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We consider dynamical systems on the space of functions taking values in a
free associative algebra. The system is said to be integrable if it possesses
an infinite dimensional Lie algebra of commuting symmetries. In this paper we
propose a new approach to the problem of quantisation of dynamical systems,
introduce the concept of quantisation ideals and provide meaningful examples.
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The {\it straight-through estimator} (STE) is commonly used to optimize
quantized neural networks, yet its contexts of effective performance are still
unclear despite empirical successes.To make a step forward in this
comprehension, we apply STE to a well-understood problem: {\it sparse support
recovery}. We introduce the {\it Support Exploration Algorithm} (SEA), a novel
algorithm promoting sparsity, and we analyze its performance in support
recovery (a.k.a. model selection) problems. SEA explores more supports than the
state-of-the-art, leading to superior performance in experiments, especially
when the columns of $A$ are strongly coherent.The theoretical analysis
considers recovery guarantees when the linear measurements matrix $A$ satisfies
the {\it Restricted Isometry Property} (RIP).The sufficient conditions of
recovery are comparable but more stringent than those of the state-of-the-art
in sparse support recovery. Their significance lies mainly in their
applicability to an instance of the STE.
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Designing coherent processes is essential for developing quantum information
technologies. We study coherent dynamics of two spatially separated electrons
in a coupled semiconductor double quantum dot (DQD), in which various two-qubit
operations are demonstrated just by adjusting the gate voltages. Especially,
second-order correlated coherent oscillations provide functional quantum
processes for making quantum correlation of separated particles. The results
encourage searching quantum entanglement in electronic devices.
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We exhibit a convex polynomial optimization problem for which the
diagonally-dominant sum-of-squares (DSOS) and the scaled diagonally-dominant
sum-of-squares (SDSOS) hierarchies, based on linear programming and
second-order conic programming respectively, do not converge to the global
infimum. The same goes for the r-DSOS and r-SDSOS hierarchies. This refutes the
claim in the literature according to which the DSOS and SDSOS hierarchies can
solve any polynomial optimization problem to arbitrary accuracy. In contrast,
the Lasserre hierarchy based on semidefinite programming yields the global
infimum and the global minimizer with the first order relaxation. We further
observe that the dual to the SDSOS hierarchy is the moment hierarchy where
every positive semidefinite constraint is relaxed to all necessary second-order
conic constraints. As a result, the number of second-order conic constraints
grows quadratically in function of the size of the positive semidefinite
constraints in the Lasserre hierarchy. Together with the counterexample, this
suggests that DSOS and SDSOS are not necessarily more tractable alternatives to
sum-of-squares.
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Policy gradient methods in actor-critic reinforcement learning (RL) have
become perhaps the most promising approaches to solving continuous optimal
control problems. However, the trial-and-error nature of RL and the inherent
randomness associated with solution approximations cause variations in the
learned optimal values and policies. This has significantly hindered their
successful deployment in real life applications where control responses need to
meet dynamic performance criteria deterministically. Here we propose a novel
phased actor in actor-critic (PAAC) method, aiming at improving policy gradient
estimation and thus the quality of the control policy. Specifically, PAAC
accounts for both $Q$ value and TD error in its actor update. We prove
qualitative properties of PAAC for learning convergence of the value and
policy, solution optimality, and stability of system dynamics. Additionally, we
show variance reduction in policy gradient estimation. PAAC performance is
systematically and quantitatively evaluated in this study using DeepMind
Control Suite (DMC). Results show that PAAC leads to significant performance
improvement measured by total cost, learning variance, robustness, learning
speed and success rate. As PAAC can be piggybacked onto general policy gradient
learning frameworks, we select well-known methods such as direct heuristic
dynamic programming (dHDP), deep deterministic policy gradient (DDPG) and their
variants to demonstrate the effectiveness of PAAC. Consequently we provide a
unified view on these related policy gradient algorithms.
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When agents interact socially with different intentions, conflicts are
difficult to avoid. Although how agents can resolve such problems autonomously
has not been determined, dynamic characteristics of agency may shed light on
underlying mechanisms. The current study focused on the sense of agency (SoA),
a specific aspect of agency referring to congruence between the agent's
intention in acting and the outcome. Employing predictive coding and active
inference as theoretical frameworks of perception and action generation, we
hypothesize that regulation of complexity in the evidence lower bound of an
agent's model should affect the strength of the agent's SoA and should have a
critical impact on social interactions. We built a computational model of
imitative interaction between a robot and a human via visuo-proprioceptive
sensation with a variational Bayes recurrent neural network, and simulated the
model in the form of pseudo-imitative interaction using recorded human body
movement data. A key feature of the model is that each modality's complexity
can be regulated differently with a hyperparameter assigned to each module. We
first searched for an optimal setting that endows the model with appropriate
coordination of multimodal sensation. This revealed that the vision module's
complexity should be more tightly regulated than that of the proprioception
module. Using the optimally trained model, we examined how changing the
tightness of complexity regulation after training affects the strength of the
SoA during interactions. The results showed that with looser regulation, an
agent tends to act more egocentrically, without adapting to the other. In
contrast, with tighter regulation, the agent tends to follow the other by
adjusting its intention. We conclude that the tightness of complexity
regulation crucially affects the strength of the SoA and the dynamics of
interactions between agents.
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Oxide interfaces exhibit a broad range of physical effects stemming from
broken inversion symmetry. In particular, they can display non-reciprocal
phenomena when time reversal symmetry is also broken, e.g., by the application
of a magnetic field. Examples include the direct and inverse Edelstein effects
(DEE, IEE) that allow the interconversion between spin currents and charge
currents. The DEE and IEE have been investigated in interfaces based on the
perovskite SrTiO$_3$ (STO), albeit in separate studies focusing on one or the
other. The demonstration of these effects remains mostly elusive in other oxide
interface systems despite their blossoming in the last decade. Here, we report
the observation of both the DEE and IEE in a new interfacial two-dimensional
electron gas (2DEG) based on the perovskite oxide KTaO$_3$. We generate 2DEGs
by the simple deposition of Al metal onto KTaO$_3$ single crystals,
characterize them by angle-resolved photoemission spectroscopy and
magnetotransport, and demonstrate the DEE through unidirectional
magnetoresistance and the IEE by spin-pumping experiments. We compare the
spin-charge interconversion efficiency with that of STO-based interfaces,
relate it to the 2DEG electronic structure, and give perspectives for the
implementation of KTaO$_3$ 2DEGs into spin-orbitronic devices.
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Precision tests of the Standard Model and searches for beyond the Standard
Model physics often require nuclear structure input. There has been a
tremendous progress in the development of nuclear ab initio techniques capable
of providing accurate nuclear wave functions. For the calculation of
observables, matrix elements of complicated operators need to be evaluated.
Typically, these matrix elements would contain spurious contributions from the
center-of-mass (COM) motion. This could be problematic when precision results
are sought. Here, we derive a transformation relying on properties of harmonic
oscillator wave functions that allows an exact removal of the COM motion
contamination applicable to any one-body operator depending on nucleon
coordinates and momenta. Resulting many-nucleon matrix elements are
translationally invariant provided that the nuclear eigenfunctions factorize as
products of the intrinsic and COM components as is the case, e.g., in the
no-core shell model approach. An application of the transformation has been
recently demonstrated in calculations of the nuclear structure recoil
corrections for the beta-decay of 6He.
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We solve closed string theory in all regular homogeneous plane-wave
backgrounds with homogeneous NS three-form field strength and a dilaton. The
parameters of the model are constant symmetric and anti-symmetric matrices
k_{ij} and f_{ij} associated with the metric, and a constant anti-symmetric
matrix h_{ij} associated with the NS field strength. In the light-cone gauge
the rotation parameters f_{ij} have a natural interpretation as a constant
magnetic field. This is a generalisation of the standard Landau problem with
oscillator energies now being non-trivial functions of the parameters f_{ij}
and k_{ij}. We develop a general procedure for solving linear but non-diagonal
equations for string coordinates, and determine the corresponding oscillator
frequencies, the light-cone Hamiltonian and level matching condition. We
investigate the resulting string spectrum in detail in the four-dimensional
case and compare the results with previously studied examples. Throughout we
will find that the presence of the rotation parameter f_{ij} can lead to
certain unusual and unexpected features of the string spectrum like new
massless states at non-zero string levels, stabilisation of otherwise unstable
(tachyonic) modes, and discrete but not positive definite string oscillator
spectra.
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Price of anarchy quantifies the degradation of social welfare in games due to
the lack of a centralized authority that can enforce the optimal outcome. At
its antipodes, mechanism design studies how to ameliorate these effects by
incentivizing socially desirable behavior and implementing the optimal state as
equilibrium. In practice, the responsiveness to such measures depends on the
wealth of each individual. This leads to a natural, but largely unexplored,
question. Does optimal mechanism design entrench, or maybe even exacerbate,
social inequality?
