating myostatin and inhibiting Akirin1. ", "Together these responses suppress MyoD expression and the participation of satellite cells in the process of muscle repair.", "\n\nSupporting Information {#s5}\n======================\n\n###### \n\n**Myostatin inhibition prevents Dex induced body and muscle weight loss**. ", "Mice were treated with Dex plus PBS or Dex plus anti-myostatin peptibody for 14 days. ", "A. Body weight changes (\\*p\\<0.05 *vs.* CTRL mice; n = 8 mice). ", "B. Gastrocnemius muscle weight (\\*p\\<0.05 *vs.* CTRL mice; n = 8 mice). ", "C. Myofiber distribution. ", "D. Representative western blots of Atrogin-1 or MuRF-1.", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\n**Dex inhibits expression of inflammatory genes in injured muscle**. ", "Mice were treated with Dex for 14 days and TA muscles were injured at different times. ", "mRNA expression of inflammatory genes was evaluated by RT-PCR. ", "Primer sequences will be sent upon request.", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\nThe authors would like to thank Dr. William E. Mitch for his critical review and Yanlan Dong for her excellent technical assistance.", "\n\n[^1]: **Competing Interests:**This study was partly funded by Satellite Health. ", "There are no patents, products in development or marketed products to declare. ", "This does not alter the authors\\' adherence to all the PLOS ONE policies on sharing data and materials.", "\n\n[^2]: Conceived and designed the experiments: YJD LPZ. ", "Performed the experiments: YJD JP LPZ. ", "Analyzed the data: YJD JP LPZ. ", "Contributed reagents/materials/analysis tools: YJD LPZ. ", "Wrote the paper: LPZ JP YJD.", "\n" ]

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[ "Isolation and characterization of HTLV-I from symptomatic family members with tropical spastic paraparesis (HTLV-I encephalomyeloneuropathy).", "\nHuman T lymphotropic virus type I (HTLV-I) was isolated from peripheral blood- and cerebrospinal fluid-derived mononuclear cells of a 13-y-old boy and from the peripheral blood lymphocytes of both his parents. ", "All three had IgG antibodies to HTLV-I and varying degrees of the clinical features of tropical spastic paraparesis (TSP). ", "The son also had IgM antibodies specific for HTLV-I in his serum. ", "Isolations were successfully made from peripheral blood lymphocytes and cerebrospinal fluid lymphocytes stimulated with interleukin-2 or cocultivated with umbilical cord blood mononuclear cells. ", "Established cell lines contained HTLV-I antigen by immunfluorescence and cell-associated virus by electron microscopy; cells became transformed in vitro as determined by their continuous growth in the absence of exogenous interleukin-2. ", "This boy is the youngest TSP patient known to be reported, and the isolation of HTLV-I from all three family members suggests the causative role of this virus in TSP." ]

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[ "<test-metadata>\n <benchmark-version>1.2</benchmark-version>\n <category>weakrand</category>\n <test-number>00314</test-number>\n <vulnerability>false</vulnerability>\n <cwe>330</cwe>\n</test-metadata>\n" ]

[ 0 ]

[ "Glia and volume transmission during physiological and pathological states.", "\nExtrasynaptic communication between neurons or neurons and glia is mediated by the diffusion of neuroactive substances through the extracellular space (ECS). ", "Structural changes and amino acid release occurring under physiological and pathological conditions result in cellular (particularly glial) swelling, leading to dynamic changes in the ECS volume and geometry that in turn affect ECS diffusion. ", "Significant changes in ECS volume and in diffusion barriers occur during development and aging. ", "They are often the result of cell death, astrogliosis, the rearrangement of astrocytic processes and changes in extracellular matrix molecules. ", "Plastic changes in ECS volume, geometry and anisotropy significantly affect the spatial relation of glial processes towards synapses, glutamate or GABA 'spillover', synaptic cross-talk and neuron-glia communication/interaction. ", "In addition, changes occurring during pathological states can be important for diagnosis, drug delivery and treatment." ]

[ 0, 0.006289308176100629, 0.00823045267489712, 0.010416666666666666, 0, 0.013157894736842105, 0 ]

[ "#!", "/bin/bash\n\nset -e\n\nfunction on_exit {\n if [ ! ", "-z \"$(jobs -p)\" ]; then\n kill $(jobs -p) >/dev/null 2>&1 || true\n fi\n}\ntrap on_exit EXIT\n\n#jobs &>/dev/null\n#exec &>/dev/null\n\ncd node_controller\n./node_controller one-shot --name Leg_01 &\n./node_controller one-shot --name Leg_02 &\n./node_controller one-shot --name Leg_03 &\n./node_controller one-shot --name Leg_04 &\n./node_controller one-shot --name Leg_05 &\n./node_controller one-shot --name Leg_06 &\n./node_controller one-shot --name Leg_07 &\n./node_controller one-shot --name Leg_08 &\n./node_controller one-shot --name Leg_09 &\n./node_controller one-shot --name Leg_10 &\ncd ../test_controller\n./test_controller ../example showtime_durable_30 --wait-for-nodes 4 --override-create-time 15\n" ]

[ 0, 0.02127659574468085, 0.014367816091954023 ]

[ "We are The Free and The Unashamed Share This:\n\nlink back to this site, however, because I intend to provide updates with anything else I receive from The Free and The Unashamed...including whatever contact information I receive permission to circulate.", "\n\n\n\n= A Declaration of Separation =\n\n\n\n==== To The Governments & People of Earth: ====\n\nWe claim the right to exist, and we will defend it. ", "We do not seek to overthrow anything. ", "We do not seek to control anything. ", "We merely wish to be left alone. ", "All we ever wanted was to live in peace with our friends and neighbors. ", "For a long, long time we bore insults to our liberty; we took blows, we did what we could to avoid injury and we worked through the system to get the offenses to stop. ", "That has now changed.", "We no longer see any benefit in working through the world’s systems. ", "At some point, working within a system becomes cowardly and immoral; for us, that point has arrived. ", "Regardless of the parties in power, their governments have continued to restrict, restrain and punish us. ", "We hereby reject them all. ", "We hereby withdraw from them all. ", "We hold the ruling states of this world and all that appertains to them to be self-serving and opposed to humanity. ", "We now withdraw our obedience and reclaim the right to strike back when struck. ", "We will not initiate force, but we do reserve the right to answer it. ", "We did not choose this – it was forced upon us.", "\n\n\n\n==== To The Governments of Earth: ====\n\nYou are building cages for all that is human. ", "In the name of protection, you have intruded into all areas of human life, far exceeding the reach of any Caesar. ", "You claim ultimate control of our property and our decisions, of our travels and even our identities. ", "You claim ownership of humanity far beyond the dreams of any Emperor of any previous era. ", "Understand clearly: We reject your authority and we reject your legitimacy. ", "We do not believe that you have any right to do the things you do. ", "You have massive power, but no right to impose it upon us and no legitimacy. ", "We have forsaken you. ", "We are no longer your citizens or your subjects. ", "Your systems are inherently anti-human, even if all their operators are not. ", "We are not merely angry young people. ", "We are fathers and mothers; aunts, uncles and grandparents; we are business owners and trusted employees; we are mechanics and engineers and farmers. ", "We are nurses and accountants and students and executives. ", "We are on every continent.", "\n\n\n\nThis is not a burst of outrage; this is a sober declaration that we no longer accept unearned suffering as our role in life. ", "For long decades we sat quietly, hoping that things would turn around. ", "We took no actions; we suffered along with everyone else. ", "But after having our limits pushed back again and again, we have given up on your systems. ", "If our fellow inhabitants of this planet wish to accept your rule, they are free to do so. ", "We will not try to stop them. ", "We, however, will no longer accept your constraints upon us. ", "From now on, when you hurt us, we will bite back. ", "If you leave us alone we will leave you alone and you can continue to rule your subjects. ", "We are happy to live quietly.", "But if you come after us, there will be consequences. ", "You caused this because of your fetish for control and power. ", "The chief men and women among you are pathologically driven to control everyone and everything that moves upon this planet. ", "You have made yourselves the judge of every human activity. ", "No god-king of the ancient world ever had the power that your systems do. ", "You have created a world where only the neutered are safe and where only outlaws are free. ", "==== To The People of Earth: ====\n\nWe seek nothing from you. ", "We do not want to rule you and we do not want to control you. ", "All we wish is to live on earth in peace. ", "As always, we will be helpful neighbors and generous acquaintances. ", "We will remain honest business partners and trustworthy employees. ", "We will continue to be loving parents and respectful children. ", "We will not, however, be sacrificial animals. ", "We reject the idea that others have a right to our lives and our property. ", "We will not demand anything from you, and we will no longer acquiesce to any demands upon us. ", "We have left that game. ", "We reject all obligations to any person or organization beyond honesty, fair dealing and a respect for human life. ", "We will shortly explain what we believe, but we are not demanding that you agree with us. ", "All we ask is that you do not try to stop us. ", "Continue to play the game if you wish; we will not try to disrupt it. ", "We have merely walked away from it. ", "We wish you peace.", "\n\n\n\n==== To Those Who Will Condemn Us: ====\n\nWe will ignore you. ", "We welcome and seek the verdict of a just God, before whom we are willing to expose our innermost thoughts. ", "Are you similarly willing? ", "We would stand openly before all mankind if it were not suicidal. ", "Perhaps some day we will have to accept slaughter for our crime of independence, but not yet. ", "Your criticism and your malice are much deeper than mere disagreements of strategy or philosophy. ", "You do not oppose our philosophy, you oppose our existence. ", "Our presence in the world means that your precious ideals are false. ", "Some of you would rather kill us than face the loss of your ideologies, just as those like you have either hated or killed every sufficiently independent human. ", "You present yourselves to the world as compassionate, tolerant and enlightened, but we know that your smooth words are costumes. ", "Oh yes, we know you, servant of the state; don’t forget, we were raised with you. ", "We played with you in the schoolyard, we sat next to you in the classroom. ", "Some of us studied at the same elite universities. ", "We watched as you had your first tastes of power. ", "We were the boys and girls standing next to you. ", "Some of us were your first victims. ", "We are not fooled by your carefully crafted public image.", "\n\n\n\n==== What We Believe ====\n\n#1: Many humans resent the responsibilities that are implied by consciousness. ", "We accept those responsibilities and we embrace consciousness. ", "Rather than letting things happen to us (avoiding consciousness), we accept consciousness and choose to act in our own interest. ", "We do not seek the refuge of blaming others, neither do we take refuge in crowds. ", "We are willing to act on our personal judgment, and we are willing to accept the consequences thereof.", "\n\n\n\n#2: We believe in negative rights for all: That all humans should be free to do whatever they wish, as long as they do not intrude upon others; that no man has a right to the life, liberty or property of another; that we oppose aggression, fraud and coercion.", "\n\n\n\n#3: We do not believe that our way of life, or any other, will make life perfect or trouble-free. ", "We expect crime and disagreements and ugliness, and we are prepared to deal with them. ", "We do not seek a strongman to step in and solve problems for us. ", "We agree to see to them ourselves.", "\n\n\n\n#4: We believe in free and unhindered commerce. ", "So long as exchanges are voluntary and honest, no other party has a right to intervene – before, during or after.", "\n\n\n\n#5: We believe that all individuals should keep their agreements.", "\n\n\n\n#6: We believe that honestly obtained property is fully legitimate and absolute.", "\n\n\n\n#7: We believe that some humans are evil and that they must be faced and dealt with. ", "We accept the fact that this is a difficult area of life.", "\n\n\n\n#8: We believe that humans can self-organize effectively. ", "We expect them to cooperate. ", "We reject impositions of hierarchy and organization.", "\n\n\n\n#9: We believe that all humans are to be held as equals in all matters regarding justice.", "\n\n\n\n#10: We believe that the more a man or woman cares about right and wrong, the more of a threat he or she is perceived to be by governments.", "\n\n\n\n#11: We believe that there are only two true classes of human beings: Those who wish to exercise power upon others - either directly or through intermediaries - and those who have no such desires.", "\n\n\n\n#12: Large organizations and centralization are inherently anti-human. ", "They must rely upon rules rather than principles, treating humans within the organization as obedient tools.", "\n\n\n\n==== Our Plans: ====\n\nWe are building our own society. ", "We will supplement traditional tools with networking, cryptography, sound money, digital currency and anonymous messaging. ", "Our society will not be centrally controlled. ", "It will rely solely on voluntary arrangements. ", "We welcome others to join us. ", "We are looking for people who are independent creators of value, people who act more than talk, and people who do the right thing because it is the right thing. ", "We will develop our own methods of dealing with injustice, built on the principles of negative rights, restitution, integrity and equal justice. ", "We do not forbid anyone from having one foot in each realm - ours and the old realm -although we demand that they do no damage to our realm. ", "We are fully opposed to any use of our realm to facilitate crime in the old realm, such as the hiding of criminal proceeds. ", "We expect to be loudly condemned, libeled and slandered by the authorities of the old regime. ", "We expect them to defend their power and their image of legitimacy with all means available to them. ", "We expect that many gullible and servile people will believe these lies, at least at first. ", "We will consider traps laid for us to be criminal offenses. ", "Any who wish to join us are encouraged to distribute this declaration, to act in furtherance of our new society, to voluntarily excel in virtues and to communicate and cooperate with other members of the new society.", "\n\n\n\nFree, unashamed men cannot be ruled.", "\n\n\n\nWe are The Free and The Unashamed. ", "Back to category overview Back to news overview Older News Newer News\n\n\n\nWe seek nothing from you. ", "We do not want to rule you and we do not want to control you. ", "All we wish is to live on earth in peace. ", "As always, we will be helpful neighbors and generous acquaintances. ", "We will remain honest business partners and trustworthy employees. ", "We will continue to be loving parents and respectful children. ", "We will not, however, be sacrificial animals. ", "We reject the idea that others have a right to our lives and our property. ", "We will not demand anything from you, and we will no longer acquiesce to any demands upon us. ", "We have left that game. ", "We reject all obligations to any person or organization beyond honesty, fair dealing and a respect for human life. ", "We will shortly explain what we believe, but we are not demanding that you agree with us. ", "All we ask is that you do not try to stop us. ", "Continue to play the game if you wish; we will not try to disrupt it. ", "We have merely walked away from it. ", "We wish you peace.", "We will ignore you. ", "We welcome and seek the verdict of a just God, before whom we are willing to expose our innermost thoughts. ", "Are you similarly willing? ", "We would stand openly before all mankind if it were not suicidal. ", "Perhaps some day we will have to accept slaughter for our crime of independence, but not yet. ", "Your criticism and your malice are much deeper than mere disagreements of strategy or philosophy. ", "You do not oppose our philosophy, you oppose our existence. ", "Our presence in the world means that your precious ideals are false. ", "Some of you would rather kill us than face the loss of your ideologies, just as those like you have either hated or killed every sufficiently independent human. ", "You present yourselves to the world as compassionate, tolerant and enlightened, but we know that your smooth words are costumes. ", "Oh yes, we know you, servant of the state; don’t forget, we were raised with you. ", "We played with you in the schoolyard, we sat next to you in the classroom. ", "Some of us studied at the same elite universities. ", "We watched as you had your first tastes of power. ", "We were the boys and girls standing next to you. ", "Some of us were your first victims. ", "We are not fooled by your carefully crafted public image.#1: Many humans resent the responsibilities that are implied by consciousness. ", "We accept those responsibilities and we embrace consciousness. ", "Rather than letting things happen to us (avoiding consciousness), we accept consciousness and choose to act in our own interest. ", "We do not seek the refuge of blaming others, neither do we take refuge in crowds. ", "We are willing to act on our personal judgment, and we are willing to accept the consequences thereof.#2: We believe in negative rights for all: That all humans should be free to do whatever they wish, as long as they do not intrude upon others; that no man has a right to the life, liberty or property of another; that we oppose aggression, fraud and coercion.#3: We do not believe that our way of life, or any other, will make life perfect or trouble-free. ", "We expect crime and disagreements and ugliness, and we are prepared to deal with them. ", "We do not seek a strongman to step in and solve problems for us. ", "We agree to see to them ourselves.#4: We believe in free and unhindered commerce. ", "So long as exchanges are voluntary and honest, no other party has a right to intervene – before, during or after.#5: We believe that all individuals should keep their agreements.#6: We believe that honestly obtained property is fully legitimate and absolute.#7: We believe that some humans are evil and that they must be faced and dealt with. ", "We accept the fact that this is a difficult area of life.#8: We believe that humans can self-organize effectively. ", "We expect them to cooperate. ", "We reject impositions of hierarchy and organization.#9: We believe that all humans are to be held as equals in all matters regarding justice.#10: We believe that the more a man or woman cares about right and wrong, the more of a threat he or she is perceived to be by governments.#11: We believe that there are only two true classes of human beings: Those who wish to exercise power upon others - either directly or through intermediaries - and those who have no such desires.#12: Large organizations and centralization are inherently anti-human. ", "They must rely upon rules rather than principles, treating humans within the organization as obedient tools.", "We are building our own society. ", "We will supplement traditional tools with networking, cryptography, sound money, digital currency and anonymous messaging. ", "Our society will not be centrally controlled. ", "It will rely solely on voluntary arrangements. ", "We welcome others to join us. ", "We are looking for people who are independent creators of value, people who act more than talk, and people who do the right thing because it is the right thing. ", "We will develop our own methods of dealing with injustice, built on the principles of negative rights, restitution, integrity and equal justice. ", "We do not forbid anyone from having one foot in each realm - ours and the old realm -although we demand that they do no damage to our realm. ", "We are fully opposed to any use of our realm to facilitate crime in the old realm, such as the hiding of criminal proceeds. ", "We expect to be loudly condemned, libeled and slandered by the authorities of the old regime. ", "We expect them to defend their power and their image of legitimacy with all means available to them. ", "We expect that many gullible and servile people will believe these lies, at least at first. ", "We will consider traps laid for us to be criminal offenses. ", "Any who wish to join us are encouraged to distribute this declaration, to act in furtherance of our new society, to voluntarily excel in virtues and to communicate and cooperate with other members of the new society.", "Free, unashamed men cannot be ruled.", "We are The Free and The Unashamed. ", "Printer Friendly Wendy McElroy - Wednesday 08 April 2009 - 04:00:00 - Permalink I received the following Declaration from an anonymous source. ", "It is a declaration of separation from all governments and from all people who wish to control others. ", "I encourage readers to post links to this Declaration far and wide. ", "The statement is posted here where comments are welcomed. ", "I request that you, however, because I intend to provide updates with anything else I receive from The Free and The Unashamed...including whatever contact information I receive permission to circulate.", "We claim the right to exist, and we will defend it. ", "We do not seek to overthrow anything. ", "We do not seek to control anything. ", "We merely wish to be left alone. ", "All we ever wanted was to live in peace with our friends and neighbors. ", "For a long, long time we bore insults to our liberty; we took blows, we did what we could to avoid injury and we worked through the system to get the offenses to stop. ", "That has now changed.", "We no longer see any benefit in working through the world’s systems. ", "At some point, working within a system becomes cowardly and immoral; for us, that point has arrived. ", "Regardless of the parties in power, their governments have continued to restrict, restrain and punish us. ", "We hereby reject them all. ", "We hereby withdraw from them all. ", "We hold the ruling states of this world and all that appertains to them to be self-serving and opposed to humanity. ", "We now withdraw our obedience and reclaim the right to strike back when struck. ", "We will not initiate force, but we do reserve the right to answer it. ", "We did not choose this – it was forced upon us.", "You are building cages for all that is human. ", "In the name of protection, you have intruded into all areas of human life, far exceeding the reach of any Caesar. ", "You claim ultimate control of our property and our decisions, of our travels and even our identities. ", "You claim ownership of humanity far beyond the dreams of any Emperor of any previous era. ", "Understand clearly: We reject your authority and we reject your legitimacy. ", "We do not believe that you have any right to do the things you do. ", "You have massive power, but no right to impose it upon us and no legitimacy. ", "We have forsaken you. ", "We are no longer your citizens or your subjects. ", "Your systems are inherently anti-human, even if all their operators are not. ", "We are not merely angry young people. ", "We are fathers and mothers; aunts, uncles and grandparents; we are business owners and trusted employees; we are mechanics and engineers and farmers. ", "We are nurses and accountants and students and executives. ", "We are on every continent.", "This is not a burst of outrage; this is a sober declaration that we no longer accept unearned suffering as our role in life. ", "For long decades we sat quietly, hoping that things would turn around. ", "We took no actions; we suffered along with everyone else. ", "But after having our limits pushed back again and again, we have given up on your systems. ", "If our fellow inhabitants of this planet wish to accept your rule, they are free to do so. ", "We will not try to stop them. ", "We, however, will no longer accept your constraints upon us. ", "From now on, when you hurt us, we will bite back. ", "If you leave us alone we will leave you alone and you can continue to rule your subjects. ", "We are happy to live quietly.", "But if you come after us, there will be consequences. ", "You caused this because of your fetish for control and power. ", "The chief men and women among you are pathologically driven to control everyone and everything that moves upon this planet. ", "You have made yourselves the judge of every human activity. ", "No god-king of the ancient world ever had the power that your systems do. ", "You have created a world where only the neutered are safe and where only outlaws are free." ]

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[ "Race Notes\n\nMERCEDES-AMG PETRONAS MOTORSPORT SCORE 30 POINTS AT SPA-FRANCORCHAMPS\n\n29.08.2018\n\nLewis Hamilton secured his 10th podium of the 2018 Formula 1™️ season at the Belgian Grand Prix as teammate Valtteri Bottas surged through the field from 17th on the grid, placing 4th overall to extend Mercedes-AMG Petronas Motorsport’s lead in the FIA Formula OneTM World Constructors’ Championship over Ferrari by 5 points.", "\n\nFollowing a Qualifying masterclass on Saturday in tricky conditions, Lewis led the pack away from pole position into La Source with Vettel close behind. ", "Car #44 started the race on the red Super Soft compound whereas Valtteri opted to use the yellow Softs to go long in the first stint.", "\n\nStrategic plans soon unravelled for the majority of the grid as a huge incident at Turn 1 took out three cars and damaged several others, Valtteri included. ", "Luckily this damage was limited to his front wing and, soon after, the Safety Car was deployed to neutralise the race. ", "Unfortunately for Lewis, this call came too late to halt the action at the front of the grid.", "\n\nVettel slipstreamed past as the leading train of cars charged up the Kemmel Straight, and for a moment the leaders were four-abreast – the two Racing Point Force Indias either side of Vettel and Lewis – before settling into single-file for the right-left-right complex of Les Combes.", "\n\nWith the Mercedes-AMG GT-R safety car now on track and slowing the field, the team pitted Valtteri for a wing change and a switch to the Super Soft compound – a much-needed ‘race reset’ from 17th with car #77 primed for attack.", "\n\nAs the race resumed, wheelspin through Blanchimont compromised leader Vettel but Lewis’s challenge for the lead was defused as he went deep into the ‘bus stop’ chicane, allowing the Ferrari to open up a safe gap between the two from La Source onward.", "\n\nThis order remained unchanged as Lewis attempted to undercut the Ferrari on Lap 22, with the team’s only planned stop for the afternoon switching car #44 to the Soft tyre compound. ", "Unfortunately, Vettel’s in-lap pace was too great to overcome and, as he re-joined the track on Lap 24 following his own stop for Softs, the Ferrari remained first overall.", "\n\nValtteri made the most of fresh rubber to enter points-paying positions by Lap 13, eventually rising as high as P4 before pitting on Lap 29 for the Soft compound tyre himself. ", "There were several stand-out moves for position in this opening stint, most notably a daring dive around the outside of Brendon Hartley entering the famed Eau Rouge corner. ", "Now placed sixth with 15 laps to go, the chase for fourth was on.", "\n\nAs Vettel and Lewis traded fastest laps at the front of the field, Valtteri passed Ocon for fifth on Lap 32 and placed his Mercedes-AMG EQ Power+ within DRS range of fourth-placed Perez by Lap 40. ", "In a move that almost mirrored the pass of 8 laps earlier, Valtteri coursed around the outside of Perez into the braking area at Les Combes to secure his fourth-place finish.", "\n\nThe chequered flag fell 4 laps later with Lewis P2, crossing the line 10 seconds adrift of Vettel, but maintaining a 17-point lead (231 points) in the Drivers’ Championship over his Ferrari rival (214 points). ", "Following his resurgent drive through the field, Valtteri now lies only 2 points behind third-placed Raikkonen (146 points). ", "Mercedes-AMG Petronas Motorsport (375 points) leads Ferrari (360 points) by 15 points in the Constructors’ Championship.", "\n\nVisit PurePitWall.com for the Italian Grand Prix this weekend to see how Pure Storage give Mercedes-AMG Petronas Motorsport and #UnfairAdvantage." ]

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[ "And it's luvverly! ", "And hot!We took Maddie for a walk (and little swim!) ", "by the lake today, and then came back and pootled in the backyard for a while. ", "Maddie was very hot, so of course the only option was to dump a bowlful of water upon her little beagle-head. ", "Of course. ", "And, of course, this moment needed to be videoed and blogged for all to see. ", "I'm trying a new video hosting service, so hopefully this'll work okay. ", "I think there might be some weird black borders on there, but other than that it's fine. ", "Look....!", "\n\nAAAAAAAAND, as if that wasn't enough value for your click, here's some footage of Jim Rennie's soccer genius, which still burns within him like a beacon of... um... genius. ", "Years from now people will say \"Look at what this guy did with his feet!\" ", "without ever knowing that I used to chew my toenails. ", "Oh, and btw - Amy asked me to assure everyone that she does not have T.B. - the heavy breathing is caused by the camera being so close to her face as she filmed.:)", "\n\nNo comments:\n\nAbout Me\n\nJim, originally from Taunton, U.K. and Amy, from Tremont, IL were married on April 7th 2006 and are currently living happily together in Tremont with Maddie the beagle and Sammy the cat. ", "They have two sons who were born prematurely and passed away, Brian William and Sawyer James. ", "In April, their first daughter, Amelie Jane, arrived safely thanks to Dr. Haney and the TAC!" ]

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[ "package net.corda.tools.shell\n\ndata class SSHDConfiguration(val port: Int) {\n companion object {\n internal const val INVALID_PORT_FORMAT = \"Invalid port: %s\"\n private const val MISSING_PORT_FORMAT = \"Missing port: %s\"\n\n /**\n * Parses a string of the form port into a [SSHDConfiguration].", "\n * @throws IllegalArgumentException if the port is missing or the string is garbage.", "\n */\n @JvmStatic\n fun parse(str: String): SSHDConfiguration {\n require(!str.isBlank()) { SSHDConfiguration.", "MISSING_PORT_FORMAT.format(str) }\n val port = try {\n str.toInt()\n } catch (ex: NumberFormatException) {\n throw IllegalArgumentException(\"Port syntax is invalid, expected port\")\n }\n return SSHDConfiguration(port)\n }\n }\n\n init {\n require(port in (0..0xffff)) { INVALID_PORT_FORMAT.format(port) }\n }\n}" ]