We study this question in nonatomic congestion games, arguably one of the
most thoroughly studied settings from the perspectives of price of anarchy as
well as mechanism design. We introduce a new model that incorporates the wealth
distribution of the population and captures the income elasticity of travel
time. This allows us to argue about the equality of wealth distribution both
before and after employing a mechanism. We start our analysis by establishing a
broad qualitative result, showing that tolls always increase inequality in
symmetric congestion games under any reasonable metric of inequality, e.g., the
Gini index. Next, we introduce the iniquity index, a novel measure for
quantifying the magnitude of these forces towards a more unbalanced wealth
distribution and show it has good normative properties (robustness to scaling
of income, no-regret learning). We analyze iniquity both in theoretical
settings (Pigou's network under various wealth distributions) as well as
experimental ones (based on a large scale field experiment in Singapore).
Finally, we provide an algorithm for computing optimal tolls for any point of
the trade-off of relative importance of efficiency and equality. We conclude
with a discussion of our findings in the context of theories of justice as
developed in contemporary social sciences.
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We derive eigenvalue bounds for the $t$-distance chromatic number of a graph,
which is a generalization of the classical chromatic number. We apply such
bounds to hypercube graphs, providing alternative spectral proofs for results
by Ngo, Du and Graham [Inf. Process. Lett., 2002], and improving their bound
for several instances. We also apply the eigenvalue bounds to Lee graphs,
extending results by Kim and Kim [Discrete Appl. Math., 2011]. Finally, we
provide a complete characterization for the existence of perfect Lee codes of
minimum distance $3$. In order to prove our results, we use a mix of spectral
and number theory tools. Our results, which provide the first application of
spectral methods to Lee codes, illustrate that such methods succeed to capture
the nature of the Lee metric.
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The in vitro and in vivo activity of diminazene (Dim), artesunate (Art) and
combination of Dim and Art (Dim-Art) against Leishmania donovani was compared
to reference drug; amphotericin B. IC50 of Dim-Art was found to be $2.28 \pm
0.24 \mu$ g/mL while those of Dim and Art were $9.16 \pm 0.3 \mu$ g/mL and
$4.64 \pm 0.48 \mu$ g/mL respectively. The IC50 for Amphot B was $0.16 \pm 0.32
\mu$ g/mL against stationary-phase promastigotes. In vivo evaluation in the L.
donovani BALB/c mice model indicated that treatments with the combined drug
therapy at doses of 12.5 mg/kg for 28 consecutive days significantly ($p <
0.001$) reduced parasite burden in the spleen as compared to the single drug
treatments given at the same dosages. Although parasite burden was slightly
lower ($p < 0.05$) in the Amphot B group than in the Dim-Art treatment group,
the present study demonstrates the positive advantage and the potential use of
the combined therapy of Dim-Art over the constituent drugs, Dim or Art when
used alone. Further evaluation is recommended to determine the most efficacious
combination ratio of the two compounds.
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We construct a stable formal model of a Lubin-Tate curve with level three,
and study the action of a Weil group and a division algebra on its stable
reduction. Further, we study a structure of cohomology of the Lubin-Tate curve.
Our study is purely local and includes the case where the characteristic of the
residue field of a local field is two.
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Exciton dynamics can be strongly affected by lattice vibrations through
electron-phonon coupling. This is rarely explored in two-dimensional magnetic
semiconductors. Focusing on bilayer CrI3, we first show the presence of strong
electron-phonon coupling through temperature-dependent photoluminescence and
absorption spectroscopy. We then report the observation of periodic broad modes
up to the 8th order in Raman spectra, attributed to the polaronic character of
excitons. We establish that this polaronic character is dominated by the
coupling between the charge-transfer exciton at 1.96 eV and a longitudinal
optical phonon at 120.6 cm-1. We further show that the emergence of long-range
magnetic order enhances the electron-phonon coupling strength by about 50$\%$
and that the transition from layered antiferromagnetic to ferromagnetic order
tunes the spectral intensity of the periodic broad modes, suggesting a strong
coupling among the lattice, charge and spin in two-dimensional CrI3. Our study
opens opportunities for tailoring light-matter interactions in two-dimensional
magnetic semiconductors.
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Friedland (1981) showed that for a nonnegative square matrix A, the spectral
radius r(e^D A) is a log-convex functional over the real diagonal matrices D.
He showed that for fully indecomposable A, log r(e^D A) is strictly convex over
D_1, D_2 if and only if D_1-D_2 != c I for any c \in R. Here the condition of
full indecomposability is shown to be replaceable by the weaker condition that
A and A'A be irreducible, which is the sharpest possible replacement condition.
Irreducibility of both A and A'A is shown to be equivalent to irreducibility of
A^2 and A'A, which is the condition for a number of strict inequalities on the
spectral radius found in Cohen, Friedland, Kato, and Kelly (1982). Such
`two-fold irreducibility' is equivalent to joint irreducibility of A, A^2, A'A,
and AA', or in combinatorial terms, equivalent to the directed graph of A being
strongly connected and the simple bipartite graph of A being connected.
Additional ancillary results are presented.
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We investigate the solvability of the Byzantine Reliable Broadcast and
Byzantine Broadcast Channel problems in distributed systems affected by Mobile
Byzantine Faults. We show that both problems are not solvable even in one of
the most constrained system models for mobile Byzantine faults defined so far.
By endowing processes with an additional local failure oracle, we provide a
solution to the Byzantine Broadcast Channel problem.
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This note gives explicit equations for the elliptic curves (in characteristic
not 2 or 3) with mod 2 representation isomorphic to that of a given one.
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In this paper, a new gradient-based optimization approach by automatically
adjusting the learning rate is proposed. This approach can be applied to design
non-adaptive learning rate and adaptive learning rate. Firstly, I will
introduce the non-adaptive learning rate optimization method: Binary Forward
Exploration (BFE), and then the corresponding adaptive per-parameter learning
rate method: Adaptive BFE (AdaBFE) is possible to be developed. This approach
could be an alternative method to optimize the learning rate based on the
stochastic gradient descent (SGD) algorithm besides the current non-adaptive
learning rate methods e.g. SGD, momentum, Nesterov and the adaptive learning
rate methods e.g. AdaGrad, AdaDelta, Adam... The purpose to develop this
approach is not to beat the benchmark of other methods but just to provide a
different perspective to optimize the gradient descent method, although some
comparative study with previous methods will be made in the following sections.
This approach is expected to be heuristic or inspire researchers to improve
gradient-based optimization combined with previous methods.
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HI intensity mapping (IM) is a novel technique capable of mapping the
large-scale structure of the Universe in three dimensions and delivering
exquisite constraints on cosmology, by using HI as a biased tracer of the dark
matter density field. This is achieved by measuring the intensity of the
redshifted 21cm line over the sky in a range of redshifts without the
requirement to resolve individual galaxies. In this chapter, we investigate the
potential of SKA1 to deliver HI intensity maps over a broad range of
frequencies and a substantial fraction of the sky. By pinning down the baryon
acoustic oscillation and redshift space distortion features in the matter power
spectrum -- thus determining the expansion and growth history of the Universe
-- these surveys can provide powerful tests of dark energy models and
modifications to General Relativity. They can also be used to probe physics on
extremely large scales, where precise measurements of spatial curvature and
primordial non-Gaussianity can be used to test inflation; on small scales, by
measuring the sum of neutrino masses; and at high redshifts where non-standard
evolution models can be probed. We discuss the impact of foregrounds as well as
various instrumental and survey design parameters on the achievable
constraints. In particular we analyse the feasibility of using the SKA1
autocorrelations to probe the large-scale signal.
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A model of the ferromagnetic origin of magnetic fields of neutron stars is
considered. In this model, the magnetic phase transition occurs inside the core
of neutron stars soon after formation. However, owing to the high electrical
conductivity the core magnetic field is initially fully screened. We study how
this magnetic field emerges for an outside observer. After some time, the
induced field that screens the ferromagnetic field decays enough to uncover a
detectable fraction of the ferromagnetic field. We conjecture that weak fields
of millisecond pulsars of 10^8-10^9 G could be identified with ferromagnetic
fields of unshielded fraction f=10^-4 resulting from the decay of screening
fields by a factor 1-f in 10^8 yr since their birth.
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A 2D approach is used to simulate the properties of positive and negative
streamers emerging from a high-voltage electrode in a long (14 cm) air gap for
standard pressure and temperature. The applied voltage varies from 100 to 500
kV. To reveal the influence of photoionization, the calculations are made for
various rates of seed electron generation in front of the streamer head. The
difference between the properties of positive and negative streamers is
associated with the different directions of the electron drift ahead of the
streamer head. As a result, the peak electric field at the streamer head and
the streamer velocity are higher for positive voltage polarity. The average
electric field in the negative streamer channel is approximately twice that in
the positive streamer channel, in agreement with available measurements in long
air gaps. It is shown that photoionization in front of the streamer head is
important not only for the development of strong positive discharges, but for
the development of strong negative discharges as well. An increase in the
photoionization rate increases the propagation velocity of the positive
streamer and retards the propagation of the negative streamer.
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Let $M$ be a hyperkahler manifold of maximal holonomy (that is, an IHS
manifold), and let $K$ be its Kahler cone, which is an open, convex subset in
the space $H^{1,1}(M, R)$ of real (1,1)-forms. This space is equipped with a
canonical bilinear symmetric form of signature $(1,n)$ obtained as a
restriction of the Bogomolov-Beauville-Fujiki form. The set of vectors of
positive square in the space of signature $(1,n)$ is a disconnected union of
two convex cones. The "positive cone" is the component which contains the
Kahler cone. We say that the Kahler cone is "round" if it is equal to the
positive cone. The manifolds with round Kahler cones have unique bimeromorphic
model and correspond to Hausdorff points in the corresponding Teichmuller
space. We prove thay any maximal holonomy hyperkahler manifold with $b_2 > 4$
has a deformation with round Kahler cone and the Picard lattice of signature
(1,1), admitting two non-collinear integer isotropic classes. This is used to
show that all known examples of hyperkahler manifolds admit a deformation with
two transversal Lagrangian fibrations, and the Kobayashi metric vanishes unless
the Picard rank is maximal.
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The effects of CP violating anomalous ZZZ and gammaZZ vertices in ZZ
production are determined. We present the differential cross-section for e+e-
-> ZZ with dependence on the spins of the Z bosons. It is shown that from the
different spin combinations those with one longitudinally and one transversally
polarized Z in the final state are the most sensitive to CP violating anomalous
couplings.
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In this paper linear canonical correlation analysis (LCCA) is generalized by
applying a structured transform to the joint probability distribution of the
considered pair of random vectors, i.e., a transformation of the joint
probability measure defined on their joint observation space. This framework,
called measure transformed canonical correlation analysis (MTCCA), applies LCCA
to the data after transformation of the joint probability measure. We show that
judicious choice of the transform leads to a modified canonical correlation
analysis, which, in contrast to LCCA, is capable of detecting non-linear
relationships between the considered pair of random vectors. Unlike kernel
canonical correlation analysis, where the transformation is applied to the
random vectors, in MTCCA the transformation is applied to their joint
probability distribution. This results in performance advantages and reduced
implementation complexity. The proposed approach is illustrated for graphical
model selection in simulated data having non-linear dependencies, and for
measuring long-term associations between companies traded in the NASDAQ and
NYSE stock markets.
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An expression for the photon condensate in quantum electrodynamics is
presented and generalized to deduce a simple relation between the gluon
condensate and the running coupling constant of quantum chromodynamics (QCD).
Ambiguities in defining the condensates are discussed. The values of the gluon
condensate from some Ans\"{a}tze for the running coupling in the literature are
compared with the value determined from QCD sum rules.
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Schweizer, Sklar and Thorp proved in 1960 that a Menger space $(G,D,T)$ under
a continuous $t$-norm $T$, induce a natural topology $\tau$ wich is metrizable.
We extend this result to any probabilistic metric space $(G,D,\star)$ provided
that the triangle function $\star$ is continuous. We prove in this case, that
the topological space $(G,\tau)$ is uniformly homeomorphic to a (deterministic)
metric space $(G,\sigma_D)$ for some canonical metric $\sigma_D$ on $G$. As
applications, we extend the fixed point theorem of Hicks to probabilistic
metric spaces which are not necessarily Menger spaces and we prove a
probabilistic Arzela-Ascoli type theorem.
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Source free domain adaptation (SFDA) aims to transfer a trained source model
to the unlabeled target domain without accessing the source data. However, the
SFDA setting faces an effect bottleneck due to the absence of source data and
target supervised information, as evidenced by the limited performance gains of
newest SFDA methods. In this paper, for the first time, we introduce a more
practical scenario called active source free domain adaptation (ASFDA) that
permits actively selecting a few target data to be labeled by experts. To
achieve that, we first find that those satisfying the properties of
neighbor-chaotic, individual-different, and target-like are the best points to
select, and we define them as the minimum happy (MH) points. We then propose
minimum happy points learning (MHPL) to actively explore and exploit MH points.
We design three unique strategies: neighbor ambient uncertainty, neighbor
diversity relaxation, and one-shot querying, to explore the MH points. Further,
to fully exploit MH points in the learning process, we design a neighbor focal
loss that assigns the weighted neighbor purity to the cross-entropy loss of MH
points to make the model focus more on them. Extensive experiments verify that
MHPL remarkably exceeds the various types of baselines and achieves significant
performance gains at a small cost of labeling.
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We present the results of the detailed surface photometry of a sample of
early-type galaxies in the Hubble Deep Field. Effective radii, surface
brightnesses and total V_606 magnitudes have been obtained, as well as U_300,
B_450, I_814, J, H and K colors, which are compared with the predictions of
chemical-spectrophotometric models of population synthesis. Spectroscopic
redshifts are available for 23 objects. For other 25 photometric redshifts are
given. In the <mu_e>-r_e plane the early-type galaxies of the HDF, once the
appropriate K+E corrections are applied, turn out to follow the `rest frame'
Kormendy relation. This evidence, linked to the dynamical information gathered
by Steidel et al.(1996), indicates that these galaxies, even at z~2-3, lie in
the Fundamental Plane, in a virial equilibrium condition. At the same redshifts
a statistically significant lack of large galaxies [i.e. with Log r_e(kpc) >
0.2] is observed.
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Lepton flavor violating Higgs decays can arise in flavor symmetry models
where the Higgs sector is responsible for both the electroweak and the flavor
symmetry breaking. Here we advocate an $S_4$ three-Higgs-doublet model where
tightly constrained flavor changing neutral currents are suppressed by a
remnant $Z_3$ symmetry. A small breaking of this $Z_3$ symmetry can explain the
$2.4\,\sigma$ excess of Higgs decay final states with a $\mu \tau $ topology
reported recently by CMS if the new neutral scalars are light. The model also
predicts sizable rates for lepton flavor violating Higgs decays in the $e\tau $
and $e \mu$ channels because of the unifying $S_4$ flavor symmetry.
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We identify the scaling limit of the backbone of the high-dimensional
incipient infinite cluster (IIC), both in the finite-range and the long-range
setting. In the finite-range setting, this scaling limit is Brownian motion, in
the long-range setting, it is a stable motion. The proof relies on a novel lace
expansion that keeps track of the number of pivotal bonds.
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The historical microlensing surveys MACHO, EROS, MOA and OGLE (hereafter
summarized in the MEMO acronym) have searched for microlensing toward the LMC
for a total duration of 27 years. We have studied the potential of joining all
databases to search for very heavy objects producing several year duration
events. We show that a combined systematic search for microlensing should
detect of the order of 10 events due to $100M_\odot$ black holes, that were not
detectable by the individual surveys, if these objects have a major
contribution to the Milky-Way halo. Assuming that a common analysis is
feasible, i.e. that the difficulties due to the use of different passbands can
be overcome, we show that the sensitivity of such an analysis should allow one
to quantify the Galactic black hole component.
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We report on a 10 ks simultaneous Chandra/HETG-NuSTAR observation of the
Bursting Pulsar, GRO J1744-28, during its third detected outburst since
discovery and after nearly 18 years of quiescence. The source is detected up to
60 keV with an Eddington persistent flux level. Seven bursts, followed by dips,
are seen with Chandra, three of which are also detected with NuSTAR. Timing
analysis reveals a slight increase in the persistent emission pulsed fraction
with energy (from 10% to 15%) up to 10 keV, above which it remains constant.
The 0.5-70 keV spectra of the persistent and dip emission are the same within
errors, and well described by a blackbody (BB), a power-law with an exponential
rolloff, a 10 keV feature, and a 6.7 keV emission feature, all modified by
neutral absorption. Assuming that the BB emission originates in an accretion
disc, we estimate its inner (magnetospheric) radius to be about 4x10^7 cm,
which translates to a surface dipole field B~9x10^10 G. The Chandra/HETG
spectrum resolves the 6.7 keV feature into (quasi-)neutral and highly ionized
Fe XXV and Fe XXVI emission lines. XSTAR modeling shows these lines to also
emanate from a truncated accretion disk. The burst spectra, with a peak flux
more than an order of magnitude higher than Eddington, are well fit with a
power-law with an exponential rolloff and a 10~keV feature, with similar fit
values compared to the persistent and dip spectra. The burst spectra lack a
thermal component and any Fe features. Anisotropic (beamed) burst emission
would explain both the lack of the BB and any Fe components.
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When there is a certain amount of field inhomogeneity, the biased
ferrimagnetic crystal will exhibit the higher-order magnetostatic (HMS) mode in
addition to the uniform-precession Kittel mode. In cavity magnonics, we show
both experimentally and theoretically the cross-Kerr-type interaction between
the Kittel mode and HMS mode. When the Kittel mode is driven to generate a
certain number of excitations, the HMS mode displays a corresponding frequency
shift and vice versa. The cross-Kerr effect is caused by an exchange
interaction between these two spin-wave modes. Utilizing the cross-Kerr effect,
we realize and integrate a multi-mode cavity magnonic system with only one
yttrium iron garnet (YIG) sphere. Our results will bring new methods to
magnetization dynamics studies and pave a way for novel cavity magnonic devices
by including the magnetostatic mode-mode interaction as an operational degree
of freedom.