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[ "---\nabstract: |\n Generalized permutohedra are deformations of regular permutohedra, and arise in many different fields of mathematics. ", "One important characterization of generalized permutohedra is the Submodular Theorem, which is related to the deformation cone of the Braid fan. ", "We lay out general techniques for determining deformation cones of a fixed polytope and apply it to the Braid fan to obtain a natural combinatorial proof for the Submodular Theorem.", "\n\n We also consider a refinement of the Braid fan, called the nested Braid fan, and construct usual (respectively, generalized) nested permutohedra which have the nested Braid fan as (respectively, refining) their normal fan. ", "We extend many results on generalized permutohedra to this new family of polytopes, including a one-to-one correspondence between faces of nested permutohedra and chains in ordered partition posets, and a theorem analogous to the Submodular Theorem. ", "Finally, we show that the nested Braid fan is the barycentric subdivision of the Braid fan, which gives another way to construct this new combinatorial object.", "\nauthor:\n- Federico Castillo and Fu Liu\nbibliography:\n- 'biblio.bib'\ntitle: Deformation Cones of nested Braid fans\n---\n\nIntroduction\n============\n\nLet $V$ be a finite dimensional real vector space, whose dimension we will always denote by $d.$ The *dual space* $W$ of $V$ is another real vector space together with a perfect pairing $\\langle\\cdot,\\cdot\\rangle:W\\times V \\to {\\mathbb{R}}$. A *polyhedron* $P \\subset V$ is the solution set of a finite set of linear inequalities: $$\\label{ineq}\nP = \\{ {\\textbf{x}}\\in V \\ : \\ \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle \\le b_i, \\ i\\in I \\},$$ where ${\\textbf{a}}_i$ are elements in $W$ and $b_i \\in {\\mathbb{R}}$ and $I$ is a finite set of indices. ", "By choosing bases, we can abbreviate the above system of linear inequalities as $$\\label{matrix}\n{\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}},$$ where ${\\textrm{A}}$ is the matrix whose row vectors are ${\\textbf{a}}_i$’s and ${\\textbf{b}}$ is the vector with components $b_i$’s. ", "A *polytope* is a bounded polyhedron. ", "A $k$-dimensional polytope $P\\subset V$ is *simple* if each vertex lies on exactly $k$ facets. ", "In this paper, we want to study special cases of the following question: For a fixed polytope $P_0 \\subset V,$ how do we characterize all “deformations” of $P_0$? ", "In the literature, there are different equivalent definitions for what we call deformations. ", "The initial approach we take here is to move facets of $P_0$ without passing a vertex (See Definition \\[defn:deform0\\]). ", "We also make use of an alternative definition in terms of normal fans; deformations corresponds to coarsenings of the normal fan of $P_0$ (See Proposition \\[prop:deform\\]). ", "Lastly, we want to mention that this notion is equivalent (via Shepard’s theorem [@grunbaum Chapter 15, Theorem 2]) to “weak Minkowski summands”, which is central to McMullen’s work on the polytope algebra (See [@mcmullen]).", "\n\nOne important family of polytopes for this paper is *generalized permutohedra*, which were originally introduced by Postnikov [@post Definition 6.1] as deformations of usual permutohedra. ", "Generalized permutohedra contain many previously known interesting families of polytopes, including Stanley-Pitman polytopes [@stanley-pitman] and matroid polytopes [@ardila]. ", "However, it turns out generalized permutohedra are translations of polymatroids (see Theorem \\[thm:polymatroid\\]), which have been studied since the 70’s. ", "Polymatroids were initially defined in the context of optimization, in particular the greedy algorithm. ", "See Edmonds’ survey [@edmonds], or Fujishige’s book [@fujishige] for a more recent perspective. ", "Since Postnikov’s work [@post], generalized permutohedra have received much research attention in the last ten years (see for example [@PosReiWil], [@suho], [@zele]). ", "More recently, relations with hopf monoids have been developed [@aguiar].", "\n\nThe motivation of this article comes from two questions related to generalized permutohedra. ", "We will discuss them in two parts below.", "\n\nSubmodular Theorem {#submodular-theorem .unnumbered}\n------------------\n\nOne well-known result on generalized permutohedra is the Submodular Theorem.", "\n\n\\[defn:submod\\] Let $E$ be a finite set. ", "A *submodular function* is a set function $f: 2^E \\to {\\mathbb{R}}$ satisfying $$f(S \\cup T) + f(S \\cap T) \\le f(S) + f(T), \\quad \\forall S, T \\subseteq E.$$\n\n\\[thm:submodular\\] There exists a bijection between generalized permutohedra of dimension at most $d$ and submodular functions $f$ on $2^{[d+1]}$ satisfying $f(\\emptyset)=0$. (Here $[d+1]=\\{1,2,\\dots,d+1\\}$.)\n\nEven though the Submodular Theorem was known well before the original definition for generalized permutohedra was given by Postnikov, we couldn’t find a direct reference for the statement and proof. ", "Research papers commonly cite to [@post] and [@PosReiWil]; but it is written in neither. ", "In [@ranktest] it appears as Proposition 15; but only the proof for one direction of the statement is provided. ", "The standard proof we can find is in [@schrijver Chapter 44, Theorem 44.3] which has the statement in terms of polymatroids. ", "However, the proof uses ideas from optimization, and we could not find a place that gives a clear statement of the connection between polymatroids and generalized permutohedra. ", "Hence, it is still interesting to find a natural combinatorial proof for the Submodular Theorem.", "\n\nIn [@PosReiWil], the authors give several equivalent definitions for generalized permutohedra, one of which states that generalized permutohedra are precisely translations of polytopes whose normal fans are coarsenings of the “Braid fan” ${\\textrm{Br}}_d$, which is the normal fan of the “centralized regular permutohedron” $\\widetilde{\\Pi_d}.$ (See Proposition \\[prop:coarser\\].) ", "As a consequence, the Submodular Theorem is closely related to the characterization for the deformation cone of the polytope $\\widetilde{\\Pi_d}$ or the fan ${\\textrm{Br}}_d.$\n\nHaving this in mind, we consider the question of determining deformation cones of a general polytope $P_0$ in Section \\[sec:prel\\]. ", "After providing a precise definition for deformations of $P_0$ using the idea of “moving facets without passing vertices”, we derive general techniques for computing the deformation cone of $P_0,$ using which we provide in Section \\[sec:GP\\] a new combinatorial proof for Theorem \\[thm:submodular\\]. ", "After the notation and machinery is introduced, the proof flows naturally, which is an indication that techniques layed out in Section \\[sec:prel\\] is a good way of attacking this kind of problems. ", "Another consequence of our techniques is a proof for the connection between polymatroids and generalized permutohedra.", "\n\nThe nested Braid fan {#the-nested-braid-fan .unnumbered}\n--------------------\n\nOne characterization for generalized permutohedra is that all the edge directions are in the form of ${\\textbf{e}}_i - {\\textbf{e}}_j$ (See Remark \\[rem:edges\\]). ", "However, if one tries to move some facet passing a vertex, edge directions in the form of ${\\textbf{e}}_i+{\\textbf{e}}_j - {\\textbf{e}}_k - {\\textbf{e}}_\\ell$ can appear. ", "Therefore, we ask whether the family of generalized permutohedra can be generalized further to allow these edge directions. ", "This motivates the work in Section \\[sec:NBF\\] of this article.", "\n\nThe maximal cones in the Braid fan ${\\textrm{Br}}_d$ are sets of points whose coordinates are given in a fixed order. ", "In Section \\[sec:NBF\\], we introduce the “nested Braid fan” ${\\textrm{Br}}_d^2,$ which is a refinement of ${\\textrm{Br}}_d$ by considering first differences of ordered coordinates. (", "See Definitions \\[defn:NBF\\] and \\[defn:NBF2\\] for detail.) ", "We show that ${\\textrm{Br}}_d^2$ is the normal fan of “usual nested permutohedra”, a subfamily of which is $\\Pi_d^2(M,N)$ (called “regular nested permutohedra”), and thus is a projective fan. (", "See Figure \\[fig:2polytopes\\] for a picture of $\\Pi_3$ and $\\Pi_3^2(4,1)$ side by side.) ", "We then use the general techniques derived in Section \\[sec:prel\\] to give a characterization for the deformation cone of ${\\textrm{Br}}_d^2$ analogous to the results for the deformation cone of ${\\textrm{Br}}_d.$\n\nOne key ingredient in our proof for the Submodular Theorem is the natural one-to-one correspondence between chains in the Boolean algebra ${{\\mathcal B}}_{d+1}$ and faces of regular permutohedron. ", "Parallely, in Section \\[sec:NBF\\], we consider the “ordered partition poset” ${{\\mathcal O}}_{d+1}$ (see Definition \\[defn:osp\\]), and show same statement holds for ${{\\mathcal O}}_{d+1}$ and the regular nested permutohedron. ", "We remark that the combinatorics of the nested Braid fan or nested permutohedra turns out to be very rich. ", "Indeed, the equations defining the deformation cone of ${\\textrm{Br}}_d^2$ are of a combinatorial nature. ", "Even though we feel we have given a thorough description for the structures of these two related geometric objects, there are still questions remained to be answer. ", "During a talk given by the first author on materials presented in Sections \\[sec:GP\\] and \\[sec:NBF\\], Victor Reiner asked whether the nested Braid fan is the barycentric subdivision of the Braid fan. ", "We give an affirmative answer to his question in Section \\[sec:chisel\\].", "\n\nOrganization of the paper {#organization-of-the-paper .unnumbered}\n-------------------------\n\nIn §\\[sec:prel\\], we will present/review definitions of deformation cones of polytopes and projective fans, and discuss general techniques for computing them from the polytopal side. ", "In §\\[sec:GP\\], we review known facts about generalized permutohedra, apply techniques derived in §\\[sec:prel\\] to find deformation cones of ${\\textrm{Br}}_d$, and give a proof for the Submodular Theorem. ", "In §\\[sec:NBF\\], we define nested Braid fan ${\\textrm{Br}}_d^2$ and nested permutohedra, and discuss their combinatorics, using which we give inequality description for nested permutohedra and determine the deformation cone of ${\\textrm{Br}}_d^2.$ In §\\[sec:chisel\\], we describe how we can obtain the nested Braid fan as the barycentric subdivision of the Braid fan, answering Victor Reiner’s question. ", "We finish the main body of this article with some questions that might be interesting for future research in §\\[sec:question\\].", "\n\nAcknowledgements {#acknowledgements .unnumbered}\n----------------\n\nThe second author is partially supported by NSF grant DMS-1265702 and a grant from the Simons Foundation \\#426756. ", "The final writing of the work was completed when both authors were attending the program “Geometric and Topological Combinatorics” at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester, and they were partially supported by the NSF grant DMS-1440140.", "\n\nThe authors would like to thank Federico Ardila and Brian Osserman for helpful discussion, and thank Alex Fink and Christian Haase for explaining Theorem \\[thm:bary1\\].", "\n\nDetermining deformation cones {#sec:prel}\n=============================\n\nWe assume familiarity with basic definitions of polyhedra and polytopes as presented in [@barvinok; @zie]. ", "The main purpose of this section is to derive a systemetic way to answer the following general question: For a fixed polytope $P_0 \\subset V,$ how do we characterize all “deformations” of $P_0$? ", "We start by setting up our question formally.", "\n\n\\[setup1\\] Let $P_0$ be a fixed full-dimensional polytope in $V$ defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}_0$, where each inequality is *facet-defining*, i.e., $\\{ {\\textbf{x}}\\in P \\ : \\ \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle = b_i\\}$ is a facet of $P.$ Suppose $P_0$ has $n$ facets $F_1, \\dots, F_m$. We may assume that the system defines $P$ is $$\\label{fineq}\n \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle \\le b_{0,i}, \\quad 1 \\le i \\le m,$$ where ${\\textbf{a}}_i$ is an normal vector to the facet $F_i.$\n\nRoughly speaking, a deformation of $P_0$ is a polytope obtained from $P_0$ by moving facets of $P_0$ “without passing any vertices”. ", "We make this more precise below.", "\n\n\\[defn:deform0\\] A polytope $Q \\subset V$ is a *deformation* of $P_0$ (described in Setup \\[setup1\\]), if there exists ${\\textbf{b}}\\in {\\mathbb{R}}^m$ such that the following two conditions are satisfied:\n\n(a) \\[item:pts\\] $Q$ is defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ (with the same matrix ${\\textrm{A}}$ as in Setup \\[setup1\\]) or equivalently, $$\\label{Qfineq}\n \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle \\le b_{i}, \\quad 1 \\le i \\le m.$$\n\n(b) \\[item:nopass\\] For any vertex $v$ of $P_0$, if $F_{i_1}, F_{i_2}, \\dots, F_{i_k}$ are the facets of $P_0$ where $v$ lies on, then the intersection of $$\\{ {\\textbf{x}}\\in V \\ : \\ \\langle {\\textbf{a}}_{i_j}, {\\textbf{x}}\\rangle = b_{i_j}\\}, \\quad 1 \\le j \\le k$$ is a vertex $u$ of $Q.$\n\nWe call ${\\textbf{b}}$ a *deforming vector* for $Q$.\n\nIt is not hard to see that any deformation $Q$ of $P_0$ is associated with a *unique* deforming vector ${\\textbf{b}}$ because conditions and imply that the entries of ${\\textbf{b}}$ must satisfy $$b_i = \\max_{{\\textbf{x}}\\in Q} \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle, \\quad \\forall 1 \\le i \\le m.$$ Thus, we say ${\\textbf{b}}$ is *the* deforming vector for $Q.$ The uniqueness of ${\\textbf{b}}$, together with condition (a), establishes a one-to-one correspondence between deformations $Q$ of $P_0$ and their associated deformation vectors. ", "Therefore, we give the following definition.", "\n\nThe *deformation cone* of $P_0$, denoted by $\\Def(P_0)$, is the collection of deforming vectors ${\\textbf{b}}\\in {\\mathbb{R}}^m$ described in Definition \\[defn:deform0\\].", "\n\nat (13,0) [$\\left(\\begin{array}{rr} -1&0 \\\\ 0&1 \\\\ 0&-1 \\\\ 1&-1 \\end{array}\\right)\\left(\\begin{array}{r} x\\\\y\\end{array}\\right) \\leq \\left(\\begin{array}{r} 1 \\\\ 2 \\\\ 1 \\\\ 2 \\end{array}\\right).$]{};\n\n(3,0)–(-3,0); (0,3)–(0,-3);\n\n(-1,-3)–(-1,3); (-3,2)–(5,2); (-3,-1)–(3,-1); (0,-2)–(5,3);\n\nat (-1,2) [$\\scriptstyle (-1,2)$]{}; at (-1,-1) [$\\scriptstyle (-1,-1)$]{}; at (1,-1) [$\\scriptstyle (1,-1)$]{}; at (4,2) [$\\scriptstyle (4,2)$]{};\n\n(-1,2) circle \\[radius=0.1\\]; (-1,-1) circle \\[radius=0.1\\]; (1,-1) circle \\[radius=0.1\\]; (4,2) circle \\[radius=0.1\\];\n\nat (0.8, 0.7) [$\\textcolor{blue}{P_0}$]{}; at (-1,0) [$F_1$]{}; at (2,2) [$F_2$]{}; at (0,-1) [$F_3$]{}; at (3,0) [$F_4$]{};\n\n(-1,-1)–(1,-1)–(4,2)–(-1,2)–cycle;\n\n(3,0)–(-3,0); (0,3)–(0,-3);\n\n(-3,-3)–(-3,3); (-3.5,2)–(5,2); (-3.5,0)–(3,0); (0.5,-2)–(5.5,3);\n\nat (-3,2) [$\\scriptstyle (-1,2)$]{}; at (-3,0) [$\\scriptstyle (-3,0)$]{}; at (2.5,0) [$\\scriptstyle (2.5,0)$]{}; at (4.5,2) [$\\scriptstyle (4.5,2)$]{};\n\n(-3,2) circle \\[radius=0.2\\]; (-3,0) circle \\[radius=0.2\\]; (2.5,0) circle \\[radius=0.2\\]; (4.5,2) circle \\[radius=0.2\\];\n\n(-3,0)–(2.5,0)–(4.5,2)–(-3,2)–cycle;\n\nat (0,-4) [${\\textbf{b}}_1=(3,2,0,2.5)$]{}; at (0.5,2.7) [$\\textcolor{blue}{Q_1}$]{};\n\n(3,0)–(-3,0); (0,3)–(0,-3);\n\n(-1,-3)–(-1,3); (-3,2)–(5,2); (-3,-1)–(3,-1); (-2,-2)–(3,3);\n\nat (-1,2) [$\\scriptstyle (-1,2)$]{}; at (-1.2,-0.3) [$\\scriptstyle (-1,-1)$]{}; at (2,2) [$\\scriptstyle (2,2)$]{};\n\n(-1,2) circle \\[radius=0.2\\]; (-1,-1) circle \\[radius=0.2\\]; (2,2) circle \\[radius=0.2\\]; (-1,-1)–(2,2)–(-1,2)–cycle;\n\nat (0,-4) [${\\textbf{b}}_2=(1,2,1,0)$]{}; at (0.5,2.7) [$\\textcolor{blue}{Q_2}$]{};\n\n(3,0)–(-3,0); (0,3)–(0,-3);\n\n(-1,-3)–(-1,3); (-3,2)–(5,2); (-3,-2)–(3,-2); (-2,-2)–(3,3);\n\nat (-1,2) [$\\scriptstyle (-1,2)$]{}; at (-1.2,-0.3) [$\\scriptstyle (-1,-1)$]{}; at (2,2) [$\\scriptstyle (2,2)$]{}; at (-1,-2) [$\\scriptstyle (-1,-2)$]{}; at (-1.5,-2) [$\\scriptstyle (-2,-2)$]{};\n\n(-1,2) circle \\[radius=0.2\\]; (-1,-1) circle \\[radius=0.2\\]; (2,2) circle \\[radius=0.2\\]; (-1,-2) circle \\[radius=0.2\\]; (-2,-2) circle \\[radius=0.2\\]; (-1,-1)–(2,2)–(-1,2)–cycle;\n\nat (0,-4) [${\\textbf{b}}_3=(1,2,2,0)$]{}; at (0.5,2.7) [$\\textcolor{blue}{Q_3}$]{};\n\n\\[ex:example\\] Let $P_0 \\subset V = {\\mathbb{R}}^2$ be the polytope on the top left of Figure \\[fig:exfigure\\], which is defined by the linear system given to its right. ", "Let ${\\textrm{A}}$ be the matrix in the linear system. ", "Any deformation $Q$ of $P_0$ can be defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ for some ${\\textbf{b}}.$ Two possible deformations $Q_1$ and $Q_2$ together with their respective deforming vectors ${\\textbf{b}}_1$ and ${\\textbf{b}}_2$ are shown on the bottom of Figure \\[fig:exfigure\\]. ", "Notice that $Q_3$ defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}_3$ is exactly the same polytope as $Q_2$, so is a deformation of $P_0$. However, ${\\textbf{b}}_3$ does not satisfy condition , and thus is not a deforming vector. ", "Hence, ${\\textbf{b}}_1, {\\textbf{b}}_2 \\in \\Def(P_0)$, but ${\\textbf{b}}_3 \\not\\in \\Def(P_0).$ (This conclusion will be proved formally in Example \\[ex:exampleprop\\].)", "\n\nThe deformation cone of $P_0$ is a natural subject to study if one is interested in deformations of the fixed polytope $P_0$. We can now rephrase our initial general question.", "\n\n\\[ques1\\] Fix a full dimensional polytope $P_0 \\subset V$. How do we find a characterization for $\\Def(P_0)?$\n\nThere is another equivalent way of defining deformations $Q$ of $P_0$ using normal fans of polytopes. (", "See Definition \\[defn:normal\\] for a formal definition of normal cones and normal fans.)", "\n\n\\[prop:deform\\] A polytope $Q \\subset V$ is a deformation of $P_0$ if and only if the normal fan $\\Sigma(Q)$ of $Q$ is a coarsening of the normal fan $\\Sigma(P_0)$ of $P_0$.\n\nThe proof of Proposition \\[prop:deform\\] is quite different from what we discuss in the rest of the paper, so will be included in Appendix \\[apd:normal\\].", "\n\nNote that in Example \\[ex:example\\], the polytope $Q_1$ has the same normal fan as $P_0$, whereas $Q_2$’s normal fan is a coarsening.", "\n\nProposition \\[prop:deform\\] implies that if two polytopes $P_1$ and $P_2$ have the same normal fan $\\Sigma$, they have exactly the same deformation cone. ", "By abusing the notation, we might denote this deformation cone by $\\Def(\\Sigma),$ and call it the *deformation cone* of $\\Sigma.$\n\nWe say a fan $\\Sigma$ is *projective* if it is the normal fan of a polytope. (", "It is not true all the fans are projective.) ", "Once we know that a projective fan $\\Sigma$ is the normal fan a polytope, one can check that the polytope is full dimensional if and only if $0 \\in \\Sigma,$ i.e., all cones in $\\Sigma$ are pointes. ", "We use these language to rewrite Setup \\[setup1\\] and Question \\[ques1\\]\n\n\\[setup2\\] Let $\\Sigma_0$ be a projective fan in $W$ such that $0 \\in \\Sigma_0$. Assume it has $m$ one dimensional cones that generated by rays ${\\textbf{a}}_1, \\dots, {\\textbf{a}}_m,$ respectively.", "\n\n\\[ques2\\] Given a fixed fan $\\Sigma_0$ as described in Setup \\[setup2\\], how do we find a characterization for $\\Def(\\Sigma_0)?$\n\nQuestions \\[ques1\\] and \\[ques2\\] are the same question in two different languages, and both have been studied, where the latter one is related to the study of toric varieties. (", "See [@cls] for general results on toric varieties.) ", "It is worth remarking that big part of the motivation and tools come from that branch of mathematics. ", "When $\\Sigma_0$ is smooth, then $\\Def(\\Sigma_0)$, modulo its lineality space, is isomorphic to $\\textrm{Nef}(\\Sigma_0)$, the cone of *numerically effective divisors* (see [@cls Chapter 6]).", "\n\nIn addition to the two definitions we have provided, there are additional different but equivalent ways of defining deformations of polytopes. ", "In particular, in the Appendix of [@PosReiWil], the authors discuss five different ways, including the normal fan version stated in Proposition \\[prop:deform\\]. ", "However, they restrict their definitions to simple polytopes only, while our definition is for *any* polytope. ", "Furthermore, it seems our Definition \\[defn:deform0\\] has not (or at least not explicitly) appeared in the literature, and actually is very important for determining deformation cones as the techniques (that will be shown below) is derived from it directly.", "\n\nThere are three main results that will be presented in the rest of this section. ", "The first result is Corollary \\[cor:ineqs\\], in which we give an explicit description for deformation cone $\\Def(P_0)$ of $P_0$ using linear equalities and inequalities. ", "This will be derived directly from Definition \\[defn:deform0\\]. ", "We then analyze inequalities in Corollary \\[cor:ineqs\\] further and apply it to simple polytopes to obtain in Proposition \\[prop:redux\\] a simpler description for $\\Def(P_0)$ using inequalities indexed by edges of $P_0$. We then give our third result - Proposition \\[prop:reduxfan\\] - by restating Proposition \\[prop:redux\\] using the language of simplicial fans, in which inequalities are indexed by pairs of adjacent maximal cones in the fan. ", "We end this section with a discussion on how to determine whether a polytope is a deformation of $P_0$ using $\\Def(P_0).$\n\nDeformation cones of (not necessarily simple) polytopes {#deformation-cones-of-not-necessarily-simple-polytopes .unnumbered}\n-------------------------------------------------------\n\nEven though condition of Definition \\[defn:deform0\\] is necessary for the definition of deformations of a fixed polytope, if one only concerns about deforming vectors, only condition is needed as stated in the following lemma.", "\n\n\\[lem:detb\\] Let ${\\textbf{b}}\\in {\\mathbb{R}}^m.$ Then ${\\textbf{b}}\\in \\Def(P_0)$ if and only if for any vertex $v$ of $P_0$, let $F_{i_1}, F_{i_2}, \\dots, F_{i_k}$ be the facets of $P_0$ that $v$ lies on and let $u_{\\textbf{b}}$ be the intersection of $$\\{ {\\textbf{x}}\\in V \\ : \\ \\langle {\\textbf{a}}_{i_j}, {\\textbf{x}}\\rangle = b_{i_j}\\}, \\quad 1 \\le j \\le k,$$ then following “NEI” (short for “non-empty-interesection”) and “no-passing” conditions are true:\n\n1. ", " $u_{\\textbf{b}}$ is nonempty, so is a point; and\n\n2. ", " it satisfies ${\\textrm{A}}u_{\\textbf{b}}\\le {\\textbf{b}},$ or equivalently, $$\\langle {\\textbf{a}}_i, u_{\\textbf{b}}\\rangle \\le b_i, \\quad \\forall i \\neq i_1,\\dots, i_k.$$\n\nThe forward implication follows directly from Definition \\[defn:deform0\\]. ", "Conversely, suppose the two conditions hold. ", "Let $Q$ be defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}.$ Condition of Definition \\[defn:deform0\\] automatically satisfied, and the NEI and no-passing conditions guarantee that $u_{\\textbf{b}}$ is a vertex of $Q$, and thus condition holds.", "\n\nThe no-passing condition can fail in different scenarios. ", "For the polytope $Q_3$ of Example \\[ex:example\\], not only the inequality $-y \\le 2$ is not facet-defining, but the hyperplane determined by $-y = 2$ does not “touch” $Q_3,$ which causes the failure of the no-passing condition. ", "Below, we show a different example where the no-passing condition fails even though all the inequalities are still facet-defining.", "\n\nSee the $3$-dimensional polytopes $P_0$ and $Q$ shown on the left of Figure \\[fig:above\\]. ", "The right of Figure \\[fig:above\\] shows how they look like when being viewed from above.", "\n\n\\[x=[(-0.2 cm, -0.1 cm)]{}, y=[(0.5 cm,0 cm)]{}, z=[(0cm, 0.5cm)]{}, scale=0.5, back/.style=[loosely dotted, thin]{}, edge/.style=[color=black!95!black, thick]{}, facet/.style=[fill=black!95!black,fill opacity=0.200]{}, vertex/.style=[inner sep=1pt,circle,draw=red!25!black,fill=red!75!black,thick,anchor=base]{}\\] (8.00000, 0.00000, 0.00000) at (8.00000, 0.00000, 0.00000); (8.00000, 10.00000, 0.00000) at (8.00000, 10.00000, 0.00000); (0.00000, 10.00000, 0.00000) at (0.00000, 10.00000, 0.00000); (4.00000, 6.00000, 4.00000) at (4.00000, 6.00000, 4.00000); (4.00000, 4.00000, 4.00000) at (4.00000, 4.00000, 4.00000); (0.00000, 0.00000, 0.00000) at (0.00000, 0.00000, 0.00000); (4.00000, 4.00000, 4.00000) – (8.00000, 0.00000, 0.00000) – (8.00000, 10.00000, 0.00000) – (4.00000, 6.00000, 4.00000) – cycle ; (4.00000, 6.00000, 4.00000) – (8.00000, 10.00000, 0.00000) – (0.00000, 10.00000, 0.00000) – cycle ; (0.00000, 0.00000, 0.00000) – (0.00000, 10.00000, 0.00000) – (4.00000, 6.00000, 4.00000) – (4.00000, 4.00000, 4.00000) – cycle ; (0.00000, 0.00000, 0.00000) – (8.00000, 0.00000, 0.00000) – (4.00000, 4.00000, 4.00000) – cycle ; (8.00000, 0.00000, 0.00000) – (8.00000, 10.00000, 0.00000); (8.00000, 0.00000, 0.00000) – (4.00000, 4.00000, 4.00000); (8.00000, 0.00000, 0.00000) – (0.00000, 0.00000, 0.00000); (8.00000, 10.00000, 0.00000) – (0.00000, 10.00000, 0.00000); (8.00000, 10.00000, 0.00000) – (4.00000, 6.00000, 4.00000); (0.00000, 10.00000, 0.00000) – (4.00000, 6.00000, 4.00000); (0.00000, 10.00000, 0.00000) – (0.00000, 0.00000, 0.00000); (4.00000, 6.00000, 4.00000) – (4.00000, 4.00000, 4.00000); (4.00000, 4.00000, 4.00000) – (0.00000, 0.00000, 0.00000); at (8.00000, 0.00000, 0.00000) ; at (8.00000, 10.00000, 0.00000) ; at (0.00000, 10.00000, 0.00000) ; at (4.00000, 6.00000, 4.00000) ; at (4.00000, 4.00000, 4.00000) ; at (0.00000, 0.00000, 0.00000) ; at (-6,-4) [$\\textcolor{blue}{P_0}$]{};\n\n\\[xshift=3.5cm, x=[(-0.2 cm, -0.1 cm)]{}, y=[(0.6 cm,0 cm)]{}, z=[(0cm, 0.4cm)]{}, scale=0.5, back/.style=[loosely dotted, thin]{}, edge/.style=[color=black!95!black, thick]{}, facet/.style=[fill=black!95!black,fill opacity=0.200]{}, vertex/.style=[inner sep=1pt,circle,draw=red!25!black,fill=red!75!black,thick,anchor=base]{}\\] (10.00000, 0.00000, 0.00000) at (10.00000, 0.00000, 0.00000); (10.00000, 8.00000, 0.00000) at (10.00000, 8.00000, 0.00000); (6.00000, 4.00000, 4.00000) at (6.00000, 4.00000, 4.00000); (4.00000, 4.00000, 4.00000) at (4.00000, 4.00000, 4.00000); (0.00000, 0.00000, 0.00000) at (0.00000, 0.00000, 0.00000); (0.00000, 8.00000, 0.00000) at (0.00000, 8.00000, 0.00000); (6.00000, 4.00000, 4.00000) – (10.00000, 0.00000, 0.00000) – (10.00000, 8.00000, 0.00000) – cycle ; (0.00000, 8.00000, 0.00000) – (10.00000, 8.00000, 0.00000) – (6.00000, 4.00000, 4.00000) – (4.00000, 4.00000, 4.00000) – cycle ; (0.00000, 8.00000, 0.00000) – (4.00000, 4.00000, 4.00000) – (0.00000, 0.00000, 0.00000) – cycle ; (0.00000, 0.00000, 0.00000) – (10.00000, 0.00000, 0.00000) – (6.00000, 4.00000, 4.00000) – (4.00000, 4.00000, 4.00000) – cycle ; (10.00000, 0.00000, 0.00000) – (10.00000, 8.00000, 0.00000); (10.00000, 0.00000, 0.00000) – (6.00000, 4.00000, 4.00000); (10.00000, 0.00000, 0.00000) – (0.00000, 0.00000, 0.00000); (10.00000, 8.00000, 0.00000) – (6.00000, 4.00000, 4.00000); (10.00000, 8.00000, 0.00000) – (0.00000, 8.00000, 0.00000); (6.00000, 4.00000, 4.00000) – (4.00000, 4.00000, 4.00000); (4.00000, 4.00000, 4.00000) – (0.00000, 0.00000, 0.00000); (4.00000, 4.00000, 4.00000) – (0.00000, 8.00000, 0.00000); (0.00000, 0.00000, 0.00000) – (0.00000, 8.00000, 0.00000); at (10.00000, 0.00000, 0.00000) ; at (10.00000, 8.00000, 0.00000) ; at (6.00000, 4.00000, 4.00000) ; at (4.00000, 4.00000, 4.00000) ; at (0.00000, 0.00000, 0.00000) ; at (0.00000, 8.00000, 0.00000) ; at (-6,-4) [$\\textcolor{blue}{Q}$]{};\n\n(0,0)–(10,0)–(10,8)–(0,8)–cycle; (0,0)–(4,4)–(6,4)–(10,0); (0,8)–(4,4)–(6,4)–(10,8); (0,0) circle \\[radius=0.2\\]; (10,0) circle \\[radius=0.2\\]; (10,8) circle \\[radius=0.2\\]; (0,8) circle \\[radius=0.2\\]; (4,4) circle \\[radius=0.2\\]; (6,4) circle \\[radius=0.2\\]; at (1.5,4) [$\\textcolor{blue}{P_0}$]{};\n\n(0,0)–(0,10)–(8,10)–(8,0)–cycle; (0,0)–(4,4)–(4,6)–(0,10); (8,0)–(4,4)–(4,6)–(8,10); (0,0) circle \\[radius=0.2\\]; (0,10) circle \\[radius=0.2\\]; (8,10) circle \\[radius=0.2\\]; (8,0) circle \\[radius=0.2\\]; (4,4) circle \\[radius=0.2\\]; (4,6) circle \\[radius=0.2\\];\n\nat (2,5) [$\\textcolor{blue}{Q}$]{};\n\n$Q$ is obtained from $P_0$ by moving the $\\textsc{left}$ and $\\textsc{right}$ facets of $P_0$ inward “too much”. ", "Notice that in $P_0$, the facets $\\textsc{front},\\textsc{back}$ and $\\textsc{right}$ intersect in a vertex, but in $Q$ they do not. ", "More precisely, the hyperplanes determined by the $\\textsc{front},\\textsc{back}$ and $\\textsc{right}$ facets of $Q$ intersect at a point outside of $Q$, and thus is on the wrong side of the hyperplane determined by the $\\textsc{left}$ facet. ", "So $Q$ is not a deformation of $P_0$ even though it can be defined using the same matrix ${\\textrm{A}}$ as $P_0.$\n\nIt is straightforward to translate conditions in Lemma \\[lem:detb\\] to explicit linear conditions. ", "We give the following notation and definition before stating Corollary \\[cor:ineqs\\].", "\n\nFor convenience, for any facet $F = F_i$ of $P_0,$ we sometimes use $F$ as the subscripts for ${\\textbf{a}}_i$ and $b_i,$ that is $${\\textbf{a}}_F = {\\textbf{a}}_i, \\quad b_F = b_i.$$\n\nLet $v$ be a vertex of $P_0.$ Suppose $F_{i_1}, F_{i_2}, \\dots, F_{i_k}$ (with $i_1 < i_2 < \\cdots < i_k$) are the facets of $P_0$ where $v$ lies on. (", "Note that we must have $k \\ge d$.) We say $F_{i_1},\\dots, F_{i_d}$ are the *first $d$ supporting facets of $v$*, and $F_{i_j}$ for $d < j \\le k$ is an *extra supporting facet of $v$*. (", "Note these definitions rely on the specific ordering we give for facets of $P_0$.)\n\nFor any ${\\textbf{b}}\\in {\\mathbb{R}}^m$, let $v_{\\textbf{b}}$ be the intersection of the hyperplanes determined by the first $d$ supporting facets of $v,$ that is, $v_{\\textbf{b}}$ is the the intersection of $$\\{ {\\textbf{x}}\\in V \\ : \\ \\langle {\\textbf{a}}_{i_j}, {\\textbf{x}}\\rangle = b_{i_j}\\}, \\quad 1 \\le j \\le d,$$ which clearly is a point.", "\n\nFor any vertex $v$ of $P_0$ and any facet $F$ of $P_0$, we associate with the pair $(v, F)$ an equality or an inequality as below: $$\\begin{aligned}\nE_{v,F}({\\textbf{b}}) :& \\quad \\langle {\\textbf{a}}_F, v_{\\textbf{b}}\\rangle = b_F, \\\\\nI_{v,F}({\\textbf{b}}) :& \\quad \\langle {\\textbf{a}}_F, v_{\\textbf{b}}\\rangle \\le b_F. \\end{aligned}$$\n\n\\[cor:ineqs\\] The deformation cone $\\Def(P_0)$ is the collection of vectors ${\\textbf{b}}$ satisfying the following two conditions:\n\n(i) All the equalities $E_{v,F}({\\textbf{b}})$ hold, where $(v,F)$ is a vertex-facet pair of $P_0$ such that $F$ is an extra supporting facet of $v$.\n\n(ii) All the inequalities $I_{v,F}({\\textbf{b}})$ holds, where $(v,F)$ is a vertex-facet pair of $P_0$ such that $F$ is not a supporting facet of $v.$\n\nTherefore, $\\Def(P_0)$ is (indeed) a polyhedral cone.", "\n\nOne sees that condition (i) is equivalent to the NEI condition, and condition (ii) is equivalent to the no-passing condition. ", "Moreover, since $v_{\\textbf{b}}$ is the solution of a linear system, it is written as a linear combinations of entries in ${\\textbf{b}}.$ Therefore, each equality or inequality is linear. ", "So the solution set of ${\\textbf{b}}$ is a polyhedral cone.", "\n\n\\[rem:nef\\] The deformation cone is related to the $\\textrm{Nef}$ cone (see [@cls Definition 6.3.18]) of the toric variety associated with $\\Sigma(P)$, as follows. ", "Any polytope whose normal fan is a coarsening of $\\Sigma(P)$ gives an *basepoint free* divisor, which for toric varieties is the same as *nef* ([@cls Theorem 6.3.12]) divisor. ", "The difference is that the $\\textrm{Nef}$ cone do not distinguish between translations of the same polytope, since they give the same divisor modulo rational equivalence. ", "Hence, the $\\textrm{Nef}$ cone is isomorphic to the deformation cone modulo translations.", "\n\nThe number of inequalities in Corollary \\[cor:ineqs\\] can be reduced. ", "Given a polytope $P_0$, we say a facet $F$ is a *neighbor* of a vertex $v$ and $(v,F)$ is a *neighboring pair* of $P_0$, if $v\\notin F$ but there exist a vertex $v'\\in F$ such that $\\{v, v'\\}$ is an edge of $P_0$.\n\n\\[prop:preredux\\] Let ${\\textbf{b}}\\in {\\mathbb{R}}^m.$ The followings are equivalent.", "\n\n1. ", " ${\\textbf{b}}\\in \\Def(P_0).$\n\n2. ", " Conditions (i) and (ii) of Corollary \\[cor:ineqs\\] are satisfied.", "\n\n3. ", " Condition (i) of Corollary \\[cor:ineqs\\] is satisified, and all the inequalities $I_{v,F}({\\textbf{b}})$ are satisfied, where $(v, F)$ is a neighboring vertex-facet pair of $P_0$.\n\n4. ", " Condition (i) of Corollary \\[cor:ineqs\\] is satisified, and for any edge $e=\\{v, v'\\}$ of $P_0$, there exists $\\lambda_e \\in {\\mathbb{R}}_{\\ge 0}$ such that $v- v' = \\lambda_e (v_{\\textbf{b}}- v'_{\\textbf{b}}).$\n\nThe equivalence between (1) and (2) are assumed by Corollary \\[cor:ineqs\\], and it is clear that (2) implies (3). ", "So it suffices to show (3) implies (4) and (4) implies (2).", "\n\nThere exist $d-1$ facets $F_{j_1},\\dots, F_{j_{d-1}}$ of $P_0,$ such that the edge $e=\\{v, v'\\}$ in $P_0$ is the intersection of them. ", "Thus $v-v'$ is in the one dimensional space that is orthgonal to the $(d-1)$-space spanned by ${\\textbf{a}}_{j_1},\\dots, {\\textbf{a}}_{j_{d-1}}.$ By the definiton of $v_{\\textbf{b}}$ and $v'_{\\textbf{b}}$ and because condition (i) of Corollary \\[cor:ineqs\\] is satisfied, one sees that $v_{\\textbf{b}}-v'_{\\textbf{b}}$ should be in the same one dimensional space. ", "Therefore, $v-v' = \\lambda_e(v_{\\textbf{b}}- v'_{\\textbf{b}})$ for some $\\lambda_e \\in {\\mathbb{R}}.$ Thus, it is left to show that $\\lambda_e \\ge 0.$\n\nLet $F$ be a facet that $v'$ lies on but $v$ does not. ", "Since $v \\in P_0$ has to satisfy the strict inequality in $I_{v,F}({\\textbf{b}}_0),$ we have that $\\langle {\\textbf{a}}_F, v \\rangle < b_{0, F} = \\langle {\\textbf{a}}_F, v' \\rangle,$ which is equivalent to $\\langle {\\textbf{a}}_F, v-v' \\rangle < 0.$ On the other hand, as $(v,F)$ is a neighboring pair, we also have $I_{v,F}({\\textbf{b}})$ holds, which is equivalent to $\\langle {\\textbf{a}}_F, v_{\\textbf{b}}-v'_{\\textbf{b}}\\rangle = \\lambda_e \\langle {\\textbf{a}}_F, v-v' \\rangle \\le 0.$ Hence, $\\lambda_e \\ge 0.$\n\nLet $(v, F)$ be a vertex-facet pair of $P_0$ such that $v$ does not lie on $F.$ Let $v_0 = v$ and pick a point ${\\textbf{x}}\\in F.$ Then $$\\langle {\\textbf{a}}_F, v_0 \\rangle < b_{0,F} = \\langle {\\textbf{a}}_F, {\\textbf{x}}\\rangle,$$ Since ${\\textbf{x}}- v_0$ is a nonnegative linear combination of rays in $\\{ u - v_0 \\ : \\ \\{v_0, u\\} \\text{ is an edge of $P_0$ } \\},$ there exists a vertex $v_1$ such that $\\{v_0,v_1\\}$ is an edge and $$\\langle {\\textbf{a}}_F, v_0 \\rangle < \\langle {\\textbf{a}}_F, v_1 \\rangle.$$ Continuing this procedure, we can construct a sequence of vertices of $P_0:$ $v_0=v, v_1, v_2, \\dots, v_\\ell$ such that $\\{v_i, v_{i+1}\\}$ is an edge of $P_0$ for each $i,$ and $$\\langle {\\textbf{a}}_F, v \\rangle < \\langle {\\textbf{a}}_F, v_1 \\rangle < \\cdots < \\langle {\\textbf{a}}_F, v_\\ell \\rangle = b_{0,F}.$$ Using the assumption of (4), we get $$\\langle {\\textbf{a}}_F, v_{\\textbf{b}}\\rangle \\le \\langle {\\textbf{a}}_F, \\left(v_1\\right)_{{\\textbf{b}}} \\rangle \\le \\cdots \\le \\langle {\\textbf{a}}_F, \\left(v_\\ell\\right)_{{\\textbf{b}}} \\rangle = b_{F},$$ which is exactly the inequality $I_{v,F}({\\textbf{b}})$ as desired.", "\n\nIn this article, we will use the equivalence between (1) and (3) of Proposition \\[prop:preredux\\] to determine the deformation cone $\\Def(P_0).$\n\nPart (3) of the proposition allows us to reduce the number of inequalities in determining the deformation cone. ", "In the toric varieties language, this correspond to the fact that it is enough to check positivity on each torus invariant curve. ", "See [@cls Theorem 6.3.12 part (c)].", "\n\nIt is undesirable to compute $v_{\\textbf{b}}$ and then compute $\\langle {\\textbf{a}}_{F}, v_{\\textbf{b}}\\rangle$ for each individual $E_{v,F}$ or $I_{v,F}$. We find the following explicit formulation useful.", "\n\n\\[lem:rewritelhs\\] Let $(v,F)$ be a vertex-facet pair of $P_0$. Suppose $F_{i_1}, F_{i_2}, \\dots, F_{i_d}$ are the first $d$ supporting facets of $v$. If ${\\textbf{a}}_F = \\sum_{j=1}^d c_j {\\textbf{a}}_{i_j} = \\sum_{j =1}^d c_j {\\textbf{a}}_{F_{i_j}},$ then the left hand side of $E_{v,F}$ and $I_{v,F}$ becomes $\\displaystyle \\sum_{j =1}^d c_j b_{{i_j}}$ or equivalently $\\displaystyle \\sum_{j =1}^d c_j b_{F_{i_j}}.$\n\n$\\displaystyle\n \\langle {\\textbf{a}}_{F}, v_{\\textbf{b}}\\rangle = \\left\\langle \\sum_{j=1}^d c_j{\\textbf{a}}_{F_{i_j}}, v_{\\textbf{b}}\\right\\rangle\n =\\sum_{j=1}^d c_j \\langle {\\textbf{a}}_{F_{i_j}}, v_{\\textbf{b}}\\rangle\n = \\sum_{j=1}^d c_j b_{F_{i_j}}.", "\n$\n\nDeformation cones of simple polytopes {#deformation-cones-of-simple-polytopes .unnumbered}\n-------------------------------------\n\nFinally, we apply our results to simple polytopes. ", "We start with the following preliminary lemma.", "\n\n\\[lem:edgeeq\\] Suppose $P_0$ is simple. ", "Let $e = \\{v, v'\\}$ be an edge of $P_0.$ Suppose $F, F_{i_1},\\dots, F_{i_{d-1}}$ are the supporting facets of $v,$ and $F', F_{i_1},\\dots, F_{i_{d-1}}$ be the supporting facets of $v'.$ There is a unique solution $(c_F, c_{F'}, c_1, \\dots, c_{d-1})$ up to scale to $$\\label{equ:edgeeq}\n \\sum_{j=1}^{d-1} c_j {\\textbf{a}}_{F_{i_j}} = c_F {\\textbf{a}}_F + c_{F'} {\\textbf{a}}_{F'}$$ such that $c_F c_{F'} > 0.$ Hence, there is a unique solution up to *positive* scale to the above equation such that $c_F > 0, c_{F'} > 0.$\n\nThe unique existence of a solution to such that $c_F c_F' \\neq 0$ follow from the fact that both the set ${\\textbf{a}}_F, {\\textbf{a}}_{F_{i_1}},$ $\\dots,$ ${\\textbf{a}}_{F_{i_{d-1}}}$ and the set ${\\textbf{a}}_{F'}, {\\textbf{a}}_{F_{i_1}}, \\dots, {\\textbf{a}}_{F_{i_{d-1}}}$ are linearly independent. ", "The numbers $c_F$ and $c_F'$ have the same sign because ${\\textbf{a}}_F$ and ${\\textbf{a}}_{F'}$ are on two different sides of the $(d-1)$-dimensional space spanned ${\\textbf{a}}_{F_{i_1}}, \\dots, {\\textbf{a}}_{F_{i_{d-1}}}$ and $\\sum_{j=1}^{d-1} c_j {\\textbf{a}}_{F_{i_j}}$ is a vector in this space.", "\n\nEquation is called the *wall condition* in [@cls Chapter 6]. ", "See [@cls Figure 17, page 301].", "\n\nAssume all the hypothesis in Lemma \\[lem:edgeeq\\] and let $(c_F, c_{F'}, c_1, \\dots, c_{d-1})$ be the unique solution up to positive scale to assumed by Lemma \\[lem:edgeeq\\]. (", "So $c_F, c_{F'} > 0$.) We associate edge $e=\\{v, v'\\}$ an inequality: $$I_e({\\textbf{b}}): \\sum_{j=1}^{d-1} c_j b_{F_{i_j}} \\le c_F b_F + c_{F'} b_{F'}.$$\n\nWe now reach the main result of this part.", "\n\n\\[prop:redux\\] Suppose $P_0$ is as given in Setup \\[setup1\\] and is simple. ", "Let ${\\textbf{b}}\\in {\\mathbb{R}}^m.$ Then ${\\textbf{b}}\\in \\Def(P_0)$ if and only if all the inequalities $I_{e}({\\textbf{b}})$ are satisfied, where $e$ is an edge of $P_0.$\n\nWe use the equivalence between (1) and (3) of Proposition \\[prop:preredux\\]. ", "Since $P_0$ is simple. ", "it is clear that condition (i) of Corollary \\[cor:ineqs\\] can be ignored. ", "Furthermore, any ordered pair of adjacent vertex $(v, v')$ of $P_0$ determines a unique neighboring vertex-facet pair $(v, F)$, where $F$ is the unique supporting facet of $v'$ that does not support $v,$ and any pair $(v,F)$ arises (not necessarily uniquely) this way. ", "Therefore, we can change the indexing of the inequalities in condition (ii) of Corollary \\[cor:ineqs\\] to $(v,v').$ Finally, one can verify if $e=\\{v, v'\\}$ is an edge, the inequality $I_e({\\textbf{b}})$ is equivalent to both the inequality associated to $(v,v')$ and the one associated to $(v', v).$ Then the conclusion follows.", "\n\n\\[ex:exampleprop\\] We go back to our Example \\[ex:example\\], illustrated in Figure \\[fig:exfigure\\]. ", "We draw the polytope $P_0$ with a labeling of its vertices, and draw the normal fan $\\Sigma(P_0)$ of $P_0$ in Figure \\[fig:normalfan\\].", "\n\n(0,0) – (-1,0); at (-1,0) [$\\scriptstyle {\\textbf{a}}_1=(-1,0)$]{}; (0,0) – (0,1); at (0,1) [$\\scriptstyle {\\textbf{a}}_2=(0,1)$]{}; (0,0) – (0,-1); at (0,-1) [$\\scriptstyle {\\textbf{a}}_3=(0,-1)$]{}; (0,0) – (1,-1); at (0.8,-0.8) [$\\scriptstyle {\\textbf{a}}_4=(1,-1)$]{}; at (-3,1)[$\\textcolor{blue}{\\Sigma(P_0)}:$]{};\n\n(6,0.5)–(8,0.5)–(7,-0.5)–(6,-0.5)–cycle; at (6,0.5) [$v$]{}; at (8,0.5)[$w$]{}; at (7,-0.5) [$x$]{}; at (6,-0.5) [$y$]{}; at (6.7,0)[$\\textcolor{blue}{P_0}$]{}; (6,-0.5) circle \\[radius=0.08\\]; (6,0.5) circle \\[radius=0.08\\]; (7,-0.5) circle \\[radius=0.08\\]; (8,0.5) circle \\[radius=0.08\\];\n\nNow we apply Proposition \\[prop:redux\\] to find the inequalities that defines $\\Def(P_0).$ Let $e_1 = \\{v, y\\}.$ The vertex $v$ lies on facets $F_1$ and $F_2$, and the vertex $y$ lies on facets $F_1$ and $F_3.$ We have $0 \\cdot {\\textbf{a}}_1={\\textbf{a}}_2 + {\\textbf{a}}_3.$ This gives the inequality $I_{e_1}: 0 \\le b_2 + b_3.$ Similarly, for $e_2 := \\{v, w\\},$ we have $-{\\textbf{a}}_2 ={\\textbf{a}}_1 + {\\textbf{a}}_4,$ which gives $I_{e_2}: - b_2 \\le b_1 + b_4;$ for $e_3 = \\{y,x\\},$ we have ${\\textbf{a}}_3={\\textbf{a}}_1 + {\\textbf{a}}_4,$ which gives $I_{e_3}: b_3 \\le b_1 + b_4;$ for $e_4 = \\{x,w\\},$ we have $0 \\cdot {\\textbf{a}}_4={\\textbf{a}}_2 + {\\textbf{a}}_3 ,$ which gives $I_{e_4}: 0 \\le b_2 + b_3.$ Note that two of the four inequalities $I_{e_1}$ and $I_{e_4}$ are the same, and $I_{e_2}$ follows from $I_{e_1}$ and $I_{e_3},$ so is redundant. ", "Therefore, $\\Def(P_0)$ is defined by two inequalities in ${\\mathbb{R}}^4:$ $$I_{e_1}=I_{e_4}: 0 \\le b_2+ b_3, \\qquad I_{e_3}: b_3 \\le b_1 + b_4.", "\n \\label{equ:exdefcone}$$ Among the three vectors given in Example \\[ex:example\\], we can verify that ${\\textbf{b}}_1=(3,2,0,2.5), {\\textbf{b}}_2=(1,2,1,0)$ satisfy the above two inequalities, and ${\\textbf{b}}_3=(1,2,2,0)$ does not satisfy the inequality $I_{e_3}.$ This agrees with the assertion that ${\\textbf{b}}_1, {\\textbf{b}}_2 \\in \\Def(P_0)$ and ${\\textbf{b}}_3 \\not\\in \\Def(P_0).$\n\nWe remark that $\\Def(P_0)$ defined by is not pointed. ", "Indeed, for any deformation $Q$ of $P_0,$ any translation of $Q$ is also a deformation of $P_0.$ We may consider two polytopes are equivalent if one is obtained from another by translation. ", "Under this equivalence, the collection of the deforming vectors gives the nef cone $\\Nef(P_0)$ of $P_0$. (See Remark \\[rem:nef\\].) ", "One sees that $\\Nef(P_0)$ is computed from $\\Def(P_0)$ by quotienting out the span of the two columns of ${\\textrm{A}}$ which are $(-1,0,0,1)^T,(0,1,-1,-1)^T.$ In this quotient we write everything in terms of $b_3,b_4$ since we have $b_1=b_4$ and $b_2=b_3+b_4$. So the nef cone $\\Nef(P_0)$ is defined by $$0 \\leq 2b_3+b_4, \\qquad 0 \\leq -b_3+2b_4,$$ where $b_3,b_4$ are the coordinates of ${\\mathbb{R}}^2$. This is always a pointed cone.", "\n\nDeformation cones of simplicial projective fans {#deformation-cones-of-simplicial-projective-fans .unnumbered}\n-----------------------------------------------\n\nA fan $\\Sigma$ is *simplicial* if every cone in it is simplicial. ", "This means that every $k$-dimensional cone in $\\Sigma$ is spanned by exactly $k$ rays. ", "One sees that $P$ being simple is equivalent to that $\\Sigma(P)$ is simplicial. ", "In particular, edges of $P$ are in bijection with a pair of adjacent maximal cones in $\\Sigma(P),$ where we say two maximal cones are *adjacent* if their spanning ray sets differ by exactly one ray. ", "We can easily translate Lemma \\[lem:edgeeq\\] and Proposition \\[prop:redux\\] to versions for simplicial fans using the connection between a simple polytope and its simplicial normal fan. ", "We omit the modified version of Lemma \\[lem:edgeeq\\], but restate Proposition \\[prop:redux\\] since the new version will be the main one we use in Sections \\[sec:GP\\] and \\[sec:NBF\\].", "\n\n\\[defn:fanineq\\] Suppose $\\Sigma_0$ is simplicial. ", "Let $\\left\\{{\\textbf{a}}_F, {\\textbf{a}}_{F_{i_1}},\\dots, {\\textbf{a}}_{F_{i_{d-1}}} \\right\\}$ and $\\Big\\{ {\\textbf{a}}_{F'}, {\\textbf{a}}_{F_{i_1}},$ $\\dots,$ ${\\textbf{a}}_{F_{i_{d-1}}} \\Big\\}$ be the sets of spanning rays of two adjacent maximal cones $\\sigma$ and $\\sigma'$ in $\\Sigma_0.$ Suppose $(c_F, c_{F'}, c_1, \\dots, c_{d-1})$ is the unique solution up to positive scale to assumed by Lemma \\[lem:edgeeq\\]. (", "So $c_F, c_{F'} > 0$.) We associate to the pair $\\{\\sigma, \\sigma'\\}$ an inequality: $$I_{ \\{\\sigma,\\sigma'\\}} ({\\textbf{b}}): \\sum_{j=1}^{d-1} c_j b_{F_{i_j}} \\le c_F b_F + c_{F'} b_{F'}.$$\n\n\\[prop:reduxfan\\] Suppose $\\Sigma_0$ is as given in Setup \\[setup2\\] and is simplicial. ", "Let ${\\textbf{b}}\\in {\\mathbb{R}}^m.$ Then ${\\textbf{b}}\\in \\Def(\\Sigma_0)$ if and only if all the inequalities $I_{ \\{\\sigma, \\sigma'\\}}({\\textbf{b}})$ are satisfied, where $\\{ \\sigma, \\sigma'\\}$ is a pair of adjacent maximal cones in $\\Sigma_0.$\n\nBack to Deformations {#back-to-deformations .unnumbered}\n--------------------\n\nWe finish this section with a discussion on how to determine whether a polytope $Q$ is a deformation of $P_0$ provided that we have a description for the deformation cone $\\Def(P_0).$ Although there is a one-to-one correspondence between deforming vectors ${\\textbf{b}}\\in \\Def(P_0)$ and deformations of $P_0,$ if we take a polytope $Q$ that is defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$, knowing ${\\textbf{b}}\\not\\in \\Def(P_0)$ is not enough to conclude that $Q$ is not a deformation of $P_0.$ Indeed, we have seen in Examples \\[ex:example\\] and \\[ex:exampleprop\\] that $Q_3$ (in Figure \\[fig:exfigure\\]) is defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}_3$ where ${\\textbf{b}}_3 \\not\\in \\Def(P_0);$ but $Q_3$ is a deformation of $P_0$. It was discussed earlier that the reason for which ${\\textbf{b}}_3$ is not a deforming vector is that the hyperplane defined by $-y=2$, i.e., the bottom horizontal line in the picture for $Q_3$, does not “touch” the polytope $Q_3.$ This turns out to be an important notion.", "\n\nSuppose a polytope $Q \\subset V$ is defined by the linear system ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}.$ We say an inequality $\\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle \\le b_i$ in the system is *tight* for $Q$, if the equality attains for some points in $Q.$ If all the inequalities in the system are tight, we say ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ is a *tight* representation for $Q.$\n\nIt is easy to see that ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ being a tight representation for $Q$ is a consequence of condition of Defintion \\[defn:deform0\\], and thus is a necessary condition for ${\\textbf{b}}$ being a deforming vector. ", "With this concept of tight representations, we can use the knowledge of deformation cone to verify whether a polytope $Q$ is a deformation of $P_0.$\n\n\\[lem:checkdeform\\] Suppose $P_0$ is as described in Setup \\[setup1\\], and $Q$ is defined by a tight representation ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}.$ Then $Q$ is a deformation of $P_0$ if and only if ${\\textbf{b}}\\in \\Def(P_0).$\n\nWe only need to show the forward implication as the backward one is obvious. ", "Suppose $Q$ is a deformation of $P_0.$ Then there exists ${\\textbf{b}}' \\in \\Def(P_0)$ such that $Q$ is defined by ${\\textrm{A}}{\\textbf{x}}\\in {\\textbf{b}}',$ which is a tight representation as well. ", "By the definition of tightness, we have $$b_i = \\max_{{\\textbf{x}}\\in Q} \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle = b_i', \\quad \\forall 1 \\le i \\le m.$$ Hence, ${\\textbf{b}}= {\\textbf{b}}' \\in \\Def(P_0).$\n\nGeneralized permutohedra and Braid Fan {#sec:GP}\n======================================\n\nIn the following two sections, we work over the vector space $V_d = \\{ {\\textbf{x}}\\in {\\mathbb{R}}^{d+1} \\ : \\langle\\1, {\\textbf{x}}\\rangle = 0\\} \\subset {\\mathbb{R}}^{d+1}$ and its dual space $W_d = {\\mathbb{R}}^{d+1}/\\1$, where $\\1 = (1, 1, \\dots, 1)$ denotes the all-one vector in ${\\mathbb{R}}^{d+1}.$ Note that the standard basis $\\{{\\textbf{e}}_1,\\cdots,{\\textbf{e}}_{d+1}\\}$ of ${\\mathbb{R}}^{d+1}$ is a canonical spanning set for $W_d$ although it is not a basis. ", "The goal of this section is to apply the techniques introduced in Section \\[sec:prel\\] to give a new combinatorial proof for Theorem \\[thm:submodular\\] by determining the deformation cone of the Braid fan. ", "We also state and prove Theorem \\[thm:polymatroid\\], which gives the connection between polymatroids and generalized permutohedra. ", "We start by introducing the fan concerned in this section.", "\n\nFor any $\\pi\\in \\fS_{d+1}$ we define a cone in $W_d$ as follows: $$C(\\pi):=\\{{\\textbf{x}}\\in W_d \\ :\\ x_{\\pi^{-1}(1)}<x_{\\pi^{-1}(2)}<\\cdots<x_{\\pi^{-1}(d+1)}\\}.$$\n\nOne checks that $C(\\pi)$ is well-defined because if $(x_1, \\dots, x_{d+1}) = (y_1, \\dots, y_{d+1})$ is in $W_d$, that is, there exists $k \\in {\\mathbb{R}}$ such that $y_i = x_i +k$ for each $i,$ then $$x_{\\pi^{-1}(1)}<x_{\\pi^{-1}(2)}<\\cdots<x_{\\pi^{-1}(d+1)} \\text{ if and only if } y_{\\pi^{-1}(1)} <y_{\\pi^{-1}(2)} <\\cdots<y_{\\pi^{-1}(d+1)}.$$ Also, for any two distinct $\\pi_1,\\pi_2 \\in \\fS_{d+1},$ the cones $C(\\pi_1)$ and $C(\\pi_2)$ are disjoint. ", "Each region $C(\\pi)$ is an open polyhedral cone. ", "Its closure, denoted by $\\sigma(\\pi)$, is obtained from $C(\\pi)$ by relaxing the strict inequalities.", "\n\nWe call the collection of cones $\\{\\sigma(\\pi): \\pi\\in \\fS_{d+1}\\}$, together with all of their faces, the *Braid fan*, denoted by ${\\textrm{Br}}_d.$\n\nIt is straightforward to show that ${\\textrm{Br}}_d$ is a complete fan in $W_d.$ However, we will prove this fact by showing ${\\textrm{Br}}_d$ is the normal fan of a family of polytopes in Proposition \\[prop:fanofusual\\] below. ", "The similar idea will be used in the next section, and we simply present it this way in preparation for late discussions.", "\n\nWe next formally introduce generalized permutohedra. ", "Given a strictly increasing sequence $\\balpha= (\\alpha_1,\\alpha_2,\\cdots,\\alpha_{d+1}) \\in {\\mathbb{R}}^{d+1}$, for any $\\pi\\in \\fS_{d+1}$, we use the following notation: $$v_\\pi^\\balpha := \\left(\\alpha_{\\pi(1)},\\alpha_{\\pi(2)},\\cdots, \\alpha_{\\pi({d+1})}\\right) = \\sum_{i=1}^{d+1} \\alpha_{i} {\\textbf{e}}_{\\pi^{-1}(i)}.$$ Then we define the *usual permutohedron* $$\\Perm(\\balpha) := {\\textrm{conv}}\\left(v_\\pi^{\\balpha}:\\quad \\pi\\in \\fS_{d+1}\\right).", "\n\\label{equ:defnusual}$$ In particular, if $\\balpha = (1, 2, \\dots, {d+1}),$ we obtain the *regular permutohedron*, denoted by $\\Pi_{d},$ $$\\Pi_{d} := \\Perm (1, 2, \\dots, d+1).$$ Note that the above definition for $\\Perm(\\balpha)$ does not directly say that the vertex set of $\\Perm(\\balpha)$ is $\\{ v_\\pi^\\balpha : \\ \\pi \\in \\fS_{d+1}\\}$. However, this is true as we will see in Proposition \\[prop:fanofusual\\] below.", "\n\nRecall that that *generalized permutohedra* are polytopes obtained from usual permutohedra by moving vertices while preserving all edge directions. ", "We see that any generalized permutohedron in ${\\mathbb{R}}^{d+1}$ lies in an affine space that is parallel to $V_d.$ However, under the setup of our article, we would like to only consider polytopes that are in $V_d.$ Thus, we give the following definition.", "\n\n\\[defn:central\\] For any polytope $P \\in {\\mathbb{R}}^{d+1}$ that lies in an affine space $V'$ that is parallel to $V_d.$ It is clear $V' =\\{ {\\textbf{x}}\\in {\\mathbb{R}}^{d+1} : \\langle \\1, {\\textbf{x}}\\rangle = N\\}$ for some (unique) $N \\in {\\mathbb{R}}.$ Then $V' = \\frac{N}{d+1} \\1 + V_d.$ We define $\\widetilde{P} := P - \\frac{N}{d+1} \\1$ to be the *centralized* version of the polytope $P,$ which lies in $V_d.$\n\n\\[ex:crp\\] The regular permutohedron $\\Pi_d$ lies in the affine space $V' = \\Big\\{ {\\textbf{x}}\\in {\\mathbb{R}}^{d+1} \\ : \\ \\langle \\1, {\\textbf{x}}\\rangle = \\frac{(d+2)(d+1)}{2}\\Big\\}.$ Hence, the *centralized regular permutohedron* is $$\\widetilde{\\Pi_d} = \\Pi_d - \\frac{d+2}{2} \\1 = \\Perm\\left( -\\frac{d}{2}, -\\frac{d-2}{2}, \\dots, \\frac{d-2}{2}, \\frac{d}{2} \\right) \\subset V_d.$$\n\nWe have the following two results relating generalized/usual permutohedra and ${\\textrm{Br}}_d.$\n\n\\[prop:fanofusual\\] If $\\balpha=(\\alpha_1,\\dots, \\alpha_{d+1})$ is strictly increasing, then for each $\\pi \\in \\fS_{d+1},$ the point $v_\\pi^\\balpha$ is a vertex of $\\Perm(\\balpha),$ and the normal cone of $\\Perm(\\balpha)$ at $v_{\\pi}^\\balpha$ is $\\sigma(\\pi).$ Therefore, the Braid fan ${\\textrm{Br}}_d$ is the normal fan of the usual permutohedron $\\Perm(\\balpha).$ Hence, ${\\textrm{Br}}_d$ is a complete projective fan in $W_d$.\n\n\\[prop:coarser\\] A polytope $P$ in $V_d$ is a (centralized) generalized permutohedron if and only if its normal fan $\\Sigma(P)$ is refined by the braid arrangement fan ${\\textrm{Br}}_d$.\n\nWe include a proof for Proposition \\[prop:fanofusual\\], which is relevant to discussion in Section \\[sec:NBF\\]. ", "The following elementary result is useful (See [@inequalities Theorem 368]).", "\n\n\\[lem:rearr\\] Suppose $x_1 \\le x_2 \\le \\cdots \\le x_n$ and $y_1 \\le y_2 \\le \\cdots \\le y_n.$ Then for any $\\pi \\in \\fS_n,$ we have $$\\sum_{i=1}^n x_i y_i \\ge \\sum_{i=1}^n x_i y_{\\pi(i)}.$$ Furthermore, if $x_1 < x_2 < \\cdots < x_n$ and $y_1 < y_2 < \\cdots < y_n$, then the equality only holds when $\\pi$ is the identity permutation.", "\n\nRecall the definition of normal cone in Definition \\[defn:normal\\]\n\nLet ${\\textbf{w}}\\in C(\\pi).$ For convenience, we let $u_i = w_{\\pi^{-1}(i)}$ so that ${\\textbf{w}}$ can be expressed as $$\\label{equ:wexp0}\n {\\textbf{w}}= \\sum_{i=1}^{d+1} u_{i}{\\textbf{e}}_{\\pi^{-1}(i)}.$$ Then ${\\textbf{w}}\\in C(\\pi)$ means that $$u_{1} < u_{2} < \\cdots < u_{d+1}.$$ Then it follows from Lemma \\[lem:rearr\\] that $\\langle {\\textbf{w}}, v_\\pi^\\balpha \\rangle > \\langle {\\textbf{w}}, v_{\\pi'}^\\balpha \\rangle,$ for any $\\pi \\neq \\pi' \\in \\fS_{d+1}.$ Hence, $v_\\pi^\\balpha$ does not lie in ${\\textrm{conv}}( v_{\\pi'}^\\balpha : \\ \\pi \\neq \\pi' \\in \\fS_{d+1});$ so $v_\\pi^\\balpha$ is a vertex of $\\Perm(\\balpha)$. Furthermore, we must have that ${\\textbf{w}}\\in \\ncone(v_\\pi^\\balpha, \\Perm(\\balpha)).$ This implies $$\\label{equ:inclusion1}\n\\sigma(\\pi) \\subseteq \\ncone(v_\\pi^\\balpha, \\Perm(\\balpha)).$$ However, the union of $\\sigma(\\pi)$ is the entire space $W_d,$ so the equality must holds in . ", "Thus, the conclusion follows.", "\n\nIt follows from Propositions \\[prop:fanofusual\\] and \\[prop:coarser\\] that the deformation cone $\\Def({\\textrm{Br}}_d)$ of ${\\textrm{Br}}_d$ is the same as the deformation cone $\\Def\\left( \\widetilde{\\Pi_d} \\right)$ of $\\widetilde{\\Pi_d}$, which gives a characterization for (centralized) generalized permutohedron.", "\n\nThe combinatorics of the Braid fan ${\\textrm{Br}}_d$ are equivalent to those of the face lattice of $\\widetilde{\\Pi_d}$, which are well-studied in the literature [@barvinokconvex Chapter VI, Proposition 2.2]. ", "We summarize relevant results in terms of the Braid fan ${\\textrm{Br}}_d$ in the proposition below. ", "Recall that the *Boolean algebra* ${{\\mathcal B}}_{d+1}$ is the poset on all subsets of $[d+1]$ ordered by containment. ", "This poset has a minimum element $\\hat{0}=\\emptyset$ and a maximum element $\\hat{1}=[d+1]$. We denote by $\\overline{{{\\mathcal B}}_{d+1}}$ the poset obtained from ${{\\mathcal B}}_{d+1}$ by removing the maximum and minimum elements. ", "For each element $S \\in {{\\mathcal B}}_{d+1}$, define $$\\displaystyle {\\textbf{e}}_S := \\sum_{i \\in S} {\\textbf{e}}_i.$$\n\n\\[prop:charbr\\] The rays, i.e., $1$-dimensional cones, of the Braid fan ${\\textrm{Br}}_d$ are given by ${\\textbf{e}}_S$ for all $S \\in \\overline{{{\\mathcal B}}_{d+1}}$. Furthermore, a $k$-set of rays $\\{{\\textbf{e}}_{S_1},\\cdots, {\\textbf{e}}_{S_k}\\}$ spans a $k$-dimensional cone in ${\\textrm{Br}}_d$ if and only if the sets $S_1,\\dots, S_k$ form a $k$-chain in $\\overline{{{\\mathcal B}}_{d+1}}$. In particular, the maximal cones in ${\\textrm{Br}}_d$ are in bijection with the maximal chains in $\\overline{{{\\mathcal B}}_{d+1}}.$ Hence, ${\\textrm{Br}}_d$ is simplicial.", "\n\nAs the one-dimensional cones are indexed by elements in $\\overline{{{\\mathcal B}}_{d+1}},$ the deformation cone of ${\\textrm{Br}}_d$ can be considered to be in ${\\mathbb{R}}^{\\overline{{{\\mathcal B}}_{d+1}}}$ which is indexed by nonempty, proper subsets $S$ of $[d+1].$\n\nWith these results in hand, we can now apply Proposition \\[prop:reduxfan\\] to compute $\\Def({\\textrm{Br}}_d)$ .", "\n\n\\[thm:centralsub\\] The deformation cone of the Braid fan (or centralized regular permutohedron) is the collection of ${\\textbf{b}}\\in {\\mathbb{R}}^{\\overline{{{\\mathcal B}}_{d+1}}}$ satisfying the following *submodular condition* on ${{\\mathcal B}}_{d+1}:$ $$\\label{equ:bsub}\nb_{S \\cup T} + b_{S \\cap T} \\le b_S + b_T, \\quad \\forall S, T \\in {{{\\mathcal B}}_{d+1}},$$ where by convention we let $b_\\emptyset = b_{[d+1]} = 0.$\n\n(0,0) circle \\[radius = 0.08\\]; (0,-1) circle \\[radius=0.08\\]; (1,1) circle \\[radius=0.08\\]; (-1,1) circle \\[radius=0.08\\]; (0,2) circle \\[radius=0.08\\]; (0,3) circle \\[radius=0.08\\]; (0,-1) – (0,0) – (1,1) – (0,2); (0,0) – (-1,1) – (0,2)–(0,3); at (0,3.2) ; at (0,-1) ; at (0,-1) [$S_{i-2}$]{}; at (0,0) [$S_{i-1}$]{}; at (1,1) [$S'_{i}$]{}; at (-1,1) [$S_{i}$]{}; at (0,2) [$S_{i+1}$]{}; at (0,3) [$S_{i+2}$]{};\n\nWe may add $\\emptyset$ and $[d+1]$ back to $\\overline{{{\\mathcal B}}_{d+1}}$ and say that the maximal cones in ${\\textrm{Br}}_d$ are in bijection with maximal chains in ${{\\mathcal B}}_{d+1}.$ Then any pair of adjacent maximal cones in ${\\textrm{Br}}_d$ corresponds to a pair of maximal chains in ${{\\mathcal B}}_{d+1}$ that only differ at a non-extreme element, and all pairs of adjacent maximal cones arise this way. ", "One sees any such pair of maximal chains in ${{\\mathcal B}}_{d+1}$ always form a “diamond” shape as shown in Figure \\[fig:poset\\]. ", "Suppose we have a pair of maximal chains shown in Figure \\[fig:poset\\]. ", "Then if we let $a = S_i \\setminus S_{i-1}$ and $b = S_{i'} \\setminus S_{i-1},$ we must have that $S_{i+1} = S_i \\cup \\{a, b\\}.$ Therefore, $$\\label{equ:eesum}\n{\\textbf{e}}_{S_{i+1}} + {\\textbf{e}}_{S_{i-1}} = {\\textbf{e}}_{S_{i}} + {\\textbf{e}}_{S_i'},$$ which is precisely the solution to assumed by Lemma \\[lem:edgeeq\\]. (", "Note that if $i=1,$ then ${\\textbf{e}}_{S_{i-1}} = {\\textbf{e}}_\\emptyset=0$, and if $i=d,$ then ${\\textbf{e}}_{S_{i+1}} = {\\textbf{e}}_{[d+1]} = \\1 = 0$ in $W_d.$ For both cases, is the expression that we need.) ", "It follows from Proposition \\[prop:reduxfan\\] that the corresponding pair of adjacent maximal cones gives us the following inequality: $$b_{S_{i+1}} + b_{S_{i-1}} \\le b_{S_{i}} + b_{S_i'}.$$ Going through all pairs of adjacent maximal cones, we see that $\\Def({\\textrm{Br}}_d)$ is defined by the following collection of inequalities: $$\\label{equ:bsubdiamond}\n b_{S \\cup \\{a,b\\}} + b_{S} \\le b_{S \\cup \\{a\\}} + b_{S \\cup \\{b\\}}, \\text{ for all $S \\subseteq [d+1]$ and $a, b \\in [d+1]\\setminus S.$}$$ Finally, each inequality given by follows from the above set of inequalities by induction on the size difference between $S \\cup T$ and $S \\cap T.$\n\n\\[rem:equivsub\\] We see from the proof of Theorem \\[thm:centralsub\\] that the submodular condition is equivalent to the “diamond” submodular condition . ", "This is a standard result on submodular functions, and will be used again in Section \\[sec:NBF\\].", "\n\nNote that points in ${\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ can be considered as set functions from $2^{[d+1]}$ to ${\\mathbb{R}}.$ We now restate the Submodular Theorem with more details and prove it.", "\n\n\\[thm:submodrestate\\] For each submodular function ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ satisfying ${\\textbf{b}}_\\emptyset=0,$ the linear system: $$\\label{equ:linear}\n \\left\\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\right\\rangle = \\left\\langle \\1, {\\textbf{x}}\\right\\rangle \\ = \\ b_{[d+1]}, \\quad \\text{and} \\quad \n \\left\\langle {\\textbf{e}}_S, {\\textbf{x}}\\right\\rangle \\ \\le \\ b_S, \\quad \\forall \\emptyset \\neq S \\subsetneq [d+1]$$ defines a generalized permutohedron in ${\\mathbb{R}}^{d+1},$ and any generalized permutohedron arises this way uniquely.", "\n\nFurthermore, if a polytope $P \\in {\\mathbb{R}}^{d+1}$ is defined by a tight representation , then $P$ is a generalized permutohedron if and only if ${\\textbf{b}}$ is a submodular function ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ satisfying ${\\textbf{b}}_\\emptyset=0.$\n\nIt follows from Theorem \\[thm:centralsub\\], Proposition \\[prop:coarser\\] and the description for rays of ${\\textrm{Br}}_d$ in Proposition \\[prop:charbr\\] that the one-to-one correspondence described by the theorem holds for centralized generalized permutohedra and submodular functions ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ satisfying ${\\textbf{b}}_\\emptyset=0$ and ${\\textbf{b}}_{[d+1]} = 0.$\n\nSuppose ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ is a set function. ", "Let $k = \\frac{b_{[d+1]}}{d+1}$ and define a new vector/function ${\\textbf{b}}'$ by $${\\textbf{b}}'_S = {\\textbf{b}}_S - k |S|, \\quad \\forall S \\subseteq [d+1].$$ Let $P$ and $Q$ be the polytopes defined by the linear system with vectors ${\\textbf{b}}$ and ${\\textbf{b}}'$ respectively. ", "It is straightforward to check the following facts are true:\n\n1. ", " ${\\textbf{b}}'_\\emptyset = {\\textbf{b}}_\\emptyset$ and ${\\textbf{b}}'_{[d+1]} =0.$\n\n2. ", " ${\\textbf{b}}'$ is a submodular function if and only if ${\\textbf{b}}$ is a submodular function.", "\n\n3. ", " $Q =\\tilde{P} = P - k \\1$ is the centralized version of $P.$\n\nThe first conclusion of the theorem follows from these facts and the arguments in the first paragraph.", "\n\nFinally, the second conclusion follows from Lemma \\[lem:checkdeform\\] and the observation that ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ is a tight representation for $P$ if and only if ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}'$ is a tight representation for $Q.$\n\n\\[rem:edges\\] We remark that other than the Submodular Theorem and Proposition \\[prop:coarser\\], there is another characterization of generalized permutohedra in terms of edges. ", "A polytope $P \\in {\\mathbb{R}}^{d+1}$ is a generalized permutohedron if and only if all of its edge directions are in the form of ${\\textbf{e}}_i-{\\textbf{e}}_j$ for $1 \\le i < j \\le d+1$. We briefly give the proof for the forward implication of the above statement, which will be used in the example we discuss below. ", "Indeed, it follows from Proposition \\[prop:coarser\\] that for each cone $\\sigma$ of codimension $1$ in the normal fan $\\Sigma(P)$ of a generalized permutohedron $P$, there exists a cone $\\sigma'$ of codimension $1$ in ${\\textrm{Br}}_d$, such that the $(d-1)$-dimensional linear space spanned by $\\sigma$ is the same of the linear space spanned by $\\sigma',$ and hence the direction of the edge associated with $\\sigma$ in $P$ has the same direction as the direction of the edge associated with $\\sigma'$ in the regular permutohedron $\\Pi_d.$ It is straightforward to verify that all the edge directions of $\\Pi_d$ are in the form of ${\\textbf{e}}_i-{\\textbf{e}}_j.$\n\n\\[ex:unexample\\] Consider the polytope $P$ in ${\\mathbb{R}}^4$ defined by the linear system with $b_{[4]} = 6$ and $b_S =3$ if $|S|=1$, $b_S=4$ if $|S|=2$, and $b_S = 6$ if $|S|=3.$ We see that $$8=4 + 4 = b_{\\{1,2\\}} + b_{\\{2,3\\}} < b_{\\{1,2,3\\}} + b_{\\{2\\}} = 6 + 3 = 9.$$ So ${\\textbf{b}}$ is not a submodular function. ", "Since the given system is a tight representation for $P$, we conclude that $P$ is a not a generalized permutohedron. ", "Indeed, $P$ is the cube whose vertices are $(1,1,1,3),(0,2,2,2)$ and their permutations. ", "The linear functional given by the vector $(1,2,3,4)$ attains its maximum at the vertices $(0,2,2,2)$ and $(1,1,1,3)$, but not at the other vertices. ", "Thus, $(0,2,2,2)$ and $(1,1,1,3)$ form an edge whose direction is parallel to $(-1,1,1,-1)$, conflicting with the condition for being a generalized permutohedron expressed in Remark \\[rem:edges\\].", "\n\nPolymatroids vs Generalized Permutohedra. {#", "subsec:polyvsperm .unnumbered}\n-----------------------------------------\n\nWe finish this sections by making the connection between polymatroids and generalized permutohedra.", "\n\n\\[defn:rank\\] A *polymatroid rank function* is a set function $r: 2^E \\to {\\mathbb{R}}$ on a finite set $E$ such that\n\n- $0\\leq r(A)$ for all $A\\subseteq E$. (Nonnegativity condition)\n\n- If $A_1\\subseteq A_2\\subseteq E$ then $r(A_1)\\leq r(A_2)$. (Monotone condition)\n\n- $r(A_1\\cup A_2) + r(A_1\\cap A_2)\\leq r(A_1) + r(A_2)$ for all $A_1,A_2\\subseteq E$. (Submodular condition)\n\nNote that we are only lifting the restriction $r(A)\\leq |A|$ from the definition of matroids. ", "To be consistent with notation used for generalized permutohedra, we may assume $E = [d+1]$, and $r = {\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}.$\n\nThe *base polymatroid* $P_{\\textbf{b}}$ associated to a polymatroid rank function ${\\textbf{b}}$ on $[d+1]$ is the polytope in ${\\mathbb{R}}^{d+1}$ defined by the linear system .", "\n\nIt turns out that we may add the constraint ${\\textbf{b}}_\\emptyset = 0$ to the above definition and still get all the base polymatroids.", "\n\n\\[lem:reduce20\\] Let ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ be a polymatroid rank function. ", "Define an associated vector ${\\textbf{b}}'$ as follows: $${\\textbf{b}}'_\\emptyset = 0, \\quad \\text{and} \\quad {\\textbf{b}}'_S = {\\textbf{b}}_S, \\forall \\emptyset \\neq S \\subseteq [d+1].$$ Then ${\\textbf{b}}'$ is a polymatroid rank function on $[d+1]$ and $P_{\\textbf{b}}= P_{{\\textbf{b}}'}.$\n\nThe proof of the lemma is straightforward, so is omitted.", "\n\n\\[thm:polymatroid\\] The bijection asserted in Theorem \\[thm:submodrestate\\] induces a bijection between base polymatroids of dimension at most $d$ and monotone submodular functions ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ satisfying ${\\textbf{b}}_\\emptyset=0.$ Moreover, every generalized permutohedron has a translation that is a base polymatroid.", "\n\nThe first assertion follows easily from Lemma \\[lem:reduce20\\], Theorem \\[thm:submodrestate\\], and the observation that the nonnegativity condition (R1) follows from the monotone condition when we assume ${\\textbf{b}}_\\emptyset=0.$\n\nWe use similar ideas presented in the proof of Theorem \\[thm:submodrestate\\] to prove the second statement. ", "Suppose $P$ is a generalized permutohedron associated to the submodular function ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ (where ${\\textbf{b}}_\\emptyset = 0$). ", "For any $k \\in {\\mathbb{R}}$, we define a new vector/function ${\\textbf{b}}^{(k)} \\in {\\mathbb{R}}^{{{\\mathcal B}}_{d+1}}$ by $${\\textbf{b}}^{(k)}_S = {\\textbf{b}}_S + k |S|, \\quad \\forall S \\subseteq [d+1].$$ Then ${\\textbf{b}}^{(k)}$ is a submodular function and the generalized permutohedron associated to ${\\textbf{b}}^{(k)}$ is a translation of $P.$ However, it is easy to see that for sufficiently large $k,$ the set function ${\\textbf{b}}^{(k)}$ is monotone. ", "Hence, the conclusion follows.", "\n\nNested Braid fan and nested permutohedra {#sec:NBF}\n========================================\n\nThe plan of this section is as follows: We will first introduce the nested Braid fan ${\\textrm{Br}}_d^2$ as a refinement of the Braid fan, and construct a family of polytopes, called usual nested permutohedra in $V_d$ by giving an explicit description for their vertices. ", "We then establish (in Proposition \\[prop:fanofusual2\\]) the connection between these two new objects by showing ${\\textrm{Br}}_d^2$ is the normal fan of any usual nested permutohedron. ", "After discussing combinatorial structure of ${\\textrm{Br}}_d^2$ (in Proposition \\[prop:charbr2\\]), we give an inequality description for usual nested permutohedra (in Theorem \\[thm:facetdes\\]). ", "Lastly, we determine deformation cones of ${\\textrm{Br}}_d^2$ and nested permutohedra and give a result that is analogous to the Submodular Theorem (see Theorems \\[thm:centralsub2\\] and \\[thm:sub2\\]).", "\n\nRecall that $\\{{\\textbf{e}}_1,\\cdots,{\\textbf{e}}_{d+1}\\}$ is the standard basis for $\\mathbb{R}^{d+1}$. For any permutation $\\pi \\in \\fS_{d+1},$ we define $${\\textbf{f}}^\\pi_i := {\\textbf{e}}_{\\pi^{-1}(i+1)} - {\\textbf{e}}_{\\pi^{-1}(i)}, \\quad \\forall 1 \\le i \\le d,$$ and for any point ${\\textbf{x}}=(x_1,\\dots,x_{d+1})$ in ${\\mathbb{R}}^{d+1}$ or $W_d$, we define $$(\\Delta {\\textbf{x}})^\\pi_i := x_{\\pi^{-1}(i+1)} - x_{\\pi^{-1}(i)}, \\quad \\forall 1 \\le i \\le d.$$\n\n\\[defn:NBF\\] For each $(\\pi,\\tau)\\in \\fS_{d+1}\\times \\fS_{d}$, let $C(\\pi,\\tau)$ be the collection of vectors ${\\textbf{x}}\\in W_d$ satisfying:\n\n1. ", " $x_{\\pi^{-1}(1)}<x_{\\pi^{-1}(2)}<\\cdots<x_{\\pi^{-1}(d+1)}$, and\n\n2. ", " $(\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(1)}<(\\Delta{\\textbf{x}})^\\pi_{\\tau^{-1}(2)}<\\cdots < (\\Delta{\\textbf{x}})^\\pi_{\\tau^{-1}(d)}$. (Note that this condition is an order of the first differences of the sequence $x_{\\pi^{-1}(1)}, x_{\\pi^{-1}(2)}, \\dots, x_{\\pi^{-1}(d+1)}$ with respect to the permutation $\\tau.$)\n\nSimilar to $C(\\pi)$ defined in the last section, one can check that $C(\\pi,\\tau)$ is well-defined, and each region $C(\\pi,\\tau)$ is an open polyehdral cone. ", "Let $\\sigma(\\pi,\\tau)$ be the closed polyhedral cone obtained from $C(\\pi,\\tau)$ by relaxing the strict inequalities.", "\n\n\\[defn:NBF2\\] We call the collection of cones $\\{\\sigma(\\pi,\\tau): (\\pi, \\tau) \\in \\fS_{d+1}\\times \\fS_{d}\\}$, together with all of their faces, the *nested Braid fan*, denoted by ${\\textrm{Br}}_d^2.$\n\nLet $(\\pi,\\tau) = (3241, 231).$ Then $(\\pi^{-1},\\tau^{-1})=(4213,312).$ Thus, the $C(\\pi,\\tau)$ is the collection of ${\\textbf{x}}\\in W_d$ satisfying\n\n1. ", " $x_4 < x_2 < x_1 < x_3$, and\n\n2. ", " $x_3-x_1<x_2-x_4<x_1-x_2.$\n\nWe will use similar idea as presented in last section to prove that ${\\textrm{Br}}_d^2$ is a complete projective fan by showing it is the normal fan of a family of polytopes, which will be constructed below. ", "We start by choosing two stricly increasing sequences $$\\balpha = (\\alpha_1, \\alpha_2, \\dots, \\alpha_{d+1}) \\in {\\mathbb{R}}^{d+1} \\quad \\text{and} \\quad \\bbeta = (\\beta_1, \\beta_2, \\dots, \\beta_{d}) \\in {\\mathbb{R}}^{d}.$$ We then pick $M, N > 0.$ The basic idea of the construction is to take the $M$-th dilation of the usual permutohedron $\\Perm(\\balpha)$ and then replace each of its vertices with an $N$-th dilation of $\\Perm(\\bbeta)$ under a correct coordinate system. ", "This will give us $d! (", "d+1)!$ vertices. ", "Below is the precise construction. ", "For any $(\\pi, \\tau) \\in \\fS_{d+1} \\times \\fS_d$, we define $$\\label{equ:defnv}\nv_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} := M \\sum_{i=1}^{d+1} \\alpha_i {\\textbf{e}}_{\\pi^{-1}(i)} + N \\sum_{i=1}^d \\beta_i {\\textbf{f}}_{\\tau^{-1}(i)}^\\pi.$$ (Note that $\\sum_{i=1}^{d+1} \\alpha_i {\\textbf{e}}_{\\pi^{-1}(i)} = v_\\pi^\\balpha$ is a vertex of $\\Perm(\\balpha).$) We omit $(\\balpha,\\bbeta)$ from the superscript, and only write $v_{\\pi,\\tau}^{(M,N)}$ if $(\\balpha,\\bbeta) = \\left( (1,2,\\dots,d+1), (1,2,\\dots, d) \\right).$\n\nAfter rearranging coordinate, we get the following expression: $$v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} = \\sum_{i=1}^{d+1} (M \\alpha_i + N(\\beta_{\\tau(i-1)} - \\beta_{\\tau(i)})) \\ {\\textbf{e}}_{\\pi^{-1}(i)},\n \\label{equ:expansion}$$ where by convention we let $\\beta_{\\tau(0)} = \\beta_{\\tau(d+1)} =0.$ We would like to have the coefficients of ${\\textbf{e}}_{\\pi^{-1}(i)}$ in the above expansion increase strictly as $i$ increases, for any $(\\pi,\\tau)$. If this happens, we say $(M,N) \\in {\\mathbb{R}}_{>0}^2$ is an *appropriate choice* for $(\\balpha, \\bbeta)$. It is not hard to see that for fixed $(\\balpha, \\bbeta)$, any pair $(M,N)$ satisfying $M >> N$ is an appropriate choice.", "\n\n\\[defn:usual2\\] Suppose $(\\balpha, \\bbeta) \\in {\\mathbb{R}}^{d+1} \\times {\\mathbb{R}}^d$ is a pair of strictly increasing sequences $(\\balpha, \\bbeta) \\in {\\mathbb{R}}^{d+1} \\times {\\mathbb{R}}^d$ and $(M,N) \\in {\\mathbb{R}}_{>0}^2$ is an *appropriate choice* for $(\\balpha, \\bbeta)$. We define the *usual nested permutohedron* $$\\Perm(\\balpha, \\bbeta; M,N) := {\\textrm{conv}}\\left(v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)}:\\quad (\\pi,\\tau) \\in \\fS_{d+1}\\times \\fS_d\\right).", "\n\\label{equ:defnusual2}$$ In particular, if $\\balpha = (1, 2,\\dots, d+1)$ and $\\bbeta=(1,2,\\dots, d),$ we call the polytope a *regular nested permutohedron*, denoted by $\\Pi_d^2(M,N).$ (So $v_{\\pi,\\tau}^{(M,N)}$ are vertices for $\\Pi_d^2(M,N).$)\n\nWe remark that similar to the definition of $\\Perm(\\balpha)$, the above definition does not directly say that each $v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,n)}$ is a vertex of $\\Perm(\\balpha, \\bbeta; M,n).$ However, it will be shown to be true in Proposition \\[prop:fanofusual2\\] below.", "\n\nOne sees that $\\Perm(\\balpha,\\bbeta;M,N)$ lies in the hyperplane $\\sum_{i=1}^{d+1} x_i = M\\sum_{i=1}^{d+1} \\alpha_i$, which is a translation of $V_d,$ and $\\Perm(\\balpha, \\bbeta; M, N)$ is centralized if and only if $\\sum_{i=1}^{d+1} \\alpha_i=0,$ which is the situation we will focus on.", "\n\n\\[ex:nestedperm\\] One can show that $(M,N)=(4,1)$ is an appropriate choice for $(\\balpha=(1,2,3,4), \\bbeta=(1,2,3))$. Thus, $\\Pi_3^2(4,1)$ is a nested regular permutohedron. ", "See Figure \\[fig:2polytopes\\] for a picture of it together with a picture of the regular permutohedron $\\Pi_3$ as a comparison. ", "Let $(\\pi,\\tau)=(3241,231)$. Then $(\\pi^{-1}, \\tau^{-1})=(4213, 312)$. Thus, the vertex of $\\Pi_3^2(4,1)$ associated to $(3241,231)$ is $$v_{3241,231}^{(4,1)}=\n4(1{\\textbf{e}}_4+2{\\textbf{e}}_2+3{\\textbf{e}}_1+4{\\textbf{e}}_3) + 1(1({\\textbf{e}}_3-{\\textbf{e}}_1)+2({\\textbf{e}}_2-{\\textbf{e}}_4)+3({\\textbf{e}}_1-{\\textbf{e}}_2)) = (14,7,17,2).$$ We can compute all vertices of $\\Pi_3^2(4,1)$ this way, and they are $$(3,7,11,19),(2,9,10,19),(1,10,11,18),(1,9,13,17),(2,7,14,17),(3,6,13,18),$$ and all of their permutations.", "\n\n\\[prop:fanofusual2\\] Suppose $(\\balpha, \\bbeta) \\in {\\mathbb{R}}^{d+1} \\times {\\mathbb{R}}^d$ is a pair of strictly increasing sequences and $(M,N) \\in {\\mathbb{R}}_{>0}^2$ is an appropriate choice for $(\\balpha, \\bbeta)$. Then for each $(\\pi,\\tau) \\in \\fS_{d+1} \\times \\fS_d,$ the point $v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)}$ is a vertex of $\\Perm(\\balpha,\\bbeta),$ and the normal cone of $\\Perm(\\balpha,\\bbeta;M,N)$ at $v_{\\pi,\\tau}^{(\\balpha,\\bbeta);(M,N)}$ is $\\sigma(\\pi,\\tau).$ Therefore, the nested Braid fan ${\\textrm{Br}}_d^2$ is the normal fan of the nested usual permutohedron $\\Perm(\\balpha, \\bbeta; M, N).$ Hence, ${\\textrm{Br}}_d^2$ is a complete projective fan in $W_d$.\n\nSimilar to the proof of Proposition \\[prop:fanofusual\\], it is enough to show that for any ${\\textbf{w}}\\in C(\\pi, \\tau)$ (assuming $(\\pi,\\tau)$ is fixed), $$\\label{equ:strictineq}\n \\left\\langle {\\textbf{w}}, v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle > \\left\\langle {\\textbf{w}}, v_{(\\pi',\\tau')}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle, \\quad \\forall (\\pi,\\tau) \\neq (\\pi',\\tau') \\in \\fS_{d+1} \\times \\fS_d.$$ We will prove the above inequality by introducing an intermediate product and showing $$\\label{equ:strictineq1}\n \\left\\langle {\\textbf{w}}, v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle > \\left\\langle {\\textbf{w}}, v_{\\pi,\\tau'}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle > \\left\\langle {\\textbf{w}}, v_{(\\pi',\\tau')}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle.$$\n\nSimilar as before, we let $u_i = w_{\\pi^{-1}(i)}$ for each $i$ and express ${\\textbf{w}}$ as in . ", "Then ${\\textbf{w}}\\in C(\\pi, \\tau)$ means that\n\n1. ", " $u_1 < u_2 < \\dots < u_{d+1}$, and\n\n2. ", " $u_{\\tau^{-1}(1)+1} - u_{\\tau^{-1}(1)} < u_{\\tau^{-1}(2)+1}-u_{\\tau^{-1}(2)} < \\cdots < u_{\\tau^{-1}(d)+1} - u_{\\tau^{-1}(d)}.$\n\nExpression , together with , allows us to compute products in easily. ", "Then the second inequality in follows from the Rearrangement Inequality (Lemma \\[lem:rearr\\]), condition (1) above and the fact that $(M,N)$ is an appropriate choice. ", "Next, we see the first inequality in holds if and only if $$\\sum_{i=1}^{d+1} u_i \\left(\\beta_{\\tau(i-1)} - \\beta_{\\tau(i)}\\right) > \\sum_{i=1}^{d+1} u_i \\left(\\beta_{\\tau'(i-1)} - \\beta_{\\tau'(i)}\\right).$$ After rearranging summations, the above inequality becomes $$\\sum_{j=1}^d \\beta_j \\left(u_{\\tau^{-1}(j)+1} - u_{\\tau^{-1}(j)}\\right) >\\sum_{j=1}^d \\beta_j \\left(u_{(\\tau')^{-1}(j)+1} - u_{(\\tau')^{-1}(j)}\\right),$$ which follows from the Rearrangement Inequality, condition (2) above and the fact that $\\bbeta$ is strictly increasing.", "\n\nProposition \\[prop:fanofusual2\\] provides one natural way to define generalized nested permutohedra.", "\n\n\\[defn:gen2\\] A polytope in $V_d$ (or in an affine plane that is a translation of $V_d$) is a *generalized nested permutohedron* if its normal fan is a coarsening of ${\\textrm{Br}}_d^2.$\n\nCombinatorics of ${\\textrm{Br}}_d^2$ {#combinatorics-of-textrmbr_d2 .unnumbered}\n------------------------------------\n\nOur next goal is to determine the combinatorics of the fan ${\\textrm{Br}}^2_d$ which is equivalent to those of the face lattice of $\\Pi_d^2(M,N)$. The following poset arises naturally in our discussion.", "\n\n\\[defn:osp\\] An *ordered (set) partition* of $[d+1]$ is an ordered tuple of disjoint subsets whose union is $[d+1]$, i.e. ${{\\mathcal T}}=(S_1,\\cdots,S_k)$ with $S_i\\subset [d+1]$ for all $1\\leq i\\leq k$ and $S_1\\sqcup\\cdots \\sqcup S_k = [d+1]$.\n\nThe *ordered (set) partition poset*, denoted by ${{\\mathcal O}}_{d+1}$, is the poset on all ordered set partitions of $[d+1]$ ordered by refinement. ", "This is a ranked poset of rank $d.$ It has a maximum, the trivial partition, $\\hat{1}=([d+1])$, but doesn’t have a minimum.", "\n\nIt has $(d+1)!$ minimal elements, one for each permutation $\\pi \\in \\fS_{d+1}$ considered as an ordered set partition of singletons: $${{\\mathcal T}}(\\pi) := ( \\{\\pi^{-1}(1)\\}, \\{\\pi^{-1}(2)\\}, \\dots, \\{\\pi^{-1}(d+1)\\}).$$\n\nWe denote by $\\overline{{{\\mathcal O}}_{d+1}}$ the poset obtained from ${{\\mathcal O}}_{d+1}$ by removing the maximum element.", "\n\nWe are going to write ordered set partitions by using numbers separated by bars. ", "For instance, the ordered partition ${{\\mathcal T}}=(\\{3,4\\},\\{1,5\\},\\{2,6,7\\})$ will be written as $34|15|267$. It is important to keep in mind that the numbers between bars form a set, hence their order is irrelevant. ", "We have ${{\\mathcal T}}(3721456) = 4|3|1|5|6|7|2 \\le 34|15|267$.\n\nRecall we define ${\\textbf{e}}_S$ for each $S \\in {{\\mathcal B}}_{d+1}.$ For each element ${{\\mathcal T}}= (S_1,\\cdots,S_k) \\in {{\\mathcal O}}_{d+1}$, we define $${\\textbf{e}}_{{{\\mathcal T}}} := \\sum_{i} i {\\textbf{e}}_{S_i}.", "\n \\label{equ:defneT}$$ For instance if ${{\\mathcal T}}=34|15|267$, then ${\\textbf{e}}_{{{\\mathcal T}}} = 1 \\cdot {\\textbf{e}}_{34} + 2 \\cdot {\\textbf{e}}_{15} + 3 \\cdot {\\textbf{e}}_{267} = (2,3,1,1,2,3,3).$ We have the following result that is analogous to Proposition \\[prop:charbr\\].", "\n\n\\[prop:charbr2\\] The rays, i.e., $1$-dimensional cones, of the Braid fan ${\\textrm{Br}}_d^2$ are given by ${\\textbf{e}}_{{\\mathcal T}}$ for all ${{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}}$. Furthermore, a $k$-set of rays $\\{{\\textbf{e}}_{{{\\mathcal T}}_1},\\cdots, {\\textbf{e}}_{{{\\mathcal T}}_k}\\}$ spans a $k$-dimensional cone in ${\\textrm{Br}}_d^2$ if and only if the sets ${{\\mathcal T}}_1,\\dots, {{\\mathcal T}}_k$ form a $k$-chain in $\\overline{{{\\mathcal O}}_{d+1}}$.\n\nIn particular, the maximal cones in ${\\textrm{Br}}_d^2$ are in bijection with the maximal chains in $\\overline{{{\\mathcal O}}_{d+1}}.$ Hence, ${\\textrm{Br}}_d^2$ is simplicial.", "\n\nAs each maximal cone $\\sigma(\\pi,\\tau)$ of ${\\textrm{Br}}_d^2$ is indexed by $(\\pi,\\tau) \\in \\fS_{d+1} \\times \\fS_d$, and maximal chains in $\\overline{{{\\mathcal O}}_{d+1}}$ are obtained from maximal chains in ${{\\mathcal O}}_{d+1}$ by removing the top element, we will prove the above proposition by providing a bijection between $(\\pi,\\tau) \\in \\fS_{d+1}\\times \\fS_d$ and maximal chains in ${{\\mathcal O}}_{d+1}.$\n\nWe first observe that the rank-$0$ element ${{\\mathcal T}}(\\pi): \\pi^{-1}(1)|\\pi^{-1}(2)|\\cdots|\\pi^{-1}(d+1)$ contains $d$ bars, and any element of rank $r$ in the interval $[{{\\mathcal T}}(\\pi), \\hat{1}]$ can be obtained from ${{\\mathcal T}}(\\pi)$ by removing an $r$-subset of the $d$ bars. ", "Conversely, any element of rank $r$ arises this way. ", "This gives the following lemma.", "\n\n\\[lem:localbool\\] For each $\\pi \\in \\fS_{d+1},$ the interval $[{{\\mathcal T}}(\\pi), \\hat{1}]$ is isomorphic to the Boolean algebra ${{\\mathcal B}}_{d}.$ Hence, the poset ${{\\mathcal O}}_{d+1}$ is *locally Boolean*, i.e., all of its intervals are Boolean algebras.", "\n\nMoreover, the discussion above provides a natural way to construct a desired bijection for the proof of Proposition \\[prop:charbr2\\].", "\n\nWe represent each $(\\pi,\\tau)$ with the following diagram, denoted by ${{\\mathcal D}}(\\pi,\\tau)$: $$\\pi^{-1}(1)\\stackrel{\\tau(1)}{|} \\pi^{-1}(2) \\stackrel{\\tau(2)}{|} \\cdots \\stackrel{\\tau(d-1)}{|} \\pi^{-1}(d) \\stackrel{\\tau(d)}{|}\\pi^{-1}(d+1).$$\n\nLet $(\\pi,\\tau) \\in \\fS_{d+1} \\times \\fS_d,$ we define $\\ch(\\pi,\\tau)$ to be the unique maximal chain in $[{{\\mathcal T}}(\\pi), \\hat{1}]$ that is obtained in the following way:\n\n1. ", " Let ${{\\mathcal D}}(\\pi,\\tau; 0) = {{\\mathcal D}}(\\pi,\\tau)$.\n\n2. ", " For each $1 \\le r \\le d,$ we let ${{\\mathcal D}}(\\pi,\\tau;r)$ be the diagram obtained from ${{\\mathcal D}}(\\pi,\\tau;r-1)$ by removing the bar labelled by $r.$\n\n3. ", " For each $0 \\le r \\le d,$ ignoring the labels on bars gives an ordered set partition in $[{{\\mathcal T}}(\\pi),\\hat{1}]$ of rank $r$, and we denote it by ${{\\mathcal T}}(\\pi,\\tau; r).$\n\n4. ", " Let $\\ch(\\pi,\\tau)$ be the maximal chain formed by $\\{ {{\\mathcal T}}(\\pi,\\tau;r) \\ : \\ 0 \\le r \\le d\\}.$\n\n\\[ex:nestedperm2\\] Let $(\\pi,\\tau) = (3241, 231).$ Then ${{\\mathcal D}}(\\pi,\\tau)$ is the diagram $$\\label{eq:diagram}\n4\\stackrel{2}{|}2\\stackrel{3}{|}1\\stackrel{1}{|}3,$$ and $\\ch(\\pi,\\tau)$ is as shown in the box on the left side of Figure \\[fig:maxchain\\], where the arrows demonstrate the procedure we describe above. ", "In the middle of the figure (or the third column of the figure), we list the rays ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;i)}$ associated with ${{\\mathcal T}}(\\pi,\\tau;r)$ for each $r.$ Finally, in the fourth column, we show the difference between any two consecutive associated rays, which turns out to be important.", "\n\nat (-2.4,3.8) [${{{\\mathcal D}}(\\pi,\\tau; r)}$]{}; at (-2.4,0) [$4\\stackrel{2}{|}2\\stackrel{3}{|}1\\stackrel{1}{|}3$]{}; at (-2.4,0.5) [$\\uparrow$]{}; at (-2.4,1) [$4\\stackrel{2}{|}2\\stackrel{3}{|}1 \\ \\ 3$]{}; at (-2.4,3/2) [$\\uparrow$]{}; at (-2.4,4/2) [$4 \\ \\ 2\\stackrel{3}{|}1 \\ \\ 3$]{}; at (-2.4,5/2) [$\\uparrow$]{}; at (-2.4,6/2) [$4 \\ \\ 2 \\ \\ 1 \\ \\ 3$]{};\n\nat (-1,0) [$\\longrightarrow$]{}; at (-1,1) [$\\longrightarrow$]{}; at (-1,2) [$\\longrightarrow$]{}; at (-1,3) [$\\longrightarrow$]{};\n\nat (0,3.8) [${{{\\mathcal T}}(\\pi,\\tau; r)}$]{}; at (0,0) [$4|2|1|3$]{}; at (0,0.5) [$|$]{}; at (0,1) [$4|2|13$]{}; at (0,3/2) [$|$]{}; at (0,4/2) [$42|13$]{}; at (0,5/2) [$|$]{}; at (0,6/2) [$4213$]{};\n\n(-0.6,-0.3) – (0.6,-0.3) – (0.6,3.3) – (-0.6,3.3) – cycle;\n\nat (3,0) [${\\textbf{e}}_4+2{\\textbf{e}}_2+3{\\textbf{e}}_1+4{\\textbf{e}}_3$]{}; at (3,1) [${\\textbf{e}}_4+2{\\textbf{e}}_2+3{\\textbf{e}}_1+3{\\textbf{e}}_3$]{}; at (3,2) [${\\textbf{e}}_4+{\\textbf{e}}_2+2{\\textbf{e}}_1+2{\\textbf{e}}_3$]{}; at (3,3) [${\\textbf{e}}_4+{\\textbf{e}}_2+{\\textbf{e}}_1+{\\textbf{e}}_3$]{}; at (3,3.8) [${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r)}$]{};\n\nat (6.6,3.8) [${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r-1)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;r)}$]{}; at (6.6, 0.5) [${\\textbf{e}}_{\\{3\\}} = {\\textbf{e}}_3$]{}; at (6.6, 1.5) [${\\textbf{e}}_{\\{213\\}} = {\\textbf{e}}_2 + {\\textbf{e}}_1 + {\\textbf{e}}_3$]{}; at (6.6, 2.5) [${\\textbf{e}}_{\\{13\\}} = {\\textbf{e}}_1 + {\\textbf{e}}_3$]{};\n\nat (10,3.8) [$\\Gamma_{\\tau^{-1}(r)}^\\pi$]{}; at (10, 0.5) [$\\Gamma_{3}^\\pi =\\{3\\}$]{}; at (10, 1.5) [$\\Gamma_{1}^\\pi = \\{213\\}$]{}; at (10, 2.5) [$\\Gamma_{2}^\\pi =\\{13\\}$]{};\n\nat (8.7, 0.5) [$\\longleftarrow$]{}; at (8.7, 1.5) [$\\longleftarrow$]{}; at (8.7, 2.5) [$\\longleftarrow$]{};\n\nOne may notice that in Figure \\[fig:maxchain\\] that the differences ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r-1)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;r)}$ can be understood in a more systemetic way. ", "We use the following notation.", "\n\nFix $\\pi \\in \\fS_{d+1}$. For $1 \\le i \\le d,$ let $$\\Gamma_i^{\\pi} := \\pi^{-1}(i, d+1] = \\{ \\pi^{-1}(j) \\ : \\ i < j \\le d+1\\}.$$\n\nThe following lemma is clear from the construction of $\\ch(\\pi,\\tau)$. So we omit its proof.", "\n\n\\[lem:diff\\] The map $(\\pi,\\tau) \\to \\ch(\\pi,\\tau)$ is a bijection from $\\fS_{d+1}\\times \\fS_d$ to maximal chains of ${{\\mathcal O}}_{d+1}$ (or equivalently, to maximal chains of $\\overline{{{\\mathcal O}}_{d+1}}$).", "\n\nFurthermore, for each $1 \\le r \\le d,$ $$\\label{equ:diff}\n{\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r-1)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;r)} = {\\textbf{e}}_{\\Gamma_{\\tau^{-1}(r)}^\\pi}.$$\n\nIn our running example, where $(\\pi,\\tau) = (3241, 231),$ we have $$\\Gamma_1^\\pi = \\{ 213\\}, \\quad \\Gamma_2^\\pi = \\{ 13\\}, \\quad \\Gamma_3^\\pi = \\{3\\}.$$ Then the differences ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r-1)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;r)}$ can be computed using as shown in the last column of Figure \\[fig:maxchain\\]. ", "For instance, $\\tau^{-1}(3)=2$ implies that ${\\textbf{e}}_{\\Gamma_2^\\pi} = {\\textbf{e}}_{\\{13\\}}$ gives the difference vector ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; 2)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;3)}$.\n\nIt is enough to show that $\\sigma(\\pi,\\tau)$ is spanned by the rays ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau; r)}$, where $0 \\le r \\le d-1,$ associated to non-maximum elements in the maximal chain $\\ch(\\pi,\\tau).$ (All the conclusions in the proposition follow from it.)", "\n\nIt follows from the definition that $\\sigma(\\pi,\\tau)$ is the collection of ${\\textbf{x}}\\in W_d$ satisfying $$\\label{eq:chainineq2}\n 0\\leq (\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(1)}\\leq (\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(2)}\\leq\\cdots \\leq (\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(d)}.$$ The rays of $\\sigma(\\pi,\\tau)$ are obtained by having one strict inequality in and equalities in the rest, i.e., by $$\\label{equ:chainineqr}\n 0 = (\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(1)}=(\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(2)}=\\cdots=(\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(r)}<(\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(r+1)} =\\cdots= (\\Delta {\\textbf{x}})^\\pi_{\\tau^{-1}(d)} =1.$$ The right hand side can be any positive constant as the solution will just be off by a scale; hence, we let it be $1.$ As there is a unique solution (if one exists) to , it is enough to verify ${\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau;r)}$ is a solution. ", "Indeed, by the construction of ${{\\mathcal T}}(\\pi,\\tau;r),$ the followings are true:\n\n1. ", " If $i \\le r,$ then $\\pi^{-1}(\\tau^{-1}(i)+1)$ is in the same block of ${{\\mathcal T}}(\\pi,\\tau;r)$ as $\\pi^{-1}(\\tau^{-1}(i))$.\n\n2. ", " If $i > r,$ then $\\pi^{-1}(\\tau^{-1}(i)+1)$ is in the block of ${{\\mathcal T}}(\\pi,\\tau;r)$ that follows the block where $\\pi^{-1}(\\tau^{-1}(i))$ is in.", "\n\nThen the desired conclusion follows from the definition of ${\\textbf{e}}_{{\\mathcal T}}$ (see ) for any ordered set partion ${{\\mathcal T}}$.\n\nAs a summary, we have associated three objects to each pair of $(\\pi,\\tau)$. The proofs of Proposition \\[prop:fanofusual2\\] and \\[prop:charbr2\\] tells us the connection between them, which are summarized in the diagram below.", "\n\nat (-1,2) [$\\fS_{d+1}\\times\\fS_d\\ni(\\pi,\\tau)$]{}; (-1,2) to \\[out=60, in=190\\] (1,3); (-1,2) circle \\[radius=0.05\\]; at (1,3) [$v_{\\pi,\\tau}^{(\\balpha,\\bbeta)(M,N)}$]{}; (3,3) to \\[out=330, in=15\\] (2.3,2.1); (2.5,1) to \\[out=30, in=345\\] (2.3,1.9); at (1,2) [$\\sigma(\\pi,\\tau)$]{}; at (4,2.4) [normal cone]{};\n\nat (1,1) [$\\ch(\\pi,\\tau)$]{}; at (5,1.6) [non-maximum elements giving]{}; at (5,1.2) [the set of spanning rays]{}; (-1,2) – (1,2); (-1,2) to \\[out=300, in=170\\] (1,1);\n\n\\[ex:nestedperm3\\] Let $(\\pi,\\tau)=(3241,231).$ As shown in Examples \\[ex:nestedperm\\] and \\[ex:nestedperm2\\] that $v_{3241,231}^{(4,1)} = (14,7,17,2)$, the maximal chain $\\ch(3241,231)$ and its associated rays are given in Figure \\[fig:maxchain\\]. ", "So the normal cone of $\\Pi_3^2(4,1)$ at the vertex $v_{3241,231}^{(4,1)}$ is $\\sigma(3241,231)$. It is spanned by the rays associated to non-maixmum elements in $\\ch(3241,231),$ which are the three vectors on the bottom of the middle column in Figure \\[fig:maxchain\\]. ", "This helps us to find three facet-defining inequalities for $\\Pi_3^2(4,1):$ $$\\begin{aligned}\n \\left\\langle {\\textbf{e}}_{42|13}, {\\textbf{x}}\\right\\rangle = 2x_1+x_2+2x_3+x_4 &\\leq \\left\\langle {\\textbf{e}}_{42|13}, (14,7,17,2) \\right\\rangle = 71\\\\\n \\left\\langle {\\textbf{e}}_{4|2|13}, {\\textbf{x}}\\right\\rangle = 3x_1+2x_2+3x_3+x_4 &\\leq\\left\\langle {\\textbf{e}}_{4|2|13}, (14,7,17,2) \\right\\rangle = 109\\\\\n \\left\\langle {\\textbf{e}}_{4|2|1|3}, {\\textbf{x}}\\right\\rangle = 3x_1+2x_2+4x_3+x_4 &\\leq\\left\\langle {\\textbf{e}}_{4|2|1|3}, (14,7,17,2) \\right\\rangle = 126.\\end{aligned}$$\n\nInequality description of usual nested permutohedra {#inequality-description-of-usual-nested-permutohedra .unnumbered}\n---------------------------------------------------\n\nIt follows from Propositions \\[prop:fanofusual2\\] and \\[prop:charbr2\\] and Definition \\[defn:gen2\\] that any generalized nested permutohedron in ${\\mathbb{R}}^{d+1}$ is defined by the linear system in the form of $$\\label{equ:linear2}\n \\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ b_{[d+1]}, \\quad \\text{and} \\quad \n \\langle {\\textbf{e}}_{{\\mathcal T}}, {\\textbf{x}}\\rangle \\ \\le \\ b_{{\\mathcal T}}, \\quad \\forall {{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}}.$$ Note that $[d+1]$ can be considered as the maximal element in ${{\\mathcal O}}_{d+1}$ which is an ordered set partition, and also can be considered as the maximal element in ${{\\mathcal B}}_{d+1}$, which is a set. ", "Either way, ${\\textbf{e}}_{[d+1]}$ represents the all-one vector $\\1.$ Hence, we may consider all the $b$’s appearing in as a vector ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$ where indices are elements in ${{\\mathcal O}}_{d+1}.$\n\nIt is interesting to obtain results that are analogous to those in Theorems \\[thm:centralsub\\] and \\[thm:submodrestate\\]. ", "We will do this in next part. ", "Before that we focus on usual nested permutohedra. ", "When we introduced usual nested permutohedra, we defined them as convex hull of all of their vertices in . ", "Now we can give an inequality description in the form of by giving explicit description for ${\\textbf{b}}$. It turns out each coordinate $b_{{\\mathcal T}}$ is determined by its structure type.", "\n\n\\[defn:type\\] Let ${{\\mathcal T}}= S_1| S_2| \\dots | S_{k+1} \\in {{\\mathcal O}}_{d+1}.$ We define the *structure type* of ${{\\mathcal T}}$, denoted by $\\Type({{\\mathcal T}})$, to be the sequence $(t_0=0, t_1, t_2, \\dots, t_{k+1}=d+1),$ where $$t_i = \\sum_{j=1}^i |S_j|, \\quad \\text{for $1 \\le i \\le k$}.$$ (We can also understand $t_i (1 \\le i \\le k)$ as the position number of the $i$th bar in ${{\\mathcal T}}.$)\n\n\\[thm:facetdes\\] Suppose $(\\balpha, \\bbeta) \\in {\\mathbb{R}}^{d+1} \\times {\\mathbb{R}}^d$ is a pair of strictly increasing sequences $(\\balpha, \\bbeta) \\in {\\mathbb{R}}^{d+1} \\times {\\mathbb{R}}^d$ and $(M,N) \\in {\\mathbb{R}}_{>0}^2$ is an appropriate choice for $(\\balpha, \\bbeta)$. Suppose ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$ is defined as follows: for each ${{\\mathcal T}}\\in {{\\mathcal O}}_{d+1},$ if $\\Type({{\\mathcal T}})=(t_0, t_1,t_2,\\dots, t_k, t_{k+1}),$ let $$b_{{{\\mathcal T}}} = M \\left( \\sum_{i=1}^{k+1} i \\sum_{j=t_{i-1}+1}^{t_i} \\alpha_j\\right) + N \\sum_{j=d-k+1}^d \\beta_j.", "\n \\label{equ:usualb}$$ Then the linear system defines the usual nested permutohedron $\\Perm(\\balpha, \\bbeta; M,N)$.\n\nAs we discussed after Definition \\[defn:usual2\\] that $\\Perm(\\balpha, \\bbeta;M,N)$ lies on the hyperplane $\\sum_{i=1}^{d+1} x_i = M \\sum_{i=1}^{d+1} \\alpha_i.$ This, together with Propositions \\[prop:fanofusual2\\] and \\[prop:charbr2\\], implies that it is enough to verify that ${\\textbf{b}}$ defined by satisfies\n\n1. ", " $b_{[d+1]} = M \\sum_{i=1}^{d+1} \\alpha_i;$ and\n\n2. ", " if ${{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}}$ is in the maximal chain $\\ch(\\pi,\\tau),$ then $b_{{\\mathcal T}}= \\left\\langle {\\textbf{e}}_{{\\mathcal T}}, v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle.$\n\nSuppose ${{\\mathcal T}}= [d+1]$ is the maximal element of ${{\\mathcal O}}_{d+1}.$ Then $k=0$ and its structure type is $(0, d+1).$ The right hand side of becomes $M \\sum_{j=1}^{d+1} \\alpha_j$ as desired.", "\n\nSuppose ${{\\mathcal T}}= S_1 | S_2 | \\cdots | S_{k+1} \\in \\overline{{{\\mathcal O}}_{d+1}}$ has structure type $(t_0, t_1, \\dots, t_{k+1}),$ and it belongs to the maximal chain $\\ch(\\pi,\\tau).$ (Note that the choice of $(\\pi,\\tau)$ is not unique.) ", "It is easy to see that ${{\\mathcal T}}$ is of rank $d-k.$ Hence, it is the rank-$(d-k)$ element ${{\\mathcal T}}(\\pi,\\tau;d-k)$ of the maximal chain $\\ch(\\pi,\\tau).$ It follows from the construction of $\\ch(\\pi,\\tau)$ that ${{\\mathcal D}}(\\pi,\\tau; d-k)$ is the following diagram: $$\\pi^{-1}(1) \\pi^{-1}(2) \\cdots \\pi^{-1}(t_1) \\stackrel{\\tau(t_1)}{|} \\pi^{-1}(t_1+1) \\cdots \\pi^{-1}(t_2) \\stackrel{\\tau(t_2)}{|} \\cdots \\cdots \\stackrel{\\tau(t_k)}{|} \\pi^{-1}(t_k+1) \\cdots \\pi^{-1}(d+1).$$ Since ${{\\mathcal T}}= {{\\mathcal T}}(\\pi,\\tau;d-k) = S_1 |S_2 |\\cdots|S_{k+1}$ is obtained from ${{\\mathcal D}}(\\pi,\\tau;d-k)$ by removing labels on the bars, and the labels on the bars have to be the largest $k$ elements in $[d].$ The followings are true $$\\begin{aligned}\n & \\{ \\tau(t_1), \\tau(t_2),\\dots, \\tau(t_k)\\} = \\{d-k+1, d-k+2, \\dots, d\\}; \\label{equ:barcond} \\\\\n& S_i = \\{ \\pi^{-1}(j) : t_{i-1}+1 \\le j \\le t_i\\} \\quad \\forall 1 \\le i \\le k+1. ", "\\label{equ:Si}\\end{aligned}$$ It follows from that ${\\textbf{e}}_{{\\mathcal T}}= \\sum_{i=1}^{k+1} i \\sum_{j=t_{i-1}+1}^{t_i} {\\textbf{e}}_{\\pi^{-1}(j)}$. Using this and , we obtain $$\\begin{aligned}\n \\left\\langle {\\textbf{e}}_{{\\mathcal T}}, v_{\\pi,\\tau}^{(\\balpha,\\bbeta),(M,N)} \\right\\rangle =& M \\left( \\sum_{i=1}^{k+1} i \\sum_{j=t_{i-1}+1}^{t_i} \\alpha_j\\right) + N \\left\\langle {\\textbf{e}}_{{\\mathcal T}}, \\sum_{i=1}^d \\beta_{\\tau(i)} {\\textbf{f}}_{i}^\\pi \\right\\rangle \\end{aligned}$$ However, $\\langle {\\textbf{e}}_{{\\mathcal T}}, {\\textbf{f}}_{i}^\\pi \\rangle = \\langle {\\textbf{e}}_{{\\mathcal T}}, {\\textbf{e}}_{\\pi^{-1}(i+1)} - {\\textbf{e}}_{\\pi^{-1}(i)} \\rangle$ is $0$ if $\\pi^{-1}(i)$ and $\\pi^{-1}(i+1)$ are in the same block of ${{\\mathcal T}}$, and is $1$ othwerwise, in which case they are in two consecutive blocks. ", "One checks that the latter situation happens if and only if $i = t_j$ for some $1 \\le j \\le k$, which is a position where a bar is placed. ", "Therefore, it follows from that $\\displaystyle \\left\\langle {\\textbf{e}}_{{\\mathcal T}}, \\sum_{i=1}^d \\beta_{\\tau(i)} {\\textbf{f}}_{i}^\\pi \\right\\rangle = \\sum_{j=d-k+1}^d \\beta_j$ as desired.", "\n\nWe apply Theorem \\[thm:facetdes\\] to the regular nested permutohedron $\\Pi_3^2(4,1)$ first studied in Example \\[ex:nestedperm\\]. ", "Clearly, the polytope lies in $$\\langle {\\textbf{e}}_{[4]}, {\\textbf{x}}\\rangle = x_1 + x_2 + x_3 + x_4 =b_{[d+1]} = M \\sum_{i=1}^4 \\alpha_i = 4 (1+2+3+4) = 40.$$ We then compute some of the inequalities: $$\\begin{aligned}\n\\langle {\\textbf{e}}_{23|4|1},{\\textbf{x}}\\rangle = 3x_1+x_2+x_3+2x_4\\leq 4\\Big(1(1+2)+2(3)+3(4)\\Big)+1\\Big(2+3\\Big)&= 90\\\\\n\\langle {\\textbf{e}}_{14|23},{\\textbf{x}}\\rangle = x_1+2x_2+2x_3+x_4\\leq 4\\Big(1(1+2)+2(3+4)\\Big)+1\\Big(3\\Big)&= 71\\\\\n\\langle {\\textbf{e}}_{4|123},{\\textbf{x}}\\rangle = 2x_1+2x_2+2x_3+x_4\\leq 4\\Big(1(1)+2(2+3+4)\\Big)+1\\Big(2+3\\Big)&= 81.\\end{aligned}$$\n\nDeformation cone of ${\\textrm{Br}}_d^2$ {#deformation-cone-of-textrmbr_d2 .unnumbered}\n---------------------------------------\n\nFinally, we are going to present results that analogous to results on $\\Def({\\textrm{Br}}_d)$ and the Submodular Theorem for generalized permutohedron discussed in Section \\[sec:GP\\]. ", "We first apply Proposition \\[prop:reduxfan\\] to determine $\\Def({\\textrm{Br}}_d^2)$, or equivalently, the deformation cone of a *centralized* usual nested permutohedron.", "\n\nIn order to apply Proposition \\[prop:reduxfan\\], one needs to describe pairs of adjacent maximal cones in ${\\textrm{Br}}_d^2.$ By Proposition \\[prop:charbr2\\], this is equivalent to describing pairs of maximal chains in ${{\\mathcal O}}_{d+1}$ that only differ at a non-maximum element. ", "Suppose $\\ch_1$ and $\\ch_2$ forms such a pair of maximal chains in ${{\\mathcal O}}_{d+1}$. Let ${{\\mathcal T}}= \\ch_1 \\setminus \\ch_2$ and ${{\\mathcal T}}'= \\ch_2\\setminus \\ch_1.$ Then ${{\\mathcal T}}$ and ${{\\mathcal T}}'$ are of same rank, say $r$, where $0 \\le r < d.$ In this case, we say $\\{ \\ch_1, \\ch_2\\}$ is a pair of *($r$-)adjacent* maximal chains in ${{\\mathcal O}}_{d+1}$.\n\n(0,0) circle \\[radius = 0.08\\]; (0,-1) circle \\[radius=0.08\\]; (1,1) circle \\[radius=0.08\\]; (-1,1) circle \\[radius=0.08\\]; (0,2) circle \\[radius=0.08\\]; (0,3) circle \\[radius=0.08\\]; (0,-1) – (0,0) – (1,1) – (0,2); (0,0) – (-1,1) – (0,2)–(0,3); at (0,3.2) ; at (0,-1) ; at (0,-1) [${{\\mathcal T}}_{r-2}$]{}; at (0,0) [${{\\mathcal T}}_{r-1}$]{}; at (1,1) [${{\\mathcal T}}'_{r}={{\\mathcal T}}'$]{}; at (-1,1) [${{\\mathcal T}}_{r}={{\\mathcal T}}$]{}; at (0,2) [${{\\mathcal T}}_{r+1}$]{}; at (0,3) [${{\\mathcal T}}_{r+2}$]{};\n\nat (-1.7,3) [$\\ch_1$]{}; at (2.1,3) [$\\ch_2$]{}; at (0,-2.5) [a diamond with $0 < r < d$]{};\n\n(1,1) circle \\[radius=0.08\\]; (-1,1) circle \\[radius=0.08\\]; (0,2) circle \\[radius=0.08\\]; (0,3) circle \\[radius=0.08\\]; (0,4) circle \\[radius=0.08\\]; (0,5) circle \\[radius=0.08\\]; (1,1) – (0,2) – (0,3)–(0,4)–(0,5); (-1,1) – (0,2); at (0,5.2) ; at (1,1) [${{\\mathcal T}}'_{r}$]{}; at (-1,1) [${{\\mathcal T}}_{r}$]{}; at (0,2) [${{\\mathcal T}}_{r+1}$]{}; at (0,3) [${{\\mathcal T}}_{r+2}$]{}; at (0,4) [${{\\mathcal T}}_{r+1}$]{}; at (0,5) [${{\\mathcal T}}_{r+2}$]{};\n\nat (-1.7,3) [$\\ch_1$]{}; at (2.1,3) [$\\ch_2$]{}; at (0,0) [a “” shape with $r=0$]{};\n\n\\[lem:adjch\\] Suppose $\\{ \\ch_1, \\ch_2\\}$ is a pair of *$r$-adjacent* maximal chains in ${{\\mathcal O}}_{d+1}$. Then (by Lemma \\[lem:diff\\]) there exists a unique pair $(\\pi_i, \\tau_i) \\in \\fS_{d+1} \\times \\fS_d$ such that $\\ch_i = \\ch(\\pi_i,\\tau_i)$ for each $i.$ There are two situations:\n\n1. ", " (The diamond situation:) If $0 < r < d,$ then $\\ch_1$ and $\\ch_2$ form a diamond shape as shown on the left of Figure \\[fig:2poss\\]. ", "Furthermore, we have $$\\label{equ:dia}\n \\pi_1 = \\pi_2, \\quad \\text{and} \\quad (r,r+1) \\circ \\tau_1 = \\tau_2,$$ where $(r,r+1)$ is the transposition that exchanges $r$ and $r+1.$\n\n2. ", " (The situation:) If $r=0,$ then $\\ch_1$ and $\\ch_2$ form a (reads “ren”) shape as shown on the right of Figure \\[fig:2poss\\]. ", "Suppose ${{\\mathcal T}}_{r+1} = {{\\mathcal T}}_1$, the minimum common element of $\\ch_1$ and $\\ch_2$, has its only $2$-element-block in $i$th position, that is, $${{\\mathcal T}}_1 =s_1|s_2|\\cdots|s_{i-1}|s_i s_i'|s_{i+1}|\\cdots|s_d. ", " \n \\label{equ:rank1}$$ Then $$\\label{equ:ren}\n \\tau_1 = \\tau_2, \\quad \\tau_1(i)=1=\\tau_2(i), \\quad \\text{and} \\quad (i,i+1) \\circ \\pi_1 = \\pi_2.$$\n\nMoreover, if $(\\pi_1,\\tau_1)$ and $(\\pi_2,\\tau_2)$ satisfy either or , then $\\ch(\\pi_1,\\tau_1)$ and $\\ch(\\pi_2,\\tau_2)$ are adjacent maximal chains in ${{\\mathcal O}}_{d+1}.$\n\nSuppose $r \\neq 0.$ Then $\\ch_1$ and $\\ch_2$ has the same minimum element, say ${{\\mathcal T}}(\\pi).$ Thus, $\\ch_1$ and $\\ch_2$ are two maximal chains in the maximal interval $[{{\\mathcal T}}(\\pi), \\hat{1}],$ and form a diamond. ", "Hence, $\\pi_1 = \\pi = \\pi_2.$ By the construction of $\\ch(\\pi,\\tau)$, we must have $$\\tau_1^{-1}(r) = \\tau_2^{-1}(r+1), \\text{ and } \\tau_1^{-1}(r+1) = \\tau_2^{-1}(r), \n \\label{equ:tautran}$$ and $\\tau_1^{-1}(i) = \\tau_2^{-1}(i)$ for $i \\neq r, r+1.$ This is equivalent to $(r, r+1) \\circ \\tau_1 = \\tau_2.$\n\nSuppose $r=0$, and $\\ch_1$ and $\\ch_2$ are as shown on the right of Figure \\[fig:2poss\\]. ", "Assume further that ${{\\mathcal T}}_1$ is given by . ", "Then the two minimal elements in $\\ch_1$ and $\\ch_2$ are $$s_1|s_2|\\cdots|s_{i-1}|s_i| s_i'|s_{i+1}|\\cdots|s_d, \\quad \\text{and} \\quad s_1|s_2|\\cdots|s_{i-1}|s_i'| s_i|s_{i+1}|\\cdots|s_d.$$ Then follows from the construction of $\\ch(\\pi,\\tau).$\n\nFinally, the last assertion can be easily verified.", "\n\nUsing the connection between adjacent chains of ${{\\mathcal O}}_{d+1}$ and adjacent vertices of the regular nested permutohedron $\\Perm(\\balpha,\\bbeta;M,N),$ we immediately have the following result.", "\n\nThe two vertices $v_{\\pi_1,\\tau_1}^{(\\balpha,\\bbeta),(M,N)}$ and $v_{\\pi_2,\\tau_2}^{(\\balpha,\\bbeta),(M,N)}$ are adjacent, i.e., form an edge, if and only if either or holds.", "\n\nEach pair of adjacent maximal chains described in Lemma \\[lem:adjch\\], via its correspondence with a pair of adjacent maximal cones in ${\\textrm{Br}}_d^2,$ is associated with an inequality as described in Definition \\[defn:fanineq\\]. ", "In the lemma below, we describe this association explicitly.", "\n\n\\[lem:adjchineq\\] Assume all the hypothesis in Lemma \\[lem:adjch\\]. ", "Let $\\sigma_i = \\sigma(\\pi_i,\\tau_i)$ be the maximal cone in ${\\textrm{Br}}_d^2$ that is in bijection with $\\ch_i$ for $i=1,2.$\n\n1. ", " (The diamond situation:) Suppose $\\ch_1$ and $\\ch_2$ form a diamond shape as shown on the left of Figure \\[fig:2poss\\]. ", "Then the associated inequality $I_{\\{\\sigma_1, \\sigma_2\\}}({\\textbf{b}})$ is $$b_{{{\\mathcal T}}_{r+1}} + b_{{{\\mathcal T}}_{r-1}} \\le b_{{{\\mathcal T}}_r} + b_{{{\\mathcal T}}'_r}.", "\n \\label{equ:diaineq}$$ We call such an inequality a *diamond submodular inequality*.", "\n\n2. ", " (The situation:) Suppose $\\ch_1$ and $\\ch_2$ form a shape as shown on the right of Figure \\[fig:2poss\\], and ${{\\mathcal T}}_1$ is given by . (", "We know that $\\tau_1=\\tau_2.$) Let $\\tau=\\tau_1=\\tau_2,$ and then let $p = \\tau(i-1)$ and $q = \\tau(i+1).$ (By convention, let $\\tau(0)=0$ and $\\tau(d+1)=d+1.$) Then the associated inequality $I_{\\{\\sigma_1, \\sigma_2\\}}({\\textbf{b}})$ is $$2b_{{{\\mathcal T}}_1} + \\underbrace{\\left(b_{{{\\mathcal T}}_{p-1}}-b_{{{\\mathcal T}}_{p}}\\right)}_{\\text{replaced with $b_{[d+1]}$ if $p=0$}} + \\underbrace{\\left(b_{{{\\mathcal T}}_{q-1}}-b_{{{\\mathcal T}}_{q}}\\right)}_{\\text{eliminated if $q=d+1$}} \\ \\le b_{{{\\mathcal T}}_0} + b_{{{\\mathcal T}}_0'}. ", " \\label{equ:renineq}$$ We call such an inequality a *inequality*.", "\n\nIn both situations, we assume $b_{[d+1]} = b_{\\hat{1}} = 0.$\n\n\\[rem:balance\\] There are (at least) two ways to see why $b_{[d+1]} =0:$ First, we are discussing the centralized permutohedra which all lie in $V_d$, where each point has its coordinates sum to $0.$ Second, ${\\textbf{e}}_{[d+1]} = 0$ in $W_d$ is a not a spanning ray of any maximal cone in ${\\textrm{Br}}_d^2.$\n\nThe reason we keep $b_{[d+1]}$ in our expression (as well as its later reformulations) is to keep the expression *balanced*, which means if we replace each $b_{{\\mathcal T}}$ with ${\\textbf{e}}_{{\\mathcal T}}$ in , then the left side gives the same vector as the right side considering both are vectors in ${\\mathbb{R}}^{d+1}$ (instead of $W_d$). (", "It will be clear from the proof of Lemma \\[lem:adjchineq\\] below why is balanced.)", "\n\nFor the diamond situation, as it was shown in the proof of Lemma \\[lem:adjch\\] that $\\tau_1$ and $\\tau_2$ satisfy . ", "Then it follows from the second part of Lemma \\[lem:diff\\] that $${\\textbf{e}}_{{{\\mathcal T}}_{r-1}} - {\\textbf{e}}_{{{\\mathcal T}}_r} = {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau_1; r-1)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau_1;r)} ={\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau_2; r)} - {\\textbf{e}}_{{{\\mathcal T}}(\\pi,\\tau_2;r+1)} = {\\textbf{e}}_{{{\\mathcal T}}'_r} - {\\textbf{e}}_{{{\\mathcal T}}_{r+1}},$$ which implies that $${\\textbf{e}}_{{{\\mathcal T}}_{r+1}} + {\\textbf{e}}_{{{\\mathcal T}}_{r-1}} = {\\textbf{e}}_{{{\\mathcal T}}_r} + {\\textbf{e}}_{{{\\mathcal T}}'_r}.$$ This gives us the diamond submodular inequality .", "\n\nWe now consider the situation. ", "Without loss of generality, we may assume $${{\\mathcal T}}_0 = s_1|s_2|\\cdots|s_{i-1}|s_i| s_i'|s_{i+1}|\\cdots|s_d, \\quad \\text{and} \\quad {{\\mathcal T}}_0' = s_1|s_2|\\cdots|s_{i-1}|s_i'| s_i|s_{i+1}|\\cdots|s_d. ", " \\label{equ:rank0}$$ Then $${\\textbf{e}}_{{{\\mathcal T}}_0} -{\\textbf{e}}_{{{\\mathcal T}}_1} = {\\textbf{e}}_{s_i'} + \\sum_{j=i+1}^d {\\textbf{e}}_{s_j} \\quad \\text{and} \\quad \n {\\textbf{e}}_{{{\\mathcal T}}_0'} -{\\textbf{e}}_{{{\\mathcal T}}_1} = {\\textbf{e}}_{s_i} + \\sum_{j=i+1}^d {\\textbf{e}}_{s_j}.", "\n \\label{equ:reneq}$$ Note that by the second part of Lemma \\[lem:diff\\], we have $$\\begin{aligned}\n {\\textbf{e}}_{s_i}+{\\textbf{e}}_{s_i'} + \\sum_{j=i+1}^d {\\textbf{e}}_{s_j} =& \\begin{cases}\n {\\textbf{e}}_{{{\\mathcal T}}_{p-1}} - {\\textbf{e}}_{{{\\mathcal T}}_p} \\quad & \\text{if $p \\neq 0$} \\\\ \n {\\textbf{e}}_{[d+1]} ={\\textbf{e}}_{\\hat{1}} \\quad & \\text{if $p=0$};\\end{cases} \\\\\n \\text{and} \\quad \\sum_{j=i+1}^d {\\textbf{e}}_{s_j} =& \\begin{cases}\n {\\textbf{e}}_{{{\\mathcal T}}_{q-1}} - {\\textbf{e}}_{{{\\mathcal T}}_q} \\quad & \\text{if $q \\neq d+1$} \\\\ \n 0 \\quad & \\text{if $q=d+1$}.\\end{cases}\n \\end{aligned}$$ One sees that the sum of the left hand sides of the above two equalities equals to the sum of the right hand sides of the two equalities in . ", "This gives us an equality involving ${\\textbf{e}}_{{{\\mathcal T}}_0}, {\\textbf{e}}_{{{\\mathcal T}}_0'}, {\\textbf{e}}_{{{\\mathcal T}}_1},$ ${\\textbf{e}}_{{{\\mathcal T}}_{p-1}} - {\\textbf{e}}_{{{\\mathcal T}}_p}$ and ${\\textbf{e}}_{{{\\mathcal T}}_{q-1}} - {\\textbf{e}}_{{{\\mathcal T}}_q}.$ Rearranging terms and applying Definition \\[defn:fanineq\\] yields the desired inequality .", "\n\nWe combine results in part (1) of Lemmas \\[lem:adjch\\] and \\[lem:adjchineq\\] to obtain the following reformulated description for diamond submodular inequalities. ", "The proof is straightforward, so is omitted.", "\n\n\\[cor:diamond\\] Let $(\\pi,\\tau) \\in \\fS_{d+1}\\times \\fS_d$ and $1 \\le r < d.$ If we let $\\tau' = (r, r+1)\\circ \\tau,$ then $\\ch(\\pi,\\tau)$ and $\\ch(\\pi, \\tau')$ form a pair of $r$-adjacent maixmal chains and their associated diamond submodular inequality can be written as: $$b_{{{\\mathcal T}}(\\pi,\\tau; r-1)} - b_{{{\\mathcal T}}(\\pi,\\tau; r)} \\le b_{{{\\mathcal T}}(\\pi,\\tau'; r)} - b_{{{\\mathcal T}}(\\pi,\\tau'; r+1)}. ", " \n \\label{equ:refdia}$$\n\nWhile the diamond submodular inequalities are in a simple form that is easy to describe, the inequalities arise from the situation are relative messy. ", "Fortunately, given the diamond submodular inequalities, in particular their reformulations given in Corollary \\[cor:diamond\\], we only need to consider a subset of the ones from the situation. ", "In fact, for each rank-$1$ ${{\\mathcal T}}_1$ element of ${{\\mathcal O}}_{d+1},$ we only need one inequality constructed from a shape containing ${{\\mathcal T}}_1.$\n\n\\[lem:ess\\] Let ${{\\mathcal T}}= {{\\mathcal T}}_1 = s_1|s_2|\\cdots|s_{i-1}|s_i s_i'|s_{i+1}|\\cdots|s_d$ be an element ${{\\mathcal O}}_{d+1}$ of rank $1.$ It covers exactly two rank-$0$ elements ${{\\mathcal T}}_0$ and ${{\\mathcal T}}_0'$ as given in . ", "We also let $${{\\mathcal S}}:= s_1 s_2 \\cdots s_{i-1} | s_i s_i' | s_{i+1}\\cdots s_d$$ be the maximum element that is above ${{\\mathcal T}}$ and still contains $\\{s_i,s_i'\\}$ as a single block. ", "Note that ${{\\mathcal S}}$ is of rank $d-1$ if $i=1$ or $d,$ and is of rank $d-2$ otherwise.", "\n\nAssume all the hypothesis in Lemma \\[lem:adjchineq\\], including those assumption in part (ii) for the situation. ", "Moreover, assume further the common rank-$1$ element of $\\ch_1$ and $\\ch_2$ is the ${{\\mathcal T}}_1$ given above. ", "Clearly, ${{\\mathcal T}}_0, {{\\mathcal T}}_0'$ are the two rank-$0$ elements.", "\n\n(a) If $S$ is a common element of $\\ch_1$ and $\\ch_2,$ then the associated inequality $I_{\\{\\sigma_1, \\sigma_2\\}}({\\textbf{b}})$ becomes: $$\\label{equ:essineq}\n 2 b_{{\\mathcal T}}+ b_{{\\mathcal S}}\\le b_{{{\\mathcal T}}_0} + b_{{{\\mathcal T}}_0'} + \\underbrace{b_{[d+1]}}_{\\text{eliminated if $i=1$}}.$$\n\n(b) If we do not assume ${{\\mathcal S}}$ is a common element of $\\ch_1$ and $\\ch_2,$ then the associated inequality $I_{\\{\\sigma_1, \\sigma_2\\}}({\\textbf{b}})$ can be deduced from the inequality and all the diamond submodular inequalities.", "\n\nWe remark that the term $b_{[d+1]}$ in can be removed even when $i \\neq 1$ as we have the assumption $b_{[d+1]}=0$. However, as we stated in Remark \\[rem:balance\\], we keep this term to make our inequality balanced.", "\n\nBoth parts of the lemma can be verified in three cases: (i) When $i=1$, and ${{\\mathcal S}}$ is of rank $d-1;$ (ii) when $i=d,$ and ${{\\mathcal S}}$ is of rank $d-1;$ (iii) when $i\\neq 1$ or $d$, and ${{\\mathcal S}}$ is of rank $d-2.$ The proofs for all cases are similar. ", "Therefore, we only present the one for case (i) where $i=1.$\n\n(a) Since $i=1,$ we immeidately have that $p = \\tau(i-1)=0.$ The element ${{\\mathcal S}}= s_1 s_1'|s_2 s_3 \\cdots s_d$ is of rank $d-1,$ and so is the second element ${{\\mathcal T}}_{d-1}$ from the top on the maximal chain $\\ch_1=\\ch(\\pi_1,\\tau_1)=\\ch(\\pi_1,\\tau).$ By the construction of $\\ch(\\pi_1,\\tau),$ the top element ${{\\mathcal T}}_d = \\hat{1}=[d+1]$ in $\\ch_1$ was obtained from ${{\\mathcal S}}$ by removing the bar at the $2$nd position, which means $q = \\tau(i+1)=\\tau(2)=d$. Plugging these information into , we obtain .", "\n\n(b) We may assume $d \\ge 2$ since if $d=1,$ there is only one inequality arising from the situation (and no diamond submodular inequalities). ", "As in the previous part, we have $p=\\tau^{-1}(i-1)=0.$ Since $d \\ge 2,$ we have $q = \\tau(i+1) = \\tau(2) \\neq d+1.$ Hence, the associated inequality is $$2b_{{{\\mathcal T}}_1} + b_{[d+1]} + \\left(b_{{{\\mathcal T}}_{q-1}}-b_{{{\\mathcal T}}_{q}}\\right) \\le b_{{{\\mathcal T}}_0} + b_{{{\\mathcal T}}_0'}.$$ Comparing it with , we see that it is enough to show the following inequality can be deduced from all the diamond submodular inequalities: $$\\label{equ:mdia} b_{{{\\mathcal T}}_{q-1}}-b_{{{\\mathcal T}}_{q}} \\le b_{{\\mathcal S}}- b_{[d+1]}.$$ Clearly, if $q=d,$ the equality holds. ", "So we assume $q < d.$ Let $\\gamma_0 = \\tau,$ and for each $1 \\le i \\le d-q,$ let $\\gamma_i = (q+i, q+i-1) \\circ \\gamma_{i-1}.$ Then $\\gamma_i(2) = q+i.$ In particular, $\\gamma_{d-q}(2) = d.$ Therefore, we have $${{\\mathcal T}}_{q-1} = {{\\mathcal T}}(\\pi_1,\\gamma_0; q-1), {{\\mathcal T}}_{q} = {{\\mathcal T}}(\\pi_1,\\gamma_0; q), \\quad \\text{and} \\quad {{\\mathcal S}}= {{\\mathcal T}}(\\pi_1, \\gamma_{d-q}; d-1), [d+1] = {{\\mathcal T}}(\\pi_1,\\gamma_{d-q}; d).$$\n\n We apply Corollary \\[cor:diamond\\] ($d-q$) times with $\\pi = \\pi_1$ and $(\\tau,\\tau') = (\\gamma_{i-1}, \\gamma_i)$ for all $1 \\le i \\le d-q,$ and obtain $d-q$ diamond submodular inequalities in the form of . ", "Adding these inequalities together yields the desired inequality .", "\n\nWe see that the inequality only depends on ${{\\mathcal T}}= {{\\mathcal T}}_1$, as ${{\\mathcal T}}_0, {{\\mathcal T}}_0'$ and ${{\\mathcal S}}$ are all determined by ${{\\mathcal T}}.$ Hence, we denote the inequality by $I_{{{\\mathcal T}}}({\\textbf{b}})$, and call it the *essential inequality* associated with the rank-$1$ element ${{\\mathcal T}}={{\\mathcal T}}_1.$\n\n\\[ex:ess\\] In Figure \\[fig:renex\\], we give an example of the proof of part (b) of Lemma \\[lem:ess\\], showing how to use diamond submodular inequalities to reduce an arbitrary inequality to an essential one. ", "We start with the pair of adjacent chains given by the circled elements, $\\ch_1= ({{\\mathcal T}}_0,{{\\mathcal T}}_1,{{\\mathcal T}}_2,{{\\mathcal T}}_3,{{\\mathcal T}}_4)$ and $\\ch_2=({{\\mathcal T}}_0',{{\\mathcal T}}_1,{{\\mathcal T}}_2,{{\\mathcal T}}_3,{{\\mathcal T}}_4)$. Their associated inequality is $$\\label{equ:exineq}\n 2b_{{{\\mathcal T}}_1}+ b_{[5]} + (b_{{{\\mathcal T}}_1} - b_{{{\\mathcal T}}_2}) \\leq b_{{{\\mathcal T}}_0}+b_{{{\\mathcal T}}_0'}.$$ However, using the two diamonds shown in Figure \\[fig:renex\\], we obtain that $$b_{{{\\mathcal T}}_1} - b_{{{\\mathcal T}}_2}\\le b_{{{\\mathcal T}}_2'} - b_{{{\\mathcal T}}_3}\\leq b_{{{\\mathcal T}}_3'}-b_{{{\\mathcal T}}_4} = b_{53|142} - b_{[5]}.$$ This shows that the inequality can be deduced from the above two diamond submodular inequalities and the following inequality: $$2b_{{{\\mathcal T}}_1}+ b_{[5]} + (b_{53|142} - b_{[5]}) = 2b_{{{\\mathcal T}}_1} + b_{53|142} \\leq b_{{{\\mathcal T}}_0}+b_{{{\\mathcal T}}_0'},$$ which is exactly the essential inequality associated to ${{\\mathcal T}}_1.$\n\n![", "Illustration of Lemma \\[lem:ess\\][]{data-label=\"fig:renex\"}](renex.eps)\n\nAll the discussion above, together with Proposition \\[prop:reduxfan\\] and Remark \\[rem:equivsub\\], gives us the first main result of this part. ", "Recall that ${{\\mathcal O}}_{d+1}$ is locally boolean (Lemma \\[lem:localbool\\]), so we can define $\\wedge$ and $\\vee$ on any pair of elements in an interval.", "\n\n\\[thm:centralsub2\\] The deformation cone of the nested Braid fan (or centralized nested regular permutohedron) is the collection of ${\\textbf{b}}\\in {\\mathbb{R}}^{\\overline{{{\\mathcal O}}_{d+1}}}$ satisfying the following conditions:\n\n1. ", " (Local submodularity) All the diamond submodular inequalities on ${{\\mathcal O}}_{d+1}$ are satisfied, or equivalently, for any maximal interval $[{{\\mathcal T}}(\\pi), \\hat{1}]$, $$\\label{equ:bsub2}\n b_{{{\\mathcal S}}\\vee {{\\mathcal T}}} + b_{{{\\mathcal S}}\\wedge {{\\mathcal T}}} \\le b_{{{\\mathcal S}}} + b_{{{\\mathcal T}}}, \\quad \\forall {{\\mathcal S}}, {{\\mathcal T}}\\in [{{\\mathcal T}}(\\pi),\\hat{1}].$$\n\n2. ", " ( condition) For any rank-$1$ element ${{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}},$ its associated essential inequality $I_{{{\\mathcal T}}}({\\textbf{b}})$ holds.", "\n\nFor both part, we assume $b_{\\hat{1}} = b_{[d+1]} = 0.$\n\nIf we remove the condition $b_{[d+1]}=0$ which corresponds to the centralized cases, we get a theorem that characeterize all generalized nested permutohedra, analogous to Theorem \\[thm:submodrestate\\].", "\n\n\\[thm:sub2\\] For ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$ satisfying the local submodularity condition and the condition described in Theorem \\[thm:centralsub2\\], the linear system: $$\\label{equ:linear3}\n \\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ b_{[d+1]}, \\quad \\text{and} \\quad \n \\langle {\\textbf{e}}_{{\\mathcal T}}, {\\textbf{x}}\\rangle \\ \\le \\ b_{{\\mathcal T}}, \\quad \\forall {{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}}$$ defines a generalized nested permutohedron in ${\\mathbb{R}}^{d+1},$ and any generalized nested permutohedron arises this way uniquely.", "\n\nFurthermore, if a polytope $P \\in {\\mathbb{R}}^{d+1}$ is defined by a tight representation , then $P$ is a generalized nested permutohedron if and only if ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$ satisfies the local submodularity condition and the condition.", "\n\nThe proof is similar to that of Theorem \\[thm:submodrestate\\], and we only give a sketch of the proof for the first part. ", "The one-to-one correspondence between centralized nested permutohedra and ${\\textbf{b}}$’s satisfying the local submodularity condition and the condition with $b_{[d+1]}=0$ is established by Theorem \\[thm:centralsub2\\].", "\n\nSuppose ${\\textbf{b}}\\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$. Let $k = \\frac{b_{[d+1]}}{d+1}$ and define a new vector/function ${\\textbf{b}}' \\in {\\mathbb{R}}^{{{\\mathcal O}}_{d+1}}$ by $${\\textbf{b}}'_{{\\mathcal T}}= {\\textbf{b}}_{{\\mathcal T}}- k \\cdot \\card({{\\mathcal T}}), \\quad \\forall {{\\mathcal T}}\\in {{\\mathcal O}}_{d+1},$$ where $\\card({{\\mathcal T}}) = \\left\\langle {\\textbf{e}}_{{{\\mathcal T}}}, \\1 \\right\\rangle = \\sum_{i} i |S_i|,$ if ${{\\mathcal T}}= (S_1,S_2 ,\\cdots ,S_k)$.\n\nLet $P$ and $Q$ be the polytopes defined by the linear system with vectors ${\\textbf{b}}$ and ${\\textbf{b}}'$ respectively. ", "Then we have the following facts:\n\n1. ", " ${\\textbf{b}}'_{[d+1]} =0.$\n\n2. ", " ${\\textbf{b}}'$ satisfies the local submodularity condtion and the condition if and only if ${\\textbf{b}}$ satisfies these two conditions as well.", "\n\n3. ", " $Q =\\tilde{P} = P - k \\1$ is the centralized version of $P.$\n\nFacts (1) and (3) are straightforward to check, and fact (2) follows from that all the inequalities we describe are balanced. (", "See Remark \\[rem:balance\\].) ", "We see the first conclusion of the theorem follows from these facts and the arguments in the first paragraph.", "\n\n\\[ex:unexampleII\\]\n\nRecall that the polytope $P \\subset {\\mathbb{R}}^4$ considered in Example \\[ex:unexample\\]. ", "We already mentioned that $P$ is the cube whose vertices are $(1,1,1,3)$ and $(0,2,2,2)$ and their permutations. ", "Furthermore, by discussing edge directions, we conclude that $P$ is not a generalized permutohedron. ", "Another way to see this is by looking at the normal cones of $P$ at each vertex. ", "For example, let $\\sigma$ be the normal cone of $P$ at the vertex $(0,2,2,2).$ One can show that $\\sigma$ is spanned by $3$ rays in ${\\textrm{Br}}_3$: ${\\textbf{e}}_{\\{2,3\\}}, {\\textbf{e}}_{\\{3,4\\}}, {\\textbf{e}}_{\\{2,4\\}}.$ However, another ray ${\\textbf{e}}_{ \\{2,3,4\\}}$ of ${\\textrm{Br}}_3$ is in the middle of $\\sigma.$ As a result, $\\sigma$ cuts through $6$ maximal cones of ${\\textrm{Br}}_3$, and thus is not a union of maximal cones in ${\\textrm{Br}}_3.$ Figure \\[fig:nonexample\\]/(A) depicts a slice of these $6$ cones where the shaped region corresponds to the normal cone $\\sigma.$ Hence, the normal fan of $P$ does not refine ${\\textrm{Br}}_3,$ and by Proposition \\[prop:coarser\\], $P$ is not a generalized permutohedron.", "\n\n[.5]{} ![", "Comparison of a normal cone $\\sigma$ in ${\\textrm{Br}}_3$ and ${\\textrm{Br}}_3^2$[]{data-label=\"fig:nonexample\"}](nonexample1.eps \"fig:\"){width=\".6\\linewidth\"}\n\n[.5]{} ![", "Comparison of a normal cone $\\sigma$ in ${\\textrm{Br}}_3$ and ${\\textrm{Br}}_3^2$[]{data-label=\"fig:nonexample\"}](nonexample2.eps \"fig:\"){width=\".6\\linewidth\"}\n\nHowever, in ${\\textrm{Br}}_3^2,$ each maximal cone of ${\\textrm{Br}}_3$ was subdivided into $6$ cones. ", "Figure \\[fig:nonexample\\]/(B) shows how the maximal cones in Figure \\[fig:nonexample\\]/(A) were subdivided, where the dark dots are rays in ${\\textrm{Br}}_3^2.$ One sees that $\\sigma$ is a union of maximal cones in ${\\textrm{Br}}_3^2.$ Similarly, all the other normal cones of $P$ are unions of maximal cones in ${\\textrm{Br}}_3^2.$ Hence, normal fan of $P$ refines ${\\textrm{Br}}_3^2$. Thus, $P$ is a generalized *nested* permutohedron.", "\n\nChiseling Constructions {#sec:chisel}\n=======================\n\nVictor Reiner asked whether it is true that ${\\textrm{Br}}_d^2$ is the barycentric subdivision of ${\\textrm{Br}}_d.$ The main purpose of this section is to give an affirmative answer to his question. ", "We start by introducing the concept of *chiseling* off faces of a polytope, which will be used to construct *barycentric subdivision*.", "\n\n\\[defn:chisel\\] Suppose $G$ is a face of a $d$-dimensional polytope $P\\subset V.$ Let $F_1,\\cdots F_l$ be the facets containing $G$ with primitive outer normals ${\\textbf{a}}_1,\\cdots, {\\textbf{a}}_l$ respectively; in other words, ${\\textbf{a}}_1,\\cdots, {\\textbf{a}}_l$ are the spanning rays of the normal cone $\\ncone(G,P)$. Define the *chiseling direction of $P$ at $G$* to be $${\\textbf{a}}_G :={\\textbf{a}}_1+\\cdots+ {\\textbf{a}}_l.$$ Furthermore, let $b_G$ be the scalar such that $G = P \\cap \\{ {\\textbf{x}}\\in V \\ : \\ \\langle {\\textbf{a}}_G, {\\textbf{x}}\\rangle = b_G \\}$; equivalently, $$b_G := \\max_{{\\textbf{x}}\\in P} \\langle {\\textbf{a}}_G, {\\textbf{x}}\\rangle.$$ For any sufficiently small $\\epsilon>0$ such that $\\{{\\textbf{x}}: \\langle {\\textbf{a}}_G,{\\textbf{x}}\\rangle < b_G-\\epsilon\\}$ contains all vertices of $P$ not in $G$, we define $P_\\epsilon:=P\\cap \\{{\\textbf{x}}\\ : \\ \\langle {\\textbf{a}}_G,{\\textbf{x}}\\rangle \\leq b_G-\\epsilon\\}$ to be the polytope obtained by *chiseling $G$ off $P$ (at distance $\\epsilon$)*. ", "We call the facet $P \\cap \\{{\\textbf{x}}: \\langle {\\textbf{a}}_G,{\\textbf{x}}\\rangle = b_G-\\epsilon\\}$ of $P_\\epsilon$ created by this process the *facet obtained by chiseling $G$ off $P$*.", "\n\nLet $G_1, \\dots, G_k$ be faces of $P.$ We say $G_1, \\dots, G_k$ can be *simultaneously chiseled off $P$ at distance $\\epsilon$* if for any $1 \\le i < j \\le k$ the facet obtained by chiseling $G_i$ off $P$ at distance $\\epsilon$ has no intersection with the facet obtained by chiseling $G_j$ off $P$ at distance $\\epsilon.$\n\nSee Figure \\[fig:chisel\\] for a picture of chiseling off a vertex from a polygon.", "\n\n![", "Chiseling off a vertex from a polygon. ", "The set $\\{{\\textbf{x}}: \\langle {\\textbf{a}}_G,{\\textbf{x}}\\rangle = b_G-\\epsilon\\}$ is given by the thick line, whereas the other is the dashed line.[]{data-label=\"fig:chisel\"}](chisel.eps)\n\nIt is easy to see that $G_1, \\dots, G_k$ can be simultaneously chiseled off $P$ at a sufficient small distant $\\epsilon>0$ if and only if $G_1,\\dots,G_k$ are pairwise disjoint.", "\n\nTo chisel a face $G$ of a polytope $P$ correspond to make a *stellar subdivision* on $\\Sigma(P)$ along $\\ncone(G,P)$ (See [@ewald Section III.2]).", "\n\nSuppose $\\Sigma$ is a projective fan in $W$ such that $0 \\in \\Sigma.$ The following algorithm gives one way to obtain the barycentric subdivision of $\\Sigma$.\n\n\\[alg:bary\\]\n\n(1) Let $P_0=P$ be a $d$-polytope whose normal fan is $\\Sigma$.\n\n(2) Let $\\epsilon_1 > 0$ be a sufficiently small number such that we can simultaneously chisel all vertices off $P_0$ at distance $\\epsilon_1$, and let $P_1$ be the polytope obtained from $P_0$ by applying these chiselings.", "\n\n(3) Let $E_1, \\dots, E_m$ be the edges of $P_1$ that come from $P_0$, that is, edges that are not created from the chiselings done in the steps above. ", "Let $\\epsilon_2>0$ be a sufficiently small number such that we can simultaneously chisel $E_1, \\dots, E_m$ off $P_1$ at distance $\\epsilon_2$, and let $P_2$ be the polytope obtained from $P_1$ by applying these chiselings.", "\n\n(4) …\n\n(5) (6) Let $F_1, \\dots, F_d$ be the $(d-1)$-dimensional faces of $P_{d-1}$ that come from $P_0.$ Let $\\epsilon_d >0$ be a sufficiently small number such that we can simultaneously chisel $F_1, \\dots, F_n$ off $P_{d-1}$ at distance $\\epsilon_d$, and let $P_d$ be the polytope obtained from $P_{d-1}$ by applying these chiselings.", "\n\nIt follows from [@ewald Definition 2.5, Section III.2] that the normal fan of $P_d$ obtained by Algorithm \\[alg:bary\\] is the *barycentric subdivision* of $\\Sigma.$\n\nFor any $k > 0, $ the set of all $k$-dimensional faces of a polytope $P$ cannot be simultaneously chiseled, since they are not pairwise disjoint. ", "However, they do become pairwise disjoint after $k$ steps of Algorithm \\[alg:bary\\]. ", "For instance, the set of all edges of $P_0$ is clearly not pairwise disjoint, but the resulting edges after chiseling all vertices of $P_0$ are pairwise disjoint and can be simultaneously chiseled.", "\n\nThe barycentric subdivision of the normal fan of a polytope should not be confused with the barycentric subdivision of the polytope itself. ", "For any polytope $P$, its barycentric subdivision is a triangulation of $P$, whereas the barycentric subdivision of a fan is again a fan. ", "Furthermore Algorithm \\[alg:bary\\] shows that it preserves projectivity.", "\n\nThe following lemma, which follows immediately from the construction of $P_d,$ will be usful in our discusion.", "\n\n\\[lem:Pd\\] The resulting polytope $P_d$ (of Algorithm \\[alg:bary\\]) is a full-dimensional polytope in the same $d$-dimensional affine space as $P_0,$ and is defined by the following linear system: $$\\langle {\\textbf{a}}_G, {\\textbf{x}}\\rangle \\le b_G - \\epsilon_{\\dim(G)+1}, \\quad \\text{for all nonempty proper faces $G$ of $P$},$$ where ${\\textbf{a}}_G$ and $b_G$ are as defined in Definition \\[defn:chisel\\], and $\\epsilon_i$’s are the chiseling distances given in Algorithm \\[alg:bary\\].", "\n\nWe are now ready to state the main result, Theorem \\[thm:bary2\\], of this section, preceded by a classical result, Theorem \\[thm:bary1\\], that is related to Reiner’s question, Recall that the *standard $d$-simplex* is $\\Delta_d := {\\textrm{conv}}\\{ {\\textbf{e}}_1, \\dots, {\\textbf{e}}_{d+1}\\}$. Theorem \\[thm:bary1\\] follows from Remark 6.6 in [@PosReiWil].", "\n\n\\[thm:bary1\\] The Braid fan ${\\textrm{Br}}_d$ is the barycentric subdivision of the normal fan $\\Sigma(\\Delta_d)$ of $\\Delta_d$.\n\n\\[thm:bary2\\] The nested Braid fan ${\\textrm{Br}}_d^2$ is the barycentric subdivision of the Braid fan ${\\textrm{Br}}_d,$ and thus is the second barycentric subdivision of $\\Sigma(\\Delta_d).$\n\nAs a warmup, we give a proof for Theorem \\[thm:bary1\\] in which we use well-known facts about faces of the standard simplices.", "\n\nWe apply Algorithm \\[alg:bary\\] to $P_0 = \\Delta_d$, making sure that the chiseling distances $\\epsilon_i$’s satisfy: $$\\epsilon_1 < \\frac{1}{2}, \\quad \\text{and for $2 \\le i \\le d,$} \\quad \\epsilon_i < \\frac{\\epsilon_{i-1}}{2}.", "\n\\label{equ:tiny}$$ It is sufficient to show that the resulting polytope $P_d$ is a usual permutohedron. ", "In order to do this, we will apply Lemma \\[lem:Pd\\] to find an inequality description for $P_d.$\n\nFirst, note that $\\Delta_d$ is a full-dimensional polytope in the affine space $$\\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ 1.$$ Next, faces of $\\Delta_d$ are naturally indexed by subsets of $[d+1]$. For each $S \\subseteq [d+1]$, the corresponding face is ${\\textrm{conv}}\\{{\\textbf{e}}_i: i\\in S\\}$, which we denote by $G_S.$ Recall that for any $\\emptyset \\neq S \\subsetneq [d+1],$ the normal cone of $\\Delta_d$ at $G_S$ is generated by $\\{-{\\textbf{e}}_j:j\\notin I\\}$. Hence, the chiseling direction of $\\Delta_d$ at $G_S$ is $\\sum_{j\\notin I} -{\\textbf{e}}_j$. As the normal fan is defined in $W_d$, where ${\\textbf{e}}_{[d+1]} = \\sum_{i\\in[d+1]} {\\textbf{e}}_i=0$, this chiseling direction can be written as ${\\textbf{e}}_S=\\sum_{i\\in S} {\\textbf{e}}_i$. Finally, let $$b_S := \\max_{{\\textbf{x}}\\in \\Delta_d} \\langle {\\textbf{e}}_S, {\\textbf{x}}\\rangle = 1.$$\n\nTherefore, by Lemma \\[lem:Pd\\], the polytope $P_d$ is given by the following linear system: $$\\label{eq:chiselex}\n \\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ 1, \\quad \\text{and} \\quad \n \\langle {\\textbf{e}}_S, {\\textbf{x}}\\rangle \\ \\le \\ b_S-\\epsilon_{\\dim(G_S)+1}=1-\\epsilon_{|S|}, \\quad \\forall \\emptyset \\neq S \\subsetneq [d+1].$$ It follows from that $$\\epsilon_d < \\epsilon_{d-1}-\\epsilon_d < \\epsilon_{d-2}-\\epsilon_{d-1} < \\cdots < \\epsilon_1- \\epsilon_2 < 1 - \\epsilon_1,\n \\label{equ:tiny1}$$ using which one can show that the right hand side of is a submodular function, so that Theorem \\[thm:submodular\\] applies. ", "More directly, one can show that $P_d$ is the usual permutohedron $\\Perm(\\balpha)$ with $$\\balpha = \\Big(\\epsilon_d, \\epsilon_{d-1}-\\epsilon_d, \\epsilon_{d-2}-\\epsilon_{d-1}, \\dots, \\epsilon_1- \\epsilon_2, 1 - \\epsilon_1\\Big).$$\n\nWe are going to prove Theorem \\[thm:bary2\\] in a parallel fashion. ", "Before that, we give the following preliminary lemma.", "\n\n\\[lem:bij\\] There exists a one-to-one correspondence between $(d-k)$-faces of $\\Pi_d$ and ordered set partitions with $k+1$ parts in $\\overline{{{\\mathcal O}}_{d+1}}$ such that if we let $G_{{\\mathcal T}}$ be the face corresponds to the ordered set partition ${{\\mathcal T}},$ then the chiseling direction of $\\Pi_d$ at $G_{{\\mathcal T}}$ is ${\\textbf{e}}_{{\\mathcal T}}.$\n\nIt follows from Propositions \\[prop:fanofusual\\] and \\[prop:charbr\\] that each $(d-k)$-dimensional face $G$ of $\\Pi_d$ corresponds with a $k$-chain in $\\overline{{{\\mathcal B}}_{d+1}}:$ $$\\label{equ:kchain} \n \\emptyset \\subsetneq S_1 \\subsetneq S_2 \\subsetneq \\cdots \\subsetneq S_k \\subsetneq [d+1]$$ such that the normal cone of $G$ is spanned by ${\\textbf{e}}_{S_1}, {\\textbf{e}}_{S_2}, \\cdots, {\\textbf{e}}_{S_k}.$\n\nFor each $k$-chain in the form of , we associate with it the ordered set partition ${{\\mathcal T}}= T_1 | T_2 | \\cdots | T_k | T_{k+1}$, where $$T_1 = [d+1] \\setminus S_k, \\quad T_2 = S_k \\setminus S_{k-1}, \\quad \\dots, \\quad T_{k} = S_2\\setminus S_1, \\quad T_{k+1} = S_1.$$ One sees that this established a bijection between $k$-chains in $\\overline{{{\\mathcal B}}_{d+1}}$ and ordered set partitions in $\\overline{{{\\mathcal O}}_{d+1}},$ and hence induces a bijection between nonempty proper faces of $\\Pi_d$ and ordered set partitions in $\\overline{{{\\mathcal O}}_{d+1}}$. Furthermore, suppose $G$ is in bijection with ordered set partition ${{\\mathcal T}}$ through the $k$-chain . ", "Then the chiseling direction of $\\Pi_d$ at $G$ is $$\\sum_{i=1}^k {\\textbf{e}}_{S_i} = \\sum_{i=1}^k \\sum_{j=k+2-i}^{k+1} {\\textbf{e}}_{T_j} = \\sum_{j=2}^{k+1} (j-1) {\\textbf{e}}_{S_j}.$$ As the normal fan is defined in $W_d$, where ${\\textbf{e}}_{[d+1]}=\\sum_{i\\in[d+1]} {\\textbf{e}}_i=0$, the above chiseling direction can be written as $$\\sum_{j=2}^{k+1} (j-1) {\\textbf{e}}_{S_j} + {\\textbf{e}}_{[d+1]} = \\sum_{j=1}^{k+1} j {\\textbf{e}}_{S_j} = {\\textbf{e}}_{{{\\mathcal T}}}.$$\n\nWe apply Algorithm \\[alg:bary\\] to $P_0 = \\Pi_d$, making sure that the chiseling distances $\\epsilon_i$’s satisfy $$\\epsilon_1 < \\frac{1}{4}, \\quad \\text{and for $2 \\le i \\le d,$} \\quad \\epsilon_i < \\frac{\\epsilon_{i-1}}{2}.", "\n \\label{equ:tiny2}$$ Similar to the proof of Theorem \\[thm:bary1\\], we will show $P_d$ is a usual nested permutohedron. ", "First, $\\Pi_d$ is a full-dimensional polytope in the affine space $$\\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ \\sum_{j=1}^{d+1} j =: b_{[d+1]}.$$ Next, for each ${{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}},$ let $G_{{\\mathcal T}}$ be its corresponding face of $\\Pi_d$ assumed by Lemma \\[lem:bij\\]. ", "Then the chiseling direction of $G_{{\\mathcal T}}$ at $\\Pi_d$ is ${\\textbf{e}}_{{\\mathcal T}}.$ By Lemma \\[lem:Pd\\], the polytope $P_d$ is defined by the linear system: $$ \\langle {\\textbf{e}}_{[d+1]}, {\\textbf{x}}\\rangle = \\langle \\1, {\\textbf{x}}\\rangle \\ = \\ b_{[d+1]}, \\quad \\text{and} \\quad \n \\langle {\\textbf{e}}_{{\\mathcal T}}, {\\textbf{x}}\\rangle \\ \\le \\ b_{{\\mathcal T}}- \\epsilon_{d-k+1}, \\quad \\forall {{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}},$$ where $b_{{{\\mathcal T}}} := \\max_{{\\textbf{x}}\\in \\Pi_d} \\langle {\\textbf{e}}_{{{\\mathcal T}}}, {\\textbf{x}}\\rangle.$ Suppose $\\Type({{\\mathcal T}})=(t_0, t_1,t_2,\\dots, t_k, t_{k+1})$ (see Defintion \\[defn:type\\] for the definition of structure type). ", "Then we can compute that $$b_{{{\\mathcal T}}} = \\left( \\sum_{i=1}^{k+1} i \\sum_{j=t_{i-1}+1}^{t_i} j\\right).$$ Note the above formula for $b_{{{\\mathcal T}}}$ not only works for ${{\\mathcal T}}\\in \\overline{{{\\mathcal O}}_{d+1}}$, also works for ${{\\mathcal T}}= [d+1].$\n\nIt follows from that $$0 < \\epsilon_d < \\epsilon_{d-1}-\\epsilon_d < \\epsilon_{d-2}-\\epsilon_{d-1} < \\cdots < \\epsilon_1- \\epsilon_2 < \\epsilon_1 < \\frac{1}{4}.$$ Hence, $$\\bbeta := \\Big( \\epsilon_2-\\epsilon_1, \\epsilon_3 - \\epsilon_2, \\dots, \\epsilon_d-\\epsilon_{d-1}, -\\epsilon_d\\Big)$$ is a strictly increasing sequence, where the abosolute value of each entry is strictly smaller than $\\frac{1}{4}.$ Therefore, letting $\\balpha:=(1,2,\\dots, d+1),$ one checks that $(M,N)=(1,1)$ is an appropriate choice for $(\\balpha,\\bbeta).$ Thus, it follows from Theorem \\[thm:facetdes\\] that $P_d$ is the usual nested permutohedron $\\Perm(\\balpha, \\bbeta;1,1).$\n\nQuestions {#sec:question}\n=========\n\nWe finish with questions that might be of interest for future research.", "\n\n1. ", " Notice that in the case of the usual permutohedron $\\Perm(\\balpha),$ we always have $v_\\pi^\\balpha \\in C(\\pi)$ for each $\\pi$, which is a property that makes notation natural. ", "It is not always the case that for a usual nested permutohedron $\\Perm(\\balpha,\\bbeta; M,N)$ we have $v_{\\pi,\\tau}^{(\\balpha,\\bbeta)(M,N)}\\in C(\\pi,\\tau)$ for each $(\\pi,\\tau)$. Does there exist any usual or generalized nested permutohedron with this property?", "\n\n2. ", " Is there a way to realize the permuto-associahedron [@zie Lecture 9.3] as a deformation of the regular nested permutohedron?", "\n\n3. ", " The nested Braid fan was defined by grouping together points with the same relative order of coordinates and their first differences. ", "One could go beyond and consider second differences, but this is **not** a subsequent barycentric subdivision. ", "Is this “doubly\" nested Braid fan a projective fan?", "\n\n4. ", " The barycentric subdivision of a fan is obtained from stellar subdivisions in a particular order. ", "If not done in the correct order the resulting fan is different. ", "Which sequences of stellar subdivisions of $\\Sigma(\\Delta_d)$ give coarsenings of ${\\textrm{Br}}_d$?", "\n\n5. ", " As mentioned before, one of the motivations of this paper was to define and study a class of polytopes whose edges are parallel to directions in the form of ${\\textbf{e}}_i+{\\textbf{e}}_j-{\\textbf{e}}_k-{\\textbf{e}}_\\ell$. The most direct way would be to first construct a fan from the hyperplane arrangement given by $x_i+x_j=x_k+x_\\ell$ for all tuples $(i,j,k,\\ell)$, including those with repeated elements, and then define a family of polytopes whose normal fans coarsen this new fan. ", "One issue that arises is that this hyperplane arrangement is not simplicial. ", "How many regions does it have? ", "Do they have a combinatorial interpretation?", "\n\nNormal cones and projective fans {#apd:normal}\n================================\n\nWe will give a proof for Proposition \\[prop:deform\\], proceeded by definitions of normal cones and normal fans. ", "Recall that $W$ is the dual space of $V.$ Thus, any ${\\textbf{w}}\\in W$ can be considered as a linear functional on $V.$\n\n\\[defn:normal\\] Suppose $P$ is a polytope in an affine space that is a translation of $V.$ Given a face $F$ of a polytope $P$, we define the *normal cone* of $P$ at $F$: $$\\ncone(F, P) := \\left\\{ {\\textbf{w}}\\in W: \\quad \\langle {\\textbf{w}}, {\\textbf{x}}\\rangle \\geq \\langle {\\textbf{w}}, {\\textbf{y}}\\rangle, \\quad \\forall {\\textbf{x}}\\in F,\\quad \\forall {\\textbf{y}}\\in P \\right\\}.$$ Therefore, $\\ncone(F,P)$ is the collection of linear functionals ${\\textbf{w}}$ in $W$ such that ${\\textbf{w}}$ attains maximum value at $F$ over all points in $P.$\n\nThe *normal fan* of $P$, denoted by $\\Sigma(P),$ is the collection of all normal cones of $P$ as we range over all faces of $P$.\n\nSince any linear functional ${\\textbf{w}}\\in W$ attains its maximum on some faces of $P$, normal fans are always complete.", "\n\nA fan $\\Sigma'$ is a *corsening* of another fan $\\Sigma$ if any cone in $\\Sigma'$ is the union of a set of cones in $\\Sigma.$ One can check that $\\Sigma'$ is a corsening of $\\Sigma$ if and only if any maximal cone in $\\Sigma'$ is the union of a set of maximal cones in $\\Sigma.$\n\nSuppose $Q$ is a deformation of $P_0$. Then there exists ${\\textbf{b}}\\in {\\mathbb{R}}^m$ such that conditions and of Definition \\[defn:deform0\\] are satisfied. ", "Let $v, u$ be described as in condition . ", "Then each of ${\\textbf{a}}_{i_1},\\dots, {\\textbf{a}}_{i_k}$ attains maximum value at $u$ over all points in $Q,$ and thus is in $\\ncone(u, Q).$ As ${\\textbf{a}}_{i_1},\\dots, {\\textbf{a}}_{i_k}$ are spanning rays of $\\ncone(v,P_0),$ we conclude that any maximal cone of $\\Sigma(P_0)$ is a subset of some maximal cone of $\\Sigma(Q)$. Since both $\\Sigma(P_0)$ and $\\Sigma(Q)$ are complete fans, we conclude that any maximal cone of $\\Sigma(Q)$ is the union of a set of maximal cones in $\\Sigma(P_0).$ Hence, $\\Sigma(Q)$ is a coarsening of $\\Sigma(P_0).$\n\nSuppose $\\Sigma(Q)$ is a coarsening of $\\Sigma(P_0).$ Let ${\\textbf{b}}= (b_i)_{i=1}^m$ where $$b_i := \\max_{{\\textbf{x}}\\in Q} \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle.", "\n\\label{equ:bi}$$ We will show that $Q$ is the deformation of $P$ with the deforming vector ${\\textbf{b}}$ by proving conditions and of Definition \\[defn:deform0\\] are satisfied.", "\n\nLet $v$ be a vertex of $P_0$ that lies on facets $F_{i_1}, F_{i_2}, \\dots, F_{i_k}$ of $P_0.$ Then $\\{ {\\textbf{a}}_{i_1}, \\dots, {\\textbf{a}}_{i_k}\\}$ are the generating rays for $\\ncone(v,P_0)$ and thus they belong to $\\ncone(u, Q)$ for some vertex $u$ of $Q$. Therefore, $$\\langle {\\textbf{a}}_{i_j}, u \\rangle = \\max_{{\\textbf{x}}\\in Q} \\langle {\\textbf{a}}_i, {\\textbf{x}}\\rangle = b_{i_j}, \\quad \\forall 1 \\le i \\le k.$$ Hence, condition of Definition \\[defn:deform0\\] follows.", "\n\nFinally, let $$Q' := \\{ {\\textbf{x}}\\in V \\ : \\ {\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}\\}.$$ It is left to show that $Q' = Q.$ One sees that it is enough to show that any vertex $u$ of $Q$ is a vertex $Q',$ and $\\ncone(u, Q) \\subseteq \\ncone(u,Q').$ Since $\\Sigma(Q)$ is a coarsening of $\\Sigma(P_0),$ we see any vertex $u$ of $Q$ arises in the way described in condition . ", "Hence, $u$ is the intersection of hyperplanes determined by taking equalities of a subset of inequlities in ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}}$ and satisfies the remaining inequalities. ", "This implies $u$ is a vertex of $Q'.$ Let $R_u := \\{ {\\textbf{a}}_{j_1}, \\dots, {\\textbf{a}}_{j_t}\\} \\subseteq \\{ {\\textbf{a}}_1, \\dots, {\\textbf{a}}_m\\}$ be the set of rays in $\\ncone(u,Q).$ Then $\\ncone(u,Q)$ is generated by rays in $R_u,$ and $$\\langle {\\textbf{a}}_{j_s}, u \\rangle = \\max_{{\\textbf{x}}\\in Q} \\langle {\\textbf{a}}_{j_s}, {\\textbf{x}}\\rangle = b_{j_s}, \\quad \\forall 1 \\le s \\le t.$$ Since $Q'$ is defined by ${\\textrm{A}}{\\textbf{x}}\\le {\\textbf{b}},$ which implies $\\langle {\\textbf{a}}_{j_s}, {\\textbf{x}}\\rangle \\le b_{j_s}$ for all ${\\textbf{x}}\\in Q$. Thus, $\\langle {\\textbf{a}}_{j_s}, u \\rangle = \\max_{{\\textbf{x}}\\in Q'} \\langle {\\textbf{a}}_{j_s},$ and so ${\\textbf{a}}_{j_s}$ belongs to $\\ncone(u,Q')$ for each $1 \\le s \\le t.$ It follows that $\\ncone(u,Q) \\subseteq \\ncone(u,Q').$\n" ]

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[ "Dotnet\n\ndotNet Protector is a powerful .NET code protection system that prevents your assemblies from being decompiled. ", "With dotNet Protector, your application is not simply obfuscated, but method bodies are encrypted. ", "EXE DLL, ASPNET and SQL assemblies can be protected. ", "You can protect a whole...\nPlatforms: Windows, Windows 8, Windows 7\n\nThis class library can be used for searching and importing various data about movies from \"Internet Movie Database\" (IMDb). ", "This library contains two main classes, for searching and for importing. ", "Search class is explained in the \"gdIMDbImporter Search\" class library.", "\nImport class can import...\nPlatforms: Windows\n\nUsing a web browser to send an SMS message can be a time consuming process, particularly if you want to send the same message or templated message to several different people. ", "Now you can use FreeSMS to automate this process from your Windows desktop. ", "FreeSMS can also be easily extended to work...\nPlatforms: Windows\n\nThe 3DChart for .NET component is a high quality native .NET component, which uses the Nevron 3D Engine for .NET to display sophisticated charts with stunning visual effects. ", "It can add interactive charts with presentation quality to your web and windows applications. ", "The key features of the...\nPlatforms: Windows\n\nLocalizer gives you everything you need to add powerful ASP.NET internationalization support to Microsoft Visual Studio 2002 / 2003, bringing the same set of localization features that Windows Forms programmers enjoy to the ASP.NET world.", "\nUntil now, a similar level of Visual Studio designer...\nPlatforms: Windows\n\nWebExtenders provide design and runtime time support for programming against javascript functions such as Alert, Confirm, Status and DefaultStatus in ASP.NET pages from within Microsoft Visual Studio.", "\nFeatures in Version 1.0.0.0\n* The ConfirmProvider component adds the ConfirmText property...\nPlatforms: Windows\n\nLingobit Localizer is a software localization tool that provides developers with an effective solution to facilitate and streamline the software localization process and communication between developers, translators and testers.", "\nUnique to Lingobit Localizer is its unified interface and...\nPlatforms: Windows\n\nDLLcc Real-Time Currency Exchange rates component provide real-time currency exchange to and from over than 150 different major currencies around the world , DLLcc is a .NET class library built entirely in C# for professional .NET developers who need to build .net e-commerce site or application...\nPlatforms: Windows\n\nCPIde is a lightweight powerful integrated development environment for Gardens Point Component Pascal. ", "It is used to develop Pascal / Oberon-style software for the Microsoft .NET framework. ", "As well as the standard programmer-oriented, text-editing features CPIde has additional language-aware...\nPlatforms: Windows\n\nDid you know that your contact database typically contains 3-10% duplicates? ", "These duplicate records result in unnecessary costs when sending out printed catalogs, create problems in the controlling, etc. ", "With classical methods you have no possibility to locate these duplicates in your database....\nPlatforms: Windows\n\nSkinCrafter skinning library, with full support for all Visual Studio .NET languages, is designed for professional .NET developers. ", "With SkinCrafter, you'll get the power to create a maximally customized interface implementing smooth and easy skinning for all standard Windows controls including...\nPlatforms: Windows\n\nSFTP (SSH File Transfer Protocol, also called Secure File Transfer Protocol) is a specialized protocol for secure file transfer over SSH channel. ", "SFTP is integral part of SSH 2 family of protocols and is supported by SSH servers. ", "SFTP doesn't have anything in common with FTP (File Transfer...\nPlatforms: Windows\n\nZipForge.", "NET is a fast and powerful ZIP compression component for .NET framework.", "\nIt lets you easily create zip files, extract files from zip archives to hard drive, add files to a zip archive, replace, move and delete files. ", "You can also read compressed files from a zip archive into memory,...\nPlatforms: Windows\n\nThe ASP .NET Barcode Web Server Control is a new drag-and-drop component that easily adds dynamic barcoding capability to Microsoft .NET Web Applications. ", "It is a server-side component that creates JPEG images, therefore all processing takes place on the server and it is compatible with all web...\nPlatforms: Windows\n\nImplement SFTP and SSH protocols in your .NET project quickly and reliably. ", "SFTP NET Managed is easy to learn and to use, and requires no experience in communication or security. ", "SFTP and SSH have never been easier in the .NET environment!", "\nDeploy your .NET server or client sooner with SFTP...\nPlatforms: Windows\n\nForm Designer .NET allows you move and resize any control on your .NET application form at runtime. ", "You need not prepare your form to use Form Designer .NET. ", "Just drop Form Designer .NET control onto any form, assign the DesignedForm property, set Active property to true and enjoy!", "\nAfter...\nPlatforms: Windows" ]