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We present a statistical study of optical warps in a sample of 540 galaxies,
about five times larger than previous samples. About 40% of all late-type
galaxies reveal S-shaped warping of their planes in the outer parts. Given the
geometrical parameters and detection sensitivity, this result suggests that at
least half of all galaxy disks might be warped. We demonstrate through
geometrical simulations that some apparent warps could be due to spiral arms in
a highly inclined galaxy. The simulations of non warped galaxies give an amount
of false warps of $\approx$ 15%, while simulations of warped galaxies suggest
that no more than 20% of the warps are missed. We find a strong positive
correlation of observed warps with environment, suggesting that tidal
interaction have a large influence in creating or re-enforcing warped
deformations.
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Decoherence of a central spin coupled to an interacting spin bath via
inhomogeneous Heisenberg coupling is studied by two different approaches,
namely an exact equations of motion (EOMs) method and a Chebyshev expansion
technique (CET). By assuming a wheel topology of the bath spins with uniform
nearest-neighbor $XX$-type intrabath coupling, we examine the central spin
dynamics with the bath prepared in two different types of bath initial
conditions. For fully polarized baths in strong magnetic fields, the
polarization dynamics of the central spin exhibits a collapse-revival behavior
in the intermediate-time regime. Under an antiferromagnetic bath initial
condition, the two methods give excellently consistent central spin decoherence
dynamics for finite-size baths of $N\leq14$ bath spins. The decoherence factor
is found to drop off abruptly on a short time scale and approach a finite
plateau value which depends on the intrabath coupling strength
non-monotonically. In the ultrastrong intrabath coupling regime, the plateau
values show an oscillatory behavior depending on whether $N/2$ is even or odd.
The observed results are interpreted qualitatively within the framework of the
EOM and perturbation analysis. The effects of anisotropic spin-bath coupling
and inhomogeneous intrabath bath couplings are briefly discussed. Possible
experimental realization of the model in a modified quantum corral setup is
suggested.
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We study supersymmetric (SUSY) responses to a photoassociation process in a
mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual
superpartners for a set of proper parameters. We consider the molecule $b$ to
be a bound state of the atom $f$ and another Fermi atom $F$ with different
species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical
lattice. The SUSY nature of the mixture can be signaled in the response to a
photon induced atom-molecule transition: While two new types of fermionic
excitations, an individual $b$ particle-$f$ hole pair continuum and the
Goldstino-like collective mode, are concomitant for a generic $b$-$f$ mixture,
the former is completely suppressed in the SUSY $b$-$f$ mixture and the
zero-momentum mode of the latter approaches to an exact eigenstate. This SUSY
response can be detected by means of the spectroscopy method, e.g., the
photoassociation spectrum which displays the molecular formation rate of $%
Ff\to b$.
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Data imbalance and open-ended distribution are two intrinsic characteristics
of the real visual world. Though encouraging progress has been made in tackling
each challenge separately, few works dedicated to combining them towards
real-world scenarios. While several previous works have focused on classifying
close-set samples and detecting open-set samples during testing, it's still
essential to be able to classify unknown subjects as human beings. In this
paper, we formally define a more realistic task as distribution-agnostic
generalized category discovery (DA-GCD): generating fine-grained predictions
for both close- and open-set classes in a long-tailed open-world setting. To
tackle the challenging problem, we propose a Self-Balanced Co-Advice
contrastive framework (BaCon), which consists of a contrastive-learning branch
and a pseudo-labeling branch, working collaboratively to provide interactive
supervision to resolve the DA-GCD task. In particular, the contrastive-learning
branch provides reliable distribution estimation to regularize the predictions
of the pseudo-labeling branch, which in turn guides contrastive learning
through self-balanced knowledge transfer and a proposed novel contrastive loss.
We compare BaCon with state-of-the-art methods from two closely related fields:
imbalanced semi-supervised learning and generalized category discovery. The
effectiveness of BaCon is demonstrated with superior performance over all
baselines and comprehensive analysis across various datasets. Our code is
publicly available.
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We show, in an elementary way, that the Julia set of one-complex-variable
entire functions is nonempty and perfect.
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In this paper, we focus on the effect of mass-transfer between compact
binaries like neutron-star-neutron-star (NS-NS) systems and
neutron-star-white-dwarf (NS-WD) systems on gravitational waves (GWs). We adopt
the mass quadrupole formula with 2.5 order Post-Newtonian (2.5 PN)
approximation to calculate the GW radiation and the orbital evolution. After a
reasonable discussion of astrophysical processes concerning our scenario, two
kinds of mass-transfer models are applied here. One is the mass overflow of the
atmosphere, where the companion star orbits into the primary's Roche limit and
its atmosphere overflows into the common envelope. The other one is the tidal
disruption of the core, which is viewed as incompressible fluid towards the
primary star, and in the near region branches into an accretion disc (AD) and
direct accretion flow. Viewing this envelope and as a background, the GW of its
spin can be calculated as a rotating non-spherically symmetric star. We
eventually obtained the corrected gravitational waveform (GWF) templates for
different initial states in the inspiral phase.
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This work presents the study of some new anomalous electromagnetic effects in
graphite-like thin carbon films. These are: The fast switching (1nanosecond) of
electrical conductivity The detection of microwave radiation and its
temperature dependence The oscillations of film stack magnetization in the
magnetic field of 1-5 T. The optical radiation under process of spasmodic
switching of conductivity Results of magnetic force microscopy (MFM), DC SQUID
magnetization, reversed Josephson effect (RJE), and resistance measurements in
thin carbon arc (CA) films are presented. The observation of a RJE induced
voltage as well as its rf frequency, input amplitude, and temperature
dependence reveals the existence of Josephson-like Junction arrays. Oscillating
behavior of the DC SQUID magnetization reminiscent of the Fraunhofer-like
behavior of superconducting (SC) critical current in the range of 10000-50000
Oe has been observed. The DC SQUID magnetization measurement indicates a
possible elementary 102 nm SC loop; this is compared to MFM direct observations
of magnetic clusters with a median size of 165 nm. The results obtained
provides a basis for non-cryogenic elecrtonic devices utilizing the Josephson
effect.
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In soccer (or association football), players quickly go from heroes to
zeroes, or vice-versa. Performance is not a static measure but a somewhat
volatile one. Analyzing performance as a time series rather than a stationary
point in time is crucial to making better decisions. This paper introduces and
explores I-VAEP and O-VAEP models to evaluate actions and rate players'
intention and execution. Then, we analyze these ratings over time and propose
use cases to fundament our option of treating player ratings as a continuous
problem. As a result, we present who were the best players and how their
performance evolved, define volatility metrics to measure a player's
consistency, and build a player development curve to assist decision-making.
|
We consider the problem of accurately recovering a matrix B of size M by M ,
which represents a probability distribution over M2 outcomes, given access to
an observed matrix of "counts" generated by taking independent samples from the
distribution B. How can structural properties of the underlying matrix B be
leveraged to yield computationally efficient and information theoretically
optimal reconstruction algorithms? When can accurate reconstruction be
accomplished in the sparse data regime? This basic problem lies at the core of
a number of questions that are currently being considered by different
communities, including building recommendation systems and collaborative
filtering in the sparse data regime, community detection in sparse random
graphs, learning structured models such as topic models or hidden Markov
models, and the efforts from the natural language processing community to
compute "word embeddings".
Our results apply to the setting where B has a low rank structure. For this
setting, we propose an efficient algorithm that accurately recovers the
underlying M by M matrix using Theta(M) samples. This result easily translates
to Theta(M) sample algorithms for learning topic models and learning hidden
Markov Models. These linear sample complexities are optimal, up to constant
factors, in an extremely strong sense: even testing basic properties of the
underlying matrix (such as whether it has rank 1 or 2) requires Omega(M)
samples. We provide an even stronger lower bound where distinguishing whether a
sequence of observations were drawn from the uniform distribution over M
observations versus being generated by an HMM with two hidden states requires
Omega(M) observations. This precludes sublinear-sample hypothesis tests for
basic properties, such as identity or uniformity, as well as sublinear sample
estimators for quantities such as the entropy rate of HMMs.
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This paper presents hydrodynamic-like model of business cycles aggregate
fluctuations of economic and financial variables. We model macroeconomics as
ensemble of economic agents on economic space and agent's risk ratings play
role of their coordinates. Sum of economic variables of agents with coordinate
x define macroeconomic variables as functions of time and coordinates x. We
describe evolution and interactions between macro variables on economic space
by hydrodynamic-like equations. Integral of macro variables over economic space
defines aggregate economic or financial variables as functions of time t only.
Hydrodynamic-like equations define fluctuations of aggregate variables. Motion
of agents from low risk to high risk area and back define the origin for
repeated fluctuations of aggregate variables. Economic or financial variables
on economic space may define statistical moments like mean risk, mean square
risk and higher. Fluctuations of statistical moments describe phases of
financial and economic cycles. As example we present a simple model relations
between Assets and Revenue-on-Assets and derive hydrodynamic-like equations
that describe evolution and interaction between these variables.
Hydrodynamic-like equations permit derive systems of ordinary differential
equations that describe fluctuations of aggregate Assets, Assets mean risks and
Assets mean square risks. Our approach allows describe business cycle aggregate
fluctuations induced by interactions between any number of economic or
financial variables.
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Traveling Salesman Problem (TSP) is a decision-making problem that is
essential for a number of practical applications. Today, this problem is solved
on digital computers exploiting Boolean-type architecture by checking one by
one a number of possible routes. In this work, we describe a special type of
hardware for the TSP solution. It is a magnonic combinatorial device comprising
magnetic and electric parts connected in the active ring circuit. There is a
number of possible propagation routes in the magnetic mesh made of phase
shifters, frequency filters, and attenuators. The phase shifters mimic cities
in TSP while the distance between the cities is encoded in the signal
attenuation. The set of frequency filters makes the waves on different
frequencies propagate through the different routes. The principle of operation
is based on the classical wave superposition. There is a number of waves coming
in all possible routes in parallel accumulating different phase shifts and
amplitude damping. However, only the wave(s) that accumulates the certain phase
shift will be amplified by the electric part. The amplification comes first to
the waves that possess the minimum propagation losses. It makes this type of
device suitable for TSP solution, where waves are similar to the salesmen
traveling in all possible routes at a time. We present the results of numerical
modeling illustrating the TSP solutions for four and six cities. Also, we
present experimental data for the TSP solution with four cities.
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The numerical solution for polarization for two-level atom in polyharmonic
field has been made. The analytical solution for partial case of symmetrical
position of carrier frequency relative to transition frequency is possible. The
results showed that the nonlinear features in polarization spectrum take place
even for small amplitudes of comb-components for small frequency distance
between them. It means that it is necessary to take into account nonlinear
effects for interpretation of spectra in comb spectroscopy.
|
Advanced data augmentation strategies have widely been studied to improve the
generalization ability of deep learning models. Regional dropout is one of the
popular solutions that guides the model to focus on less discriminative parts
by randomly removing image regions, resulting in improved regularization.
However, such information removal is undesirable. On the other hand, recent
strategies suggest to randomly cut and mix patches and their labels among
training images, to enjoy the advantages of regional dropout without having any
pointless pixel in the augmented images. We argue that such random selection
strategies of the patches may not necessarily represent sufficient information
about the corresponding object and thereby mixing the labels according to that
uninformative patch enables the model to learn unexpected feature
representation. Therefore, we propose SaliencyMix that carefully selects a
representative image patch with the help of a saliency map and mixes this
indicative patch with the target image, thus leading the model to learn more
appropriate feature representation. SaliencyMix achieves the best known top-1
error of 21.26% and 20.09% for ResNet-50 and ResNet-101 architectures on
ImageNet classification, respectively, and also improves the model robustness
against adversarial perturbations. Furthermore, models that are trained with
SaliencyMix help to improve the object detection performance. Source code is
available at https://github.com/SaliencyMix/SaliencyMix.
|
The degree anti-Ramsey number $AR_d(H)$ of a graph $H$ is the smallest
integer $k$ for which there exists a graph $G$ with maximum degree at most $k$
such that any proper edge colouring of $G$ yields a rainbow copy of $H$. In
this paper we prove a general upper bound on degree anti-Ramsey numbers,
determine the precise value of the degree anti-Ramsey number of any forest, and
prove an upper bound on the degree anti-Ramsey numbers of cycles of any length
which is best possible up to a multiplicative factor of $2$. Our proofs involve
a variety of tools, including a classical result of Bollob\'as concerning cross
intersecting families and a topological version of Hall's Theorem due to
Aharoni, Berger and Meshulam.
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The heightened sensitivity observed in non-Hermitian systems at exceptional
points (EPs) has garnered significant attention. Typical EP sensor
implementations rely on precise measurements of spectra and importantly, for
real time sensing measurements, the EP condition ceases to hold as the
perturbation increases over time, thereby preventing the use of high
sensitivity at the EP point. In this work, we present an new approach to EP
sensing which goes beyond these two traditional constraints. Firstly, instead
of measuring the spectra, our scheme of EP based sensing is based on the
observation of decay length of the optical mode in finite size gratings, which
is validated via coupled mode theory as well as full wave electrodynamic
simulations. Secondly, for larger perturbation strengths, the EP is spectrally
shifted instead of being destroyed -- this spectral shift of the EP is
calibrated and using this look-up table, we propose continuous real time
detection by varying the excitation laser wavelength. As a proof of principle
of our technique, we present an application to the sensing of coronavirus
particles, which shows unprecedented limit of detection. These findings will
contribute to the expanding field of exceptional point based sensing
technologies for real time applications beyond spectral measurements.
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The recently reported precise experimental determination of the dipole
polarizability of the H_2^+ molecular ion ground state [P.L. Jacobson, R.A.
Komara, W.G. Sturrus, and S.R. Lundeen, Phys. Rev. A 62, 012509 (2000)] reveals
a discrepancy between theory and experiment of about 0.0007a_0^3, which has
been attributed to relativistic and QED effects. In present work we analyze an
influence of the relativistic effects on the scalar dipole polarizability of an
isolated H_2^+ molecular ion. Our conclusion is that it accounts for only 1/5
of the measured discrepancy.
|
Weak Supervision (WS) techniques allow users to efficiently create large
training datasets by programmatically labeling data with heuristic sources of
supervision. While the success of WS relies heavily on the provided labeling
heuristics, the process of how these heuristics are created in practice has
remained under-explored. In this work, we formalize the development process of
labeling heuristics as an interactive procedure, built around the existing
workflow where users draw ideas from a selected set of development data for
designing the heuristic sources. With the formalism, we study two core problems
of how to strategically select the development data to guide users in
efficiently creating informative heuristics, and how to exploit the information
within the development process to contextualize and better learn from the
resultant heuristics. Building upon two novel methodologies that effectively
tackle the respective problems considered, we present Nemo, an end-to-end
interactive system that improves the overall productivity of WS learning
pipeline by an average 20% (and up to 47% in one task) compared to the
prevailing WS approach.
|
The quest towards expansion of the MAX design space has been accelerated with
the recent discovery of several solid solution and ordered phases involving at
least two MAX end members. Going beyond the nominal MAX compounds enables not
only fine tuning of existing properties but also entirely new functionality.
This search, however, has been mostly done through painstaking experiments as
knowledge of the phase stability of the relevant systems is rather scarce. In
this work, we report the first attempt to evaluate the finite-temperature
pseudo-binary phase diagram of the Ti2AlC-Cr2AlC via first-principles-guided
Bayesian CALPHAD framework that accounts for uncertainties not only in ab
initio calculations and thermodynamic models but also in synthesis conditions
in reported experiments. The phase stability analyses are shown to have good
agreement with previous experiments. The work points towards a promising way of
investigating phase stability in other MAX Phase systems providing the
knowledge necessary to elucidate possible synthesis routes for MAX systems with
unprecedented properties.
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Quantum technologies are developing powerful tools to generate and manipulate
coherent superpositions of different energy levels. Envisaging a new generation
of energy-efficient quantum devices, here we explore how coherence can be
manipulated without exchanging energy with the surrounding environment. We
start from the task of converting a coherent superposition of energy
eigenstates into another. We identify the optimal energy-preserving operations,
both in the deterministic and in the probabilistic scenario. We then design a
recursive protocol, wherein a branching sequence of energy-preserving filters
increases the probability of success while reaching maximum fidelity at each
iteration. Building on the recursive protocol, we construct efficient
approximations of the optimal fidelity-probability trade-off, by taking
coherent superpositions of the different branches generated by probabilistic
filtering. The benefits of this construction are illustrated in applications to
quantum metrology, quantum cloning, coherent state amplification, and
ancilla-driven computation. Finally, we extend our results to transitions where
the input state is generally mixed and we apply our findings to the task of
purifying quantum coherence.
|
Let $G$ be a finite group and $N\unlhd G$ with $|G: N|=p$ for some prime $p$.
In this note, to compute $m_{G,N}$ directly, we construct a class poset
$\mathfrak{T}_{C}(G)$ of $G$ for some cyclic subgroup $C$. And we find a
relation between $m_{G,N}$ and the Euler characteristic of the nerve space
$|N(\mathfrak{T}_{C}(G))|$ (see the Theorem 1.3). As an application, we compute
$m_{S_5, A_5}=0$ directly, and get $S_5$ is a $B$-group.