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[ "The eleventh version of the vintage Andrews’ illnesses of the outside, by means of Drs. ", "William D. James, Timothy G. Berger and Dirk M. Elston, presents the final word origin in dermatology with entire counsel to successfully diagnose and deal with a variety of pores and skin stipulations. ", "those hugely revered authors stability evidence-based remedy instructions with recommendation from their very own scientific adventure, supplying a pragmatic and sensible scientific point of view. ", "up-to-date all through with the most recent dermatologic findings and a brand new bankruptcy on beauty surgical concepts, this name is helping you retain present, increase your talents, and get ready for checks. ", "it's also on-line entry to the full textual content, photos, and bonus illustrations making this an fundamental, handy reference for trainees and training dermatologists.", "\n\nThe final word visible compendium of optimum suturing and wound fix perform, masking seventy five must-know techniquesAtlas of Suturing recommendations: techniques to Surgical Wound, Laceration, and Wound fix offers the construction blocks of suturing and wound fix in an at-a-glance, within your means atlas layout. ", "In its pages, the writer stocks his massive services and it truly is his goal to aid physicians throughout many specialties to enhance results for sufferers requiring fix of any wound.", "\n\nThe surface is the most important human organ procedure. ", "lack of dermis integrity as a result of damage or disorder leads to a considerable physiologic imbalance and eventually in critical incapacity or dying. ", "From burn sufferers to surgical scars and cosmetic surgery, the treatments as a result of epidermis tissue engineering and regenerative medication are vital to a wide spectrum of sufferers.", "\n\nA part of the sensible and dynamic approaches in beauty Dermatology sequence, Botulinum Toxin, 4th version, brings physicians in any respect degrees of expertise up to the mark with today’s top injection concepts. ", "This well-organized textual content presents present, authoritative information on renowned strategies together with masseter hypertrophy and darker dermis forms, the healing makes use of of botulinum pollutants, and their destiny in dermatology.", "\n\nInjections are minimally invasive and for that reason relatively well-liked by either plastic surgeons and dermatologists - in addition to the other practitioners devoted to the cultured box - with quicker methods and speedier restoration time. ", "This entire textbook, from a crew of specialists, records the preferred injection remedies - botulinum pollutants, fillers, and volumetric implants - and indicates how they might even be mixed for the easiest effects." ]

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[ "Pharmacokinetics and safety of intravenously administered citrulline in children undergoing congenital heart surgery: potential therapy for postoperative pulmonary hypertension.", "\nPulmonary hypertension may complicate surgical correction of congenital heart defects, resulting in increased morbidity and mortality. ", "We have previously shown that plasma levels of the nitric oxide precursors citrulline and arginine drop precipitously after congenital cardiac surgery and that oral citrulline supplementation may be protective against the development of pulmonary hypertension. ", "In this study, we assessed the safety and pharmacokinetic profile of intravenous citrulline as a potential therapy for postoperative pulmonary hypertension. ", "The initial phase of this investigation was a dose-escalation study of intravenously administered citrulline in infants and children undergoing one of five congenital cardiac surgical procedures (phase 1). ", "The primary safety outcome was a 20% drop in mean arterial blood pressure from the baseline pressure recorded after admission to the intensive care unit. ", "Based on our previous work, the target circulating plasma citrulline trough was 80 to 100 micromol/L. Each patient was given two separate doses of citrulline: the first in the operating room immediately after initiation of cardiopulmonary bypass and the second 4 hours later in the pediatric intensive care unit. ", "Stepwise dose escalations included 50 mg/kg, 100 mg/kg, and 150 mg/kg. ", "After model-dependent pharmacokinetic analysis, we enrolled an additional 9 patients (phase 2) in an optimized dosing protocol that replaced the postoperative dose with a continuous infusion of citrulline at 9 mg/(kg.h) for 48 hours postoperatively. ", "The initial stepwise escalation protocol (phase 1) revealed that an intravenous citrulline dose of 150 mg/kg given after initiation of cardiopulmonary bypass yielded a trough level of in the target range of approximately 80 to 100 micromol/L 4 hours later. ", "The postoperative dose revealed that the clearance of intravenously administered citrulline was 0.6 L/(h.kg), with a volume of distribution of 0.9 L/kg and estimated half-life of 60 minutes. ", "Because of the short half-life, we altered the protocol to replace the postoperative dose with a continuous infusion of 9 mg/(kg.h). ", "An additional 9 patients were studied with this continuous infusion protocol (phase 2). ", "Mean plasma citrulline levels were maintained at approximately 125 mumol/L, with a calculated clearance of 0.52 L/(h.kg). ", "None of the 17 patients studied had a 20% drop in mean arterial blood pressure from baseline. ", "In this first report of the use of intravenous citrulline in humans, we found citrulline to be both safe and well tolerated in infants and young children undergoing congenital cardiac surgery. ", "Because of the rapid clearance, the optimal dosing regimen was identified as an initial bolus of 150 mg/kg given at the initiation of cardiopulmonary bypass, followed 4 hours later by a postoperative infusion of 9 mg/(kg.h) continued up to 48 hours. ", "Using this regimen, plasma arginine, citrulline, and nitric oxide metabolite levels were well maintained. ", "Intravenous citrulline needs to be studied further as a potential therapy for postoperative pulmonary hypertension." ]

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[ "Since he won his first Grand Slam title in 2005, Rafael Nadal has accomplished everything tennis has to offer. ", "The 33-year-old has dominated the French Open, winning 12 times. ", "He’s won Wimbledon twice and the U.S. Open four times. ", "He helped Spain to the Davis Cup title five times. ", "He won Olympic gold in 2008 in singles and 2016 in doubles.", "\n\nSimply put, Nadal is extraordinary in every way. ", "There’s just one weak spot, and it makes no sense: The man who has solved every puzzle in tennis can’t figure out the Australian Open.", "\n\nNadal has a perfect 12-0 record in French Open finals and a 4-1 record in the finals of the U.S. Open. ", "At Wimbledon, he is 2-3 in finals. ", "At the Australian, he is only 1-4.", "\n\nNadal prevailed (6-3, 3-6, 7-6, 7-6) on Monday over Nick Kyrgios. ", "He is now three wins away from his 20th Grand Slam singles title, which would tie him with Roger Federer for the record among the men. ", "If he won the Australian and went on to win the French Open for the 13th time, he would surpass Federer. ", "But first, he needs to conquer Melbourne again.", "\n\nNadal won his only Australian Open title in 2009, at just 22 years old. ", "He was young, fit and determined. ", "It seemed like he would win the major at least a few more times. ", "But then his struggles started.", "\n\nIn 2012, Nadal came up short against Novak Djokovic in a thrilling final that lasted nearly six hours. ", "Nadal led 4-2 in the final set and was up 30-15 in that seventh game, needing only to hit a wide-open backhand right at the net to go up 40-15. ", "It was a freebie shot that, somehow, he missed. ", "Djokovic recovered and won the fifth set 7-5, taking his third Australian Open title.", "\n\nTwo years later, Nadal was a favorite in the final. ", "He had beaten Federer in the semifinals, three sets to none, and his final opponent, Stan Wawrinka, had upset Djokovic in the quarterfinals. ", "Wawrinka was expected to be nervous in his first Slam final. ", "But he shocked the world and beat Nadal, who was suffering from a back injury. (", "To Nadal’s credit, he applauded Wawrinka. “", "I’m very happy for him,” Nadal said. “", "He’s a great, great guy.”)", "\n\nThe final in 2017 looked like a lock for Nadal. ", "His opponent, Federer, had not played a match since July 2016 before entering the tournament — six months in all. ", "Worse still, Federer hadn’t beaten Nadal in a Grand Slam match since Wimbledon in 2007. ", "So when Federer fell behind 3-1 in the fifth set — and called for a trainer — he seemed doomed. ", "But then, like magic, Federer didn’t lose another game.", "\n\nAustralia was unkind to Nadal the past two years, too. ", "Nadal retired in the fifth set of the 2018 quarterfinal against Marin Čilić after leading two sets to one. ", "In 2019, Nadal had another surprise: He met Djokovic again in the final, and his rival leveled him in just two hours and four minutes, 6-3, 6-2, 6-3. ", "Nadal had not lost a set leading up to the final.", "\n\nNadal’s struggles are all the more strange because most of the top stars have won a big chunk of their Slam titles at the Australian Open. ", "Djokovic has seven Australian titles, while Federer has six. ", "Andre Agassi won four times, including his last three major titles, while Pete Sampras won twice. ", "Mats Wilander won three titles in Melbourne, and Jim Courier won two of his four Slam titles there. ", "The Australian Open rewards top players by letting them play their best tennis after an offseason of rest and recovery. ", "Nadal rests too, of course, but he hasn’t found the same reward lately.", "\n\nCan Nadal get over the hump this year in Australia? ", "His next opponent: Dominic Thiem, who has looked strong. ", "Nadal will need to play as well as possible to reach the semifinals.", "\n\n“I like him a lot, the way that he works, the way that he plays, and the way that he tries his best always,” Nadal said. “[", "It’s] a match that’s going to be a tough one, but will be interesting, no?”" ]

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[ "Introduction {#Sec1}\n============\n\nIn recent years, phosphodiesterase (PDE) inhibitors have been frequently tested as a potential treatment in sepsis and some autoimmune disorders (Harada et al. [", "@CR20]; Yang et al. [", "@CR64]; González-García et al. [", "@CR18]). ", "Especially, selective PDE4, PDE7, or dual PDE4/7 inhibitors are widely studied as immunomodulatory agents (Jankowska et al. [", "@CR25]). ", "Progression of sepsis and autoimmune diseases depends on various factors, but in both cases, the balance between T helper 1 (Th1) and T helper 2 (Th2) lymphocytes has been indicated as the most important one (Ferguson et al. [", "@CR15]; Kunz and Ibrahim [@CR29]). ", "Th1 lymphocytes produce pro-inflammatory cytokines such as interferon-γ (INF-γ), interleukin-2 (IL-2) or tumour necrosis factor α (TNF-α), while Th2 lymphocytes release anti-inflammatory cytokines, such as IL-4 and IL-5. ", "Depending on which cytokines predominate in plasma and target tissues, progression or remission of the disease is observed (Selmi [@CR47]; Noack and Miossec [@CR41]; László et al. [", "@CR30]). ", "The current treatment of sepsis and autoimmune diseases is not always efficient and often associated with severe side effects; therefore, a search for new anti-inflammatory drugs is needed in order to improve the therapeutic outcome in these diseases.", "\n\nOne of the most important steps in research and development of new drugs is to find a suitable marker of pharmacological response. ", "In experimental animal models of immune disorders, cytokines such as interleukins (e.g. IL-6, IL-10) and TNF-α or nitric oxide (NO) are usually used for this purpose (Gozzi et al. [", "@CR19]; Chakraborty et al. [", "@CR8]; Wyska [@CR57]; Lon et al. [", "@CR35]). ", "However, these biomarkers have some limitations. ", "First of all, their levels measured in different species and in different individuals of the same species differ significantly. ", "Moreover, the increase in their concentrations is observed with some delay relative to the stimulus (Lon et al. [", "@CR35]). ", "For these reasons, there is a need to search for new biomarkers that are closely correlated with the observed pharmacological effect in a dose-dependent manner.", "\n\nPDEs are responsible for 3′,5′-cyclic adenosine monophosphate (cAMP) and 3′,5′-cyclic guanosine monophosphate (cGMP) degradation; thus, the main mechanism of action of PDE inhibitors is related to an increase in levels of these nucleotides. ", "Some PDE families are cGMP-specific (PDE5, 6 and 9), some hydrolyse both cAMP and cGMP (PDE1, 2, 3, 10 and 11) and others are cAMP-specific (PDE4, 7 and 8). ", "Due to ubiquitous expression of PDE4 in mammalian organisms, this enzyme is primarily responsible for the cAMP degradation in the human body (Houslay et al. [", "@CR22]; Francis et al. [", "@CR16]). ", "The clinical impact of changes in cAMP levels remains not entirely clarified, but nevertheless, it has been shown that an increase in cAMP amounts has an immune-weakening potential. ", "On the other hand, the reduction of cAMP levels has an immunostimulatory effect (Raker et al. [", "@CR44]).", "\n\nPentoxifylline (PTX) and lisofylline (LSF) are non-selective PDE inhibitors that undergo metabolic interconversion (Wyska et al. [", "@CR59]). ", "Thus, irrespective of which one is administered, both compounds are present in blood. ", "For many years, they have been widely used in animal studies on inflammation and autoimmune disorders (Rice et al. [", "@CR46]; Bright et al. [", "@CR7]; Yang et al. [", "@CR62], [@CR63]; Wyska [@CR57]). ", "PTX is a drug commonly used in the treatment of intermittent claudication. ", "Moreover, it has been tested clinically in the treatment of diseases, such as sepsis or pulmonary sarcoidosis in humans (NCT02163174, NCT00001877). ", "R-(-)-LSF is an enantiomer of PTX metabolite M1 recently investigated as a potential treatment of autoimmune diabetes (NCT01603121).", "\n\nIt is well known that PDE inhibitors exert their anti-inflammatory activity, at least in part, by increasing concentrations of cAMP. ", "Therefore, it seems that this nucleotide may serve as a marker of drug response in experimental models of inflammatory disorders. ", "To confirm this assumption, we evaluated the influence of two non-selective PDE inhibitors: PTX and (±)-LSF on cAMP levels in plasma of rats with lipopolysaccharide (LPS)-induced endotoxemia. ", "Based on these data, two pharmacokinetic/pharmacodynamic (PK/PD) models were developed to describe the relationship between plasma concentrations of both compounds and their active metabolites and pharmacological response. ", "The potencies of PTX and both enantiomers of LSF as inhibitors of human recombinant PDE4B (hrPDE4B) and PDE7A (hrPDE7A) were preliminarily assessed using an in vitro assay. ", "To select an appropriate PK/PD model, the nature of interaction between PTX and R-(-)-LSF or PTX and (±)-LSF was evaluated in vitro using human recombinant PDE4B enzyme by the combination index (CI) analysis. ", "The validity of cAMP as a biomarker was verified by measuring TNF-α levels in plasma of endotoxemic rats treated with the studied compounds.", "\n\nMaterials and methods {#Sec2}\n=====================\n\nReagents {#Sec3}\n--------\n\ncAMP sodium salt, PTX (1-(5-oxohexyl)-3,7-dimethylpurine-2,6-dione), dimethyl sulfoxide (DMSO), LPS (*Escherichia coli* 055:B5) and 50% 2-chloroacetaldehyde water solution were purchased from Sigma-Aldrich (Germany). ", "Temazepam (7-chloro-3-hydroxy-1-methyl-5-phenyl-3H-1,4-benzodiazepin-2-one) was a gift from Polfa (Poland). ", "IBMX (1-methyl-3-(2-methylpropyl)-7H--purine-2,6-dione) was purchased from Santa Cruz Biotechnology (USA). (", "±)-LSF ((±)-1-(5-hydroxyhexyl)-3,7-dimethylpurine-2,6-dione) was obtained from the Department of Organic Chemistry, Faculty of Chemistry, Jagiellonian University (Cracow, Poland). ", "R-(-)-LSF and S-(+)-LSF were isolated by chromatographic separation of racemate using a chiral semi-preparative Chiralpak AD column (Daicel Corp., Japan). ", "Other chemicals were of high-performance liquid chromatography or analytical reagent grade and were purchased from Merck (Germany).", "\n\nIn vitro PDE assay {#Sec4}\n------------------\n\nThe PDE inhibitory activity of PTX, R-(-)-LSF and S-(+)-LSF was evaluated using the PDE-Glo Phosphodiesterase Assay according to the manufacturer's instruction (Promega Corporation, Madison, WI, USA). ", "Briefly, 1,5 μl of 1× PDE-Glo reaction buffer containing 10 mU of purified hrPDE4B or hrPDE7A (SignalChem, Richmond, Canada) was pipetted into 384-well plate wells (Thermo Scientific, USA). ", "The tested compounds were dissolved in DMSO, and a serial dilution of the inhibitors was performed using 1× PDE-Glo reaction buffer. ", "Then, 1 μL of diluted inhibitors and 2.5 μL of cAMP solution were added to each well. ", "After 10 min of incubation in 30 °C, 2.5 μL of PDE-Glo™ Termination Buffer and 2.5 μL of PDE-Glo™ Detection Solution were added and the plate was incubated for 20 min at room temperature. ", "Finally, 10 μL of Kinase-Glo® Reagent was pipetted to each well and after 10 min of incubation, the luminescence was measured using a microplate luminometer (POLARstar Omega, BMG LABTECH, Ortenberg, Germany). ", "All data points are the average of two determinations.", "\n\nCombination index analysis {#Sec5}\n--------------------------\n\nCompuSyn (ComboSyn, Inc., Paramus, NJ, USA) computer program was used in the calculation of the CI of non-constant ratio combinations of PTX with R-(-)-LSF or PTX with (±)-LSF as hrPDE4B inhibitors. ", "The CI was evaluated based on the Combination Index-Isobologram Theorem (Chou [@CR10]). ", "CI values = 1, \\>1 and \\<1 indicate an additive effect, antagonism and synergism, respectively. ", "However, values between 0.9 and 1.1 are considered as nearly additive. ", "To this end, four concentrations of each drug producing between 25 and 75% of the maximal inhibitory potency (data obtained from the single compound study) were chosen. ", "In the next step, four concentrations of PTX and R-(-)-LSF or PTX and (±)-LSF were mixed with each other to produce 32 combinations of investigated compounds (16 combinations for each pair of compounds). ", "The inhibitory potencies of all combinations were measured using the described above PDE-Glo Phosphodiesterase Assay.", "\n\nAnimals {#Sec6}\n-------\n\nMale Wistar rats weighting 250--300 g were housed in conditions of the constant temperature with a 12:12 h light--dark cycle with free access to food and water. ", "The animals were implanted with catheters (SAI Infusion Technologies, USA) in the jugular vein under ketamine/xylazine anaesthesia 2 days prior to the experiment. ", "Before drug administration, the rats were fasted overnight with free access to water. ", "All animal procedures were approved by the First Local Ethical Committee on Animal Testing at the Jagiellonian University. ", "All applicable international, national and/or institutional guidelines for the care and use of animals were followed.", "\n\nIn vivo experimental design {#Sec7}\n---------------------------\n\nAll compounds were directly dissolved in 0.9% sterile saline and used within 1 day of preparation. ", "The animals were divided into five groups (*n* = 3--4). ", "The control group received LPS alone at a dose of 1 mg kg^−1^, whereas the other four groups received one of the tested compounds (PTX or (±)-LSF) at a dose of 40 or 80 mg kg^−1^ simultaneously with LPS given at a dose of 1 mg kg^−1^. All injections (1 mL kg^−1^) were given to the tail vein of the rat under isoflurane anaesthesia. ", "Blood samples were collected from the jugular vein catheter into snap-cap propylene tubes containing heparin at 0, 15, 30, 60, 75 and 90 min following administration of PTX and at 0, 15, 30, 60, 90 and 120 min following (±)-LSF dosing. ", "Subsequently, samples were kept on ice and centrifuged for 10 min at 3000×*g* at 4 °C (EBA 12 R, Hettich, Germany). ", "The individual plasma samples were harvested and stored at −80 °C until analysis.", "\n\nAnalytical methods {#Sec8}\n------------------\n\nIn order to isolate studied compounds and their metabolites from plasma, to 100 μL of plasma (or plasma spiked with methanol standard solution of PTX or (±)-LSF), 10 μL of temazepam (internal standard) solution in methanol and 20 μL of 1 M hydrochloric acid water solution were added. ", "Then, the samples were extracted with 3 mL of dichloromethane for 20 min on a shaker (VXR Vibrax, IKA, Germany). ", "Subsequently, all tubes were centrifuged (2000×*g*, 15 min) and organic layers were transferred to new glass tubes and evaporated under gentle stream of nitrogen at 37 °C. ", "Dry residues were dissolved in 100 μL of mobile phase and placed in the autosampler vials. ", "The volume of injection was set to 50 μL. The HPLC system (LaChrom Elite, Merck-Hitachi, Darmstadt, Germany) consisted of an L-2130 pump, an L-2200 autosampler, an L-2450 diode array detector and an L-2350 column oven. ", "EZChrome Elite v. 3.2 (Merck-Hitachi) software was used for data acquisition. ", "The analysis was performed on a LiChrospher 100 RP-18 column (250 mm × 4 mm) with a particle size of 5 μm protected with a LiChroCART (4 mm × 4 mm) guard column (Merck, Germany). ", "The mobile phase consisted of dioxan, acetonitrile and aqueous solution of acetic acid (pH = 3.0) mixed at the ratio of 6.5:6.5:87 (*v*/*v*/*v*), respectively, and pumped at a flow rate of 1.2 mL min^−1^. Analytical wavelength was set to 275 nm and temperature of separation was 35 °C. ", "In these conditions, the retention times were found to be 15.5 min for temazepam, 17.5 min for PTX and 21 min for (±)-LSF.", "\n\nThe levels of cAMP in rat plasma were measured using the same HPLC system and a fluorescence detector (model FL-2485). ", "The analysis was performed after incubation of plasma with 2-chloroacetaldehyde as a derivatization reagent in elevated temperature to form the fluorescing derivative---1,N^6^-etheno-cAMP. ", "To 100 μL of plasma (or plasma spiked with water standard solution of cAMP), 15 μL of 2 M 2-chloroacetaldehyde solution and 50 μL of 0.5 M acetate buffer (pH = 4.5) were added to a snap-cap tubes. ", "Samples were then vortex-mixed (Reax top, Heidolph, Germany) for 20 s and incubated at 80 °C for 20 min. ", "Thereafter, the reaction mixture was cooled on ice, the samples were centrifuged (3000×*g*, 10 min) and 100 μL of supernatants was placed in the autosampler vials. ", "The volume of injection was 50 μL. The separation was performed at isocratic conditions at 35 °C using the mobile phase composed of 20 mM citric-phosphate buffer (pH = 3.2) and methanol mixed at the ratio of 91:9 (*v*/*v*) and pumped at a flow rate of 1.3 mL min^−1^. The excitation and emission wavelengths were set to 280 and 420 nm, respectively. ", "In these conditions, the retention time of 1,N^6^-etheno-cAMP was 6 min.", "\n\nNo interfering peaks were observed at the retention times of the analytes and the internal standard. ", "The calibration curves for (±)-LSF and PTX constructed by plotting the peak area ratios of the analytes to the internal standard versus corresponding concentrations of analytes were linear in a range of 0.1 to 125 μg mL^−1^. For cAMP, the calibration curve was obtained by plotting the peak areas of cAMP versus corresponding concentrations of this nucleotide and it was linear in a range of 10 to 500 pmol mL^−1^. All values for accuracy and precision were within the recommended limits (EMA [@CR14]).", "\n\nPlasma TNF-α levels were measured by rat TNF-α Quantikine ELISA kit (R&D Systems, Minneapolis, MN, USA) according to the manufacturer's protocol. ", "The limit of quantification was 12.5 pg mL^−1^.\n\nPharmacokinetics {#Sec9}\n----------------\n\nTwo independent PK models were developed for each parent drug, namely PTX or (±)-LSF, and their active metabolites following intravenous (i.v.) ", "route of administration. ", "To this end, one- or two-compartment pharmacokinetic models with linear or Michaelis--Menten type saturable elimination from the central compartment were tested. ", "Both dose levels in each case were simultaneously fitted to obtain a single set of parameters. ", "The final pharmacokinetic models for PTX and (±)-LSF were selected on the basis of visual inspection of the fitting, examination of residuals, parameter precision, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and analysis of the correlation matrix. ", "Pharmacokinetic analysis was performed using Phoenix WinNonlin v. 6.3 (Pharsight Corp, Certara*,* St. Louis, MO, USA).", "\n\nPharmacodynamics {#Sec10}\n----------------\n\nThe indirect response (IDR) model II was employed to describe pharmacodynamics of PTX and (±)-LSF as non-selective PDE inhibitors (Fig. [", "1](#Fig1){ref-type=\"fig\"}). ", "This selection was based on the fact that both compounds inhibit degradation of cAMP used in this study as a marker of drug response.", "Fig. ", "1Schematic representations of the proposed pharmacodynamic models following intravenous administration of PTX or (±)-LSF to endotoxemic rats: the simple IDR model II (**a**) and the additive interaction IDR model II (**b**)\n\nChanges in plasma cAMP concentrations (C~cAMP~) over time following each compound administration may be described by the following equation:\n\n$$\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym} \n \\usepackage{amsfonts} \n \\usepackage{amssymb} \n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$$ \\frac{dC_{cAMP}}{dt}={k}_{in}-{k}_{out}\\cdot I(t)\\cdot {C}_{cAMP} $$\\end{document}$$\n\nwhere *k* ~*in*~ is zero-order cAMP production rate constant and *k* ~*out*~ is the first-order cAMP elimination rate constant. ", "In the absence of drug, the response stays at the baseline value (R~0~):\n\n$$\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym} \n \\usepackage{amsfonts} \n \\usepackage{amssymb} \n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$$ {R}_0=\\frac{k_{in}}{k_{out}} $$\\end{document}$$\n\nThus, k~in~ can be calculated as *R* ~0~ k~out~, where *R* ~0~ is the mean cAMP concentration measured before drug administration. ", "The joint effect of PTX and (±)-LSF as parent drugs and metabolites was modelled using two approaches.", "\n\nThe first approach (Fig. [", "1](#Fig1){ref-type=\"fig\"}a) was based on the assumption that both compounds, PTX and (±)-LSF, act with similar potencies; thus, inhibitory function may be described by the following equation:\n\n$$\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym} \n \\usepackage{amsfonts} \n \\usepackage{amssymb} \n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$$ I(t)=1-\\frac{I_{\\max}\\cdot {C_p}^{\\gamma }}{{IC_{50}}^{\\gamma }+{C_p}^{\\gamma }} $$\\end{document}$$\n\nwhere *C* ~*p*~ is a sum of PTX and (±)-LSF plasma concentrations, *I* ~max~ is the maximum ability of both compounds to inhibit k~out~, *IC* ~50~ is plasma concentration of the combination of parent compound and metabolite at which inhibition is half-maximal, and *γ* is the Hill coefficient.", "\n\nThe second approach assumes that both compounds under investigation act with different potencies. ", "Based on the results of the in vitro study, an additive interaction model was used (Eq. [", "4](#Equ4){ref-type=\"\"}):\n\n$$\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym} \n \\usepackage{amsfonts} \n \\usepackage{amssymb} \n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$$ I(t)=\\left(1-\\frac{I_{\\max, PTX}\\cdot {C_{PTX}}^{\\gamma_{PTX}}}{{IC_{50,PTX}}^{\\gamma_{PTX}}+{C_{PTX}}^{\\gamma_{PTX}}}\\right)\\cdot \\left(1-\\frac{I_{\\max, LSF}\\cdot {C_{LSF}}^{\\gamma_{LSF}}}{{IC_{50,LSF}}^{\\gamma_{LSF}}+{C_{LSF}}^{\\gamma_{LSF}}}\\right) $$\\end{document}$$\n\nwhere *I* ~max,*PTX*~ and *I* ~max,LSF~, are the maximum ability of PTX and (±)-LSF, respectively, to inhibit *k* ~*out*~; *IC* ~50,PTX~ and *IC* ~50,LSF~ are the concentrations of PTX and (±)-LSF producing 50% of the maximum inhibition; *C* ~*PTX*~ and *C* ~*LSF*~ are plasma concentrations of PTX and (±)-LSF and γ~PTX~ and γ~LSF~ are the Hill coefficients. *", "I* ~max~ and *γ* in Eqs. ([", "3](#Equ3){ref-type=\"\"}) and ([4](#Equ4){ref-type=\"\"}) were fixed to 1 during fitting procedure. ", "To obtain a single set of pharmacodynamic parameters for each model, cAMP plasma concentrations following administration of PTX or (±)-LSF at both dose levels (40 or 80 mg kg^−1^) were fitted simultaneously.", "\n\nStatistical analysis {#Sec11}\n--------------------\n\nThe peak cAMP and TNF-α plasma levels following administration of LPS alone or LPS simultaneously with both doses of each compound were compared using a one-way ANOVA and Tukey's HSD post hoc test. ", "The normality of data distribution was checked by Shapiro*--*Wilk test. ", "The relationship between decimal logarithms of peak cAMP and TNF-α plasma concentrations was verified by least squares linear regression analysis. ", "All statistical analyses were performed using Statistica v. 12 (StatSoft Inc., USA). ", "The significance level *p* was set at 0.05.", "\n\nResults {#Sec12}\n=======\n\nPDE inhibitory activity and CI analysis {#Sec13}\n---------------------------------------\n\nAs presented in Fig. [", "2](#Fig2){ref-type=\"fig\"}a, b, and in Table [1](#Tab1){ref-type=\"table\"}, both enantiomers of (±)-LSF inhibited hrPDE4B in the in vitro assay with similar potencies. ", "PTX in the same test acted slightly weaker. ", "R-(-)-LSF and S-(+)-LSF act also as weak inhibitors of hrPDE7A, whereas PTX as an inhibitor of this enzyme was ineffective. ", "IBMX, a non-selective PDE inhibitor used as a reference compound in this study, reached PDE7A IC~50~ value about 3 and 4 times lower than those of R-(-)-LSF and S-(+)-LSF, respectively. ", "Moreover, this compound acted two times stronger than PTX and similarly to both enantiomers of LSF as a hrPDE4B inhibitor.", "Fig. ", "2Observed (*symbols*) vs. predicted (*lines*) hrPDE4B (**a**) or hrPDE7A (**b**) activity (%) in the presence of the investigated compounds at different concentrations; CI plots of 16 combinations of PTX and R-(-)-LSF (**c**) or PTX and (±)-LSF (**d**) as hrPDE4B inhibitors Table 1IC~50~ values of studied inhibitors estimated by non-linear regression using data obtained from in vitro studyCompoundPDE4B IC~50~ (μM)PDE7A IC~50~ (μM)R-(-)-LSF49.1266.1S-(+)-LSF52.5328.2PTX91.3\\>500.0IBMX46.677.7\n\nCI values of each compound combination were plotted on CI plots, where the effect value (x axis) is a summary % of hrPDE4B inhibition of each combination (Fig. [", "2](#Fig2){ref-type=\"fig\"}c, d). ", "CI values obtained for seven of the 16 combinations of PTX and R-(-)-LSF (Fig. [", "2](#Fig2){ref-type=\"fig\"}c) and for 11 of 16 combinations of PTX and (±)-LSF (Fig. [", "2](#Fig2){ref-type=\"fig\"}d) were in the range of 0.9--1.1, indicating the existence of simple additive interaction. ", "CI calculated for other combinations slightly exceeded the range of 0.9--1.1 indicating the presence of weak antagonism or synergism. ", "However, the mean CI value obtained for all combinations of PTX and R-(-)-LSF was 1.02 (±0.12), and for PTX and (±)-LSF combinations, it was 0.95 (±0.14).", "\n\nPharmacokinetics {#Sec14}\n----------------\n\nPharmacokinetic analysis revealed that a one-compartment model with linear elimination from the central compartment (Fig. [", "3](#Fig3){ref-type=\"fig\"}a) best described PTX and (±)-LSF (as metabolite) concentration versus time profiles after i.v. ", "administration of PTX to rats. ", "In turn, a one-compartment model with Michaelis-Menten type elimination from the central compartment (Fig. [", "3](#Fig3){ref-type=\"fig\"}b) was most appropriate to fit the plasma concentration versus time data of (±)-LSF and PTX (as metabolite) after (±)-LSF i.v. ", "administration to rats. ", "In both models, a mutual interconversion of the parent compounds and their metabolites was taken into account.", "Fig. ", "3Schematic representations of the proposed pharmacokinetic models of PTX (**a**) and (±)-LSF (**b**) following intravenous administration of each compound to rats; C~**PTX**~ and C~**LSF**~, plasma concentrations of PTX and (±)-LSF; V~**PTX**~ and V~**LSF**~, volumes of PTX and (±)-LSF compartments, respectively; V~PTXm~ and V~LSFm~, volumes of PTX and (±)-LSF metabolite compartments, respectively; k~m12~, first-order conversion rate constant of parent compound into metabolite; k~m21~, first-order conversion rate constant of metabolite into parent compound; k~e~, first-order rate constant for disappearance of parent compound; f~m~, fraction of parent compound metabolized; k~em~, first-order elimination rate constant of metabolite; V~max~, maximal elimination rate constant; K~m~, drug concentration at which the elimination rate is half-maximal\n\nAs presented in Fig. [", "4](#Fig4){ref-type=\"fig\"}, the proposed models very well captured the concentration versus time data of both parent compounds and their respective metabolites.", "Fig. ", "4Mean (±SD) observed (*symbols*) and model predicted (*lines*) PTX and (±)-LSF plasma concentrations after PTX (**a**) or (±)-LSF (**b**) administration at two doses (40 or 80 mg kg^−1^) to rats (*n* = 3--4)\n\nThe estimates of pharmacokinetic parameters are listed in Table [2](#Tab2){ref-type=\"table\"}.Table 2Estimated values of pharmacokinetic parameters of PTX or (±)-LSF as parent compounds(±)-LSF (parent drug)PTX (parent drug)ParameterFinal estimate (CV%)ParameterFinal estimate (CV%)V~LSF~ (L kg^−1^)1.22 (3.44)V~PTX~ (L kg^−1^)1.07 (1.24)V~PTXm~ (L kg^−1^)2.01 (9.48)V~LSFm~/f~m~ (L kg^−1^)1.77 (15.23)V~max~ (mg min^−1^ kg^−1^)0.433 (56.85)k~e~ (min^−1^)0.056 (3.04)K~m~ (mg L^−1^)6.02 (91.82)k~m21~ (min^−1^)0.015 (9.89)k~m12~ (min^−1^)0.203 (12.74)k~em~ (min^−1^)0.157 (15.34)k~m21~ (min^−1^)0.095 (12.87)k~em~ (min^−1^)0.116 (9.75)\n\nPharmacodynamics {#Sec15}\n----------------\n\nThe administration of investigated compounds to rats caused an inhibition of PDEs and a subsequent increase in cAMP levels in rat plasma in a dose-dependent manner with the peak concentration attained between 30 and 60 min post-(±)-LSF or PTX dosing. ", "The first tested PK/PD model (Fig. [", "1](#Fig1){ref-type=\"fig\"}a) is a basic IDR model II, where C~p~ is a sum of the parent drug and its active metabolite concentrations. ", "The second tested model (Fig. [", "1](#Fig1){ref-type=\"fig\"}b) is an additive interaction IDR model II, where the occurrence of a simple additive interaction between studied compounds is assumed. ", "Both models describing endogenous cAMP levels consisted of one zero-order input (k~in~) and one first-order cAMP elimination rate constant (k~out~).", "\n\nThe appropriateness of these models was evaluated on the basis of goodness-of-fit criteria*.* ", "The second model (Fig. [", "1](#Fig1){ref-type=\"fig\"}b) was found to better characterize changes in cAMP levels over time in the presence of both PDE inhibitors. ", "An improvement in the fitting was observed, when comparing to the first tested model, as can be determined by visual inspection of the fitting (Fig. [", "5](#Fig5){ref-type=\"fig\"}). ", "Moreover, the AIC and BIC values for the interaction model (229.2 and 232.7, respectively) were lower in comparison with the values estimated for basic IDR model II (232.9 and 235.3, respectively). ", "Pharmacodynamic parameters estimated using both models are listed in Table [3](#Tab3){ref-type=\"table\"}.Fig. ", "5Mean (±SD) observed (*symbols*) and predicted (*lines*) based on the basic IDR model II (**a**) and additive interaction IDR model II (**b**) plasma cAMP concentrations after PTX or (±)-LSF administration at two doses (40 or 80 mg kg^−1^) to rats (*n* = 3--4) Table 3Pharmacodynamic parameters estimated using both tested pharmacodynamic models following intravenous administration of PTX or (±)-LSF to rats challenged with LPSBasic indirect response model IIInteraction indirect response model IIParameterFinal estimate (CV%)Final estimate (CV%)k~in~ (pmol mL^−1^ min^−1^)9.709 (NE^a^)6.650 (NE^a^)k~out~ (min^−1^)0.511 (14.06)0.350 (10.54)IC~50,\\ PTX~ (mg L^−1^)--4.478 (22.24)IC~50,\\ LSF~ (mg L^−1^)--3.428 (19.07)IC~50~ (mg L^−1^)2.243 (9.28)--^**a**^Not estimated\n\nA slightly lower value of IC~50~ estimated using the interaction model for (±)-LSF suggests that this compound may be more potent than PTX as an inhibitor of PDEs in vivo.", "\n\nTo verify whether cAMP levels increased in a dose-dependent manner, the peak cAMP plasma concentrations following administration of LPS only and LPS simultaneously with two different doses of either compound were compared statistically (Fig. [", "6](#Fig6){ref-type=\"fig\"}a, b).Fig. ", "6Effects of different doses of PTX and (±)-LSF on the peak cAMP plasma concentrations (±SD) (*n* = 4) (**a**, **b**) and on TNF-α plasma concentrations (±SD) (**c**, **d**) at 90 min following i.v. ", "administration of each compound concomitantly with LPS (*n* = 4)\n\nSurprisingly, (±)-LSF administered at a dose of 40 mg kg^−1^ did not increase (*p* \\> 0.05) the peak cAMP level in comparison with the group receiving LPS only. ", "The lack of statistical difference in this case may be partially explained by a small sample size. ", "In contrast, the peak TNF-α levels following LPS administration were significantly lower (*p* \\< 0.05) in the presence of both compounds administered at two dose levels (Fig. [", "6](#Fig6){ref-type=\"fig\"}c, d). ", "The results of linear regression analysis indicate the occurrence of correlation between the decimal logarithms of peak cAMP and TNF-α plasma levels (Fig. [", "7](#Fig7){ref-type=\"fig\"}).Fig. ", "7Double logarithmic plot of TNF-α plasma peak levels as a function of cAMP plasma maximal concentrations in rats with endotoxemia receiving LPS alone or simultaneously with PTX or (±)-LSF\n\nEach data point was plotted using TNF-α and cAMP concentrations obtained from the same rat. ", "The correlation between plasma levels of cAMP and those of a commonly used biomarker of inflammation---TNF-α confirms the validity of cAMP as a marker of pharmacological response following administration of non-selective PDE inhibitors.", "\n\nDiscussion {#Sec16}\n==========\n\nPK/PD modelling is widely used in the pharmaceutical industry worldwide not only for quantitative effect-time data analysis but also for predictions of pharmacological response over time in new experimental conditions, such as different dose, dosing schedule, new routes of administration or in the case of decreased function of elimination organs. ", "Properly selected biomarker that reflects the clinical effect is the key to success in the development of a new drug. ", "Biomarker is defined as a measure that characterizes, in a quantitative manner, a process, which is located on the path between drug administration and effect (Danhof et al. [", "@CR13]). ", "A good biomarker should exhibit \"consistent characteristics with an acceptable sensitivity and specificity representing a specific toxicity or therapeutic effect of the drug, a specific physiological response to a treatment, a pathological progression or a physiological factor\" (Bai et al. [", "@CR3]). ", "As shown in this study, cAMP measured in plasma after administration of non-selective PDE inhibitors meets these criteria.", "\n\nLiterature data indicate that in experimental models of inflammatory diseases, PK/PD models were built using TNF-α, IFN-γ, IL-10 or NO as markers of pharmacological response (Gozzi et al. [", "@CR19]; Chakraborty et al. [", "@CR8]; Wyska [@CR57]). ", "The major drawback of using cytokines as biomarkers to evaluate anti-inflammatory drug effects is that their concentrations in blood are highly variable between different individuals of the same species*.* ", "The results presented in literature show a large inter-study variation in the values of cytokine levels (several times differences), despite similar experimental conditions. ", "For example, after intraperitoneal injection of LPS at an identical dose to the same strain of mice, the reported levels of TNF-α differed several times (Gozzi et al. [", "@CR19]; Wyska [@CR57]). ", "This diversity may be due to the methods of blood sampling and further processing of the biological material (e.g., time and temperature of centrifugation, use of anticoagulants, sample storage conditions or the time allowed for blood clotting). ", "A similar effect has been found in studies involving the CLP-induced model of sepsis (Otero-Antón et al. [", "@CR42]; Singleton et al. [", "@CR50]). ", "cAMP as a non-protein biomarker seems to be less prone to these factors. ", "As a result, the values of endogenous concentrations of this nucleotide observed in the present study are close to those found in the literature (Gomaa et al. [", "@CR17]; Itoh et al. [", "@CR24]). ", "Another disadvantage of using cytokines as markers of pharmacological effect is that the increase in their levels is observed with a delay relative to the stimulus, which may be somewhat problematic in PK/PD modelling, as it requires using an additional tlag (lag time) parameter (Lon et al. [", "@CR35]). ", "cAMP is not burdened with this disadvantage because the increase in its levels begins immediately after administration of cAMP-elevating compounds, and it attains the peak level between 30 and 60 min thereafter.", "\n\ncAMP has been frequently measured in in vitro studies, including those on pharmacodynamics of PDE inhibitors (D'Alessandro et al. [", "@CR12]; Huang et al. [", "@CR23]; Massimi et al. [", "@CR37]). ", "Moreover, there are several examples of measuring its concentrations in animal tissues (Kitazawa et al. [", "@CR27]; Jin et al. [", "@CR26]; Park et al. [", "@CR43]) or plasma (Cheng et al. [", "@CR9]; Tanahashi et al. [", "@CR53]). ", "However, the pharmacodynamic data obtained in these studies have not been analysed quantitatively. ", "The only exception is the study of Jusko and coworkers, where cAMP levels in liver following acute and chronic methylprednisolone administration in adrenalectomized rats were modelled using the IDR model II (Jin et al. [", "@CR26]). ", "cAMP plasma levels have been also monitored in humans. ", "Baseline levels of cAMP in plasma of healthy subjects obtained from different studies vary from 13 to 25 pmol mL^−1^ (Nishikimi et al. [", "@CR40]; Amado et al. [", "@CR1]; Cocks et al. [", "@CR11]; Li and Liu [@CR32]). ", "Elevated levels of cAMP were observed in patients with major blunt trauma (Cocks et al. [", "@CR11]), heart failure (Nishikimi et al. [", "@CR40]), after thoracic epidural analgesia (Li and Liu [@CR32]), after heart surgery under cardiopulmonary bypass, which triggers a systemic inflammatory response (Amado et al. [", "@CR1]), as well as in patients treated with antiplatelet drug---ticagrelor (Li et al. [", "@CR33]). ", "Furthermore, melatonin (pineal hormone) administered orally significantly augmented cAMP plasma levels in humans 1 h following its administration (Zhdanova and Raz [@CR65]). ", "The extent of mean cAMP level elevation in these conditions and treatments was not higher than two times in comparison to that observed in control groups. ", "Following intravenous infusion of PTX at a dose of 300 mg in 1 h to healthy subjects, cAMP plasma levels measured 1 h from the beginning of infusion were elevated by approximately 50% when compared to the placebo group (Kruuse et al. [", "@CR28]). ", "To our knowledge, there is a lack of information in the literature about the influence of sepsis state on cAMP levels in human plasma; thus, this issue needs further research. ", "Due to the potential use of PDE inhibitors in the treatment of a wide range of inflammatory diseases, it would be necessary to investigate the effect of these diseases on cAMP levels in plasma before applying cAMP as a marker of pharmacological response in PK/PD modelling. ", "Our own unpublished data show that in cecal ligation and puncture (CLP)-induced model of sepsis, which is probably the most frequently used as it closely resembles the progression and characteristics of human sepsis, cAMP serum concentrations in mice were reduced at 24 and 72 h following CLP procedure and were 26.4 (±3.5), 28.9 (±0.5), 18.0 (±0.4) and 9.3 pmol mL^−1^ (±0.5) in the control group and at 8, 24 and 72 h after CLP procedure, respectively. ", "Therefore, when using this model of sepsis and cAMP as a biomarker, the baseline response should be described by a more complex equation.", "\n\nIt is well known that cAMP participates in multiple downstream pathways, but one of its most important actions is activation of the cAMP-dependent protein kinase A (PKA) I (Walsh et al. [", "@CR56]). ", "This nucleotide binds to the regulatory subunits of PKA I, leading to its dissociation into the regulatory and catalytic subunits. ", "Subsequently, catalytic subunits of PKA I phosphorylate specific residues on multiple target proteins initiating the appropriate signalling pathways (Walsh and Van Patten [@CR55]). ", "cAMP-activated PKA I binds and phosphorylates cAMP-responsive transcription factors, such as cAMP-response element binding protein (CREB) (Shaywitz and Greenberg [@CR49]), activating transcription factor-1 (ATF-1) (Rehfuss et al. [", "@CR45]), nuclear factor kappa-light-chain-enhancer of activated B cells (NFκB) (Houslay et al. [", "@CR22]) and nuclear receptors (Martin et al. [", "@CR36]; Liu et al. [", "@CR34]). ", "This pathway is responsible for the regulation of immune response and the production of inflammatory cytokines (Jankowska et al. [", "@CR25]). ", "Moreover, elevated levels of cAMP cause down-regulation of T cell proliferation and effector functions. ", "The mechanism of this activity is not entirely clarified, but there are some indications that it may be associated with the inducible cAMP early repressor (ICER) (Bodor et al. [", "@CR6]).", "\n\nTill today, two independent studies have shown that inhibition of PDE4 isoform is responsible for the elevated levels of cAMP in animal blood. ", "Rolipram (a selective PDE4 inhibitor) but no cilostamide (a selective PDE3 inhibitor) elevated plasma cAMP concentration in dogs in a dose-dependent manner (Tanahashi et al. [", "@CR53]). ", "Similarly, CP-80,633 and rolipram, selective PDE4 inhibitors administered at the same dose of 10 mg kg^−1^ p.o., ", "increased plasma cAMP concentrations in mice. ", "In the same study, selective inhibitors of PDE1 (vinpocetine), PDE2 (dipyridamole), PDE3 (SKF-94,120), and PDE5 (zaprinast), given at a 10 times higher dose than that of the PDE4 inhibitors, failed to alter cAMP levels significantly (*p* \\< 0.05) in these tests. ", "Moreover, a non-selective PDE inhibitor theophylline, when administered orally at a dose of 100 mg kg^−1^ to mice, increased plasma levels of cAMP up to 296.9 pmol mL^−1^ at 20 min post-dose (Cheng et al. [", "@CR9]), whereas after i.p. ", "dose of 50 mg kg^−1^ to rats with endotoxemia, it elevated concentrations of this nucleotide to 228.22 pmol mL^−1^ 0.5 h after drug administration (our own unpublished data). ", "It is quite possible that basophiles, mast cells, neutrophils, eosinophils, monocytes and lymphocytes, which contain PDE4 and PDE7 enzymes (Torphy and Undem [@CR54]; Smith et al. [", "@CR51]), are involved in the accumulation and efflux of cAMP as a result of the treatment with non-selective as well as PDE4 and PDE7-selective PDE inhibitors (Cheng et al. [", "@CR9]). ", "Taken together, these data suggest that plasma concentrations of cAMP elevated by PDE inhibitors may be connected with an increased cAMP export from PDE4-sensitive immune cells and PDE7 inhibition may enhance this effect.", "\n\nIn the in vitro study conducted using human recombinant PDE4B and PDE7A, the main cAMP-hydrolysing enzymes, the IC~50~ values of IBMX as a reference compound were similar to those found in literature (Hatzelmann et al. [", "@CR21]; Smith et al. [", "@CR52]). ", "We noticed a higher PDE inhibitory potency of (±)-LSF enantiomers in comparison to PTX. ", "Moreover, both R-(-)-LSF and S-(+)-LSF demonstrated comparable IC~50~ values as PDE4B and PDE7A inhibitors. ", "Therefore, in the pharmacodynamic models employed in this study, it was assumed that both enantiomers of LSF exhibit the same PDE inhibitory potency. ", "Up to date, it has been believed that only R-(-)-enantiomer of (±)-LSF exhibits pharmacological activity (Nicklasson et al. [", "@CR39]). ", "For example, it has been demonstrated that R-(-)-LSF, unlike S-(+)-LSF, inhibited IL-12-induced murine T helper 1 (Th1) differentiation in a dose-dependent manner (Bright et al. [", "@CR7]). ", "In this paper, we demonstrated for the first time that both enantiomers of (±)-LSF act with a similar potency at least as PDE4B and PDE7A inhibitors. ", "Thus, the differences observed in previous studies may arise from other mechanisms of anti-inflammatory activity of R-(-)-LSF. ", "It has been shown that this enantiomer may act through multiple mechanisms, among which inhibition of STAT-4 (Yang et al. [", "@CR63]) or phosphatidic acid generation (Bleich et al. [", "@CR5]) can be mentioned as examples. ", "However, little is known about properties of S-(+)-LSF, leaving a gap for further research. ", "As PTX and (±)-LSF undergo metabolic interconversion in blood (Nicklasson et al. [", "@CR39]; Wyska et al. [", "@CR59]) and both compounds exert anti-inflammatory effects, we made an attempt to assess the nature of possible interaction that might occur. ", "CI values calculated using CompuSyn software for PTX and R-(-)-LSF as well as for PTX and (±)-LSF oscillated around 1, indicating existence of additive (zero) interaction between both investigated compounds. ", "This observation was taken into account during pharmacodynamic model building and finally, the additive interaction model was used in PK/PD analysis.", "\n\nAs mentioned above, PTX and R-(-)-LSF are prone to metabolic interconversion. ", "The reduction of PTX to R-(-)-LSF is mediated by an enzyme independent on cytochrome P450, namely carbonyl reductase; on the other hand, the opposite reaction is catalysed by CYP1A2 (Lee and Slattery [@CR31]). ", "Moreover, PTX is metabolised to S-(+)-LSF. ", "Thereby, after administration of PTX or (±)-LSF to rats, all three compounds, namely PTX and both enantiomers of (±)-LSF, occur in blood. ", "Therefore, our PK models have some limitations. ", "As we used a non-chiral method for determination of (±)-LSF concentrations, the parameter values obtained for (±)-LSF in fact relate to the combination of the two enantiomers co-occurring in rat plasma. ", "The results of the previous study indicated that interconversion rates of PTX and R-(-)-LSF, as well as PTX and S-(+)-LSF, are different and that this process plays a minor role in the pharmacokinetics of both compounds (Wyska et al. [", "@CR59]). ", "Despite the simplification of pharmacokinetic models in this study, both pharmacokinetic models very well captured changes in concentrations of the tested compounds in rat plasma. ", "The pharmacokinetic analysis confirmed the results of previous research on mice indicating the presence of non-linear pharmacokinetics of R-(-)-LSF administered alone or concomitantly with LPS (Wyska [@CR57]; Wyska et al. [", "@CR60]). ", "Unlike PTX, this compound is metabolized in mice principally by cytochrome P450 (Lee and Slattery [@CR31]; Wyska [@CR58]); thus, the saturation of metabolism at higher doses may occur. ", "Both PTX and (±)-LSF are rapidly eliminated from the rat body, as demonstrated by the fast decline of the terminal phase of the concentration versus time profiles. ", "The elimination half-life (t~0.5~) of PTX equalled 16.4 min, and it was two times longer than that observed in mice (Wyska et al. [", "@CR61]). ", "In turn, the values of K~m~ or V~max~ of (±)-LSF estimated in rats (Table [2](#Tab2){ref-type=\"table\"}) were somehow lower than those obtained for R-(-)-LSF in mice (15.08 mg L^−1^ and 2.33 mg min^−1^ kg^−1^, respectively) (Wyska et al. [", "@CR61]).", "\n\nIn this study, we used cAMP as a marker of pharmacological response after administration of compounds that modulate the level of this nucleotide and evaluated the in vivo potency of the investigated compounds using PK/PD modelling. ", "As demonstrated in this paper, after administration of both PDE inhibitors, cAMP levels changed in a dose-dependent manner. ", "The proposed PK/PD models are based on the assumption that both compounds (PTX and (±)-LSF) cause a reduction in degradation of cAMP by PDE (principally PDE4) inhibition. ", "The first tested PK/PD model, which is the basic IDR model II (Fig. [", "1](#Fig1){ref-type=\"fig\"}a) is simpler and can be successfully used in a situation where only one compound, which exhibits pharmacological activity, occurs in blood. ", "The second model---the interaction IDR model II (Fig. [", "1](#Fig1){ref-type=\"fig\"}b)---reflects a more complex situation when two active compounds are present in blood, and they undergo additive interaction. ", "Furthermore, each compound has a different potency. ", "This approach is based on the additive drug--drug interaction model developed by Ariens et al. ([", "@CR2]). ", "The PK/PD analysis revealed that the second model (Fig. [", "1](#Fig1){ref-type=\"fig\"}b) better described changes of cAMP levels over time following administration of studied compounds. ", "It may be justified by the fact that both parent compounds and their active metabolites occur in rat blood, and they exhibit pharmacological activity as PDE inhibitors. ", "Basic assumptions of this model are that both parent compounds and their respective active metabolites exhibit additive (zero) interaction (as it can be concluded from the results of CI analysis), and both enantiomers of (±)-LSF have the same potency as PDE inhibitors (based on the similar IC~50~ values obtained in the in vitro study). ", "As the investigated compounds at higher concentrations fully inhibited activity of the enzymes in the in vitro test, in both compared pharmacodynamic models, I~max~ value was fixed to 1. ", "The employed PK/PD models allowed for assessment of the PDE inhibitory potency of tested compounds in vivo. ", "Based on the obtained results, it seems that (±)-LSF is a slightly stronger inhibitor of PDEs in rats compared to PTX, as demonstrated by approximately 20% lower IC~50~ value (Table [2](#Tab2){ref-type=\"table\"}). ", "Also, the results of the in vitro test confirmed the observation that both (±)-LSF enantiomers acted stronger as hrPDE4B and hrPDE7A inhibitors compared to PTX. ", "IC~50~ values of R-(-)-LSF and S-(+)-LSF versus PTX as hrPDE4B inhibitors were about two times lower. ", "Moreover, IC~50~ values of PTX and (±)-LSF calculated using PK/PD model after conversion to μM are of the same order of magnitude as IC~50~ values assessed for both compounds using hrPDE4B (main cAMP hydrolysing enzyme) in the in vitro experiment and were equal 16.09 and 12.23 μM for PTX and (±)-LSF, respectively. ", "Although enzymes used in the in vitro assay are human recombinant proteins, it has been demonstrated that PDE4 inhibitors have very similar IC~50~ values in relation to human and rat recombinant PDE4B (Bian et al. [", "@CR4]). ", "However, it must be kept in mind that PDE4 activity in rat blood leukocytes is higher in comparison to that in human cells, probably as a result of approximately 25 times higher expression of PDE4 in rat leukocytes. ", "Anti-inflammatory potency of PTX and R-(-)-LSF has been assessed earlier using TNF-α as a marker of pharmacological response and different PK/PD models (Wyska [@CR57]). ", "The results of these studies indicated the presence of dose-dependent relationship between PTX or R-(-)-LSF exposure and inhibition of TNF-α production in serum of LPS-treated mice. ", "The value of TNF-α IC~50~ for PTX estimated in that experiment was lower than that observed for R-(-)-LSF, but the influence of S-(+)-LSF or (±)-LSF on TNF-α levels was not investigated. ", "In this study, we evaluated the influence of PTX and (±)-LSF administration on TNF-α plasma levels in endotoxemic rats. ", "These compounds at both doses caused a significant decrease (*p* \\< 0.05) in TNF-α concentrations. ", "It may be concluded that the elevated levels of cAMP in rat plasma correspond with the decreased TNF-α levels after administration of both investigated PDE inhibitors simultaneously with LPS. ", "Moreover, in this study, the correlation between decimal logarithms of peak TNF-α and cAMP plasma levels in endotoxemic rats was demonstrated, indicating the potential utility of cAMP as a marker of non-selective PDE inhibitors' effect in inflammatory diseases. ", "This observation is in line with the results of in vitro study where a correlation has been found between the decimal logarithms of cAMP accumulation potency (EC~50~) and IC~50~ of TNF-α suppressive action for a series of non-selective PDE inhibitors (Semmler et al. [", "@CR48]). ", "However, these observations are not in agreement with the results of in vitro studies using immune cells from patients suffering from Gram-negative bacterial pneumonia, where the elevated intracellular levels of cAMP observed in human leukocytes were not correlated with the suppression of TNF-α levels (Matsumoto et al. [", "@CR38]).", "\n\nIn conclusion, the results of this study indicated that both non-selective PDE inhibitors, PTX and (±)-LSF, differ in pharmacokinetic and pharmacodynamic characteristics. ", "The proposed PK/PD additive interaction IDR model II accurately described the concentration--effect relationship between PTX or (±)-LSF concentrations and cAMP plasma levels. ", "The proposed PK/PD models may serve as a tool for assessing PDE inhibitory activity of new non-selective PDE or PDE4-selective inhibitors in vivo. ", "Moreover, due to cAMP immune weakening potential, they can be used in studies on new immunomodulatory drugs, which mechanism of action is based on the elevation of cAMP levels.", "\n\nWe thank Krzysztof Pociecha, MSc, for his excellent technical assistance. ", "This work was supported by Statutory Funds of the Jagiellonian University Medical College, Cracow, Poland (K/ZDS/004706 and K/DSC/003548).", "\n\nAll the experimental procedures and protocols involving animals were approved by the First Local Ethical Committee on Animal Testing at the Jagiellonian University in Cracow and were conducted in accordance with the European Communities Council Directive of 22 September 2010 (2010/63/EU).", "\n\nConflict of interest {#FPar1}\n====================\n\nThe authors declare that they have no conflict of interest.", "\n" ]