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We study and classify the purely parabolic discrete subgroups of
$PSL(3,\Bbb{C})$. This includes all discrete subgroups of the Heisenberg group
${\rm Heis}(3,\Bbb{C})$. While for $PSL(2,\Bbb{C})$ every purely parabolic
subgroup is Abelian and acts on $\Bbb{P}^1_\Bbb{C}$ with limit set a single
point, the case of $PSL(3,\Bbb{C})$ is far more subtle and intriguing. We show
that there are five families of purely parabolic discrete groups in
$PSL(3,\Bbb{C})$, and some of these actually split into subfamilies. We
classify all these by means of their limit set and the control group. We use
first the Lie-Kolchin Theorem and Borel's fixed point theorem to show that all
purely parabolic discrete groups in $PSL(3,\Bbb{C})$ are virtually
triangularizable. Then we prove that purely parabolic groups in
$PSL(3,\Bbb{C})$ are virtually solvable and polycyclic, hence finitely
presented. We then prove a slight generalization of the Lie-Kolchin Theorem for
these groups: they are either virtually unipotent or else Abelian of rank 2 and
of a very special type. All the virtually unipotent ones turn out to be
conjugate to subgroups of the Heisenberg group ${\rm Heis}(3,\Bbb{C})$. We
classify these using the obstructor dimension introduced by Bestvina, Kapovich
and Kleiner. We find that their Kulkarni limit set is either a projective line,
a cone of lines with base a circle or else the whole $\Bbb{P}^2_\Bbb{C}$. We
determine the relation with the Conze-Guivarc'h limit set of the action on the
dual projective space $\check{\Bbb{P}}^2_\Bbb{C}$ and we show that in all cases
the Kulkarni region of discontinuity is the largest open set where the group
acts properly discontinuously.
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We propose a scheme to perform a fundamental two-qubit gate between two
trapped ions using ideas from atom interferometry. As opposed to the scheme
considered by J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995), it
does not require laser cooling to the motional ground state.
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This work deals with the modeling of nonsmooth vibro-impact motion of a
continuous structure against a rigid distributed obstacle. Galerkin's approach
is used to approximate the solutions of the governing partial differential
equations of the structure, which results in a system of ordinary differential
equations (ODEs). When these ODEs are subjected to unilateral constraints and
velocity jump conditions, one must use an event detection algorithm to
calculate the time of impact accurately. Event detection in the presence of
multiple simultaneous impacts is a computationally demanding task. Ivanov
proposed a nonsmooth transformation for a vibro-impacting
multi-degree-of-freedom system subjected to a single unilateral constraint.
This transformation eliminates the unilateral constraints from the problem and,
therefore, no event detection is required during numerical integration. Ivanov
used his transformation to make analytical calculations for the stability and
bifurcations of vibro-impacting motions; however, he did not explore its
application for simulating distributed collisions in spatially continuous
structures. We adopt Ivanov's transformation to deal with multiple unilateral
constraints in spatially continuous structures. Also, imposing the velocity
jump conditions exactly in the modal coordinates is nontrivial and challenging.
Therefore, in this work we use a modal-physical transformation to convert the
system from modal to physical coordinates on a spatially discretized grid. We
then apply Ivanov's transformation on the physical system to simulate the
vibro-impact motion of the structure. The developed method is demonstrated by
modeling the distributed collision of a nonlinear string against a rigid
distributed surface. For validation, we compare our results with the well-known
penalty approach.
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Learning sensorimotor control policies from high-dimensional images crucially
relies on the quality of the underlying visual representations. Prior works
show that structured latent space such as visual keypoints often outperforms
unstructured representations for robotic control. However, most of these
representations, whether structured or unstructured are learned in a 2D space
even though the control tasks are usually performed in a 3D environment. In
this work, we propose a framework to learn such a 3D geometric structure
directly from images in an end-to-end unsupervised manner. The input images are
embedded into latent 3D keypoints via a differentiable encoder which is trained
to optimize both a multi-view consistency loss and downstream task objective.
These discovered 3D keypoints tend to meaningfully capture robot joints as well
as object movements in a consistent manner across both time and 3D space. The
proposed approach outperforms prior state-of-art methods across a variety of
reinforcement learning benchmarks. Code and videos at
https://buoyancy99.github.io/unsup-3d-keypoints/
|
We propose a new type of bistable device for silicon photonics, using the
self-electro-optic effect within an optical cavity. Since the bistability does
not depend on the intrinsic optical nonlinearity of the material, but is
instead engineered by means of an optoelectronic feedback, it appears at low
optical powers. This bistable device satisfies all the basic criteria required
in an optical switch to build a scalable digital optical computing system.
|
In the intracluster medium (ICM) of galaxy clusters, heat and momentum are
transported almost entirely along (but not across) magnetic field lines. We
perform the first fully self-consistent Braginskii-MHD simulations of galaxy
clusters including both of these effects. Specifically, we perform local and
global simulations of the magnetothermal instability (MTI) and the
heat-flux-driven buoyancy instability (HBI) and assess the effects of viscosity
on their saturation and astrophysical implications. We find that viscosity has
only a modest effect on the saturation of the MTI. As in previous calculations,
we find that the MTI can generate nearly sonic turbulent velocities in the
outer parts of galaxy clusters, although viscosity somewhat suppresses the
magnetic field amplification. At smaller radii in cool-core clusters, viscosity
can decrease the linear growth rates of the HBI. However, it has less of an
effect on the HBI's nonlinear saturation, in part because three-dimensional
interchange motions (magnetic flux tubes slipping past each other) are not
damped by anisotropic viscosity. In global simulations of cool core clusters,
we show that the HBI robustly inhibits radial thermal conduction and thus
precipitates a cooling catastrophe. The effects of viscosity are, however, more
important for higher entropy clusters. We argue that viscosity can contribute
to the global transition of cluster cores from cool-core to non cool-core
states: additional sources of intracluster turbulence, such as can be produced
by AGN feedback or galactic wakes, suppress the HBI, heating the cluster core
by thermal conduction; this makes the ICM more viscous, which slows the growth
of the HBI, allowing further conductive heating of the cluster core and a
transition to a non cool-core state.
|
Two modest-sized symbolic corpora of post-tonal and post-metric keyboard
music have been constructed, one algorithmic, the other improvised. Deep
learning models of each have been trained and largely optimised. Our purpose is
to obtain a model with sufficient generalisation capacity that in response to a
small quantity of separate fresh input seed material, it can generate outputs
that are distinctive, rather than recreative of the learned corpora or the seed
material. This objective has been first assessed statistically, and as judged
by k-sample Anderson-Darling and Cramer tests, has been achieved. Music has
been generated using the approach, and informal judgements place it roughly on
a par with algorithmic and composed music in related forms. Future work will
aim to enhance the model such that it can be evaluated in relation to
expression, meaning and utility in real-time performance.
|
Point Projection Microscopy (PPM) is used to image suspended graphene using
low-energy electrons (100-200eV). Because of the low energies used, the
graphene is neither damaged or contaminated by the electron beam. The
transparency of graphene is measured to be 74%, equivalent to electron
transmission through a sheet as thick as twice the covalent radius of
sp^2-bonded carbon. Also observed is rippling in the structure of the suspended
graphene, with a wavelength of approximately 26 nm. The interference of the
electron beam due to the diffraction off the edge of a graphene knife edge is
observed and used to calculate a virtual source size of 4.7 +/- 0.6 Angstroms
for the electron emitter. It is demonstrated that graphene can be used as both
anode and substrate in PPM in order to avoid distortions due to strong field
gradients around nano-scale objects. Graphene can be used to image objects
suspended on the sheet using PPM, and in the future, electron holography.
|
A \emph{private proximity retrieval} (\emph{PPR}) scheme is a protocol which
allows a user to retrieve the identities of all records in a database that are
within some distance $r$ from the user's record $x$. The user's \emph{privacy}
at each server is given by the fraction of the record $x$ that is kept private.
In this paper, this research is initiated and protocols that offer trade-offs
between privacy and computational complexity and storage are studied. In
particular, we assume that each server stores a copy of the database and study
the required minimum number of servers by our protocol which provides a given
privacy level. Each server gets a query in the protocol and the set of queries
forms a code. We study the family of codes generated by the set of queries and
in particular the minimum number of codewords in such a code which is the
minimum number of servers required for the protocol. These codes are closely
related to a family of codes known as \emph{covering designs}. We introduce
several lower bounds on the sizes of such codes as well as several
constructions. This work focuses on the case when the records are binary
vectors together with the Hamming distance. Other metrics such as the Johnson
metric are also investigated.
|
The simulation of Micro Pattern Gaseous Detectors (MPGDs) signal response is
an important and powerful tool for the design and optimization of such
detectors. However, several attempts to simulate exactly the effective charge
gain have not been completely successful. Namely, the gain stability over time
has not been fully understood. Charging-up of the insulator surfaces have been
pointed as one of the responsible for the difference between experimental and
Monte Carlo results. This work describes two iterative methods to simulate the
charging-up in one MPGD device, the Gas Electron Multiplier (GEM). The first
method uses a constant step for avalanches time evolution, very detailed, but
slower to compute. The second method uses a dynamic step that improves the
computing time. Good agreement between both methods was reached. Despite of
comparison with experimental results shows that charging-up plays an important
role in detectors operation, should not be the only responsible for the
difference between simulated and measured effective gain, but explains the time
evolution in the effective gain.
|
Science opportunities and recommendations concerning optical/infrared
polarimetry for the upcoming decade in the field of extragalactic astrophysics.
Community-based White Paper to Astro2010 in response to the call for such
papers.
|
Deep learning approaches to breast cancer detection in mammograms have
recently shown promising results. However, such models are constrained by the
limited size of publicly available mammography datasets, in large part due to
privacy concerns and the high cost of generating expert annotations. Limited
dataset size is further exacerbated by substantial class imbalance since
"normal" images dramatically outnumber those with findings. Given the rapid
progress of generative models in synthesizing realistic images, and the known
effectiveness of simple data augmentation techniques (e.g. horizontal
flipping), we ask if it is possible to synthetically augment mammogram datasets
using generative adversarial networks (GANs). We train a class-conditional GAN
to perform contextual in-filling, which we then use to synthesize lesions onto
healthy screening mammograms. First, we show that GANs are capable of
generating high-resolution synthetic mammogram patches. Next, we experimentally
evaluate using the augmented dataset to improve breast cancer classification
performance. We observe that a ResNet-50 classifier trained with GAN-augmented
training data produces a higher AUROC compared to the same model trained only
on traditionally augmented data, demonstrating the potential of our approach.
|
We propose a model-free algorithm for learning efficient policies capable of
returning table tennis balls by controlling robot joints at a rate of 100Hz. We
demonstrate that evolutionary search (ES) methods acting on CNN-based policy
architectures for non-visual inputs and convolving across time learn compact
controllers leading to smooth motions. Furthermore, we show that with
appropriately tuned curriculum learning on the task and rewards, policies are
capable of developing multi-modal styles, specifically forehand and backhand
stroke, whilst achieving 80\% return rate on a wide range of ball throws. We
observe that multi-modality does not require any architectural priors, such as
multi-head architectures or hierarchical policies.
|
Related to Shank's notion of simplest cubic fields, the family of
parametrised Diophantine equations,
\[ x^3 - (n-1) x^2 y - (n+2) xy^2 - 1 = \left( x - \lambda_0 y\right)
\left(x-\lambda_1 y\right) \left(x - \lambda_2 y\right) = \pm 1,
\] was studied and solved effectively by Thomas and later solved completely
by Mignotte.
An open conjecture of Levesque and Waldschmidt states that taking these
parametrised Diophantine equations and twisting them not only once but twice,
in the sense that we look at
\[ f_{n,s,t}(x,y) = \left( x - \lambda_0^s \lambda_1^t y \right) \left( x -
\lambda_1^s\lambda_2^t y \right) \left( x - \lambda_2^s\lambda_0^t y \right) =
\pm 1,
\] retains a result similar to what Thomas obtained in the original or
Levesque and Waldschidt in the once-twisted ($t = 0$) case; namely, that
non-trivial solutions can only appear in equations where the parameters are
small. We confirm this conjecture, given that the absolute values of the
exponents $s, t$ are not too large compared to the base parameter $n$.
|
Rotational velocity, lithium abundance, and the mass depth of the outer
convective zone are key parameters in the study of the processes at work in the
stellar interior, in particular when examining the poorly understood processes
operating in the interior of solar-analog stars. We investigate whether the
large dispersion in the observed lithium abundances of solar-analog stars can
be explained by the depth behavior of the outer convective zone masses, within
the framework of the standard convection model based on the local mixing-length
theory. We also aims to analyze the link between rotation and lithium abundance
in solar-analog stars. We computed a new extensive grid of stellar evolutionary
models, applicable to solar-analog stars, for a finely discretized set of mass
and metallicity. From these models, the stellar mass, age, and mass depth of
the outer convective zone were estimated for 117 solar-analog stars, using Teff
and [Fe/H] available in the literature, and the new HIPPARCOS trigonometric
parallax measurements. We determine the age and mass of the outer convective
zone for a bona fide sample of 117 solar-analog stars. No significant on-to-one
correlation is found between the computed convection zone mass and published
lithium abundance, indicating that the large A(Li) dispersion in solar analogs
cannot be explained by the classical framework of envelope convective mixing
coupled with lithium depletion at the bottom of the convection zone. These
results illustrate the need for an extra-mixing process to explain lithium
behavior in solar-analog stars, such as, shear mixing caused by differential
rotation. To derive a more realistic definition of solar-analog stars, as well
as solar-twin, it seems important to consider the inner physical properties of
stars, such as convection, hence rotation and magnetic properties.
|
The corona splash due to the impact of a liquid drop on a smooth dry
substrate is investigated with high speed photography. A striking phenomenon is
observed: splashing can be completely suppressed by decreasing the pressure of
the surrounding gas. The threshold pressure where a splash first occurs is
measured as a function of the impact velocity and found to scale with the
molecular weight of the gas and the viscosity of the liquid. Both experimental
scaling relations support a model in which compressible effects in the gas are
responsible for splashing in liquid solid impacts.
|
To examine the evolution of the early-type galaxy population in the rich
cluster Abell 2390 at z=0.23 we have gained spectroscopic data of 51 elliptical
and lenticular galaxies with MOSCA at the 3.5 m telescope on Calar Alto
Observatory. This investigation spans both a broad range in luminosity
(-19.3>M_B>-22.3) and uses a wide field of view of 10'x10', therefore the
environmental dependence of different formation scenarios can be analysed in
detail as a function of radius from the cluster centre. Here we present results
on the surface brightness modelling of galaxies where morphological and
structural information is available in the F814W filter aboard the Hubble Space
Telescope (HST) and investigate for this subsample the evolution of the
Fundamental Plane.
|
If an artificial intelligence aims to maximise risk-adjusted return, then
under mild conditions it is disproportionately likely to pick an unethical
strategy unless the objective function allows sufficiently for this risk. Even
if the proportion ${\eta}$ of available unethical strategies is small, the
probability ${p_U}$ of picking an unethical strategy can become large; indeed
unless returns are fat-tailed ${p_U}$ tends to unity as the strategy space
becomes large. We define an Unethical Odds Ratio Upsilon (${\Upsilon}$) that
allows us to calculate ${p_U}$ from ${\eta}$, and we derive a simple formula
for the limit of ${\Upsilon}$ as the strategy space becomes large. We give an
algorithm for estimating ${\Upsilon}$ and ${p_U}$ in finite cases and discuss
how to deal with infinite strategy spaces. We show how this principle can be
used to help detect unethical strategies and to estimate ${\eta}$. Finally we
sketch some policy implications of this work.
|
We investigate the survival rate of an initial momentum anisotropy
(${v}_2^{ini}$), not spatial anisotropy, to the final state in a multi-phase
transport (AMPT) model in Au+Au collisions at $\sqrt{s_{NN}}$=200~GeV. It is
found that both the final-state parton and charged hadron $v_2$ show a linear
dependence versus $v_2^{ini}\{\rm PP\}$ with respect to the participant plane
(PP). It is found that the slope of this linear dependence (referred to as the
survive rate) increases with transverse momentum ($p_T$), reaching~$\sim$100\%
at $p_T$$\sim$2.5 GeV/c for both parton and charged hadron. The survival rate
decreases with collision centrality and energy, indicating decreasing survival
rate with increasing interactions. It is further found that a $v_2^{ini}\{\rm
Rnd\}$ with respect to a random direction does not survive in $v_2\{\rm PP\}$
but in the two-particle cumulant $v_2\{2\}$. The dependence of $v_2\{2\}$ on
$v_2^{ini}\{\rm Rnd\}$ is quadratic rather than linear.
|
In the realm of Boltzmann-Gibbs statistical mechanics there are three well
known isomorphic connections with random geometry, namely (i) the
Kasteleyn-Fortuin theorem which connects the $\lambda \to 1$ limit of the
$\lambda$-state Potts ferromagnet with bond percolation, (ii) the isomorphism
which connects the $\lambda \to 0$ limit of the $\lambda$-state Potts
ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism
which connects the $n \to 0$ limit of the $n$-vector ferromagnet with
self-avoiding random walk in linear polymers. We provide here strong numerical
evidence that a similar isomorphism appears to emerge connecting the energy
$q$-exponential distribution $\propto e_q^{-\beta_q \varepsilon}$ (with $q=4/3$
and $\beta_q \omega_0 =10/3$) optimizing, under simple constraints, the
nonadditive entropy $S_q$ with a specific geographic growth random model based
on preferential attachment through exponentially-distributed weighted links,
$\omega_0$ being the characteristic weight.
|
We report the proof that the expression of extended Gibrat's law is unique
and the probability distribution function (pdf) is also uniquely derived from
the law of detailed balance and the extended Gibrat's law. In the proof, two
approximations are employed that the pdf of growth rate is described as
tent-shaped exponential functions and that the value of the origin of growth
rate is constant. These approximations are confirmed in profits data of
Japanese companies 2003 and 2004. The resultant profits pdf fits with the
empirical data with high accuracy. This guarantees the validity of the
approximations.
|
Joint models for longitudinal and time-to-event data constitute an attractive
modeling framework that has received a lot of interest in the recent years.