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[ "MANILA, Philippines (Update 2, 11:52 a.m.) — Sen. Antonio Trillanes IV is facing yet another case as a local prosecutor charged the senator with grave threat from a complaint filed by Labor Undersecretary Jing Paras.", "\n\nA state prosecutor found probable cause to indict Trillanes on violation of Article 282 of the Revised Penal Code. ", "The Department of Labor and Employment official said that Trillanes, on May 29, 2018, threatened to kill him.", "\n\nREAD: Labor exec Paras slaps Trillanes with grave threat rap\n\nThe information or charge sheet included the following quotes Trillanes allegedly told Paras at the sidelines of a Senate hearing:\n\n“Ang lakas ng loob mo. ", "Hindi magtatanggol ang amo mo. ", "Matatapos din yan. ", "Yayariin kita. ", "Mersenaryo ka. ", "Yayariin kita.”", "\n\n(You’re gutsy. ", "Your master won’t protect you. ", "That will end. ", "I will finish you. ", "You are a mercenary. ", "I will finish you.)", "\n\n“Tatawa-tawa ka pa. ", "May araw ka din. ", "Yayariin kita.”", "\n\n(Go on, laugh. ", "You will have your end. ", "I will end you.)", "\n\n“Suwerte mo... mabait itong... secretary kun’di yayariin kita eh.”", "\n\n(You’re lucky... this secretary is nice, if he was not, I will finish you.)", "\n\nThe purportedly statements of Trillanes “[created] fear and anxiety on the mind of [Paras] that the threats will be carried out,” read the document signed by Assistant City Prosecutor Janette Herras-Baggas.", "\n\nThe case was raffled off to the sala of Pasay Metropolitan Trial Court Branch 47 Acting Presiding Judge Joeven Dellosa on December 7.", "\n\nDellosa set the arraignment and preliminary conference of the case in the morning of February 15.", "\n\nThe order dated Dec. 14, 2018 was made public only on Friday.", "\n\n“The private complainant (Paras) is directed to appear before the Court on the same date for purposes of plea bargaining, where allowed, and notification of trial dates,” Dellosa said in his one-page order.", "\n\nTrillanes: I will face latest suit squarely\n\n“Like all the other harassment cases filed against me, I will face this squarely,” the senator said in a statement.", "\n\nTrillanes said that he has returned to the country on Wednesday, January 9.", "\n\nThe senator went to Europe in December for a series of speaking engagements in Amsterdam, Barcelona and London.", "\n\nHe is due to leave again on January 27 to Feb. 10, 2019 for a series of activities in California, Washington D.C. and Maryland.", "\n\nThe grave threat case is just one of the suits Trillanes is facing.", "\n\nParas and lawyer Manuelito Luna filed inciting to sedition and conspiracy or proposal to commit coup d’etat before a Pasay prosecutor.", "\n\nThe senator is also facing a libel case before a Davao court.", "\n\nMakati Regional Trial Court Branch 150 earlier upheld its issuance of a warrant against the senator over a revived rebellion case over his involvement in the 2007 Manila Peninsula incident.", "\n\nMakati Judge Elmo Alameda stood by his earlier ruling that President Rodrigo Duterte’s Proclamation 572, which declared Trillanes’ amnesty as void from the beginning, had factual basis.", "\n\nTrillanes is one of the staunchest critics of the president." ]

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[ "Electrical potential control makes it possible in rotating machines, such as for example generators or high-voltage motors, to minimize electrical voltages (potential differences), thereby allowing the occurrence of partial and/or corona discharges to be reduced or avoided entirely.", "\nIn rotating electrical machines, the reliability of the insulating system is decisively responsible for their operational reliability. ", "The insulating system has the task of permanently insulating electrical conductors (wires, coils, bars) from one another and from the laminated stator core or the surroundings. ", "Outer potential control has the task of making electrical contact between the laminated stator core at ground potential and the outer side of the main insulation. ", "This ensures that no partial discharges occur in voids in the region of the boundary layer of the insulation and the laminated core.", "\nA distinction must be made here between outer corona protection (OCP) for generator winding bars that have been produced by single bar production (OCP-S) and outer corona protection (OCP) for generator winding bars that have been produced by means of the GVPI process (OCP-G). ", " \nIn the case of globally impregnated stator windings (Global Vacuum Pressure Impregnation GVPI), the entire laminated core with a fully fitted winding is impregnated and cured altogether. ", "As a result, the adhesive bonding of the winding in the slots of the laminated core is so strong that the different coefficients of expansion of the copper, iron and insulation lead to high thermomechanical stresses between the copper, insulation and iron, which after a certain number of thermal cycles (starts and stops of the generator) may lead to tearing open of the boundary surfaces. ", "In order to prevent the gaps from being subject to a difference in electrical potential, and the partial discharges igniting there from destroying the insulation, an outer potential control (outer corona protection, OCP) is used, in the prior art represented in FIG. ", "20 as a double-layered outer corona protection, such as is used for the potential control of machines processed by means of G-VPI.", "\nAn insulating base winding 70 of fine-mica tape is applied over the current-carrying Roebel bar of copper conductor elements 40, smoothing and increasing the edge radii of the thin copper conductor elements 40.", "\nWound thereover is a first graphite-containing conductive nonwoven tape 100, which is only connected at one point to the high-voltage potential of the copper conductor element 40 by way of a contact strip 130.", "\nIt is only thereupon that the main insulation 160 of fine-mica glass is wound. ", "Instead of the copper conductor elements, the first conductive nonwoven tape 100 thus forms the high-voltage electrode. ", "It is permanently adhesively bonded to the main insulation 160.", "\nFollowing on top of the main insulation 160 is the inner outer corona protection winding 110 according to the prior art, an outermost separating tape 190′ and an outer outer corona protection winding 200. ", "An outer corona protection tape 140, which is woven in the outermost separating tape 190′, connects the inner outer corona protection winding 110 and the outer outer corona protection winding 200.", "\nThe thermomechanical stresses occurring between the copper conductor assembly and the insulation during the starting and stopping of the generator may after a certain operating time lead to local detachments of the insulating sheath from the conductor, without the feared partial discharges igniting in the gaps that are produced. ", "The region of the delamination is potential-free, because the high-voltage potential has been transferred to the conductive nonwoven tape that becomes baked fast on the main insulation. ", "This IPC design at the highly stressed inner boundary layer between the conductor and the insulation allows turbogenerators to be operated at peak load for decades without any notable partial discharge aging.", "\nThe object of the invention is therefore to solve the aforementioned problems.", "\nThe object is achieved by an insulation system according to, with an outer corona protection according to the invention and an electrical machine according to the invention." ]

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[ "Theresa May has struck a deal with George Osborne agreeing to cut Home Office\nspending but protect the police's budget for tackling terrorism\n\nMrs May, the Home Secretary, has agreed to substantial cuts to her department, but the counter-terrorism budget will be ring-fenced.", "\n\nShe was one of several ministers fighting to protect her budget agaisnt the Treasury's efforts to secure £11.5 billion of cuts from Whitehall departments for the year 2015/16.", "\n\nToday, the Treasury announced six departments have reached settlements totaling £1.1 billion, including pledges from Owen Paterson, the Environment Secretary, and Maria Miller, the Culture and Media Secretary.", "\n\nIt amounts to an eight per cent cut to the budgets of across all six departments, which also include the Scotland Office, Wales Office and the Law Officers Department.", "\n\nThis means Mr Osborne has managed £3.6 billion of cuts - meaning he is about a third of his way to his goal. ", "The latest ministers to sign up to cuts adds to departments who signed up to cuts £1.5 bilion of cuts last month and £1 billion of cuts in announced in the Budget.", "\n\nMore than half of all departments have signed up to a provisional settlement setting out savings. ", "However, some of the biggest and trickiest deals are still to come from 10 more departments, including controversial cuts to the Ministry of Defence.", "\n\nDanny Alexander, Chief Secretary to the Treasury, said the settlements \"show we continue to make real progress towards the savings we need while protecting priority areas\".", "\n\n\"Counter terrorism policing is a crucial part of our national security and I took no convincing of the need to protect this area. ", "Given recent events in Woolwich, we cannot compromise on our national security,\" he said.", "\n\n“None of the spending choices we make are easy, but ensuring the UK can pay its way in the world is vital to our long terms prosperity. ", "Settling over half of Departments with two weeks to go shows how committed the whole of Government is to dealing with the deficit.”" ]

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[ "\"Llys Meddyg... is perfectly placed for foraging — from seashore to forest — and specialises in the collection of razor clams. ", "Each day ends with a professionally cooked meal, made with items you have found.\" ", "Barney Desmazery in BBC Good Food Magazine\n\nShort Courses\n\nUpdate: Nov 25th, 2016\n\nExperience the heart of Llys Meddyg\n\nThis cosy gem of a hotel has established itself on some fine principles: local, seasonal, approachable, family. ", "We are pushing out a new way of sharing the best of these with you, offering a range of fun and informative short courses giving you the chance to experience the things that make Llys Meddyg special.", "\nOur popular foraging days continue with Ed Sykes looking for and cooking the wild food of our local Pembrokeshire countryside and seashore. ", "Our new courses include a hands-on introduction to the art of butchery, smoking and curing, with our longer courses to include fishing and shooting." ]

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[ "/*\nCopyright 2014 The Kubernetes Authors.", "\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.", "\nYou may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.", "\nSee the License for the specific language governing permissions and\nlimitations under the License.", "\n*/\n\npackage clock\n\nimport (\n\t\"sync\"\n\t\"time\"\n)\n\n// PassiveClock allows for injecting fake or real clocks into code\n// that needs to read the current time but does not support scheduling\n// activity in the future.", "\ntype PassiveClock interface {\n\tNow() time.", "Time\n\tSince(time.", "Time) time.", "Duration\n}\n\n// Clock allows for injecting fake or real clocks into code that\n// needs to do arbitrary things based on time.", "\ntype Clock interface {\n\tPassiveClock\n\tAfter(time.", "Duration) <-chan time.", "Time\n\tNewTimer(time.", "Duration) Timer\n\tSleep(time.", "Duration)\n\tNewTicker(time.", "Duration) Ticker\n}\n\n// RealClock really calls time.", "Now()\ntype RealClock struct{}\n\n// Now returns the current time.", "\nfunc (RealClock) Now() time.", "Time {\n\treturn time.", "Now()\n}\n\n// Since returns time since the specified timestamp.", "\nfunc (RealClock) Since(ts time.", "Time) time.", "Duration {\n\treturn time.", "Since(ts)\n}\n\n// After is the same as time.", "After(d).", "\nfunc (RealClock) After(d time.", "Duration) <-chan time.", "Time {\n\treturn time.", "After(d)\n}\n\n// NewTimer returns a new Timer.", "\nfunc (RealClock) NewTimer(d time.", "Duration) Timer {\n\treturn &realTimer{\n\t\ttimer: time.", "NewTimer(d),\n\t}\n}\n\n// NewTicker returns a new Ticker.", "\nfunc (RealClock) NewTicker(d time.", "Duration) Ticker {\n\treturn &realTicker{\n\t\tticker: time.", "NewTicker(d),\n\t}\n}\n\n// Sleep pauses the RealClock for duration d.\nfunc (RealClock) Sleep(d time.", "Duration) {\n\ttime.", "Sleep(d)\n}\n\n// FakePassiveClock implements PassiveClock, but returns an arbitrary time.", "\ntype FakePassiveClock struct {\n\tlock sync.", "RWMutex\n\ttime time.", "Time\n}\n\n// FakeClock implements Clock, but returns an arbitrary time.", "\ntype FakeClock struct {\n\tFakePassiveClock\n\n\t// waiters are waiting for the fake time to pass their specified time\n\twaiters []fakeClockWaiter\n}\n\ntype fakeClockWaiter struct {\n\ttargetTime time.", "Time\n\tstepInterval time.", "Duration\n\tskipIfBlocked bool\n\tdestChan chan time.", "Time\n}\n\n// NewFakePassiveClock returns a new FakePassiveClock.", "\nfunc NewFakePassiveClock(t time.", "Time) *FakePassiveClock {\n\treturn &FakePassiveClock{\n\t\ttime: t,\n\t}\n}\n\n// NewFakeClock returns a new FakeClock\nfunc NewFakeClock(t time.", "Time) *FakeClock {\n\treturn &FakeClock{\n\t\tFakePassiveClock: *NewFakePassiveClock(t),\n\t}\n}\n\n// Now returns f's time.", "\nfunc (f *FakePassiveClock) Now() time.", "Time {\n\tf.lock.", "RLock()\n\tdefer f.lock.", "RUnlock()\n\treturn f.time\n}\n\n// Since returns time since the time in f.\nfunc (f *FakePassiveClock) Since(ts time.", "Time) time.", "Duration {\n\tf.lock.", "RLock()\n\tdefer f.lock.", "RUnlock()\n\treturn f.time.", "Sub(ts)\n}\n\n// SetTime sets the time on the FakePassiveClock.", "\nfunc (f *FakePassiveClock) SetTime(t time.", "Time) {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\tf.time = t\n}\n\n// After is the Fake version of time.", "After(d).", "\nfunc (f *FakeClock) After(d time.", "Duration) <-chan time.", "Time {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\tstopTime := f.time.", "Add(d)\n\tch := make(chan time.", "Time, 1) // Don't block!", "\n\tf.waiters = append(f.waiters, fakeClockWaiter{\n\t\ttargetTime: stopTime,\n\t\tdestChan: ch,\n\t})\n\treturn ch\n}\n\n// NewTimer is the Fake version of time.", "NewTimer(d).", "\nfunc (f *FakeClock) NewTimer(d time.", "Duration) Timer {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\tstopTime := f.time.", "Add(d)\n\tch := make(chan time.", "Time, 1) // Don't block!", "\n\ttimer := &fakeTimer{\n\t\tfakeClock: f,\n\t\twaiter: fakeClockWaiter{\n\t\t\ttargetTime: stopTime,\n\t\t\tdestChan: ch,\n\t\t},\n\t}\n\tf.waiters = append(f.waiters, timer.waiter)\n\treturn timer\n}\n\n// NewTicker returns a new Ticker.", "\nfunc (f *FakeClock) NewTicker(d time.", "Duration) Ticker {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\ttickTime := f.time.", "Add(d)\n\tch := make(chan time.", "Time, 1) // hold one tick\n\tf.waiters = append(f.waiters, fakeClockWaiter{\n\t\ttargetTime: tickTime,\n\t\tstepInterval: d,\n\t\tskipIfBlocked: true,\n\t\tdestChan: ch,\n\t})\n\n\treturn &fakeTicker{\n\t\tc: ch,\n\t}\n}\n\n// Step moves clock by Duration, notifies anyone that's called After, Tick, or NewTimer\nfunc (f *FakeClock) Step(d time.", "Duration) {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\tf.setTimeLocked(f.time.", "Add(d))\n}\n\n// SetTime sets the time on a FakeClock.", "\nfunc (f *FakeClock) SetTime(t time.", "Time) {\n\tf.lock.", "Lock()\n\tdefer f.lock.", "Unlock()\n\tf.setTimeLocked(t)\n}\n\n// Actually changes the time and checks any waiters. ", "f must be write-locked.", "\nfunc (f *FakeClock) setTimeLocked(t time.", "Time) {\n\tf.time = t\n\tnewWaiters := make([]fakeClockWaiter, 0, len(f.waiters))\n\tfor i := range f.waiters {\n\t\tw := &f.waiters[i]\n\t\tif !", "w.targetTime.", "After(t) {\n\n\t\t\tif w.skipIfBlocked {\n\t\t\t\tselect {\n\t\t\t\tcase w.destChan <- t:\n\t\t\t\tdefault:\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tw.destChan <- t\n\t\t\t}\n\n\t\t\tif w.stepInterval > 0 {\n\t\t\t\tfor !", "w.targetTime.", "After(t) {\n\t\t\t\t\tw.targetTime = w.targetTime.", "Add(w.stepInterval)\n\t\t\t\t}\n\t\t\t\tnewWaiters = append(newWaiters, *w)\n\t\t\t}\n\n\t\t} else {\n\t\t\tnewWaiters = append(newWaiters, f.waiters[i])\n\t\t}\n\t}\n\tf.waiters = newWaiters\n}\n\n// HasWaiters returns true if After has been called on f but not yet satisfied (so you can\n// write race-free tests).", "\nfunc (f *FakeClock) HasWaiters() bool {\n\tf.lock.", "RLock()\n\tdefer f.lock.", "RUnlock()\n\treturn len(f.waiters) > 0\n}\n\n// Sleep pauses the FakeClock for duration d.\nfunc (f *FakeClock) Sleep(d time.", "Duration) {\n\tf.Step(d)\n}\n\n// IntervalClock implements Clock, but each invocation of Now steps the clock forward the specified duration\ntype IntervalClock struct {\n\tTime time.", "Time\n\tDuration time.", "Duration\n}\n\n// Now returns i's time.", "\nfunc (i *IntervalClock) Now() time.", "Time {\n\ti.Time = i.Time.", "Add(i.", "Duration)\n\treturn i.Time\n}\n\n// Since returns time since the time in i.\nfunc (i *IntervalClock) Since(ts time.", "Time) time.", "Duration {\n\treturn i.Time.", "Sub(ts)\n}\n\n// After is currently unimplemented, will panic.", "\n// TODO: make interval clock use FakeClock so this can be implemented.", "\nfunc (*IntervalClock) After(d time.", "Duration) <-chan time.", "Time {\n\tpanic(\"IntervalClock doesn't implement After\")\n}\n\n// NewTimer is currently unimplemented, will panic.", "\n// TODO: make interval clock use FakeClock so this can be implemented.", "\nfunc (*IntervalClock) NewTimer(d time.", "Duration) Timer {\n\tpanic(\"IntervalClock doesn't implement NewTimer\")\n}\n\n// NewTicker is currently unimplemented, will panic.", "\n// TODO: make interval clock use FakeClock so this can be implemented.", "\nfunc (*IntervalClock) NewTicker(d time.", "Duration) Ticker {\n\tpanic(\"IntervalClock doesn't implement NewTicker\")\n}\n\n// Sleep is currently unimplemented; will panic.", "\nfunc (*IntervalClock) Sleep(d time.", "Duration) {\n\tpanic(\"IntervalClock doesn't implement Sleep\")\n}\n\n// Timer allows for injecting fake or real timers into code that\n// needs to do arbitrary things based on time.", "\ntype Timer interface {\n\tC() <-chan time.", "Time\n\tStop() bool\n\tReset(d time.", "Duration) bool\n}\n\n// realTimer is backed by an actual time.", "Timer.", "\ntype realTimer struct {\n\ttimer *time.", "Timer\n}\n\n// C returns the underlying timer's channel.", "\nfunc (r *realTimer) C() <-chan time.", "Time {\n\treturn r.timer.", "C\n}\n\n// Stop calls Stop() on the underlying timer.", "\nfunc (r *realTimer) Stop() bool {\n\treturn r.timer.", "Stop()\n}\n\n// Reset calls Reset() on the underlying timer.", "\nfunc (r *realTimer) Reset(d time.", "Duration) bool {\n\treturn r.timer.", "Reset(d)\n}\n\n// fakeTimer implements Timer based on a FakeClock.", "\ntype fakeTimer struct {\n\tfakeClock *FakeClock\n\twaiter fakeClockWaiter\n}\n\n// C returns the channel that notifies when this timer has fired.", "\nfunc (f *fakeTimer) C() <-chan time.", "Time {\n\treturn f.waiter.destChan\n}\n\n// Stop conditionally stops the timer. ", " If the timer has neither fired\n// nor been stopped then this call stops the timer and returns true,\n// otherwise this call returns false. ", " This is like time.", "Timer::Stop.", "\nfunc (f *fakeTimer) Stop() bool {\n\tf.fakeClock.lock.", "Lock()\n\tdefer f.fakeClock.lock.", "Unlock()\n\t// The timer has already fired or been stopped, unless it is found\n\t// among the clock's waiters.", "\n\tstopped := false\n\toldWaiters := f.fakeClock.waiters\n\tnewWaiters := make([]fakeClockWaiter, 0, len(oldWaiters))\n\tseekChan := f.waiter.destChan\n\tfor i := range oldWaiters {\n\t\t// Identify the timer's fakeClockWaiter by the identity of the\n\t\t// destination channel, nothing else is necessarily unique and\n\t\t// constant since the timer's creation.", "\n\t\tif oldWaiters[i].destChan == seekChan {\n\t\t\tstopped = true\n\t\t} else {\n\t\t\tnewWaiters = append(newWaiters, oldWaiters[i])\n\t\t}\n\t}\n\n\tf.fakeClock.waiters = newWaiters\n\n\treturn stopped\n}\n\n// Reset conditionally updates the firing time of the timer. ", " If the\n// timer has neither fired nor been stopped then this call resets the\n// timer to the fake clock's \"now\" + d and returns true, otherwise\n// this call returns false. ", " This is like time.", "Timer::Reset.", "\nfunc (f *fakeTimer) Reset(d time.", "Duration) bool {\n\tf.fakeClock.lock.", "Lock()\n\tdefer f.fakeClock.lock.", "Unlock()\n\twaiters := f.fakeClock.waiters\n\tseekChan := f.waiter.destChan\n\tfor i := range waiters {\n\t\tif waiters[i].destChan == seekChan {\n\t\t\twaiters[i].targetTime = f.fakeClock.time.", "Add(d)\n\t\t\treturn true\n\t\t}\n\t}\n\treturn false\n}\n\n// Ticker defines the Ticker interface\ntype Ticker interface {\n\tC() <-chan time.", "Time\n\tStop()\n}\n\ntype realTicker struct {\n\tticker *time.", "Ticker\n}\n\nfunc (t *realTicker) C() <-chan time.", "Time {\n\treturn t.ticker.", "C\n}\n\nfunc (t *realTicker) Stop() {\n\tt.ticker.", "Stop()\n}\n\ntype fakeTicker struct {\n\tc <-chan time.", "Time\n}\n\nfunc (t *fakeTicker) C() <-chan time.", "Time {\n\treturn t.c\n}\n\nfunc (t *fakeTicker) Stop() {\n}\n" ]

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[ "Calvo commutes sentences of two more convicts so they can be deported\n\nGovernor's spokeswoman speaks on the federal immigration officials working with Gov. Calvo on the deportation of non-U.S. citizens incarcerated at the Department of Corrections.", "\nRick Cruz & Masako Watanabe/PDN\n\nHartman was convicted of fourth-degree criminal sexual conduct and two counts of tampering with witnesses, the release stated.", "\n\nNaich was convicted of aggravated assault as a second-degree felony, possession and use of a deadly weapon in the commission of a felon and terrorizing as a third-degree felony, the release stated.", "\n\nOnce the governor signs an Order of Commutation of Sentence, the detainee is transferred to federal officials, who carry out the deportation process, the release stated. ", "The administration said it continues to work with federal partners to deport non-U.S. citizens who fail to abide by the laws of Guam and the United States.", "\n\nThis action brings the total number of criminals whose sentences the commuted for either removal or deportation to 44, the release states." ]

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[ "Tomato Garlic Chutney Recipe Spicy Momos Sauce\n\nSpicy Tomato Garlic Chutney or red chili Momo sauce for chinese Veg or chicken momo. ", "Momos Chatni can also be served with Indian dosa, Idli or Parantha.", "\n\n2 min Prep\n\n10 min Cook\n\nYield 250 gms\n\nAs evident from its name, the Tomato Garlic Chutney is made with loads of Tomato and Garlic is added for a twist in taste.", "\n\nIf you are the fan of chinese style Indian made momo, you would have definitely sweat yourself while dipping that spicy red chili chatni with momos.", "\n\nEven though it is mainly associated with Momos, you can enjoy it with south Indian Dosa or Idli. ", "This is not exactly same red Chatni served with Dosa or Idli in restaurants. ", "The one we share here is specifically for serving red chatni with veg Momos or the chicken ones but there is no reason that you can't serve it with others.", "\n\nAs a matter of fact, we have served it with Paratha as well to ditch the main course sabzi. ", "You can seriously make it a lunch deal if you just wrap the Aloo paratha with the tomato garlic chutney.", "\n\nTomato Garlic Chutney has various versions and everybody likes to make it their way. ", "This is our tried and tested version and dedicated to Maahi's passion for eating the Veg momos. ", "She has tried many while she was in Delhi and particularly liked the ones sold in the Rohini's M2K (a movie hall) complex. ", "The vendor is a street side cart located next to the 'Bittu tikki' shop.", "\n\nThis recipe is an attempt to re-create the same spicy red chutney at home and we believe we have got quite close to it." ]

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[ "Once More, Media Twists Weld’s Words\n\nBy: Elias J. Atienza\n\nLibertarian VP nominee Bill Weld has been making headlines for all the wrong reasons once again. ", "Several articles have had the headlines, such as Talking Point Memo, that Bill Weld told voters to vote for Clinton.", "\n\nWeld delivered a statement at a press conference in Boston where he said that the Libertarian Party has made “great strides” in becoming part of the “national political dialogue.”", "\n\n“We are making strides toward breaking the two-party monopoly, and America will be stronger when we do, but given the position of the Commission on Presidential Debates, the deck is still stacked against even a credible third-party ticket with two proven former Governors,” Weld said in the statement.", "\n\nHis remarks focused on Trump and how he was unfit for office. ", "He tore into Trump’s statements on illegal immigrants, rhetoric on minorities and trade, childish behavior, and other faults he had found. ", "He then finished with this.", "\n\n“In the final days of this very close race, every citizen must be aware of the power and responsibility of each individual vote. ", "This is not the time to cast a jocular or feel-good vote for a man whom you may have briefly found entertaining. ", "Donald Trump should not, cannot, and must not be elected President of the United States.”", "\n\nNowhere did he admit defeat. ", "Nowhere did he say vote for Clinton. ", "He is calling on every voter to not vote for Donald Trump. ", "Weld is calling for voters to choose the Libertarian Party over Trump so that they can present a credible option against Clinton.", "\n\nWeld himself has gone to great lengths in dissuading voters from voting for Clinton. ", "Two weeks ago he sat down with TLR to talk about the recent Wikileaks emails and how they proved Clinton was not telling the truth.", "\n\nHe told TLR:\n\n“I thought there were two statements in the Goldman and Sachs speech that are worthy of attention. ", "The first was her assurance to the Wall Street bankers that she has a public opinion, which they knew about, and a private opinion, that’s telling me that she doesn’t really hold that position. ", "She’s saying ‘I will do anything, as long as you pay me enough money, but I have to hold a different position with the public.’ ", "She’s not telling the truth. ", "The second thing that’s alarming is that she said the people who know best what regulations are appropriate for national services, are the people who work in the industry, ‘people like yourselves, so that’s what I’m going to be looking at for guidance as I decide regulations.’ ", "Again, translation: ‘I will do anything, as long as you keep the bank roll going.”", "\n\nWeld has not conceded. ", "Don’t let the media tell you otherwise. ", "Weld is also holding a rally in Anchorage, Alaska on October 27th." ]

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[ "Wave at Saturn Certificate\n\nThank you for joining the Cassini team for the \"Wave at Saturn\" event.", "\n\nFor those who joined in the \"Wave at Saturn\" event, we thank you, and we hope you enjoyed getting your customized certificate.", "\n\nThank you again for joining us in the \"Wave at Saturn\" event. ", "To save the image above, most browsers will provide a \"save image as\" option when using a right-click while your curser is over the image. ", "To view a version of this image sized for printing, please click here. ", "To view the text version of the image, please click here." ]

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[ "Diving Anilao\n\nDiving Anilao is a must-do for any diver that likes weird and wonderful small stuff. ", "Only 3 hours drive from Manila Airport, it’s a macro diving paradise.", "\n\nJust a three hour drive from Manila airport is a macro photographer’s underwater paradise – Anilao. ", "Its like the Philippines’s version of Indonesia’s Lembeh Strait – a small area of scrubby reef and sand that holds a smorgasbord of weird and wonderful marine life. ", "If critters are your thing, Anilao is a must dive kind of place.", "\n\nThere are numerous resorts along the coast at Anilao as it’s a popular weekend getaway for Manilans. ", "We stayed at Crystal Blue resort which is dedicated to macro diving and photography and run by the affable Mike Bartick, a pro underwater photographer.", "\n\nThe resort is basic but comfortable, built on several levels up the side of the cliffs that form Anilao’s shoreline. ", "There’s a lovely sea view restaurant with hearty helpings of food, which overlooks the small tender boats that take divers out each morning, afternoon and evening.", "\n\nThere’s also a very spacious and well setup camera room which makes all the difference if you have a big rig.", "\n\nThe staff are helpful and the dive guides excellent at finding the otherwise expertly hidden wildlife. ", "Give them a wish list and they’ll probably find all of it for you over the course of a visit.", "\n\nI’m not a particular fan of night dives but they’re very rewarding at Anilao – especially as, given the shallow depth of most dives you can go out at dusk, night dive for an hour and still be home in time for dinner at 7ish.", "\n\nIf you like frogfish, then Anilao is going to be piscine-amphibian heaven for you. ", "Painted, hairy, velvet, outsize, tiny – there are frogfish on almost every dive and one relatively new site, Mato Point, has already been nicknamed Too Many Frogfish as we found no less than 8 of them, of all sizes, colours and types, within a five square metre area, clinging onto a near vertical wall.", "\n\nFrom a rarity point of view, the trip highlight was hands-down seeing a black hairy frogfish. ", "I had no idea they even existed and our guide Johmer said it was only the second time he’d seen one in 10 years of diving Anilao. ", "It had been spotted on another new site, Sun View, thus proving it’s always worth the gamble of exploring an unknown area.", "\n\nThe topography of most Anilao sites is as you’d expect – very shallow and sandy, usually close to the shore. ", "Coconut Bay was a standout with just non stop sightings from the moment we got in the water. ", "Nudibranches were everywhere, including one amorous couple, and there were no less than three sea horses, each one a good mature size.", "\n\nThe sheltered calm water acts as the perfect spot for breeding and nursing young, and we found a tiny cuttlefish and later its adult counterpart half buried in the sand. ", "These seemingly barren monotonous stretches of aquatic scrubland are full of life.", "\n\nIt’s not all flatlands though – the Daryl Laot wreck provides an interesting lattice of steel encrusted in coral with a resident school of batfish. ", "Layag Layag has a decent section of reef albeit with a lot of trash in the water, while out at the island Aphol provides the rarity of a bit of Current with even more nudibranches.", "\n\nThe night dives were a real highlight too, with the much vaunted Town Pier site – basically an utterly flat stretch of sand at 6 metres depth – and Secret Bay delivering evening performances by hairy frogfish and mimic octopus.", "\n\nFour days diving just didn’t seem enough by the time we reached the end of our trip. ", "Anilao is super easy diving – walk straight down from your room onto the boat, no more than 30 minutes out to the dive sites, usually a lot less, regular bottom times of 90 minutes due to the shallow depths of most sites, and just non-stop critter action thanks to the guides. ", "And as it’s only a 3 hour drive straight from Manila Airport, it’s the easiest place to go diving in the Philippines too. ", "What’s not to like? ", "For sure I’ll be back.", "\n\nHow To Get To Anilao\n\nFrom Manila Airport it’s a straight 3 hour drive to Anilao. ", "Any resort can organise a driver to be waiting for you at Arrivals. ", "Check for the cheapest flights to Manila with Skyscanner.", "\n\nWhere To Stay In Anilao\n\nThere are literally scores of resorts in Anilao – it’s a popular area for Manilans to visit at the weekend. ", "Many resorts are hotels first with a dive operation tacked on, rather than a dedicated diving resort. ", "Be aware that Anilao resorts in general are quite expensive for what you get in terms of amenities and food – read previous guest reviews carefully to manage your own expectations.", "\n\nAnilao Liveaboards\n\nBest Time To Dive Anilao\n\nOctober to May is the main dive season for Anilao. ", "July and August is when monsoon season is in full effect. ", "Check your calendar for major public holidays in the Philippines as the resorts are likely to be crowded during Easter holidays and so on.", "\n\nWhat Dive Insurance Do I need For The Philippines?", "\n\nWorld Nomads provide travel insurance if you’re travelling in the Philippines that covers you both on land during travels to and from Anilao and also while diving. ", "Their insurance policy provides coverage for certified divers who don’t go below 40 meters and are diving with qualified guides or instructors. ", "World Nomads are recommended by Lonely Planet and National Geographic among others. ", "Diving insurance is mandatory and proof of purchase needs to be shown along with certification cards and log books.", "\n\nOther Places For Macro Photography\n\nMake Sure You Have Diving And Travel Insurance\n\nWorld Nomads is one of the leading travel insurance providers and their coverage also includes scuba diving to 40 metres too if you select the relevant options. ", "Make sure you're covered insurance-wise both above and below water.", "\n\nMy Book: Thailand’s Underwater World\n\nExperience Thailand’s amazing marine life up close in this beautiful book by Chris Mitchell and Jez Tryner. ", "More info\n\nDisclosure: Divehappy.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com and amazon.co.uk)." ]

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[ "Q:\n\nc++ get other windows messages\n\nim learning to make things to other windows like resize the ie or any type of window. ", "the only problem i don't know how i can get or give messages to other windows.", "\nso like i pressed a key in ie i would like to get that message to my program too!", "\nany idea\n\nA:\n\nTo get the messages that are sent to windows programs you have to install a hook in order to listen to the messages you want. ", "You do this via the SetWindowsHookEx function.", "\nHowever, I believe that you should read a book about this kind of behaviour, since there are certain rules you have to apply. ", "For instance, before returning from your callback function, you have to call CallNextHookEx in order to let the other hooks handle the message. ", "This is the first hit in books.google.com when searching for setwindowshookex.", "\n\n" ]

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[ "Abdallah ibn Khazim al-Tamimi\n\nAbdallah ibn Khazim () was a son of the famed Khurasani Arab general Khazim ibn Khuzayma al-Tamimi and a senior official in the Abbasid Caliphate.", "\n\nKhuzayma was the son of Khazim ibn Khuzayma, a Khurasani Arab who became an early follower of the Abbasids and played an instrumental rule in their rise to power both during and after the Abbasid Revolution. ", "Through Khazim, the family achieved a prominent place among the Khurasaniyya, the Khurasani soldiers who had come west during the Revolution and formed the main power-base of the early Abbasid regime. ", "Abdallah served as chief of security (sahib al-shurta) for the Caliph al-Mahdi (r. 775–785) in 781 CE, for al-Mahdi's son and heir-apparent al-Hadi (r. 785–786) during his campaign in Jurjan. ", "Caliph Harun al-Rashid (r. 786–809) appointed him governor of Tabaristan on the Caspian Sea. ", "In the civil war that broke out after Harun's death between al-Amin (r. 809–813) and al-Ma'mun (r. 813–833), he, along with his brothers, sided with al-Amin, and even served as his sahib al-shurta towards the end of his reign. ", "As al-Ma'mun's forces laid siege to Baghdad in 812, he and his family abandoned the city and fled to nearby Mada'in.", "\n\nReferences\n\nSources \n \n \n\nCategory:8th-century births\nCategory:9th-century deaths\nCategory:Generals of the Abbasid Caliphate\nCategory:Governors of the Abbasid Caliphate\nCategory:8th-century Arabs\nCategory:9th-century Arabs\nCategory:Banu Tamim" ]

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[ "Q:\n\nNeed to see if I can use my read statements to accomplish 3 types of output?", "\n\nI have been asked to write program to process 2 input files (customer and employee), matching the keys of both files and producing the following 3 output files:\n\nFile-1: records that are on both files\nFile-2: records that are on the customer file but not the employee file\nFile-3: records that are on the employee file but not the customer file\n\nMy loop is set so that it checks one record in customer file against every record in the employee file and then gets another key-pair value from the customer file and starts the process over.", "\nCurrently:\n\nMatching Records - Must be in File1 and File2 (This works)\nRecords that are in File1 but not in File2 (Not working)\nRecords that are in File2 but not in File1 (Not working)\n\nQuestions: Is there a way to use the same read paragraphs as I have currently to accomplish all of my tasks at one time, without having to rerun the JCL for each file compare type\nThe code that I have posted works for ONLY the matching case\nCode: (Record Layout -- This all works)\n01 MAIN-LINE1. ", " \n 05 FILLER PIC X(03). ", "<-- won't use in comparison \n 05 ID-1 PIC X(09). ", " \n 05 FILLER PIC X(01). ", " \n 05 KEY-1 PIC X(20). ", " \n 05 FILLER PIC X(47). ", " \n\n01 MAIN-LINE2. ", " \n 05 ID-2 PIC X(09). ", " \n 05 FILLER PIC X(55). ", " \n 05 KEY-2 PIC X(20). ", " \n 05 FILLER PIC X(66). ", " \n\nRead statements below. ", "This is called from one Perform Match-Infile1... which does work.", "\nThis code below works for a Matching situation in the files.", "\nMATCH-INFILE1. ", " \n READ INFILE1 INTO MAIN-LINE1 \n AT END \n MOVE 'Y' TO EOF1 \n GO TO X-INFILE1 \n NOT AT END \n PERFORM READ-INFILE2 THRU X-INFILE2 UNTIL EOF2 = 'Y' \n END-READ. ", " \nX-INFILE1. ", "EXIT. ", " \n\nREAD-INFILE2. ", " \n READ INFILE2 INTO MAIN-LINE2 \n AT END \n MOVE 'Y' TO EOF2 \n GO TO X-INFILE2 \n NOT AT END \n\n PERFORM COMP-FILE THRU X-COMP-FILE <-- I did not include this because \n I forgot to but can add it in in \n the morning when I have access \n to the mainframe. (", "simple compare) \n END-READ. ", " \nX-INFILE2. ", "EXIT.", "\n\nRecord Layout\nCustomer Layout:\n**107458982** ****FM00000000000713432****CH <-- discard the CH\n\nEmployee Layout:\n(discard the SD two byte fields)\nSD **331067113** **FFM00000000004556402**\n\nA:\n\nI do not think it is possible to do all three tasks with your current code. ", "Also what would happen if the files contained 1,000,000 records. ", "You would be reading a file 1,000,000 times. ", "It would take forever to finish (assuming the hard-disks survived).", "\n\nFor this type of processing I would suggest a sort-merge process:\n\nSort the files into key sequence\nDo a merge on the 2 files (for 3 files the process is similar, you just have more complicated evaluate).", "\n\nThe processing logic for 2 files in key sequence becomes:\n while not eof\n evaluate true\n when key-file1 < key-file2\n Write file1-record to output-file-2\n read file1\n when key-file1 > key-file2\n Write file2-record to output-file-3\n read file2\n when key-file1 = key-file2\n /* match processing, \n will involve reading at least one of the files */ \n move key-file1 to hold-key\n while key-file1 = hold-key\n Write Output-File-1\n read file1\n end\n while key-file2 = hold-key\n read file2\n end\n end\n end\n\nThere will be End-of-file logic to add in\nNote: It is unclear from the question how multiple entries for the same key should be handled\n\n" ]

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[ "Serotonergic reinnervation of the hamster suprachiasmatic nucleus and intergeniculate leaflet without functional circadian rhythm recovery.", "\nIntraventricular injections of the neurotoxin, 5,7-dihydroxytryptamine (DHT), were used to lesion hamster forebrain serotonin systems. ", "The entrained circadian wheelrunning rhythm was studied for up to 20 weeks post-lesion as was the extent of reinnervation of nuclei regulating circadian rhythmicity. ", "Reinnervation of the suprachiasmatic nucleus and intergeniculate leaflet by serotonergic fibers begins by 8 weeks and progresses to substantial, but not complete, levels by week 20. ", "Four measures of the nocturnal activity phase of the circadian rhythm were rapidly modified by the lesions, but in contrast to the morphology, persisted unchanged during the entire 20 week test period. ", "The circadian rhythm system of hamsters may be fundamentally different from other behavioral or neuroendocrine systems studied in rats with respect to its inability to recover from damage to its serotonergic innervation. ", "Alternatively, the failure to demonstrate functional recovery may reflect a species difference or insufficient recovery time." ]

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[ "Round Marcasite\n\nThese round pyrite gemstones are great\ngenuine gemstones that you can add to your collection of loose\ngemstones at your jeweler’s workbench. ", "Each of these faceted marcasite\nstones is a high quality gemstone, and is available in shades of metallic\ngrey. ", "These loose round marcasites will match any jewelry design you are\nworking on or repairing. ", "These loose silver marcasites will help you\ncreate beautiful finished jewelry every time." ]

[ 0, 0, 0, 0 ]

[ "Q:\n\nGroup by records by date\n\nI am using SQL Server 2008 R2. ", "I am having a database table like below : \n+--+-----+---+---------+--------+----------+-----------------------+\n|Id|Total|New|Completed|Assigned|Unassigned|CreatedDtUTC |\n+--+-----+---+---------+--------+----------+-----------------------+\n|1 |29 |1 |5 |6 |5 |2014-01-07 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|2 |29 |1 |5 |6 |5 |2014-01-07 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|3 |29 |1 |5 |6 |5 |2014-01-07 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|4 |30 |1 |3 |2 |3 |2014-01-08 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|5 |30 |0 |3 |4 |3 |2014-01-09 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|6 |30 |0 |0 |0 |0 |2014-01-10 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n|7 |30 |0 |0 |0 |0 |2014-01-11 06:00:00.000|\n+--+-----+---+---------+--------+----------+-----------------------+\n\nNow, I am facing a strange problem while grouping the records by CreatedDtUTC column. ", "\nI want the distinct records from this table. ", "Here you can observe that the first three records are duplicates created at the same date time. ", "I want the distinct records so I had ran the query given below : \nSELECT Id, Total, New, Completed, Assigned, Unassigned, MAX(CreatedDtUTC) \nFROM TblUsage \nGROUP BY CreatedDtUTC\n\nBut it gives me error : \nColumn 'TblUsage.", "Id' is invalid in the select list because it is not contained in either an aggregate function or the GROUP BY clause.", "\nI also have tried DISTINCT for CreatedDtUTC column, but had given the same error. ", "Can anyone let me know how to get rid of this? ", "\nP.S. I want the CreatedDtUTC coumn in CONVERT(VARCHAR(10), CreatedDtUTC,101) format. ", "\n\nA:\n\nThe error message itself is very explicit. ", "You can't put a column without applying an aggregate function to it into SELECT clause if it's not a part of GROUP BY. ", "And the reason behind is very simple SQL Server doesn't know which value for that column within a group you want to select. ", "It's not deterministic and therefore prohibited.", "\nYou can either put all the columns besides Id in GROUP BY and use MIN() or MAX() on Id or you can leverage windowing function ROW_NUMBER() in the following way\nSELECT Id, Total, New, Completed, Assigned, Unassigned, CONVERT(VARCHAR(10), CreatedDtUTC,101) CreatedDtUTC\n FROM\n(\n SELECT t.*, ROW_NUMBER() OVER (PARTITION BY Total, New, Completed, Assigned, Unassigned, CreatedDtUTC \n ORDER BY id DESC) rnum\n FROM TblUsage t\n) q\n WHERE rnum = 1\n\nOutput:\n\n| ID | TOTAL | NEW | COMPLETED | ASSIGNED | UNASSIGNED | CREATEDDTUTC |\n|----|-------|-----|-----------|----------|------------|--------------|\n| 3 | 29 | 1 | 5 | 6 | 5 | 01/07/2014 |\n| 6 | 30 | 0 | 0 | 0 | 0 | 01/10/2014 |\n| 7 | 30 | 0 | 0 | 0 | 0 | 01/11/2014 |\n| 5 | 30 | 0 | 3 | 4 | 3 | 01/09/2014 |\n| 4 | 30 | 1 | 3 | 2 | 3 | 01/08/2014 |\n\nHere is SQLFiddle demo\n\n" ]

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[ "The present invention relates generally to the field of electrosurgery, and more particularly to surgical devices and methods which employ high frequency electrical energy to treat tissue in regions of the head and neck, such as the ear, nose and throat. ", "The present invention is particularly suited for treating obstructive sleep disorders, such as sleep-apnea, snoring and the like.", "\nSleep-apnea syndrome is a medical condition characterized by daytime hypersomnolence, intellectual deterioration, cardiac arrhythmias, snoring and thrashing during sleep. ", "This syndrome is typically divided into two types. ", "One type, termed xe2x80x9ccentral sleep apnea syndromexe2x80x9d, is characterized by repeated loss of respiratory effort. ", "The second type, termed obstructive sleep apnea syndrome, is characterized by repeated apneic episodes during sleep resulting from obstruction of the patient\"\"s upper airway.", "\nTreatment for sleep apnea has included various medical, surgical and physical measures. ", "Medical measures include the use of medications and the avoidance of central nervous system depressants, such as sedatives or alcohol. ", "These measures are sometimes helpful, but rarely completely effective. ", "Physical measures have included weight loss, opening nasopharygeal airways, nasal CPAP and various tongue retaining devices used nocturnally. ", "These measures are cumbersome, uncomfortable and difficult to use for prolonged periods of time. ", "In particular, CPAP devices, which act essentially as a pneumatic xe2x80x9csplintxe2x80x9d to the airway to alleviate the obstruction, must be used for the entire patient\"\"s lifetime, and typically requires close to 100% usage of the device while sleeping and napping. ", "These factors result in limited patient compliance with CPAP devices, reducing the effectiveness of the therapy.", "\nSurgical interventions have included uvulopalatopharyngoplasty (UPPP), laser-assisted uvuloplasty procedures (LAUP), tonsillectomy, surgery to correct severe retrognathia and tracheostomy. ", "The LAUP procedures involve the use a CO2 laser to excise and vaporize excess tissue in the region of the palate and uvula. ", "In UPPP procedures, a scalpel or conventional electrocautery device is typically employed to remove portions of the uvula, palate, pharynx and/or tonsils. ", "While these procedures are effective, the risk of surgery in some patients is often prohibitive. ", "In addition, UPPP and LAUP procedures performed with conventional electrocautery or laser devices typically generate extreme post-operative pain which may be unacceptable to the patient.", "\nRecently, RF energy has been used to selectively destroy portions of the tongue and soft palate to treat air passage disorders, such as sleep apnea. ", "This procedure, which was developed by Somnus Medical Technologies of Sunnyvale, Calif., involves the use of a monopolar electrode that directs RF current into the target tissue to desiccate or destroy submucosal tissue in the patient\"\"s mouth. ", "Of course, such monopolar devices suffer from the disadvantage that the electric current will flow through undefined paths in the patient\"\"s body, thereby increasing the risk of unwanted electrical stimulation to portions of the patient\"\"s body. ", "In addition, since the defined path through the patient\"\"s body has a relatively high impedance (because of the large distance or resistivity of the patient\"\"s body), large voltage differences must typically be applied between the return and active electrodes in order to generate a current suitable for ablation or cutting of the target tissue. ", "This current, however, may inadvertently flow along body paths having less impedance than the defined electrical path, which will substantially increase the current flowing through these paths, possibly causing damage to or destroying surrounding tissue or neighboring peripheral nerves.", "\nAnother disadvantage of conventional RF devices, such as the Somnus monopolar electrode, is that these devices typically operate by creating a voltage difference between the active electrode and the target tissue, causing an electrical arc to form across the physical gap between the electrode and tissue. ", "At the point of contact of the electric arcs with tissue, rapid tissue heating occurs due to high current density between the electrode and tissue. ", "This high current density causes cellular fluids to rapidly vaporize into steam, thereby producing a xe2x80x9ccutting effectxe2x80x9d along the pathway of localized tissue heating. ", "Thus, the tissue is parted along the pathway of evaporated cellular fluid, inducing undesirable collateral tissue damage in regions surrounding the target tissue site. ", "This collateral tissue damage often causes indiscriminate destruction of tissue, resulting in the loss of the proper function of the tissue. ", "In addition, the device does not remove any tissue directly, but rather depends on destroying a zone of tissue and allowing the body to eventually remove the destroyed tissue.", "\nYet another disadvantage with the Somnus technology is that the procedure typically takes a long time, often requiring the electrical energy to be applied to the submucosal tissue for a period of longer than a minute. ", "This can be quite uncomfortable to the patient, who is typically awake during the procedure.", "\nThe present invention provides systems, apparatus and methods for selectively applying electrical energy to structures in the head and neck of a patient\"\"s body, such as tissue within the ear, nose and throat. ", "The systems and methods of the present invention are particularly useful for treating obstructive sleep disorders, such as snoring or sleep apnea. ", "The present invention includes a channeling technique in which small holes or channels are formed within tissue structures in the mouth, such as the tonsils, tongue, palate and uvula, and thermal energy is applied to the tissue surface immediately surrounding these holes or channels to cause thermal damage to the tissue surface, thereby stiffening the surrounding tissue structure. ", "Applicant has discovered that such stiffening of certain tissue structures in the mouth and throat helps to prevent the tissue structure from obstructing the patient\"\"s upper airway during sleep.", "\nMethods of the present invention include introducing one or more active electrode(s) into the patient\"\"s mouth, and positioning the active electrode(s) adjacent the target tissue, e.g., selected portions of the tongue, tonsils, soft palate tissues (e.g., the uvula and pharynx), hard tissue or other mucosal tissue. ", "High frequency voltage is applied between the active electrode(s) and one or more return electrode(s) to volumetrically remove or ablate at least a portion of the target tissue, and the active electrode(s) are advanced through the space left by the ablated tissue to form a channel, hole, divot or other space in the target tissue. ", "The active electrode(s) are then removed from the channel, and other channels or holes may be formed at suitable locations in the patient\"\"s mouth or throat. ", "In preferred embodiments, high frequency voltage is applied to the active electrode(s) as they are removed from the hole or channel. ", "The high frequency voltage is below the threshold for ablation of tissue to effect hemostasis of severed blood vessels within the tissue surface surrounding the hole. ", "In addition, the high frequency voltage effects a controlled depth of thermal heating of the tissue surrounding the hole to thermally damage at least the surface of this tissue without destroying or otherwise debulking the underlying tissue. ", "This thermal damage stiffens the tissue structure, thereby reducing obstructions to the patient\"\"s air passages.", "\nIn a specific configuration, electrically conductive media, such as isotonic saline or an electrically conductive gel, is delivered to the target site within the mouth to substantially surround the active electrode(s) with the media. ", "The media may be delivered through an instrument to the specific target site, or the entire target region may be filled with conductive media such that the electrode terminal(s) are submerged during the procedure. ", "Alternatively, the distal end of the instrument may be dipped or otherwise applied to the conductive media prior to introduction into the patient\"\"s mouth. ", "In all of these embodiments, the electrically conductive media is applied or delivered such that it provides a current flow path between the active and return electrode(s). ", "In other embodiments, the intracellular conductive fluid in the patient\"\"s tissue may be used as a substitute for, or as a supplement to, the electrically conductive media that is applied or delivered to the target site. ", "For example, in some embodiments, the instrument is dipped into conductive media to provide a sufficient amount of fluid to initiate the requisite conditions for ablation. ", "After initiation, the conductive fluid already present in the patient\"\"s tissue is used to sustain these conditions.", "\nIn the representative embodiments, the active electrode(s) are advanced into the target tissue in the ablation mode, where the high frequency voltage is sufficient to ablate or remove the target tissue through molecular dissociation or disintegration processes. ", "In these embodiments, the high frequency voltage applied to the electrode terminal(s) is sufficient to vaporize an electrically conductive fluid (e.g., gel, saline and/or intracellular fluid) between the electrode terminal(s) and the tissue. ", "Within the vaporized fluid, a ionized plasma is formed and charged particles (e.g., electrons) are accelerated towards the tissue to cause the molecular breakdown or disintegration of several cell layers of the tissue. ", "This molecular dissociation is accompanied by the volumetric removal of the tissue. ", "The short range of the accelerated charged particles within the plasma layer confines the molecular dissociation process to the surface layer to minimize damage and necrosis to the underlying tissue. ", "This process can be precisely controlled to effect the volumetric removal of tissue as thin as 10 to 150 microns with minimal heating of, or damage to, surrounding or underlying tissue structures. ", "A more complete description of this phenomena is described in commonly assigned U.S. Pat. ", "No. ", "5,697,882 the complete disclosure of which is incorporated herein by reference.", "\nThe active electrode(s) are usually removed from the holes or channels in the subablation or thermal heating mode, where the high frequency voltage is below the threshold for ablation as described above, but sufficient to coagulate severed blood vessels and to effect thermal damage to at least the surface tissue surrounding the holes. ", "In some embodiments, the active electrode(s) are immediately removed from the holes after being placed into the subablation mode. ", "In other embodiments, the physician may desire to control the rate of removal of the active electrode(s) and/or leave the active electrode(s) in the hole for a period of time, e.g., on the order of about 1 to 10 seconds, in the subablation mode to increase the depth of thermal damage to the tissue.", "\nIn one method, high frequency voltage is applied, in the ablation mode, between one or more active electrode(s) and a return electrode spaced axially from the active electrode(s), and the active electrode(s) are advanced into the tissue to form a hole or channel as described above. ", "High frequency voltage is then applied between the return electrode and one or more third electrode(s), in the thermal heating mode, as the electrosurgical instrument is removed from the hole. ", "In one embodiment, the third electrode is a dispersive return pad on the external surface of the skin. ", "In this embodiment, the thermal heating mode is a monopolar mode, in which current flows from the return electrode, through the patient\"\"s body, to the return pad. ", "In other embodiments, the third electrode(s) are located on the electrosurgical instrument and the thermal heating mode is bipolar. ", "In all of the embodiments, the third electrode(s) are designed to increase the depth of current penetration in the tissue over the ablation mode so as to increase the thermal damage.", "\nIn another method, the third or coagulation electrode is placed in the thermal heating mode at the same time that the active electrode(s) is placed in the ablation mode. ", "In this embodiment, electric current is passed from the coagulation electrode, through the tissue surrounding the hole, to the return electrode at the same time that current is passing between the active and return electrodes. ", "In a specific configuration, this is accomplished by reducing the voltage applied to the coagulation electrode with a passive or active element coupled between the power supply and the coagulation electrode. ", "In this manner, the instrument will immediately begin to coagulate and heat the tissue surrounding the hole as soon as the coagulation electrode enters the hole so that the tissue can close the electric circuit between the coagulation and return electrodes.", "\nIn one method, an electrosurgical instrument having an electrode assembly is dipped into electrically conductive fluid such that the conductive fluid is located around and between both active and return electrodes in the electrode assembly. ", "The instrument is then introduced into the patient\"\"s mouth to the back of the tongue, and a plurality of holes are formed across the base of the tongue as described above. ", "The instrument is removed from each hole in the thermal heating mode to create thermal damage and to coagulate blood vessels. ", "Typically, the instrument will be dipped into the conductive fluid after being removed from each hole to ensure that sufficient conductive fluid exists for plasma formation and to conduct electric current between the active and return electrodes. ", "This procedure stiffens the base of the tongue, which inhibits the tongue from obstructing breathing as the patient sleeps.", "\nSystems according to the present invention generally include an electrosurgical instrument having a shaft with proximal and distal ends, an electrode assembly at the distal end and one or more connectors coupling the electrode assembly to a source of high frequency electrical energy. ", "The electrode assembly includes one or more active electrode(s) configured for tissue ablation, a return electrode spaced from the active electrode(s) on the instrument shaft and a third, coagulation electrode spaced from the return electrode on the instrument shaft. ", "The system further includes a power source coupled to the electrodes on the instrument shaft for applying a high frequency voltage between the active and return electrodes, and between the coagulation and return electrodes, at the same time. ", "The voltage applied between the coagulation and return electrodes is substantially lower than the voltage applied between the active and return electrodes to allow the former to coagulation severed blood vessels and heat tissue, while the latter ablates tissue.", "\nThe active electrode(s) may comprise a single active electrode, or an electrode array, extending from an electrically insulating support member, typically made of an inorganic material such as ceramic, silicone or glass. ", "The active electrode will usually have a smaller exposed surface area than the return and coagulation electrodes such that the current densities are much higher at the active electrode than at the other electrodes. ", "Preferably, the return and coagulation electrodes have relatively large, smooth surfaces extending around the instrument shaft to reduce current densities, thereby minimizing damage to adjacent tissue.", "\nIn one embodiment, the system comprises a voltage reduction element coupled between the power source and the coagulation electrode to reduce the voltage applied to the coagulation electrode. ", "The voltage reduction element will typically comprise a passive element, such as a capacitor, resistor, inductor or the like. ", "In the representative embodiment, the power supply will apply a voltage of about 150 to 350 volts rms between the active and return electrodes, and the voltage reduction element will reduce this voltage to about 20 to 90 volts rms to the coagulation electrode. ", "In this manner, the voltage delivered to the coagulation electrode is below the threshold for ablation of tissue, but high enough to coagulation and heat the tissue.", "\nThe apparatus may further include a fluid delivery element for delivering electrically conducting fluid to the electrode terminal(s) and the target site. ", "The fluid delivery element may be located on the instrument, e.g., a fluid lumen or tube, or it may be part of a separate instrument. ", "Alternatively, an electrically conducting gel or spray, such as a saline electrolyte or other conductive gel, may be applied to the electrode assembly or the target site. ", "In this embodiment, the apparatus may not have a fluid delivery element. ", "In both embodiments, the electrically conducting fluid will preferably generate a current flow path between the electrode terminal(s) and the return electrode(s)." ]

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[ "Order Michigan Supreme Court\n Lansing, Michigan\n\n February 4, 2015 Robert P. Young, Jr.,\n Chief Justice\n\n 149562 Stephen J. Markman\n Mary Beth Kelly\n Brian K. Zahra\n Bridget M. McCormack\n David F. Viviano\n PEOPLE OF THE STATE OF MICHIGAN, Richard H. Bernstein,\n Plaintiff-Appellee, Justices\n\n v SC: 149562\n COA: 319705\n Wayne CC: 08-008020-FC\n JOHNATHAN FORD,\n Defendant-Appellant.", "\n\n ____________________________________/\n\n On order of the Court, the application for leave to appeal the June 3, 2014 order of\n the Court of Appeals is considered, and it is DENIED, because the defendant has failed to\n meet the burden of establishing entitlement to relief under MCR 6.508(D).", "\n\n\n\n\n I, Larry S. Royster, Clerk of the Michigan Supreme Court, certify that the\n foregoing is a true and complete copy of the order entered at the direction of the Court.", "\n February 4, 2015\n h0128\n Clerk\n\f" ]

[ 0.004851425106124924, 0.006578947368421052, 0.018433179723502304, 0.006756756756756757 ]

[ "\"\"\" Util functions for SMPL\n@@batch_skew\n@@batch_rodrigues\n@@batch_lrotmin\n@@batch_global_rigid_transformation\n\"\"\"\n\nfrom __future__ import absolute_import\nfrom __future__ import division\nfrom __future__ import print_function\n\nimport tensorflow as tf\n\n\ndef batch_skew(vec, batch_size=None, name=''):\n \"\"\"\n vec is N x 3, batch_size is int\n\n returns N x 3 x 3. ", "Skew_sym version of each matrix.", "\n \"\"\"\n with tf.name_scope(name, \"batch_skew\", [vec]):\n if batch_size is None:\n batch_size = vec.shape.as_list()[0]\n col_inds = tf.constant([1, 2, 3, 5, 6, 7])\n indices = tf.reshape(\n tf.reshape(tf.range(0, batch_size) * 9, [-1, 1]) + col_inds,\n [-1, 1])\n updates = tf.reshape(\n tf.stack(\n [\n -vec[:, 2], vec[:, 1], vec[:, 2], -vec[:, 0], -vec[:, 1],\n vec[:, 0]\n ],\n axis=1), [-1])\n out_shape = [batch_size * 9]\n res = tf.scatter_nd(indices, updates, out_shape)\n res = tf.reshape(res, [batch_size, 3, 3])\n\n return res\n\n\ndef batch_rodrigues(theta, name='', dtype=tf.float64):\n \"\"\"\n Theta is N x 3\n \"\"\"\n with tf.name_scope(name, \"batch_rodrigues\", [theta]):\n batch_size = theta.shape.as_list()[0]\n angle = tf.expand_dims(tf.clip_by_value(tf.norm(theta, axis=1), 1e-16, 1e16), -1)\n r = tf.expand_dims(tf.math.divide_no_nan(theta, angle), -1)\n\n angle = tf.expand_dims(angle, -1)\n cos = tf.cos(angle)\n sin = tf.sin(angle)\n\n outer = tf.matmul(r, r, transpose_b=True, name=\"outer\")\n eyes = tf.tile(tf.expand_dims(tf.eye(3, dtype=dtype), 0), [batch_size, 1, 1])\n R = cos * eyes + (1 - cos) * outer + sin * batch_skew(r, batch_size=batch_size)\n return R\n\n\ndef batch_lrotmin(theta, name=''):\n \"\"\" NOTE: not used bc I want to reuse R and this is simple.", "\n Output of this is used to compute joint-to-pose blend shape mapping.", "\n Equation 9 in SMPL paper.", "\n\n\n Args:\n pose: `Tensor`, N x 72 vector holding the axis-angle rep of K joints.", "\n This includes the global rotation so K=24\n\n Returns\n diff_vec : `Tensor`: N x 9*(num_joints-1) rotation matrix of (K-1) joints with identity subtracted.,", "\n \"\"\"\n with tf.name_scope(name, \"batch_lrotmin\", [theta]):\n with tf.name_scope(\"ignore_global\"):\n theta = theta[:, 3:]\n\n # N*23 x 3 x 3\n Rs = batch_rodrigues(tf.reshape(theta, [-1, 3]))\n lrotmin = tf.reshape(Rs - tf.eye(3), [-1, 207])\n\n return lrotmin\n\n\ndef batch_global_rigid_transformation(Rs, Js, parent, rotate_base=False, name=''):\n \"\"\"\n Computes absolute joint locations given pose.", "\n\n rotate_base: if True, rotates the global rotation by 90 deg in x axis.", "\n if False, this is the original SMPL coordinate.", "\n\n Args:\n Rs: N x num_joints x 3 x 3 rotation vector of K joints\n Js: N x num_joints x 3, joint locations before posing\n parent: num_joints holding the parent id for each index\n\n Returns\n new_J : `Tensor`: N x num_joints x 3 location of absolute joints\n A : `Tensor`: N x num_joints 4 x 4 relative joint transformations for LBS.", "\n \"\"\"\n\n num_joints = parent.shape[0]\n with tf.name_scope(name, \"batch_forward_kinematics\", [Rs, Js]):\n N = Rs.shape[0].value\n if rotate_base:\n print('Flipping the SMPL coordinate frame!!!!')", "\n rot_x = tf.constant([[1, 0, 0], [0, -1, 0], [0, 0, -1]], dtype=Rs.dtype)\n rot_x = tf.reshape(tf.tile(rot_x, [N, 1]), [N, 3, 3])\n root_rotation = tf.matmul(Rs[:, 0, :, :], rot_x)\n else:\n root_rotation = Rs[:, 0, :, :]\n\n # Now Js is N x num_joints x 3 x 1\n Js = tf.expand_dims(Js, -1)\n\n def make_A(R, t, name=''):\n # Rs is N x 3 x 3, ts is N x 3 x 1\n with tf.name_scope(name, \"Make_A\", [R, t]):\n R_homo = tf.pad(R, [[0, 0], [0, 1], [0, 0]])\n t_homo = tf.concat([t, tf.ones([N, 1, 1], dtype=t.dtype)], 1)\n return tf.concat([R_homo, t_homo], 2)\n\n A0 = make_A(root_rotation, Js[:, 0])\n results = [A0]\n for i in range(1, parent.shape[0]):\n j_here = Js[:, i] - Js[:, parent[i]]\n A_here = make_A(Rs[:, i], j_here)\n res_here = tf.matmul(results[parent[i]], A_here, name=\"propA%d\" % i)\n results.append(res_here)\n\n results = tf.stack(results, axis=1)\n\n new_J = results[:, :, :3, 3]\n\n # --- Compute relative A: Skinning is based on\n # how much the bone moved (not the final location of the bone)\n # but (final_bone - init_bone)\n # ---\n Js_w0 = tf.concat([Js, tf.zeros([N, num_joints, 1, 1], dtype=Js.dtype)], 2)\n init_bone = tf.matmul(results, Js_w0)\n # Append empty 4 x 3:\n init_bone = tf.pad(init_bone, [[0, 0], [0, 0], [0, 0], [3, 0]])\n A = results - init_bone\n\n return new_J, A\n" ]

[ 0.010899182561307902, 0, 0.010561056105610561, 0, 0.03333333333333333, 0.011363636363636364, 0.005747126436781609, 0.008968609865470852, 0, 0.038461538461538464, 0.008264462809917356, 0.004464285714285714, 0.004487179487179487 ]

[ "Q:\n\nIs there official clarification how firbolg's Hidden Step interacts with delayed damage/save effects?", "\n\nThe playable Firbolg race from Volo's Guide to Monsters has the Hidden Step racial feature (emphasis mine):\n\nHidden Step. ", "As a bonus action, you can magically turn invisible until the start of your next turn or until you attack, make a damage roll, or force someone to make a saving throw. ", "Once you use this trait, you can't use it again until you finish a short or long rest.", "\n\nI can see how the text says it works, but there are situations where its wording ends invisibility without you taking any offensive action. ", "That's really unusual for invisibility effects.", "\n(For example, the spell Booming Blade makes you make a damage roll for the spell later, but it's not you personally taking new offensive action: it deals damage when a previously-hit opponent moves before the caster's next turn.)", "\nTherefore my question: Have any errata or developer statements been made that clarify if “passive” delayed damage rolls or saving throws aren't meant to end Hidden Step?", "\nI'm specifically looking for official statements clarifying this exact kind of interaction. ", "Interpretations based on the text aren't useful answers because I can already see how the interaction works absent errata, and speculation on the intention aren't official clarification.", "\nI myself have been unable to find an official statement that clarifies this issue, only this statement, which confirms that you are allowed to cast beneficial spells.", "\n\nA:\n\nYes, there is now an (un)official statement\nJeremy Crawford has clarified in a Tweet:\n\nQ: A firbolg PC casts booming blade then uses hidden step to go invisible. ", "The creature that is hit with booming blade moves away and\nthus takes damage. ", "Does hidden step deactivate?", "\nA: Hidden Step ends if you make a damage roll, no matter when you make\nit.", "\nQ: So it doesn't matter if a spell/effect is initiated by you before\nhidden step was activated? ", "As long as you make a creature do a saving\nthrow or attack or roll damage for any reason then hidden step ends?", "\nA: That's correct.", "\n\nSo, passive or not, as long as a creature is making a saving throw or taking damage from an effect you initiated (no matter when you initiated it) for any reason, hidden step will end.", "\nThis matches the intent we can understand when reading the ability itself.", "\nIntent is clear from reading as well: if the user causes a harmful effect, hidden step deactivates.", "\nThe ability is explicitly written to restrict just about every way you can damage or harm an opponent (regardless of when said effect was initiated), so it seems clear that the intent was to prevent the user from doing harmful things. ", "As such, allowing a loophole for spells and effects cast/initiated before the user used hidden step runs counter to that intent.", "\nIt may also be helpful to note that the designers also intentionally wrote this ability so as not to restrict beneficial spells and abilities being used.", "\nThe ability is already quite powerful and from a DM standpoint this argument would seem like an attempt to cheese additional power out of the ability by circumventing its primary restrictions.", "\nThis also seems wholly fair. ", "In the example of booming blade, the only reason to cast such a spell is to try to cause damage. ", "If you also choose to use hidden step you are taking the risk that the opponent triggers that damage and thus cancels your ability. ", "It was player choice to cast the spell and to use the ability.", "\nAllowing this opens the door for plenty of bad things/cheese\nOur heroic firbolgs casts delayed blast fireball at a group of 4 enemies, uses hidden step, then immediately stops concentrating on the spell. ", "It takes no action to stop concentrating on a spell so this is the exact same scenario as with booming blade. ", "This causes 4 saving throws and 4 creatures to take up to 12d6 damage.", "\nDoes it seem to be intended to allow such an effect to not break hidden step? ", "This seems like an overtly harmful action and I really do not think for one second that the designers intended this to be the case.", "\nAnd this is only a cursory look at one spell. ", "I'm sure that there are many more and possibly even worse spells/effects one could get away with through this loophole.", "\nNeither RAW nor RAI support allowing a loophole for effects initiated before hidden step is activated.", "\nAs always, a DM may, of course, allow this if they want to for any reason.", "\n\n" ]

[ 0.01904761904761905, 0.016129032258064516, 0, 0, 0, 0, 0.004347826086956522, 0, 0, 0.005376344086021506, 0, 0.005952380952380952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Formed in 2002, Duo Transatlantique combines the prize-winning talents of guitarists Benjamin Beirs and Maud Laforest. ", "Soon after beginning their studies at the Peabody Institute of the Johns Hopkins University in Baltimore, MD, the two decided to form a guitar duo, under the guidance of Julian Gray, an acclaimed chamber musician and founder of the Gray-Pearl guitar duo. ", "In 2005, Ben embarked on his first journey to France, where the duo won first prize in the Union Française des Artistes Musiciens Guitar Duo Competition and played a concert in the American Cathedral in Paris. ", "Since then, they have continued touring annually. ", "Currently, Ms. Laforest lives in Reims, France, while Mr. Beirs has stayed in Baltimore.", "\n\nTheir newly-released second album is entitled “From Moment to Moment.” ", "It features arrangements of the French film score “Amelie” by Yann Tiersen and includes music by Penicaud, Joplin, Bellinati, Scarlatti, L'Hoyer, and Franck. ", "The French magazine Guitare Classique writes, “The sonority is rich and one of the most flattering we’ve ever heard...don't hesitate to buy this CD!” ", "Classical Music Sentinel says, “The versatility in their playing is reflected in the variety and different styles of pieces...by versatility, I mean the flexible, expressive approach and playing techniques they bring to every different piece, from the Baroque clarity of the Scarlatti, to the simple fun of the Joplin, and the melancholy of the Tiersen...performed here in a superb arrangement.” ", "Their debut album, entitled \"Le Gris et le Vert\" (The Grey and the Green) includes music of Debussy, Scarlatti, Petit, Albeniz, and Villoldo. ", "Visit http://www.duotransatlantique.com for more information." ]

[ 0.025210084033613446, 0.01568627450980392, 0.004761904761904762, 0, 0.022727272727272728, 0, 0.02531645569620253, 0.006666666666666667, 0.007575757575757576, 0.014084507042253521, 0.01639344262295082 ]

[ "<?", "xml version=\"1.0\" encoding=\"utf-8\" ?", ">\n\n<chapter id=\"fixtures\">\n <title>Fixtures</title>\n\n <para>\n <indexterm><primary>Fixture</primary></indexterm>\n\n L'une des parties les plus consommatrices en temps lors de l'écriture\n de tests est d'écrire le code pour configurer le monde dans un état connu\n puis de le remettre dans son état initial quand le test est terminé. ", "Cet état\n connu est appelé la <emphasis>fixture</emphasis> du test.", "\n </para>\n\n <para>\n Dans <xref linkend=\"writing-tests-for-phpunit.examples.", "StackTest.php\" />, la\n fixture était simplement le tableau sauvegardé dans la variable <literal>$fixture</literal>.", "\n La plupart du temps, cependant, la fixture sera beaucoup plus complexe\n qu'un simple tableau, et le volume de code nécessaire pour la mettre en place\n croîtra dans les mêmes proportions. ", "Le contenu effectif du test sera perdu\n dans le bruit de configuration de la fixture. ", "Ce problème s'aggrave quand \n vous écrivez plusieurs tests doté de fixtures similaires. ", "Sans l'aide du\n framework de test, nous aurions à dupliquer le code qui configure la fixture\n pour chaque test que nous écrivons.", "\n </para>\n\n <para>\n <indexterm><primary>Méthode canevas</primary></indexterm>\n <indexterm><primary>setUp()</primary></indexterm>\n <indexterm><primary>tearDown()</primary></indexterm>\n\n PHPUnit gère le partage du code de configuration. ", "Avant qu'une méthode de test ne soit\n lancée, une méthode canevas appelée <literal>setUp()</literal> est invoquée.", "\n <literal>setUp()</literal> est l'endroit où vous créez les objets sur lesquels\n vous allez passer les tests. ", "Une fois que la méthode de test est finie, qu'elle ait\n réussi ou échoué, une autre méthode canevas appelée\n <literal>tearDown()</literal> est invoquée. ", "<literal>tearDown()</literal>\n est l'endroit où vous nettoyez les objets sur lesquels vous avez passé les tests.", "\n </para>\n\n <para>\n Dans <xref linkend=\"writing-tests-for-phpunit.examples.", "StackTest2.php\" /> nous avons\n utilisé la relation producteur-consommateur entre les tests pour partager une fixture. ", "Ce\n n'est pas toujours souhaitable ni même possible. ", "<xref linkend=\"fixtures.examples.", "StackTest.php\"/>\n montre comme nous pouvons écrire les tests de <literal>PileTest</literal> de telle façon\n que ce n'est pas la fixture elle-même qui est réutilisée mais le code qui l'a créée.", "\n D'abord nous déclarons la variable d'instance, <literal>$pile</literal>, que nous\n allons utiliser à la place d'une variable locale à la méthode. ", "Puis nous plaçons\n la création de la fixture <literal>tableau</literal> dans la méthode \n <literal>setUp()</literal>. ", "Enfin, nous supprimons le code redondant des méthodes\n de test et nous utilisons la variable d'instance nouvellement introduite.", "\n <literal>$this->pile</literal>, à la place de la variable locale à la méthode\n <literal>$pile</literal> avec la méthode d'assertion <literal>assertEquals()</literal>.", "\n </para>\n\n <example id=\"fixtures.examples.", "StackTest.php\">\n <title>Using setUp() to create the stack fixture</title>\n <programlisting><![CDATA[<?php\nclass PileTest extends PHPUnit_Framework_TestCase\n{\n protected $pile;\n\n protected function setUp()\n {\n $this->pile = array();\n }\n\n public function testVide()\n {\n $this->assertTrue(empty($this->pile));\n }\n\n public function testPush()\n {\n array_push($this->pile, 'foo');\n $this->assertEquals('foo', $this->pile[count($this->pile)-1]);\n $this->assertFalse(empty($this->pile));\n }\n\n public function testPop()\n {\n array_push($this->pile, 'foo');\n $this->assertEquals('foo', array_pop($this->pile));\n $this->assertTrue(empty($this->pile));\n }\n}\n?", ">]]></programlisting>\n </example>\n\n <para>\n <indexterm><primary>Méthode canevas</primary></indexterm>\n <indexterm><primary>setUpBeforeClass()</primary></indexterm>\n <indexterm><primary>setUp()</primary></indexterm>\n <indexterm><primary>tearDown()</primary></indexterm>\n <indexterm><primary>tearDownAfterClass()</primary></indexterm>\n\n Les méthodes canevas <literal>setUp()</literal> et <literal>tearDown()</literal>\n sont exécutées une fois pour chaque méthode de test (et pour les nouvelles instances)\n de la classe de cas de test.", "\n </para>\n\n <para>\n <indexterm><primary>Méthode canevas</primary></indexterm>\n <indexterm><primary>setUpBeforeClass()</primary></indexterm>\n <indexterm><primary>setUp()</primary></indexterm>\n <indexterm><primary>assertPreConditions()</primary></indexterm>\n <indexterm><primary>assertPostConditions()</primary></indexterm>\n <indexterm><primary>tearDown()</primary></indexterm>\n <indexterm><primary>tearDownAfterClass()</primary></indexterm>\n <indexterm><primary>onNotSuccessfulTest()</primary></indexterm>\n\n De plus, les méthodes canevas <literal>setUpBeforeClass()</literal> et\n <literal>tearDownAfterClass()</literal> sont appelées respectivement avant \n que le premier test de la classe de cas de test ne soit exécuté et après\n que le dernier test de la classe de test a été exécuté.", "\n </para>\n\n <para>\n <indexterm><primary>Méthode canevas</primary></indexterm>\n\n L'exemple ci-dessous montre toutes les méthodes canevas qui sont disponibles\n dans une classe de cas de test.", "\n </para>\n\n <example id=\"fixtures.examples.", "TemplateMethodsTest.php\">\n <title>Exemple montrant toutes les méthodes canevas disponibles</title>\n <programlisting><![CDATA[<?php\nclass TemplateMethodsTest extends PHPUnit_Framework_TestCase\n{\n public static function setUpBeforeClass()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n protected function setUp()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n protected function assertPreConditions()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n public function testOne()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n $this->assertTrue(TRUE);\n }\n\n public function testTwo()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n $this->assertTrue(FALSE);\n }\n\n protected function assertPostConditions()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n protected function tearDown()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n public static function tearDownAfterClass()\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n }\n\n protected function onNotSuccessfulTest(Exception $e)\n {\n fwrite(STDOUT, __METHOD__ . \"", "\\n\");\n throw $e;\n }\n}\n?", ">]]></programlisting>\n <screen><userinput>phpunit TemplateMethodsTest</userinput><![CDATA[\nPHPUnit 5.0.0 by Sebastian Bergmann and contributors.", "\n\nTemplateMethodsTest::setUpBeforeClass\nTemplateMethodsTest::setUp\nTemplateMethodsTest::assertPreConditions\nTemplateMethodsTest::testOne\nTemplateMethodsTest::assertPostConditions\nTemplateMethodsTest::tearDown\n.TemplateMethodsTest::setUp\nTemplateMethodsTest::assertPreConditions\nTemplateMethodsTest::testTwo\nTemplateMethodsTest::tearDown\nTemplateMethodsTest::onNotSuccessfulTest\nFTemplateMethodsTest::tearDownAfterClass\n\n\nTime: 0 seconds, Memory: 5.25Mb\n\nThere was 1 failure:\n\n1) TemplateMethodsTest::testTwo\nFailed asserting that <boolean:false> is true.", "\n/home/sb/TemplateMethodsTest.php:30\n\nFAILURES!", "\nTests: 2, Assertions: 2, Failures: 1.]]></screen>\n </example>\n\n <section id=\"fixtures.more-setup-than-teardown\">\n <title>Plus de setUp() que de tearDown()</title>\n\n <para>\n <literal>setUp()</literal> et <literal>tearDown()</literal> sont sympathiquement\n symétriques en théorie mais pas en pratique. ", "En pratique, vous n'avez besoin \n d'implémenter <literal>tearDown()</literal> que si vous avez alloué\n des ressources externes telles que des fichiers ou des sockets dans\n <literal>setUp()</literal>. ", "Si votre <literal>setUp()</literal> ne crée simplement\n que de purs objets PHP, vous pouvez généralement ignorer <literal>tearDown()</literal>. ", "\n Cependant, si vous créez de nombreux objets dans votre <literal>setUp()</literal>, vous\n pourriez vouloir libérer (<literal>unset()</literal>) les variables pointant vers\n ces objets dans votre <literal>tearDown()</literal> de façon à ce qu'ils puissent être\n récupérés par le ramasse-miettes. ", "Le nettoyage des objets de cas de test n'est pas \n prévisible.", "\n </para>\n </section>\n\n <section id=\"fixtures.variations\">\n <title>Variantes</title>\n\n <para>\n Que se passe-t'il si vous avez deux tests avec deux setups légèrement\n différents ? ", "Il y a deux possibilités :\n </para>\n\n <itemizedlist>\n <listitem>\n <para>\n Si le code des <literal>setUp()</literal> ne diffère que légèrement, extrayez le\n code qui diffère du code de <literal>setUp()</literal> pour le mettre dans la méthode\n de test.", "\n </para>\n </listitem>\n\n <listitem>\n <para>\n Si vous avez vraiment deux <literal>setUp()</literal> différentes, vous\n avez besoin de classes de cas de test différentes. ", "Nommez les classes selon\n les différences constatées dans les setup.", "\n </para>\n </listitem>\n </itemizedlist>\n </section>\n\n <section id=\"fixtures.sharing-fixture\">\n <title>Partager les Fixtures</title>\n\n <para>\n Il existe quelques bonnes raisons pour partager des fixtures entre les tests,\n mais dans la plupart des cas la nécessité de partager une fixture entre plusieurs\n tests résulte d'un problème de conception non résolu.", "\n </para>\n\n <para>\n Un bon exemple de fixture qu'il est raisonnable de partager entre plusieurs\n tests est une connexion à une base de données : vous vous connectez une fois\n à la base de données et vous réutilisez cette connexion au lieu d'en créer \n une nouvelle pour chaque test. ", "Ceci rend vos tests plus rapides.", "\n </para>\n\n <para>\n <indexterm><primary>setUpBeforeClass</primary></indexterm>\n <indexterm><primary>tearDownAfterClass</primary></indexterm>\n\n <xref linkend=\"fixtures.sharing-fixture.examples.", "DatabaseTest.php\" />\n utilise les méthodes canevas <literal>setUpBeforeClass()</literal> et\n <literal>tearDownAfterClass()</literal> pour respectivement établir la connexion à la \n base de données avant le premier test de la classe de cas de test et pour\n de déconnecter de la base de données après le dernier test du cas de test.", "\n </para>\n\n <example id=\"fixtures.sharing-fixture.examples.", "DatabaseTest.php\">\n <title>Partager les fixtures entre les tests d'une série de tests</title>\n <programlisting><![CDATA[<?php\nclass DatabaseTest extends PHPUnit_Framework_TestCase\n{\n protected static $dbh;\n\n public static function setUpBeforeClass()\n {\n self::$dbh = new PDO('sqlite::memory:');\n }\n\n public static function tearDownAfterClass()\n {\n self::$dbh = NULL;\n }\n}\n?", ">]]></programlisting>\n </example>\n\n <para>\n On n'insistera jamais assez sur le fait que partager les fixtures\n entre les tests réduit la valeur de ces tests. ", "Le problème de conception\n sous-jacent est que les objets ne sont pas faiblement couplés. ", "Vous pourrez\n obtenir de meilleurs résultats en résolvant le problème de conception\n sous-jacent puis en écrivant des tests utilisant des bouchons \n (voir <xref linkend=\"test-doubles\" />), plutôt qu'en créant\n des dépendances entre les tests à l'exécution et en ignorant l'opportunité\n d'améliorer votre conception.", "\n </para>\n </section>\n\n <section id=\"fixtures.global-state\">\n <title>Etat global</title>\n\n <para>\n <ulink url=\"http://googletesting.blogspot.com/2008/05/tott-using-dependancy-injection-to.html\">Il est difficile de tester du code qui utilise des singletons.</ulink>\n La même chose est vraie pour le code qui utilise des variables globales. ", "Typiquement,\n le code que vous voulez tester est fortement couplé avec une variable globale et \n vous ne pouvez pas contrôler sa création. ", "Un problème additionnel réside dans le fait\n qu'un test qui modifie une variable globale peut faire échouer un autre test.", "\n </para>\n\n <para>\n En PHP, les variables globales fonctionnent comme ceci :\n </para>\n\n <itemizedlist>\n <listitem><para>Une variable globale <literal>$foo = 'bar';</literal> est enregistrée comme <literal>$GLOBALS['foo'] = 'bar';</literal>.</para></listitem>\n <listitem><para>La variable <literal>$GLOBALS</literal> est une variable appelée <emphasis>super-globale</emphasis>.</para></listitem>\n <listitem><para>Les variables super-globales sont des variables internes qui sont toujours disponibles dans toutes les portées.</para></listitem>\n <listitem><para>Dans la portée d'une fonction ou d'une méthode, vous pouvez accéder à la variable globale <literal>$foo</literal> soit en accédant directement à <literal>$GLOBALS['foo']</literal> soit en utilisant <literal>global $foo;</literal> pour créer une variable locale faisant référence à la variable globale.</para></listitem>\n </itemizedlist>\n\n <para>\n A part les variables globales, les attributs statiques des classes font\n également partie de l'état global.", "\n </para>\n\n <para>\n <indexterm><primary>Variables globales</primary></indexterm>\n <indexterm><primary>Indépendance des tests</primary></indexterm>\n\n Par défaut, PHPUnit exécute vos tests de façon à ce que des modifications\n aux variables globales et super-globales (\n <literal>$GLOBALS</literal>,\n <literal>$_ENV</literal>, <literal>$_POST</literal>,\n <literal>$_GET</literal>, <literal>$_COOKIE</literal>,\n <literal>$_SERVER</literal>, <literal>$_FILES</literal>,\n <literal>$_REQUEST</literal>) n'affectent pas les autres tests. ", "Optionnellement,\n cette indépendance peut être étendue aux attributs statiques des classes.", "\n </para>\n\n <note>\n <para>\n L'implémentation des opérations de sauvegarde et de restauration des attributs\n statiques des classes nécessite PHP 5.3 (ou supérieur).", "\n </para>\n <para>\n L'implémentation des opérations de sauvegarde et de restauration des variables\n globales et des attributs statiques des classes utilise \n <literal>serialize()</literal> et <literal>unserialize()</literal>.", "\n </para>\n <para>\n Les objets de certaines classes qui sont fournis pas PHP lui-même, tel que\n <literal>PDO</literal> par exemple, ne peuvent pas être sérialisés si bien que\n l'opération de sauvegarde va échouer quand un tel objet sera enregistré dans le tableau\n <literal>$GLOBALS</literal>, par exemple.", "\n </para>\n </note>\n\n <para>\n <indexterm><primary><literal>@backupGlobals</literal></primary></indexterm>\n <indexterm><primary><literal>$backupGlobalsBlacklist</literal></primary></indexterm>\n\n L'annotation <literal>@backupGlobals</literal> qui est discutée dans \n <xref linkend=\"appendixes.annotations.backupGlobals\"/> peut être utilisée pour \n contrôler les opérations de sauvegarde et de restauration des variables globales.", "\n Alternativement, vous pouvez fournir une liste noire des variables globales qui doivent\n être exclues des opérations de sauvegarde et de restauration comme ceci :\n <programlisting>class MonTest extends PHPUnit_Framework_TestCase\n{\n protected $backupGlobalsBlacklist = array('globalVariable');\n\n // ...\n}</programlisting>\n </para>\n\n <note>\n <para>\n Merci de noter que le réglage de l'attribut <literal>$backupGlobalsBlacklist</literal>\n à l'intérieur de la méthode <literal>setUp()</literal>, par exemple, n'a aucun effet.", "\n </para>\n </note>\n\n <para>\n <indexterm><primary><literal>@backupStaticAttributes</literal></primary></indexterm>\n <indexterm><primary><literal>$backupStaticAttributesBlacklist</literal></primary></indexterm>\n\n L'annotation <literal>@backupStaticAttributes</literal> qui est discutée dans \n <xref linkend=\"appendixes.annotations.backupStaticAttributes\"/> peut être utilisée pour \n contrôler les opérations de sauvegarde et de restauration des attributs statiques.", "\n Alternativement, vous pouvez fournir une liste noire des attributs statiques qui doivent\n être exclus des opérations de sauvegarde et de restauration comme ceci :\n <programlisting>class MonTest extends PHPUnit_Framework_TestCase\n{\n protected $backupStaticAttributesBlacklist = array(\n 'className' => array('attributeName')\n );\n\n // ...\n}</programlisting>\n </para>\n\n <note>\n <para>\n Merci de noter que le réglage de l'attribut <literal>$backupStaticAttributesBlacklist</literal>\n à l'intérieur de la méthode <literal>setUp()</literal>, par exemple, n'a aucun effet.", "\n </para>\n </note>\n </section>\n</chapter>\n" ]

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[ "Does accounting for mitochondrial genetic variation improve the fit of genetic models?", "\nWe describe a simple variance component model for estimating the effect of mitochondrial DNA (mtDNA) inheritance on quantitative trait variation. ", "The model is applied to quantitative trait Q5 in the simulated general population data from Genetic Analysis Workshop (GAW) 12. ", "Although the mitochondrial effect on Q5 is small (5.3%) and the power of the method to detect the effect is correspondingly low, analysis over the available population replicates demonstrates that the effect of maternal relatedness can be detected and estimated accurately." ]

[ 0, 0, 0.0078125, 0 ]

[ "Building of the Alexander Podvorie (Moscow)\n\nThe building of the Alexander Podvorie () is a masonry built in the end of the 17th century in Moscow The building was built in the backyard of the Assumption Monastery of Alexandrov Sloboda and the Florischevoy Desert. ", "It is located in the center of the city (Starovagankovsky Lane, 23) and has the status of an object of cultural heritage of federal significance.", "\n\nHistory \nThe Chambers at Starovagankovsky Lane were built in the late 17th century. ", "Since 1679, they housed the farmsteads of the Assumption Monastery of Alexandrov Sloboda and the Florischevaya Desert. ", "The premises were rented out. ", "In the 1890s, Moscow historian Alexei Alexandrovich Martynov lived in the building. ", "In 1978, restoration work was carried out by I. I. Kazakevich and V. V. Putyatin. ", "Currently, the building houses offices.", "\n\nArchitecture \nThe two-story building is constructed of stone. ", "It includes two different rooms, separated by a corridor, which is typical for residential buildings of that time. ", "The original vaulted ceilings were preserved on the ground floor and in the basement. ", "The front entrance is located on the south side, from the courtyard. ", "The porch is not preserved; its existence now resembles a doorway on the second floor, where an external staircase originally led. ", "After the restoration in the 1970s, profiled interstitial towers and cornices, platbands, lattices on windows, as well as a high four-pitched roof with attic projections were restored.", "\n\nReferences \n\nCategory:Cultural heritage monuments in Moscow" ]

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[ "Above: A picture of Dekker (blue shirt) with his family from the world premiere in 1987.", "\n\n/Film: The Monster Squad celebrates its silver anniversary today. ", "Where were you on opening day, 25 years ago and what were the expectations at the time? ", "When did those expectations change?", "\n\nThere’s a tradition among filmmakers of taking a limo from theater to theater to check audience reactions. ", "My hopes were that we had made a terrific movie that people would enjoy and would do good business. ", "Those expectations changed at the first theater we came to. ", "The audience seemed to be loving it, but you could count the patrons on two hands. ", "That was the tenor of the rest of the evening, and the ultimate box office — at theater after theater, an appreciative but anemically small audience. ", "It was a disaster.", "\n\nWhen was the last time you watched the film in full and how do you think it has aged?", "\n\nThe last time I watched it from start to finish was at the Eastman House in Rochester, New York. ", "The cons: some of the kids’ wardrobe and haircuts, some clunky pacing and awkwardness in the early reels, some general cheese (and that damn song under the montage!). ", "The pros: I’m really pleased with the tone of the film. ", "It’s self-aware, but not goofy, and ultimately heartfelt. ", "Every time there’s something bordering on camp (Wolfman’s got you know-whats), something scary or touching happens, and vice versa. ", "I think this puts it a cut above, and has aged it well. ", "And I think the final reels are terrific. ", "In some ways, I think it would fare better now than it did then.", "\n\nWhy do you think the film took so long its find its audience and now, 25 years later, has it reached – or eclipsed – your wildest expectations?", "\n\nLet’s face it, it’s a sophisticated kid’s movie — and when it opened, kids couldn’t get in without their parents (it was rated PG-13). ", "So the audience was mostly kids watching it on home video and cable and taking it to heart.", "\n\nThe film has experienced a resurgence over the past 5 years or so thanks to the Alamo screening, DVD/Blu-ray release, etc but even before that, the film had a cult following on video. ", "Has it been difficult to process the fact that it took so long for the film to finally get the recognition it so rightfully deserves?", "\n\nYes.", "\n\nCan you tell us a bit about the whereabouts of some of the key cast members?", "\n\nRyan Lambert (Rudy) is a rock musician in the San Francisco Bay Area. ", "We’re always looking for something to work on together. ", "Andre Gower (Sean) lives in North Carolina and works as a film festival promoter. ", "Ashley Bank (Phoebe) is in L.A. and has worked as a producer and stand-up comic. ", "She recently got married. ", "Michael Faustino (Eugene) is a technician in TV and movies, and recently had a son that looks just like him. ", "Brent Chalem (Horace), sadly, died in the ’90s. ", "Liam Neeson (who was cast as Dracula’s doppelganger in a scene we never shot) and Shane Black (my co-screenwriter) have sadly both faded into obscurity.", "\n\nObviously, it has ebs and flows, but overall – in the 25 years since the release of The Monster Squad, how often do you find yourself talking about the movie or thinking about the experience?", "\n\nI’m asked to show the movie at least three times a year, and it’s always fun to reminisce.", "\n\nThe general perception of your career is that, after RoboCop 3, you got placed in “director jail?” ", "Would you agree with that assessment and how do you spend your days, these days?", "\n\nThat perception is pretty spot-on. ", "I had written and was casting a comedy called MR. ", "COOL for Paramount when ROBOCOP 3 was released, and the plug was pulled shortly thereafter. ", "Since then I have mostly been working as a writer, including several unmade pilots and feature projects for James Cameron, Neal Moritz, Fox, TNT, Dreamworks and others — and the TV series ‘Star Trek: Enterprise,’ on which I was a writer and consulting producer. ", "But mostly, I’ve been hoping somebody will call and offer me a movie to direct.", "\n\nA remake of The Monster Squad has been in development for some years. ", "Do you think it’ll actually happen and if you could be involved, what would be your dream participation?", "\n\nI hope not and my dream participation would be to make as much money as humanly possible for doing nothing whatsoever.", "\n\nI’d like to thank Fred Dekker for agreeing to my quick email interview as well as writing and directing one of the defining movies of my childhood. ", "It helped introduce me to a world of genre films I’d never known about and has remained one of my favorite movies ever. ", "Mummy came in my house and changed my life.", "\n\nHappy 25th birthday, Monster Squad. ", "Time to blow a whole in limbo." ]

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[ "/*\n * Copyright (C) 2006 Martin Willi\n * HSR Hochschule fuer Technik Rapperswil\n * Copyright (C) 2001 Jari Ruusu.", "\n *\n * Ported from strongSwans implementation written by Jari Ruusu.", "\n *\n * This program is free software; you can redistribute it and/or modify it\n * under the terms of the GNU General Public License as published by the\n * Free Software Foundation; either version 2 of the License, or (at your\n * option) any later version. ", " See <http://www.fsf.org/copyleft/gpl.txt>.", "\n *\n * This program is distributed in the hope that it will be useful, but\n * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY\n * or FITNESS FOR A PARTICULAR PURPOSE. ", " See the GNU General Public License\n * for more details.", "\n */\n\n#include <string.h>\n\n#include \"sha2_hasher.h\"\n\n\ntypedef struct private_sha512_hasher_t private_sha512_hasher_t;\n\n/**\n * Private data structure with hashing context for SHA384 and SHA512\n */\nstruct private_sha512_hasher_t {\n\t/**\n\t * Public interface for this hasher.", "\n\t */\n\tsha2_hasher_t public;\n\n\tunsigned char sha_out[128]; /* results are here, bytes 0..47/0..63 */\n\tuint64_t sha_H[8];\n\tuint64_t sha_blocks;\n\tuint64_t sha_blocksMSB;\n\tint sha_bufCnt;\n};\n\n\ntypedef struct private_sha256_hasher_t private_sha256_hasher_t;\n\n/**\n * Private data structure with hashing context for SHA256\n */\nstruct private_sha256_hasher_t {\n\t/**\n\t * Public interface for this hasher.", "\n\t */\n\tsha2_hasher_t public;\n\n\tunsigned char sha_out[64]; /* results are here, bytes 0...31 */\n\tuint32_t sha_H[8];\n\tuint64_t sha_blocks;\n\tint sha_bufCnt;\n};\n\n\nstatic const uint32_t sha224_hashInit[8] = {\n\t0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939, 0xffc00b31, 0x68581511,\n\t0x64f98fa7, 0xbefa4fa4\n};\n\nstatic const uint32_t sha256_hashInit[8] = {\n\t0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c,\n\t0x1f83d9ab, 0x5be0cd19\n};\n\nstatic const uint32_t sha256_K[64] = {\n\t0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1,\n\t0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3,\n\t0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786,\n\t0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,\n\t0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147,\n\t0x06ca6351, 0x14292967, 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13,\n\t0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b,\n\t0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,\n\t0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a,\n\t0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208,\n\t0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2\n};\n\nstatic const uint64_t sha512_hashInit[8] = {\n\t0x6a09e667f3bcc908ULL, 0xbb67ae8584caa73bULL, 0x3c6ef372fe94f82bULL,\n\t0xa54ff53a5f1d36f1ULL, 0x510e527fade682d1ULL, 0x9b05688c2b3e6c1fULL,\n\t0x1f83d9abfb41bd6bULL, 0x5be0cd19137e2179ULL\n};\n\nstatic const uint64_t sha384_hashInit[8] = {\n\t0xcbbb9d5dc1059ed8ULL, 0x629a292a367cd507ULL, 0x9159015a3070dd17ULL,\n\t0x152fecd8f70e5939ULL, 0x67332667ffc00b31ULL, 0x8eb44a8768581511ULL,\n\t0xdb0c2e0d64f98fa7ULL, 0x47b5481dbefa4fa4ULL\n};\n\nstatic const uint64_t sha512_K[80] = {\n\t0x428a2f98d728ae22ULL, 0x7137449123ef65cdULL, 0xb5c0fbcfec4d3b2fULL,\n\t0xe9b5dba58189dbbcULL, 0x3956c25bf348b538ULL, 0x59f111f1b605d019ULL,\n\t0x923f82a4af194f9bULL, 0xab1c5ed5da6d8118ULL, 0xd807aa98a3030242ULL,\n\t0x12835b0145706fbeULL, 0x243185be4ee4b28cULL, 0x550c7dc3d5ffb4e2ULL,\n\t0x72be5d74f27b896fULL, 0x80deb1fe3b1696b1ULL, 0x9bdc06a725c71235ULL,\n\t0xc19bf174cf692694ULL, 0xe49b69c19ef14ad2ULL, 0xefbe4786384f25e3ULL,\n\t0x0fc19dc68b8cd5b5ULL, 0x240ca1cc77ac9c65ULL, 0x2de92c6f592b0275ULL,\n\t0x4a7484aa6ea6e483ULL, 0x5cb0a9dcbd41fbd4ULL, 0x76f988da831153b5ULL,\n\t0x983e5152ee66dfabULL, 0xa831c66d2db43210ULL, 0xb00327c898fb213fULL,\n\t0xbf597fc7beef0ee4ULL, 0xc6e00bf33da88fc2ULL, 0xd5a79147930aa725ULL,\n\t0x06ca6351e003826fULL, 0x142929670a0e6e70ULL, 0x27b70a8546d22ffcULL,\n\t0x2e1b21385c26c926ULL, 0x4d2c6dfc5ac42aedULL, 0x53380d139d95b3dfULL,\n\t0x650a73548baf63deULL, 0x766a0abb3c77b2a8ULL, 0x81c2c92e47edaee6ULL,\n\t0x92722c851482353bULL, 0xa2bfe8a14cf10364ULL, 0xa81a664bbc423001ULL,\n\t0xc24b8b70d0f89791ULL, 0xc76c51a30654be30ULL, 0xd192e819d6ef5218ULL,\n\t0xd69906245565a910ULL, 0xf40e35855771202aULL, 0x106aa07032bbd1b8ULL,\n\t0x19a4c116b8d2d0c8ULL, 0x1e376c085141ab53ULL, 0x2748774cdf8eeb99ULL,\n\t0x34b0bcb5e19b48a8ULL, 0x391c0cb3c5c95a63ULL, 0x4ed8aa4ae3418acbULL,\n\t0x5b9cca4f7763e373ULL, 0x682e6ff3d6b2b8a3ULL, 0x748f82ee5defb2fcULL,\n\t0x78a5636f43172f60ULL, 0x84c87814a1f0ab72ULL, 0x8cc702081a6439ecULL,\n\t0x90befffa23631e28ULL, 0xa4506cebde82bde9ULL, 0xbef9a3f7b2c67915ULL,\n\t0xc67178f2e372532bULL, 0xca273eceea26619cULL, 0xd186b8c721c0c207ULL,\n\t0xeada7dd6cde0eb1eULL, 0xf57d4f7fee6ed178ULL, 0x06f067aa72176fbaULL,\n\t0x0a637dc5a2c898a6ULL, 0x113f9804bef90daeULL, 0x1b710b35131c471bULL,\n\t0x28db77f523047d84ULL, 0x32caab7b40c72493ULL, 0x3c9ebe0a15c9bebcULL,\n\t0x431d67c49c100d4cULL, 0x4cc5d4becb3e42b6ULL, 0x597f299cfc657e2aULL,\n\t0x5fcb6fab3ad6faecULL, 0x6c44198c4a475817ULL\n};\n\n\n/* set macros for SHA256 */\n#define Ch(x,y,z) (((x) & (y)) ^ ((~(x)) & (z)))\n#define Maj(x,y,z) (((x) & (y)) ^ ((x) & (z)) ^ ((y) & (z)))\n#define R(x,y) ((y) >> (x))\n\n#define S(x,y) (((y) >> (x)) | ((y) << (32 - (x))))\n#define uSig0(x) ((S(2,(x))) ^ (S(13,(x))) ^ (S(22,(x))))\n#define uSig1(x) ((S(6,(x))) ^ (S(11,(x))) ^ (S(25,(x))))\n#define lSig0(x) ((S(7,(x))) ^ (S(18,(x))) ^ (R(3,(x))))\n#define lSig1(x) ((S(17,(x))) ^ (S(19,(x))) ^ (R(10,(x))))\n\n/**\n * Single block SHA256 transformation\n */\nstatic void sha256_transform(private_sha256_hasher_t *ctx,\n\t\t\t\t\t\t\t const unsigned char *datap)\n{\n\tregister int j;\n\tuint32_t a, b, c, d, e, f, g, h;\n\tuint32_t T1, T2, W[64], Wm2, Wm15;\n\n\t/* read the data, big endian byte order */\n\tj = 0;\n\tdo {\n\t\tW[j] = (((uint32_t)(datap[0]))<<24) | (((uint32_t)(datap[1]))<<16) |\n\t\t\t\t(((uint32_t)(datap[2]))<<8 ) | ((uint32_t)(datap[3]));\n\t\tdatap += 4;\n\t} while(++j < 16);\n\n\t/* initialize variables a...h */\n\ta = ctx->sha_H[0];\n\tb = ctx->sha_H[1];\n\tc = ctx->sha_H[2];\n\td = ctx->sha_H[3];\n\te = ctx->sha_H[4];\n\tf = ctx->sha_H[5];\n\tg = ctx->sha_H[6];\n\th = ctx->sha_H[7];\n\n\t/* apply compression function */\n\tj = 0;\n\tdo\n\t{\n\t\tif(j >= 16)\n\t\t{\n\t\t\tWm2 = W[j - 2];\n\t\t\tWm15 = W[j - 15];\n\t\t\tW[j] = lSig1(Wm2) + W[j - 7] + lSig0(Wm15) + W[j - 16];\n\t\t}\n\t\tT1 = h + uSig1(e) + Ch(e,f,g) + sha256_K[j] + W[j];\n\t\tT2 = uSig0(a) + Maj(a,b,c);\n\t\th = g; g = f; f = e;\n\t\te = d + T1;\n\t\td = c; c = b; b = a;\n\t\ta = T1 + T2;\n\t} while(++j < 64);\n\n\t/* compute intermediate hash value */\n\tctx->sha_H[0] += a;\n\tctx->sha_H[1] += b;\n\tctx->sha_H[2] += c;\n\tctx->sha_H[3] += d;\n\tctx->sha_H[4] += e;\n\tctx->sha_H[5] += f;\n\tctx->sha_H[6] += g;\n\tctx->sha_H[7] += h;\n\n\tctx->sha_blocks++;\n}\n\n/**\n * Update SHA256 hash\n */\nstatic void sha256_write(private_sha256_hasher_t *ctx,\n\t\t\t\t\t\t const unsigned char *datap, int length)\n{\n\twhile(length > 0)\n\t{\n\t\tif(!ctx->sha_bufCnt)\n\t\t{\n\t\t\twhile(length >= sizeof(ctx->sha_out))\n\t\t\t{\n\t\t\t\tsha256_transform(ctx, datap);\n\t\t\t\tdatap += sizeof(ctx->sha_out);\n\t\t\t\tlength -= sizeof(ctx->sha_out);\n\t\t\t}\n\t\t\tif(!length) return;\n\t\t}\n\t\tctx->sha_out[ctx->sha_bufCnt] = *datap++;\n\t\tlength--;\n\t\tif(++ctx->sha_bufCnt == sizeof(ctx->sha_out))\n\t\t{\n\t\t\tsha256_transform(ctx, &ctx->sha_out[0]);\n\t\t\tctx->sha_bufCnt = 0;\n\t\t}\n\t}\n}\n\n/**\n * finalize SHA256 hash\n */\nstatic void sha256_final(private_sha256_hasher_t *ctx, u_char *buf, size_t len)\n{\n\tregister int j;\n\tuint64_t bitLength;\n\tuint32_t i;\n\tunsigned char padByte, *datap;\n\n\tbitLength = (ctx->sha_blocks << 9) | (ctx->sha_bufCnt << 3);\n\tpadByte = 0x80;\n\tsha256_write(ctx, &padByte, 1);\n\n\t/* pad extra space with zeroes */\n\tpadByte = 0;\n\twhile(ctx->sha_bufCnt !", "= 56)\n\t{\n\t\tsha256_write(ctx, &padByte, 1);\n\t}\n\n\t/* write bit length, big endian byte order */\n\tctx->sha_out[56] = bitLength >> 56;\n\tctx->sha_out[57] = bitLength >> 48;\n\tctx->sha_out[58] = bitLength >> 40;\n\tctx->sha_out[59] = bitLength >> 32;\n\tctx->sha_out[60] = bitLength >> 24;\n\tctx->sha_out[61] = bitLength >> 16;\n\tctx->sha_out[62] = bitLength >> 8;\n\tctx->sha_out[63] = bitLength;\n\tsha256_transform(ctx, &ctx->sha_out[0]);\n\n\tdatap = buf;\n\tj = 0;\n\tdo {\n\t\ti = ctx->sha_H[j];\n\t\tdatap[0] = i >> 24;\n\t\tdatap[1] = i >> 16;\n\t\tdatap[2] = i >> 8;\n\t\tdatap[3] = i;\n\t\tdatap += 4;\n\t} while(++j < len / 4);\n}\n\n/* update macros for SHA512 */\n#undef S\n#undef uSig0\n#undef uSig1\n#undef lSig0\n#undef lSig1\n#define S(x,y) (((y) >> (x)) | ((y) << (64 - (x))))\n#define uSig0(x) ((S(28,(x))) ^ (S(34,(x))) ^ (S(39,(x))))\n#define uSig1(x) ((S(14,(x))) ^ (S(18,(x))) ^ (S(41,(x))))\n#define lSig0(x) ((S(1,(x))) ^ (S(8,(x))) ^ (R(7,(x))))\n#define lSig1(x) ((S(19,(x))) ^ (S(61,(x))) ^ (R(6,(x))))\n\n/**\n * Single block SHA384/SHA512 transformation\n */\nstatic void sha512_transform(private_sha512_hasher_t *ctx,\n\t\t\t\t\t\t\t const unsigned char *datap)\n{\n\tregister int j;\n\tuint64_t a, b, c, d, e, f, g, h;\n\tuint64_t T1, T2, W[80], Wm2, Wm15;\n\n\t/* read the data, big endian byte order */\n\tj = 0;\n\tdo {\n\t\tW[j] = (((uint64_t)(datap[0]))<<56) | (((uint64_t)(datap[1]))<<48) |\n\t\t\t\t(((uint64_t)(datap[2]))<<40) | (((uint64_t)(datap[3]))<<32) |\n\t\t\t\t(((uint64_t)(datap[4]))<<24) | (((uint64_t)(datap[5]))<<16) |\n\t\t\t\t(((uint64_t)(datap[6]))<<8 ) | ((uint64_t)(datap[7]));\n\t\tdatap += 8;\n\t} while(++j < 16);\n\n\t/* initialize variables a...h */\n\ta = ctx->sha_H[0];\n\tb = ctx->sha_H[1];\n\tc = ctx->sha_H[2];\n\td = ctx->sha_H[3];\n\te = ctx->sha_H[4];\n\tf = ctx->sha_H[5];\n\tg = ctx->sha_H[6];\n\th = ctx->sha_H[7];\n\n\t/* apply compression function */\n\tj = 0;\n\tdo {\n\t\tif(j >= 16) {\n\t\t\tWm2 = W[j - 2];\n\t\t\tWm15 = W[j - 15];\n\t\t\tW[j] = lSig1(Wm2) + W[j - 7] + lSig0(Wm15) + W[j - 16];\n\t\t}\n\t\tT1 = h + uSig1(e) + Ch(e,f,g) + sha512_K[j] + W[j];\n\t\tT2 = uSig0(a) + Maj(a,b,c);\n\t\th = g; g = f; f = e;\n\t\te = d + T1;\n\t\td = c; c = b; b = a;\n\t\ta = T1 + T2;\n\t} while(++j < 80);\n\n\t/* compute intermediate hash value */\n\tctx->sha_H[0] += a;\n\tctx->sha_H[1] += b;\n\tctx->sha_H[2] += c;\n\tctx->sha_H[3] += d;\n\tctx->sha_H[4] += e;\n\tctx->sha_H[5] += f;\n\tctx->sha_H[6] += g;\n\tctx->sha_H[7] += h;\n\n\tctx->sha_blocks++;\n\tif(!ctx->sha_blocks) ctx->sha_blocksMSB++;\n}\n\n/**\n * Update a SHA384/SHA512 hash\n */\nstatic void sha512_write(private_sha512_hasher_t *ctx,\n\t\t\t\t\t\t const unsigned char *datap, int length)\n{\n\twhile(length > 0)\n\t{\n\t\tif(!ctx->sha_bufCnt)\n\t\t{\n\t\t\twhile(length >= sizeof(ctx->sha_out))\n\t\t\t{\n\t\t\t\tsha512_transform(ctx, datap);\n\t\t\t\tdatap += sizeof(ctx->sha_out);\n\t\t\t\tlength -= sizeof(ctx->sha_out);\n\t\t\t}\n\t\t\tif(!length) return;\n\t\t}\n\t\tctx->sha_out[ctx->sha_bufCnt] = *datap++;\n\t\tlength--;\n\t\tif(++ctx->sha_bufCnt == sizeof(ctx->sha_out))\n\t\t{\n\t\t\tsha512_transform(ctx, &ctx->sha_out[0]);\n\t\t\tctx->sha_bufCnt = 0;\n\t\t}\n\t}\n}\n\n/**\n * Finalize a SHA384/SHA512 hash\n */\nstatic void sha512_final(private_sha512_hasher_t *ctx, u_char *buf, size_t len)\n{\n\tregister int j;\n\tuint64_t bitLength, bitLengthMSB;\n\tuint64_t i;\n\tunsigned char padByte, *datap;\n\n\tbitLength = (ctx->sha_blocks << 10) | (ctx->sha_bufCnt << 3);\n\tbitLengthMSB = (ctx->sha_blocksMSB << 10) | (ctx->sha_blocks >> 54);\n\tpadByte = 0x80;\n\tsha512_write(ctx, &padByte, 1);\n\n\t/* pad extra space with zeroes */\n\tpadByte = 0;\n\twhile(ctx->sha_bufCnt !", "= 112)\n\t{\n\t\tsha512_write(ctx, &padByte, 1);\n\t}\n\n\t/* write bit length, big endian byte order */\n\tctx->sha_out[112] = bitLengthMSB >> 56;\n\tctx->sha_out[113] = bitLengthMSB >> 48;\n\tctx->sha_out[114] = bitLengthMSB >> 40;\n\tctx->sha_out[115] = bitLengthMSB >> 32;\n\tctx->sha_out[116] = bitLengthMSB >> 24;\n\tctx->sha_out[117] = bitLengthMSB >> 16;\n\tctx->sha_out[118] = bitLengthMSB >> 8;\n\tctx->sha_out[119] = bitLengthMSB;\n\tctx->sha_out[120] = bitLength >> 56;\n\tctx->sha_out[121] = bitLength >> 48;\n\tctx->sha_out[122] = bitLength >> 40;\n\tctx->sha_out[123] = bitLength >> 32;\n\tctx->sha_out[124] = bitLength >> 24;\n\tctx->sha_out[125] = bitLength >> 16;\n\tctx->sha_out[126] = bitLength >> 8;\n\tctx->sha_out[127] = bitLength;\n\tsha512_transform(ctx, &ctx->sha_out[0]);\n\n\tdatap = buf;\n\tj = 0;\n\tdo {\n\t\ti = ctx->sha_H[j];\n\t\tdatap[0] = i >> 56;\n\t\tdatap[1] = i >> 48;\n\t\tdatap[2] = i >> 40;\n\t\tdatap[3] = i >> 32;\n\t\tdatap[4] = i >> 24;\n\t\tdatap[5] = i >> 16;\n\t\tdatap[6] = i >> 8;\n\t\tdatap[7] = i;\n\t\tdatap += 8;\n\t} while(++j < len / 8);\n}\n\nMETHOD(hasher_t, reset224, bool,\n\tprivate_sha256_hasher_t *this)\n{\n\tmemcpy(&this->sha_H[0], &sha224_hashInit[0], sizeof(this->sha_H));\n\tthis->sha_blocks = 0;\n\tthis->sha_bufCnt = 0;\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, reset256, bool,\n\tprivate_sha256_hasher_t *this)\n{\n\tmemcpy(&this->sha_H[0], &sha256_hashInit[0], sizeof(this->sha_H));\n\tthis->sha_blocks = 0;\n\tthis->sha_bufCnt = 0;\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, reset384, bool,\n\tprivate_sha512_hasher_t *this)\n{\n\tmemcpy(&this->sha_H[0], &sha384_hashInit[0], sizeof(this->sha_H));\n\tthis->sha_blocks = 0;\n\tthis->sha_blocksMSB = 0;\n\tthis->sha_bufCnt = 0;\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, reset512, bool,\n\tprivate_sha512_hasher_t *this)\n{\n\tmemcpy(&this->sha_H[0], &sha512_hashInit[0], sizeof(this->sha_H));\n\tthis->sha_blocks = 0;\n\tthis->sha_blocksMSB = 0;\n\tthis->sha_bufCnt = 0;\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, get_hash224, bool,\n\tprivate_sha256_hasher_t *this, chunk_t chunk, uint8_t *buffer)\n{\n\tsha256_write(this, chunk.ptr, chunk.len);\n\tif (buffer !", "= NULL)\n\t{\n\t\tsha256_final(this, buffer, HASH_SIZE_SHA224);\n\t\treset224(this);\n\t}\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, get_hash256, bool,\n\tprivate_sha256_hasher_t *this, chunk_t chunk, uint8_t *buffer)\n{\n\tsha256_write(this, chunk.ptr, chunk.len);\n\tif (buffer !", "= NULL)\n\t{\n\t\tsha256_final(this, buffer, HASH_SIZE_SHA256);\n\t\treset256(this);\n\t}\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, get_hash384, bool,\n\tprivate_sha512_hasher_t *this, chunk_t chunk, uint8_t *buffer)\n{\n\tsha512_write(this, chunk.ptr, chunk.len);\n\tif (buffer !", "= NULL)\n\t{\n\t\tsha512_final(this, buffer, HASH_SIZE_SHA384);\n\t\treset384(this);\n\t}\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, get_hash512, bool,\n\tprivate_sha512_hasher_t *this, chunk_t chunk, uint8_t *buffer)\n{\n\tsha512_write(this, chunk.ptr, chunk.len);\n\tif (buffer !", "= NULL)\n\t{\n\t\tsha512_final(this, buffer, HASH_SIZE_SHA512);\n\t\treset512(this);\n\t}\n\treturn TRUE;\n}\n\nMETHOD(hasher_t, allocate_hash224, bool,\n\tprivate_sha256_hasher_t *this, chunk_t chunk, chunk_t *hash)\n{\n\tchunk_t allocated_hash = chunk_empty;\n\n\tif (hash)\n\t{\n\t\t*hash = allocated_hash = chunk_alloc(HASH_SIZE_SHA224);\n\t}\n\treturn get_hash224(this, chunk, allocated_hash.ptr);\n}\n\nMETHOD(hasher_t, allocate_hash256, bool,\n\tprivate_sha256_hasher_t *this, chunk_t chunk, chunk_t *hash)\n{\n\tchunk_t allocated_hash = chunk_empty;\n\n\tif (hash)\n\t{\n\t\t*hash = allocated_hash = chunk_alloc(HASH_SIZE_SHA256);\n\t}\n\treturn get_hash256(this, chunk, allocated_hash.ptr);\n}\n\nMETHOD(hasher_t, allocate_hash384, bool,\n\tprivate_sha512_hasher_t *this, chunk_t chunk, chunk_t *hash)\n{\n\tchunk_t allocated_hash = chunk_empty;\n\n\tif (hash)\n\t{\n\t\t*hash = allocated_hash = chunk_alloc(HASH_SIZE_SHA384);\n\t}\n\treturn get_hash384(this, chunk, allocated_hash.ptr);\n}\n\nMETHOD(hasher_t, allocate_hash512, bool,\n\tprivate_sha512_hasher_t *this, chunk_t chunk, chunk_t *hash)\n{\n\tchunk_t allocated_hash = chunk_empty;\n\n\tif (hash)\n\t{\n\t\t*hash = allocated_hash = chunk_alloc(HASH_SIZE_SHA512);\n\t}\n\treturn get_hash512(this, chunk, allocated_hash.ptr);\n}\n\nMETHOD(hasher_t, get_hash_size224, size_t,\n\tprivate_sha256_hasher_t *this)\n{\n\treturn HASH_SIZE_SHA224;\n}\n\nMETHOD(hasher_t, get_hash_size256, size_t,\n\tprivate_sha256_hasher_t *this)\n{\n\treturn HASH_SIZE_SHA256;\n}\n\nMETHOD(hasher_t, get_hash_size384, size_t,\n\tprivate_sha512_hasher_t *this)\n{\n\treturn HASH_SIZE_SHA384;\n}\n\nMETHOD(hasher_t, get_hash_size512, size_t,\n\tprivate_sha512_hasher_t *this)\n{\n\treturn HASH_SIZE_SHA512;\n}\n\nMETHOD(hasher_t, destroy, void,\n\tsha2_hasher_t *this)\n{\n\tfree(this);\n}\n\n/*\n * Described in header.", "\n */\nsha2_hasher_t *sha2_hasher_create(hash_algorithm_t algorithm)\n{\n\tswitch (algorithm)\n\t{\n\t\tcase HASH_SHA224:\n\t\t{\n\t\t\tprivate_sha256_hasher_t *this;\n\n\t\t\tINIT(this,\n\t\t\t\t.public = {\n\t\t\t\t\t.hasher_interface = {\n\t\t\t\t\t\t.reset = _reset224,\n\t\t\t\t\t\t.get_hash_size = _get_hash_size224,\n\t\t\t\t\t\t.get_hash = _get_hash224,\n\t\t\t\t\t\t.allocate_hash = _allocate_hash224,\n\t\t\t\t\t\t.destroy = _destroy,\n\t\t\t\t\t},\n\t\t\t\t},\n\t\t\t);\n\t\t\treset224(this);\n\t\t\treturn &this->public;\n\t\t}\n\t\tcase HASH_SHA256:\n\t\t{\n\t\t\tprivate_sha256_hasher_t *this;\n\n\t\t\tINIT(this,\n\t\t\t\t.public = {\n\t\t\t\t\t.hasher_interface = {\n\t\t\t\t\t.reset = _reset256,\n\t\t\t\t\t.get_hash_size = _get_hash_size256,\n\t\t\t\t\t.get_hash = _get_hash256,\n\t\t\t\t\t.allocate_hash = _allocate_hash256,\n\t\t\t\t\t.destroy = _destroy,\n\t\t\t\t\t},\n\t\t\t\t},\n\t\t\t);\n\t\t\treset256(this);\n\t\t\treturn &this->public;\n\t\t}\n\t\tcase HASH_SHA384:\n\t\t{\n\t\t\tprivate_sha512_hasher_t *this;\n\n\t\t\tINIT(this,\n\t\t\t\t.public = {\n\t\t\t\t\t.hasher_interface = {\n\t\t\t\t\t.reset = _reset384,\n\t\t\t\t\t.get_hash_size = _get_hash_size384,\n\t\t\t\t\t.get_hash = _get_hash384,\n\t\t\t\t\t.allocate_hash = _allocate_hash384,\n\t\t\t\t\t.destroy = _destroy,\n\t\t\t\t\t},\n\t\t\t\t},\n\t\t\t);\n\t\t\treset384(this);\n\t\t\treturn &this->public;\n\t\t}\n\t\tcase HASH_SHA512:\n\t\t{\n\t\t\tprivate_sha512_hasher_t *this;\n\n\t\t\tINIT(this,\n\t\t\t\t.public = {\n\t\t\t\t\t.hasher_interface = {\n\t\t\t\t\t.reset = _reset512,\n\t\t\t\t\t.get_hash_size = _get_hash_size512,\n\t\t\t\t\t.get_hash = _get_hash512,\n\t\t\t\t\t.allocate_hash = _allocate_hash512,\n\t\t\t\t\t.destroy = _destroy,\n\t\t\t\t\t},\n\t\t\t\t},\n\t\t\t);\n\t\t\treset512(this);\n\t\t\treturn &this->public;\n\t\t}\n\t\tdefault:\n\t\t\treturn NULL;\n\t}\n}\n" ]

[ 0.017699115044247787, 0.014705882352941176, 0.0078125, 0.023255813953488372, 0.0051813471502590676, 0, 0, 0, 0.0039332913782252985, 0.0034552260293694214, 0.002477700693756194, 0.00784313725490196, 0.011764705882352941, 0.00784313725490196, 0.0017371163867979154, 0.0019672131147540984 ]

[ "Supreme Court Justice Sonia Sotomayor was tended to by paramedics at her District of Columbia home for \"symptoms of low blood sugar\" Friday morning, a Supreme Court spokeswoman said Friday.", "\n\n“Justice Sotomayor experienced symptoms of low blood sugar at her home this morning,” Kathy Arberg, a spokeswoman for the court, told the Washington Examiner. “", "She was treated by D.C. Emergency Medical Services and is doing fine.”", "\n\nArberg said Sotomayor, 63, came to work and “resumed her usual schedule.” ", "The justices met Friday in their weekly closed-door conference.", "\n\nShe will continue with her planned activities Saturday and Sunday, Arberg said.", "\n\nSotomayor was diagnosed with Type 1 diabetes as a child. ", "She told Diabetes Forecast magazine in a 2013 interview she carries with her glucose tablets and a blood glucose meter, and is “super vigilant” when in court." ]

[ 0.015873015873015872, 0.018518518518518517, 0.014285714285714285, 0, 0, 0.012345679012345678, 0, 0.006329113924050633 ]

[ "Summary and Info\n\nThis new work form Jon A. Maguire provides an in-depth examination of personal flight clothing and equipment used by United States Army Air Force flyers in World War II. ", "Included are: flight helmets, oxygen masks, goggles, clothing, boots, gloves, flak ar" ]

[ 0.015957446808510637, 0 ]

[ "Nanoparticles of nickel oxide and nickel hydroxide using lyophilisomes of fibrinogen as template.", "\nStable lyophilisomes of fibrinogen at pH 7.5 have been prepared by the method of a rapid freezing-heating and annealing sequence. ", "Reduction of the lyophilisomes of the nickel-fibrinogen complex coated on solid substrates and subsequent heating showed formation of nickel hydroxide and finally nickel oxide. ", "Ultraviolet-visible spectroscopy has been used to monitor the thin films of pure fibrinogen microcapsules, as well as the subsequent nucleation and growth of nanoparticles within the supramolecular structure. ", "Transmission electron microscopy showed initially a thread-like structure which disappeared on continued heating, resulting in nanoparticles ranging from 10 to 50 nm. ", "Particle-size distribution of product was analyzed by using X-ray diffraction (XRD), transmission electron microscopy (TEM) and the corresponding selected area electron diffraction (SAED), and Brunauer-Emmett-Teller (BET) N(2) adsorption. ", "The results suggest that the NiO particles have a body-centered cubic structure and are well dispersed. ", "The particle-size distribution ranges from 10 to 50 nm with an average particle size about 28 nm, and the specific surface area is 34 m(2)/g. ", "Magnetic study carried out on the prepared nanoparticles showed a ferromagnetic behavior." ]

[ 0, 0, 0, 0, 0, 0.016736401673640166, 0.009615384615384616, 0, 0 ]

[ "Q:\n\nIssue with GremlinPipeline\n\nI am creating lots of Gremlin pipelines using the following command to query titan graph vertex:\nGremlinPipeline pipeline = new GremlinPipeline();\nSince I am unable to find any method to release or reset my pipeline, I am creating new instance for each and every vertex that needs to be queried. ", "This is creating a memory hot spot. ", "Is there a way to re-use or reset the pipeline without creating new instance?", "\nI tried using methods pipeline.remove() and pipeline.reset() but no luck.", "\nRegards,\nKarthik\n\nA:\n\nConsider starting your pipeline with the childVertices. ", " In Gremlin Groovy that would be:\nchildVertices._().outE().has(SCORE).or(...\n\nor I guess if you were using GremlinPipeline directly, then something like:\nnew GremlinPipeline(childVertices).has(SCORE).or(....\n\n" ]

[ 0.006097560975609756, 0, 0, 0, 0, 0.009569377990430622 ]

[ "Computer museum seeks BBC Micro fixers Published duration 29 June 2015\n\nimage copyright TNMOC image caption The exhibition at the museum gives schoolchildren a hands-on lesson in 8-bit computing\n\nA public appeal for people who can repair BBC Micro computers has been launched by a museum.", "\n\nThe National Museum of Computing (TNMOC) needs help to maintain the stock of BBC machines it uses in education programmes and exhibits.", "\n\nIt is looking for people familiar with the computer and its peripherals including monitors and disk drives.", "\n\nThe 8-bit BBC Micro was launched in 1981 and gave many people their first taste of home computing.", "\n\nBasic instructions\n\nThe museum, which is located on the Bletchley Park estate, has about 80 BBC Micro computers, said Chris Monk, learning co-ordinator at the organisation. ", "Some of these are in display cases, he said, but the majority form part of an interactive exhibit that recreates a 1980s classroom.", "\n\nMany times a week school groups visit this exhibit to find out about the social history of micro computers and to get a taste of what machines could do in the days before tablets, smartphones and laptops, said Mr Monk.", "\n\n\"We want to find out whether people have got skills out there that can keep the cluster alive as long as we can,\" he said. ", "Anyone with appropriate skills can contact the museum via its website.", "\n\nSome students studying computer science get a chance to use the machines and programme simple games in BBC Basic, he added, saying that using the language can be a revelation.", "\n\n\"A lot of the students are used to using Python and they know how fussy that can be when you do not put your indents in the right place,\" said Mr Monk. \"", "But BBC basic does not care as it was designed to be quite tolerant of spacing and it tries to give them sensible error messages.\"", "\n\nValerie Quaye, an ICT teacher from the Kings of Wessex Academy in Cheddar, Somerset, who regularly takes students to TNMOC to try the BBC machines, said the hands-on experience was \"invaluable\".", "\n\nimage caption A replica of the Colossus computer is also at the National Museum of Computing\n\n\"We do teach programming but it is much more text-based,\" she said. \"", "They do not see the output until they have written a lot of code.\"", "\n\nBy contrast, she said, working on the BBC Micro was much more immediate.", "\n\n\"It hooks them in even though it's quite basic,\" said Ms Quaye. \"", "They get over the basic graphics very quickly.\"", "\n\nOwen Grover, a volunteer at the museum who currently helps maintain the cluster of BBC Micro machines, said they held up well despite being more than 30 years old.", "\n\nThe BBC Micro was \"pretty robust\", he said, because it was designed to be used in classrooms. ", "This meant that refurbishing machines for use in the hands-on exhibit was usually fairly straightforward.", "\n\n\"The main problem we need to sort out is the power supply,\" he said. \"", "There are two capacitors that dry out and if we do not replace them they tend to explode and stink the place out. ", "So we change them as a matter of course.\"", "\n\nGeneral maintenance on the machines includes replacing keys that stick and the occasional component that fails. ", "Thankfully, he said, there were few custom-built components in the machine so getting spares is easy. ", "Harder-to-obtain parts are cannibalised from broken or faulty machines the museum has in its stores.", "\n\n\"The good thing about them is that they are repairable,\" said Mr Grover. \"", "We are not going to be repairing power supplies in modern equipment in 30 years' time because they are not designed to be opened up and replaced.\"" ]

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[ "Comments (17)\n\nWe take our dog for walks, we color, we watch Baby Einstein every morning while I have my cup of coffee, we go to the grocery store, she \"helps\" me with laundry and sweeping, we read books, sing songs, dance, we play with her kitchen set and name all the colors and different objects, etc. ", "We have another neighbor who is a SAHM with a 2 year old so if my DH is working the late shift, then we let the kids play outside together for a couple hours before our husbands get home. ", "If DH is working a 14 hr shift, then halfway through the day, we stop by his work for a couple minutes so she can give her daddy a hug and kiss. ", "Her ped was very impressed with my dd's communication skills since she has put two and three words together occasionally to talk to us, so I feel like I must be doing something right. ", "We are hardly ever bored and if it isn't too cold out, then I take her to the park to play. ", "If it is cold, then once or twice a month, we go to the mall and play in the kids area there. ", "We occasionally go on playdates and have church on Wednesday nights and Sundays. ", "She is very active and social.", "\n\nI stay home a lot like you. ", "We do the occasional playgroup once a week and grocery runs, but kosty just stay home and play. ", "There is nothing that will be more positive than spending time with your LO, whether it's at home or out of the house. ", "Being at home gives them a predictable and one on one experience which is great for their development. ", "It's great to be social and go out, but it's not better or worse! ", "They learn so much by being at home with you! ", "Although, sometimes you need to get out for your own sanity! ", "That's what we do sometimes!", "\n\nWe stay at home too, I think it is a pain to take LO out. ", "We do sensory bins, we play together, I clean and he plays by himself, nap, eat and before I know it DH is home. ", "When the weather is nice we go for walks or play outside.", "\n\nI stay home a lot, but try to get out with the girls once twice a week. ", "It 's harder because I dont have a car during the day and the weather is starting to get really cold\n\nBut we go to the park and the store when the weather is nice. ", "I walk to my sisters once or twice a week, but its like a 30 minute up a big hill with a double stroller... the more pregnant I get the harder that is :(\n\nwe also spend lots of time at home and i think its better to be with me than anyone else but she does get tired of me and loves to be outside and spend time with other babies, just try to balance it out.", "\n\nI'm rarely home for more than a few hours at a time.", "\nOur things we do varies but we usually go eat lunch with my mom and little siblings once a week, lunch with hubby one a week or once every two weeks, I split my grocery trips up to twice as week, go to the bank, and soon we will be Christmas shopping too.", "\nI visit a friend and my sister or have them come over, go to the library for bouncing babies, and we have church Sunday mornings." ]

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[ "Dear Neighbors,\n\nIn case you would prefer to pick-up your groceries curbside or have them delivered right to your front door, we offer curbside pick-up as well as delivery!", "\n\nOur new curbside & delivery schedule is Monday-Friday.", "\n\nClick here to place your curbside or delivery order! ", "We deliver to the following zip codes: 20001, 20005, 20007, 20008, 20009, 20036, 20037, and 20010.", "\n\nThank you, and please stay safe and well!!" ]

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[ "Real Ghost Poltergeist Activity Caught On Tape\n\nYou need to a flashplayer enabled browser to view this YouTube video\n\nThis poltergeist activity was caught on tape inside a deli that is said to have been a rum running location during prohibition. ", "The owner couldnt figure out how his store kept getting out of order during the night. ", "He set up a camera and turned over the security tape to police who had no explanation and no culprit. ", "Is this real poltergeist or Ghost activity?" ]

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[ "Introduction {#sec1-1}\n============\n\nAcute myeloid leukemia (AML) is a clonal, hematological malignancy of myeloid progenitor cells. ", "These progenitor blast cells accumulate in the bone marrow and peripheral blood, eventually disrupting normal hematopoiesis and leading clinically to anemia, neutropenia and thrombocytopenia.^[@ref1]^ The prognosis for AML is variable, and reflects a number of clinical and genetic factors.^[@ref2]^\n\nCurrently, AML is considered treatable and curative in many cases with a remissioninduction chemotherapy regimen followed by consolidative chemotherapy and, in many cases, hematopoietic stem cell transplant in first or subsequent remissions. ", "In 1973, a standard regimen of 7 days of continuous infusion cytarabine and 3 days of daunorubicin was established. ", "The initial remission rates have varied from 55-90% of patients after 7+3 therapy in patient cohorts with a median age of 50;^[@ref3],[@ref4]^ however, 20-30% of young patients and 40-50% of older patients will experience primary induction failure.^[@ref5]^ The 5-year survival rate for recurrent AML is only 11%.^[@ref2]^ There still remains considerable variability in assigning appropriate treatment for primary-refractory and recurrent leukemia.^[@ref6]^\n\nAzacitidine is a hypomethylating agent shown to be more effective compared to best support care in elderly patients or patients with poor performance state and serious co-morbidities.^[@ref7]^ Azacitidine acts by inhibiting DNA methyltranferase once it is incorporated in the growing DNA strand.^[@ref8]^ The drug's limited efficacy in AML was demonstrated as far back as the 1970's.^[@ref9]^ Nevertheless, it did not become commercially available until 2004 when approved as the first drug for the treatment of myelodysplastic syndromes (MDS). ", "Renewed interest in its potential to treat AML quickly followed. ", "Several additional clinical studies have demonstrated its efficacy in treating relapsed or refractory AML.^[@ref6],[@ref10],[@ref11]^ We recently treated a patient whose case illuminates the potential of azacitidine therapy in refractory AML with monocytic features under severely adverse conditions.", "\n\nCase Report {#sec1-2}\n===========\n\nA 57-year-old Filipino man presented with de novo AML, hyperuricemia, fulminant acute renal failure with a creatinine of 9.9 mg/dL and leukocytosis (80.6×10^[@ref3]^/mm^[@ref3]^), features associated with an increased risk of early death.^[@ref12]^ He initially presented to the Emergency Department complaining of progressive dyspnea, anorexia and a 20-pound weight loss over the prior three to four weeks. ", "His past medical history was significant for mitral valve replacement for mitral valve prolapse, seizure disorder, hyperlipidemia, cigarette smoking and heavy alcohol use. ", "He denied fever, night sweats, pruritus, rash, or cough. ", "His family history was non-contributory. ", "His vital signs and body temperature were normal. ", "Physical exam was significant for a grade II/VI systolic ejection murmur in left upper sternal border, bibasilar crackles on lung auscultation and trace pretibial edema. ", "No lymphadenopathy or hepatosplenomegaly were noted. ", "His admission CBC was significant for a white blood cell count (WBC) of 80.6×10^[@ref3]^/mm^[@ref3]^ with differential of 13% segmented neutrophils, 3% bands, 4% lymphocytes, and 75% monocytes with many immature forms and a platelet count of 88×10^[@ref3]^/mm^[@ref3]^. These results represent a marked change from his CBC done only four months previously. ", "At that time, his CBC demonstrated a WBC of 7.9×10^[@ref3]^/mm^[@ref3]^ with a normal differential, a platelet count of 150×10^[@ref3]^/mm^[@ref3]^ and a hemoglobin of 14.6 g/dL. Bone marrow aspiration with flow cytometry, cytogenetics and fluorescent in-situ hybridization (FISH) studies demonstrated acute myeloid leukemia, WHO classification not otherwise specified (with monocytic differentiation), with 84% blasts, 3% segmented neutrophils, 2% nucleated red blood cells, 3% lymphocytes and 5% monocytes. ", "Cytogenetic studies revealed a normal karyotype and FISH demonstrated no mutations (5q12, 5q31, 7cen, 7q31. ", "8cen, and 20q12) commonly observed in AML or MDS. *", "JAK2* mutational studies were likewise negative. ", "He received rasburicase for hyperuricemia and underwent acute hemodialysis. ", "His hyperuricemia and acute renal failure resolved.", "\n\nThe patient initially received non-anthracycline based induction therapy with fludarabine (15 mg/m^[@ref2]^ IV BID for 4 days) and cytarabine (500mg/m^[@ref2]^ IV BID for 4 days) because echocardiography had demonstrated decreased cardiac contractility and an ejection fraction (EF) of 40-45%. ", "After the first induction, his bone marrow remained hypercellular with 94% monoblasts and a normal karyotype. ", "There were no mutations commonly seen in AML (FISH negative for MLL, BCR-ABL1, PDGRA, and PDGRB rearrangements), and atypical megakaryocytes that were not present on the initial diagnostic marrow. ", "A MUGA later demonstrated an EF of 64%. ", "He was re-induced with infusional cytarabine (100 mg/mg CIVI d1-7) and daunorubicin (60 mg/m2/d IV d1-3). ", "After his second induction course, the day 15 bone marrow continued to demonstrate 22% monoblasts with a normal karyotype, no common MDS mutations seen by FISH and megakaryocytes with atypia. ", "The patient failed to achieve a complete remission after these two cycles of induction chemotherapy. ", "Within 16 days following completion of the second induction, his leukocyte count rose again to greater than 100×10^[@ref3]^/mm^[@ref3]^ with 30% segmented neutrophils, 17% monocytes, and 53% blasts and platelets rose higher than 500×10^[@ref3]^/mm^[@ref3]^ ([Figure 1](#fig001){ref-type=\"fig\"}). ", "Hyper-leukocytosis was managed briefly with hydroxyurea, followed by azacitidine (75 mg/m^[@ref2]^) subcutaneously for 7-days every 28 days. ", "His blood counts rapidly normalized. ", "Following 5 cycles of azacitidine, a bone marrow aspirate and biopsy demonstrated a morphologic complete response (CR) with 0% blasts, 11.5% myelocytes, 10.5% metamyelocytes, 18.5% segmented neutrophils, 47.5% erythroid precursors, 4% lymphocytes, 1% monocytes, 4% eosinophils, and 1% basophils with normal cytogenetics and FISH. ", "He is currently continuing azacitidine maintenance therapy and remains in complete remission after ten additional cycles.", "\n\nDiscussion and Conclusions {#sec1-3}\n==========================\n\nResponse of refractory AML to azacitidine has been documented as far back as the 1970s.^[@ref8]^ A recent clinical study assessed the efficacy of hypomethylating agents (azacitidine and decitabine) as induction, salvage, or consolidation therapy for AML.^[@ref9]^ They reported that hypomethylating agents used as induction therapy resulted in a response rate of 26%; however, as salvage therapy, only one of 28 patients achieved a CR. ", "In another study, 21% of patients treated with azacitidine for recurrent or refractory disease achieved a CR. ", "Of this group, six patients later underwent a hematopoietic stem cell transplant (HSCT).^[@ref6]^ Both studies showed a similar median overall survival (OS) of the whole cohort of 8 and 9 months, respectively; however, among the patients that achieved a CR, median OS was not reached. ", "These results suggest that the complete responses achieved may be durable. ", "Furthermore, a French study of 141 patients with refractory AML after intensive chemotherapy reported a 9% complete response rate following azacitidine based therapy.^[@ref11]^ Among their cohort with a normal karyotype the one-year survival was 42.5%. ", "These studies underline the efficacy of hypomethylating agents in the treatment of selected patients with relapsed or refractory AML.", "\n\nFurthermore, combinations of azacitidine with other agents including epigenetic modifiers and other targeted chemotherapeutic agents have shown particular promise. ", "A phase II trial demonstrated increased response rate in MDS with azacitidine and the HDAC inhibitor, vorinostat, compared to historic controls.^[@ref13]^ Another clinical trial has shown that a combination of azacitidine and the non-specific tyrosine kinase inhibitor sorafenib may be particularly effective in treating relapsed AML with a *FLT-3* mutation. ", "^[@ref14]^ Combination chemotherapy of azacitidine with gemtuzumab ozogamicin for elderly patients not qualifying for intensive induction chemotherapy has achieved a 35% CR rate in a phase II clinical trial.^[@ref3]^\n\nOur patient is unusual because of his critical condition at presentation with extreme leukocytosis, hyperuricemia, associated acute renal failure and borderline low cardiac EF. ", "He had cytogenetically normal AML, the most common cytogenetic risk group, which is associated with variable outcomes.^[@ref15],[@ref16]^ While there is little data on association between response to azacitidine and AML with monocytic differentiation, there is evidence that azacitidine is an effective agent in the management of chronic myelomonocytic leukemia.^[@ref17]^ It would be of interest to investigate further whether a monocytic phenotype is particularly responsive to azacitidine therapy. ", "The aggressiveness of his leukemia is notable as well with the rapid rise of his white blood count to over 100×10^[@ref3]^/mm^[@ref3]^ only two weeks after completing his second induction course. ", "Far more surprising, he developed significant thrombocytosis following two consecutive cycles of induction chemotherapy, a phenomenon observed in the 3q21q26 syndrome,^[@ref18]^ although he had cytogenetically normal AML. ", "Another possible cause for his thrombocytosis is damage to megakaryocytes after chemotherapy, which explains the newly present atypical megakaryocytes in his bone marrow after the first round of induction chemotherapy. ", "Regardless of the etiology, his platelet count returned to normal levels after azacitidine therapy. ", "Our patient also did not experience the dose-limiting toxicities of azacitidine, such as severe bone marrow suppression and infection. ", "There are only a few reports of patients achieving a complete remission following azacitidine after failing initial remission-induction therapy.^[@ref6]^\n\nAzacitidine may, in select cases, become a preferred agent for salvage therapy in refractory or recurrent AML especially as a bridge to HSCT.^[@ref10]^ Further prospective clinical trials with a focus on the clinical and molecular behavior are needed to assess further the optimal use of hypomethylating agents in the management of refractory AML.", "\n\nThe authors would like to thank Dr. Jeremy Pantin for his editorial suggestions. ", "This material is the result of work supported with resources and the use of facilities at the Charlie Norwood Veterans Affairs Medical Center, Augusta, Georgia. ", "The contents do not represent the views of the Department of Veterans Affairs nor the United States Government.", "\n\n{#fig001}\n\n[^1]: Contributions: the authors contributed equally.", "\n\n[^2]: Conflicts of interest: the authors declare no potential conflicts of interest.", "\n" ]

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[ "Far-right German porn star sacked as face of neo-Nazi party because she made film with a black man now banned by porn industry... because she is a neo-Nazi\n\nIna Groll, or 'Kitty Blair', was face of National Democratic Party of Germany\n\nShe encouraged men to join far-right party by dressing in revealing outfits\n\nBut she has been fired after senior NDP officials watched her new porn film\n\nIn the movie, titled 'Kitty Discovers Sperm,' she has sex with a black man\n\n\n\nThe far-right porn star sacked from Germany's neo-Nazi NPD party when they found out she made a film with a black man has now been banned by the porn industry... because she is a neo-Nazi.", "\n\nIna Groll, who works under the porn name 'Kitty Blair', had been widely featured in a high-profile campaign by the National Democratic Party of Germany (NDP), encouraging men to join the group by standing outside polling stations dressed in revealing outfits.", "\n\nBut when party chiefs saw her latest porn film they were horrified to see her having sex with a black adult actor and sacked her as the face of the party.", "\n\n\n\nNow, according to German porn industry spokesman John Thompson, who is also boss of the Berlin porn film company 'GGG', there had been a unanimous decision to boycott the blonde actress.", "\n\nSacked: Ina Groll (pictured, left, taking a selfie and, right, as her porn alias, 'Kitty Blair') was fired as the face of the country's National Democratic Party - because she has sex with a black man in her latest porn film\n\n\n\nPorn star: Ms Groll had been widely featured in a high-profile campaign by NDP, which was founded in 1964\n\nHe said: 'In the porn film industry, we welcome participants with all skin colours, and all nationalities, but we don't welcome Nazis. ", "If we had known about her political activities, we would have sent her home straight away.'", "\n\nThe porn industry ban follows on from a ban from using her in promotional stunts for the far right National Democratic Party of Germany (NDP) or from appearing at events with senior NDP officials, after she was found to have had sex with a black man in her latest porn film, 'Kitty Discovers Sperm'.", "\n\nRepresentative: She encouraged men to join the party by standing outside election polls dressed in revealing outfits. ", "Above, Ms Groll poses with a member of the NDP, which is widely perceived as a neo-Nazi organisation\n\nConfident: But the model has now been fired after NDP officals watched her film, titled: 'Kitty Discovers Sperm'\n\nThe NDP leadership had apparently been happy to use images of the 28-year-old blonde in their various campaigns and promotional material until then, believing she would lure male fans to vote for the NDP.", "\n\n\n\nShe became friends with many of the senior neo-Nazis in the country and senior NDP officials but all that changed when one of the men sat down to watch one of her videos - and was horrified to find she was having sex with a black man in the film titled 'Kitty discovers Sperm'.", "\n\nOnce the fact was made public a Facebook page was even formed to get rid of Groll from the party. ", "One wrote: 'Those who sell their body for money and disgrace their race have no place in our party.'", "\n\nPosing: Ms Groll was sacked following a number of lengthy discussions and a NDP party meeting\n\nThe matter was also raised with senior NDP officials and after a party meeting it was decided that the political group would sever all ties with Groll, who goes under the porn name of Kitty Blair.", "\n\nAnother German porn industry insider, Axel Schaffrath, who was the former partner of top German porn star Gina Wild, said: 'The popular view is that she needs to be locked up, no one needs someone like her with her perverted view of the world.", "\n\n\n\nShe certainly has no chance of filming any more porn movies after her Nazi links were revealed. ", "I personally advised the producers to keep her as far away as possible, people like her need to be ignored by everyone.", "\n\nFounded in 1964, the NDP identifies itself as Germany's 'only significant patriotic force'.", "\n\n\n\nThe party, widely perceived as a neo-Nazi organisation, is currently represented in two of the country's 16 state parliaments.", "\n\n" ]

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[ "\n363 S.E.2d 642 (1988)\n88 N.C. App. ", "476\nTroy W. HORNE, d/b/a Troy's Mobile Homes\nv.\nNOBILITY HOMES, INCORPORATED and Bellefonte Underwriters Insurance Company.", "\nNo. ", "8725SC648.", "\nCourt of Appeals of North Carolina.", "\nJanuary 19, 1988.", "\n*643 Stephen T. Daniel & Associates, P.A. by Stephen T. Daniel, Morganton, for plaintiff-appellant.", "\nPatton, Starnes, Thompson, Aycock & Teele, P.A. by Robert L. Thompson, Morganton, for defendants-appellees.", "\nSMITH, Judge.", "\nThe order from which plaintiff appeals is interlocutory. \"", "An interlocutory order is one made during the pendency of an action, which does not dispose of the case, but leaves it for further action by the trial court in order to settle and determine the entire controversy.\" ", "Veazey v. Durham, 231 N.C. 357, 362, 57 S.E.2d 377, 381, reh'g. ", "denied, 232 N.C. 744, 59 S.E.2d 429 (1950). ", "Accord McKinney v. Royal Globe Insur. ", "Co., 64 N.C.App. ", "370, 307 S.E.2d 390 (1983). ", "An order setting aside a default judgment is interlocutory as \"it does not finally dispose of the case and requires further action by the trial court.\" ", "Bailey v. Gooding, 301 N.C. 205, 209, 270 S.E.2d 431, 434 (1980).", "\nNo appeal lies from an interlocutory order unless it affects a substantial right and will result in injury if not reviewed before final judgment. ", "G.S. 1-277(a); G.S. 7A-27(d); Waters v. Personnel, Inc., 294 N.C. 200, 240 S.E.2d 338 (1978). ", "Accord Fraser v. Di Santi, 75 N.C.App. ", "654, 331 S.E.2d 217, disc. ", "rev. ", "denied, 315 N.C. 183, 337 S.E.2d 856 (1985). ", "If the appellant's rights \"would be fully and adequately protected by an exception to the order that could then be assigned as error on appeal after final judgment,\" there is no right to an immediate appeal. ", "Bailey v. Gooding, supra, 301 N.C. at 210, 270 S.E.2d at 434.", "\nPlaintiff contends our refusal to hear this appeal will deny a substantial right. ", "By affidavit, plaintiff's counsel submits that Nobility's Reidsville plant has been closed and is now for sale. ", "Plaintiff argues that a dismissal of this appeal will result in irreparable harm to plaintiff in that Nobility's remaining assets will be beyond the jurisdiction of North Carolina courts thus hindering recovery on a final judgment. ", "We disagree. ", "Plaintiff has not shown that the attachment provisions of G.S. 1-440.1 et seq. ", "afford no relief as to Nobility's assets. ", "Accordingly, plaintiff has not shown that it will be deprived of a substantial right.", "\nIn this case, plaintiff's objection to the order setting aside the default judgment is protected by its exception to the order. ", "Avoidance of a trial is not a substantial right entitling plaintiff to an immediate appeal. ", "Waters v. Personnel, Inc., supra; Bailey v. Gooding, supra. ", "No right will be lost by delaying the appeal until after a final judgment is entered. ", "As the appeal is premature, it must be dismissed. ", "Bailey v. Gooding, supra.", "\nAppeal dismissed.", "\nARNOLD and WELLS, JJ., ", "concur.", "\n" ]

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[ "One of the most effective ways of raising and lowering a screw operated vehicle lifting jack is by use of a crank. ", "A crank provides a desired mechanical advantage for turning the screw and also results in ease of operation as a consequence of the simple cranking action.", "\nCranks are however, undesirably large and present a stowage problem in view of their bulky nature. ", "Additionally, cranks have usually been provided as items separate from the jack. ", "This has often resulted in loss of the crank.", "\nThe present invention provides the combination of a lifting jack with an integral stowable crank. ", "The crank includes some features which have been proposed in the past but not included in a single combination. ", "For example, the crank of the present invention is foldable. ", "It is desirable to have a foldable crank in order that the crank is long enough to fit easily under a vehicle while at the same time being foldable for stowage. ", "Foldable or telescoping cranks have been suggested in U.S. Pat. ", "Nos. ", "1,326,451 issued Dec. 30, 1919 to H. S. Jillson et al, 1,286,161 issued Nov. 26, 1918 to A. F. Wagner, 2,557,465 issued June 19, 1951 to J. C. Rauscher, Sr., ", "1,193,126 issued Aug. 1, 1916 to E. M. Cumings and 1,361,593 issued Dec. 7, 1920 to A. B. Lang. ", "However, these patents do not teach means for permanently connecting the crank to the lifting jack while at the same time permitting the crank to be swung into the jack for storage purposes.", "\nIt is also desired, for maximum turning torque, that the crank turning arm be in alignment with the jack screw and be connected to the jack screw by means of a universal-type joint connection to permit tilting of the crank away from the ground to avoid hitting the ground as the crank is turned and permitting the user to adopt a comfortable kneeling or bending position while manipulating the lifting jack. ", "The desirability of this type of connection is taught in U.S. Pat. ", "Nos. ", "1,468,771 issued Sept. 25, 1923 to E. E. Arnold, 1,901,915 issued Mar. 21, 1933 to M. H. Loughridge and 2,479,362 issued Aug. 16, 1984 to W. Jackson. ", "However, again, the provision of a foldable crank swingable onto the jack for stowage is not suggested.", "\nIn accordance with the present invention, a combination as above described having the following four desirable features is provided:\n1. ", "A foldable crank.", "\n2. ", "Means permitting the folded crank to be swung into the jack for storage.", "\n3. ", "A permanent connection of the crank to the jack.", "\n4. ", "A universal-type connection of the crank to the jack." ]

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[ "Former President Barack Obama Barack Hussein ObamaThe Memo: Trump's strengths complicate election picture Obama shares phone number to find out how Americans are planning to vote Democrats' troubling adventure in a 'Wonderland' without 'rule of law' MORE’s post-White House memoir will likely not be published this year, increasing the chances that the book will be released in the middle of the 2020 presidential campaign.", "\n\nPublisher Penguin Random House has started reaching out to foreign partners and others about the book’s status, according to the Associated Press. ", "The AP reported that Obama has been writing the book himself, writing out a first draft on legal pads, the same method he employed for several White House speeches and his last memoir, “Dreams from My Father,” which was a best-seller.", "\n\nADVERTISEMENT\n\nPenguin Random House did not immediately respond to a request for comment from The Hill.", "\n\nThe former president and his wife, former first lady Michelle Obama Michelle LeVaughn Robinson ObamaBlack stars reimagine 'Friends' to get out the vote Obama shares phone number to find out how Americans are planning to vote Michelle Obama: 'Don't listen to people who will say that somehow voting is rigged' MORE, first signed profitable deals with the publisher in 2017. ", "Michelle Obama’s memoir “Becoming” was released last year and quickly became one of the most popular political memoirs ever, selling over 10 million copies.", "\n\nA person with knowledge of the matter told the AP that Penguin Random House did not update its partners on a launch date.", "\n\nA 2020 launch could thrust the former president, still one of the most revered figures in the Democratic Party, back into the political spotlight just as the party is trying to find its next leader.", "\n\nBeyond a number of campaigns in the 2018 midterm cycle, Obama has taken pains since he departed the White House to stay out of the limelight as the party continues to find itself in the throes of a war between centrists and progressives, an internal division that was split wide open in the 2016 election.", "\n\nThe former president has thus far declined to endorse any presidential contender, including his former vice president Joe Biden Joe BidenBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' ", "Democratic groups using Bloomberg money to launch M in Spanish language ads in Florida Harris faces pivotal moment with Supreme Court battle MORE." ]

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[ "Music\n\nLlyn Foulkes marches to the beat of his own drum — and bass, xylophone, car horn and cowbell. ", "The idiosyncratic painter…is also an accomplished musician. ", "And his instrument of choice is, well, all of them.", "\n\nFoulkes plays a homemade contraption called the Machine, a dense, wraparound nest of scavenged and invented instruments whose crowning glory is a clump of old-fashioned car and bicycle horns.", "\n\nTo play his original compositions, Foulkes squeezes the horns’ black rubber bulbs, triggers a drum with one foot, strums an electric bass with the other and picks up a pair of mallets to tap out a melody on a swirl of xylophone keys and cowbells. ", "Sometimes he beats an empty plastic water jug. ", "Oh, and he sings too. ", "The results are both cacophonous and catchy, evoking the sideshow carny stylings of Tom Waits and the sound-effect-laden novelty songs of Foulkes’ first idol, the 1940s musical satirist Spike Jones.", "\n\nThis return to the sounds of his childhood is the culmination of a long musical evolution. “", "From ’65 to ’71, I was a drummer in a rock band — played all over the [Sunset] Strip, at the Whisky [a Go Go], next to the Doors, the Byrds and all — but I got tired of rock music because rock music all became about how loud it is,” he says. ", "After a stint leading his own group, the Rubber Band [featured on the Tonight Show in ’74], he struck out on his own in 1980 and has been playing the Machine ever since. ", "Now, at 74, he hopes to focus more on his music and has grown a bit weary of the art world. “", "You’ve got billionaire real estate developers defining what art is and saying this is the great art and it’s worth this much money,” he says. “", "I just want to have fun and people like my stuff. ", "That’s all.” — ", "Los Angeles Times — Sharon Mizota\n\nTune in to United Art Scene Tuesday evenings for live webcasts of music from the Church of Art and check back here soon for music downloads." ]

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[ "Q:\n\nComputation difference between function and manual computation\n\nI am facing a mystery right now. ", "I get strange results in some program and I think it may be related to the computation since I got different results with my functions compared to manual computation.", "\nThis is from my program, I am printing the values pre-computation :\nprint(\"\\nPrecomputation:\\nmatrix\\n:\", matrix)\ntmp = likelihood_left * likelihood_right\nprint(\"\\nconditional_dep:\", tmp)\nprint(\"\\nfinal result:\", matrix @ tmp)\n\nI got the following output:\nPrecomputation:\nmatrix: \n[array([0.08078721, 0.5802404 , 0.16957052, 0.09629893, 0.07310294])\n array([0.14633129, 0.45458744, 0.20096238, 0.02142105, 0.17669784])\n array([0.41198731, 0.06197812, 0.05934063, 0.23325626, 0.23343768])\n array([0.15686545, 0.29516415, 0.20095091, 0.14720275, 0.19981674])\n array([0.15965914, 0.18383683, 0.10606946, 0.14234812, 0.40808645])]\n\nconditional_dep: [0.01391123 0.01388155 0.17221067 0.02675524 0.01033257]\nfinal result: [0.07995043 0.03485223 0.02184015 0.04721548 0.05323298]\n\nThe thing is when I compute the following code:\nmatrix = [np.array([0.08078721, 0.5802404 , 0.16957052, 0.09629893, 0.07310294]),\n np.array([0.14633129, 0.45458744, 0.20096238, 0.02142105, 0.17669784]), \n np.array([0.41198731, 0.06197812, 0.05934063, 0.23325626, 0.23343768]), \n np.array([0.15686545, 0.29516415, 0.20095091, 0.14720275, 0.19981674]), \n np.array([0.15965914, 0.18383683, 0.10606946, 0.14234812, 0.40808645])]\n\ntmp = np.asarray([0.01391123, 0.01388155, 0.17221067, 0.02675524, 0.01033257])\n\nmatrix @ tmp\n\nThe values in use are exactly the same as they should be in the computation before but I get the following result:\narray([0.04171218, 0.04535276, 0.02546353, 0.04688848, 0.03106443])\n\nThis result is then obviously different than the previous one and is the true one (I computed the dot product by hand).", "\nI have been facing this problem the whole day and I did not find anything useful online. ", "If any of you have any even tiny idea where it can come from I'd be really happy :D\nThank's in advance\nYann\nPS: I can show more of the code if needed.", "\nPS2: I don't know if it is relevant but this is used in a dynamic programming algorithm.", "\n\nA:\n\nTo recap our discussion in the comments, in the first part (\"pre-computation\"), the following is true about the matrix object:\n>>> matrix.shape\n(5,)\n>>> matrix.dtype\ndtype('O') # aka object\n\nAnd as you say, this is due to matrix being a slice of a larger, non-uniform array. ", "Let's recreate this situation:\n>>> matrix = np.array([[], np.array([0.08078721, 0.5802404 , 0.16957052, 0.09629893, 0.07310294]), np.array([0.14633129, 0.45458744, 0.20096238, 0.02142105, 0.17669784]), np.array([0.41198731, 0.06197812, 0.05934063, 0.23325626, 0.23343768]), np.array([0.15686545, 0.29516415, 0.20095091, 0.14720275, 0.19981674]), np.array([0.15965914, 0.18383683, 0.10606946, 0.14234812, 0.40808645])])[1:]\n\nIt is now not a matrix with scalars in rows and columns, but a column vector of column vectors. ", "Technically, matrix @ tmp is an operation between two 1-D arrays and hence NumPy should, according to the documentation, calculate the inner product of the two. ", "This is true in this case, with the convention that the sum be over the first axis:\n>>> np.array([matrix[i] * tmp[i] for i in range(5)]).sum(axis=0)\narray([0.07995043, 0.03485222, 0.02184015, 0.04721548, 0.05323298])\n>>> matrix @ tmp\narray([0.07995043, 0.03485222, 0.02184015, 0.04721548, 0.05323298])\n\nThis is essentially the same as taking the transpose of the proper 2-D matrix before the multiplication:\n>>> np.stack(matrix).T @ tmp\narray([0.07995043, 0.03485222, 0.02184015, 0.04721548, 0.05323298])\n\nEquivalently, as noted by @jirasssimok:\n>>> tmp @ np.stack(matrix)\narray([0.07995043, 0.03485222, 0.02184015, 0.04721548, 0.05323298])\n\nHence the erroneous or unexpected result.", "\nAs you have already resolved to do in the comments, this can be avoided in the future by ensuring all matrices are proper 2-D arrays.", "\n\n" ]

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[ "Scientists say bones formerly identified as Massospondylus are from a different species\n\nFossil hunters have discovered a new species of dinosaur that has been hidden in plain sight in a South African museum collection for 30 years.", "\n\nThe fossilised bones had been misidentified as a peculiar specimen of Massospondylus, one of the first named dinosaurs.", "\n\nBut a detailed analysis of the 200m-year-old skeleton, which includes an almost complete skull, led researchers to conclude that the remains not only represented a new species but belonged to an entirely new genus too.", "\n\nNamed Ngwevu intloko, which is Xhosa for “grey skull”, the creature measured about 4m from the tip of its snout to the end of its tail and may have weighed as much as 300kg (660lb).", "\n\nIt walked on its hind legs and had a barrel-shaped body, a long, slender neck and a small, boxy skull. ", "Though predominantly a plant-eater, Ngwevu may have taken small animals too when the opportunity arose.", "\n\nPaul Barrett and his PhD student Kimberley Chapelle at the Natural History Museum in London identified the new species after comparing the bones with a haul of other museum specimens. ", "Details of the discovery are published in the journal PeerJ.\n\nThe near-complete fossil was collected from a farm in the Fouriesburg area in Free State, South Africa, in 1978 and has been in the collection at the Evolutionary Studies Institute (ESI), part of the University of the Witwatersrand in Johannesburg, ever since.", "\n\n“A few of us harboured suspicions that it might be something new and different,” Barrett said. “", "In particular, the skull of Ngwevu is much broader and boxier than that of Massospondylus, which is much narrower and taller in proportions.”", "\n\nBecause Massospondylus was so common in South Africa, the researchers had a number of specimens of different ages with which to compare the Ngwevu bones. “", "Based on this, we were able to rule out age as a possible explanation for the differences we see,” Chapelle said.", "\n\nThe dinosaur appears to have been fully grown when it died at about 10 years old, and was smaller than the 5m to 6m-long adult Massospondylus.", "\n\nNgwevu belonged to a diverse population of early dinosaurs that were related to the massive plant-eating sauropods such as diplodocus. ", "Ngwevu lived in a world of ferns, horsetails and conifers watered by a few large permanent rivers. ", "Of all the predators it had to watch out for, the carnivore Dracovenator probably came top.", "\n\n“This is a dinosaur that’s been hiding in plain sight,” Barrett said of Ngwevu. “", "We recognised it by going back through museum collections and doing detailed comparisons between the available specimens. ", "It makes the point that museum collections, even those that are heavily studied, often have the potential to surprise us with finds of brand new species.”" ]

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[ " NUMBER 13-16-00683-CR\n\n COURT OF APPEALS\n\n THIRTEENTH DISTRICT OF TEXAS\n\n CORPUS CHRISTI - EDINBURG\n____________________________________________________________\n\nNOHEMI GABRIELA GONZALEZ, Appellant,\n\n v.\n\nTHE STATE OF TEXAS, Appellee.", "\n____________________________________________________________\n\n On appeal from the 370th District Court\n of Hidalgo County, Texas.", "\n____________________________________________________________\n\n MEMORANDUM OPINION\n Before Justices Rodriguez, Longoria, and Hinojosa\n Memorandum Opinion by Justice Longoria\n\n This appeal was abated by this Court on November 9, 2017, because appellant\n\nfailed to file a brief. ", "This cause is now before the court because counsel for appellant\n\nhas filed a motion to dismiss the appeal. ", "Accordingly, this case is hereby REINSTATED.", "\n\f In an affidavit attached to the motion to dismiss appeal, appellant states that she\n\nno longer wishes to pursue her appeal. ", "We find the motion and affidavit together meet\n\nthe requirement of Texas Rule of Appellate Procedure 42.2(a) that appellant and her\n\nattorney must sign a written motion to dismiss the appeal. ", "See TEX. ", "R. APP. ", "P. 42.2(a).", "\n\nWithout passing on the merits of the case, we GRANT the motion to dismiss pursuant to\n\nTexas Rule of Appellate Procedure 42.2(a) and dismiss the appeal. ", "Having dismissed\n\nthe appeal at appellant's request, no motion for rehearing will be entertained, and our\n\nmandate will issue forthwith.", "\n\n NORA L. LONGORIA\n Justice\n\n\nDo not publish.", "\nSee TEX. ", "R. APP. ", "P. 47.2(b).", "\n\nDelivered and filed the\n14th day of December, 2017.", "\n\n\n\n\n 2\n\f" ]

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