This paper presents the capabilities of the R package JMbayes for fitting these
models under a Bayesian approach using Markon chain Monte Carlo algorithms.
JMbayes can fit a wide range of joint models, including among others joint
models for continuous and categorical longitudinal responses, and provides
several options for modeling the association structure between the two
outcomes. In addition, this package can be used to derive dynamic predictions
for both outcomes, and offers several tools to validate these predictions in
terms of discrimination and calibration. All these features are illustrated
using a real data example on patients with primary biliary cirrhosis.
|
We present a generalized Landau-Brazovskii free energy for the solidification
of chiral molecules on a spherical surface in the context of the assembly of
viral shells. We encounter two types of icosahedral solidification transitions.
The first type is a conventional first-order phase transition from the uniform
to the icosahedral state. It can be described by a single icosahedral spherical
harmonic of even $l$. The chiral pseudo-scalar term in the free energy creates
secondary terms with chiral character but it does not affect the thermodynamics
of the transition. The second type, associated with icosahedral spherical
harmonics with odd $l$, is anomalous. Pure odd $l$ icosahedral states are
unstable but stability is recovered if admixture with the neighboring $l+1$
icosahedral spherical harmonic is included, generated by the non-linear terms.
This is in conflict with the principle of Landau theory that symmetry-breaking
transitions are characterized by only a \textit{single} irreducible
representation of the symmetry group of the uniform phase and we argue that
this principle should be removed from Landau theory. The chiral term now
directly affects the transition because it lifts the degeneracy between two
isomeric mixed-$l$ icosahedral states. A direct transition is possible only
over a limited range of parameters. Outside this range, non-icosahedral states
intervene. For the important case of capsid assembly dominated by $l=15$, the
intervening states are found to be based on octahedral symmetry.
|
We investigate the use of high-dimensional quantum key distribution (HD-QKD)
in wireless access to hybrid quantum classical networks. We study the
distribution of d-dimensional time-phase encoded states between an indoor
wireless user and the central office on the other end of the access network. We
evaluate the performance in the case of transmitting quantum and classical
signals over the same channel by accounting for the impact of background noise
induced by the Raman-scattered light on the QKD receiver. We also take into
account the loss and background noise that occur in indoor environments as well
as finite key effects in our analysis. We show that an HD-QKD system with d = 4
can outperform its qubit-based counterpart.
|
We study the interior regularity of solutions to the Dirichlet problem $Lu=g$
in $\Omega$, $u=0$ in $\R^n\setminus\Omega$, for anisotropic operators of
fractional type $$ Lu(x)= \int_{0}^{+\infty}\,d\rho
\int_{S^{n-1}}\,da(\omega)\,
\frac{ 2u(x)-u(x+\rho\omega)-u(x-\rho\omega)}{\rho^{1+2s}}.$$ Here, $a$ is
any measure on~$S^{n-1}$ (a prototype example for~$L$ is given by the sum of
one-dimensional fractional Laplacians in fixed, given directions).
When $a\in C^\infty(S^{n-1})$ and $g$ is $C^\infty(\Omega)$, solutions are
known to be $C^\infty$ inside~$\Omega$ (but not up to the boundary). However,
when $a$ is a general measure, or even when $a$ is $L^\infty(S^{n-1})$,
solutions are only known to be $C^{3s}$ inside $\Omega$.
We prove here that, for general measures $a$, solutions are
$C^{1+3s-\epsilon}$ inside $\Omega$ for all $\epsilon>0$ whenever $\Omega$ is
convex. When $a\in L^{\infty}(S^{n-1})$, we show that the same holds in all
$C^{1,1}$ domains. In particular, solutions always possess a classical first
derivative.
The assumptions on the domain are sharp, since if the domain is not convex
and the spectral measure is singular, we construct an explicit counterexample
for which $u$ is \emph{not} $C^{3s+\epsilon}$ for any $\epsilon>0$ -- even if
$g$ and $\Omega$ are $C^\infty$.
|
The extremely precise extraction of the proton radius by Pohl et al. from the
measured energy difference between the 2P and 2S states of muonic hydrogen
disagrees significantly with that extracted from electronic hydrogen or elastic
electron-proton scattering. This is the proton radius puzzle. The origins of
the puzzle and the reasons for believing it to be very significant are
explained. Various possible solutions of the puzzle are identified, and future
work needed to resolve the puzzle is discussed.
|
We analyze the effective action describing the linearised gravitational
self-action for a classical superconducting string in a curved spacetime. It is
shown that the divergent part of the effective action is equal to zero for the
both Nambu-Goto and chiral superconducting string.
|
The use of propagandistic techniques in online contents has increased in
recent years aiming to manipulate online audiences. Efforts to automatically
detect and debunk such content have been made addressing various modeling
scenarios. These include determining whether the content (text, image, or
multimodal) (i) is propagandistic, (ii) employs one or more propagandistic
techniques, and (iii) includes techniques with identifiable spans. Significant
research efforts have been devoted to the first two scenarios compared to the
latter. Therefore, in this study, we focus on the task of detecting
propagandistic textual spans. Specifically, we investigate whether large
language models (LLMs), such as GPT-4, can effectively perform the task.
Moreover, we study the potential of employing the model to collect more
cost-effective annotations. Our experiments use a large-scale in-house dataset
consisting of annotations from human annotators with varying expertise levels.
The results suggest that providing more information to the model as prompts
improves its performance compared to human annotations. Moreover, our work is
the first to show the potential of utilizing LLMs to develop annotated datasets
for this specific task, prompting it with annotations from human annotators
with limited expertise. We plan to make the collected span-level labels from
multiple annotators, including GPT-4, available for the community.
|
The common terahertz time-domain spectroscopy (THz-TDS) based on
photoconductive antenna (PCA) needs two separate PCA chips. One PCA works as an
emitter, and the other works as a receiver. For a reflection-type measurement,
the technique called 'attenuated total reflection' usually is needed to enhance
the reflection sensitivity. These make the system bulk and complicated for the
reflection-type measurement. In this paper, we propose a novel THz-TDS
endoscope that is specifically designed for reflection-type measurement. This
THz-TDS endoscope is benefited from an integrated photoconductive antenna (we
call it iPCA), which integrates the emitter and receiver on a single antenna
chip. Therefore, the dimension of the endoscope can be shrunk as much as
possible for practical usage. We present the design and working principle of
this THz-TDS endoscope in details. It may open a promising way for the THz-TDS
application in biomedical fields.
|
This work develops non-asymptotic theory for estimation of the long-run
variance matrix and its inverse, the so-called precision matrix, for
high-dimensional time series under general assumptions on the dependence
structure including long-range dependence. The estimation involves shrinkage
techniques which are thresholding and penalizing versions of the classical
multivariate local Whittle estimator. The results ensure consistent estimation
in a double asymptotic regime where the number of component time series is
allowed to grow with the sample size as long as the true model parameters are
sparse. The key technical result is a concentration inequality of the local
Whittle estimator for the long-run variance matrix around the true model
parameters. In particular, it handles simultaneously the estimation of the
memory parameters which enter the underlying model. Novel algorithms for the
considered procedures are proposed, and a simulation study and a data
application are also provided.
|
This survey of alternating permutations and Euler numbers includes
refinements of Euler numbers, other occurrences of Euler numbers, longest
alternating subsequences, umbral enumeration of classes of alternating
permutations, and the cd-index of the symmetric group.
|
Direct photon production is an important process at hadron colliders, being
relevant both for precision measurement of the gluon density, and as background
to Higgs and other new physics searches. Here we explore the implications of
recently derived results for high energy resummation of direct photon
production for the interpretation of measurements at the Tevatron and the LHC.
The effects of resummation are compared to various sources of theoretical
uncertainties like PDFs and scale variations. We show how the high--energy
resummation procedure stabilizes the logarithmic enhancement of the cross
section at high--energy which is present at any fixed order in the perturbative
expansion starting at NNLO. The effects of high--energy resummation are found
to be negligible at Tevatron, while they enhance the cross section by a few
percent for $p_T \lsim 10$ GeV at the LHC. Our results imply that the
discrepancy at small $p_T$ between fixed order NLO and Tevatron data cannot be
explained by unresummed high--energy contributions.
|
The folding rates of two-state proteins have been found to correlate with
simple measures of native-state topology. The most prominent among these
measures is the relative contact order (CO), which is the average CO or
'localness' of all contacts in the native protein structure, divided by the
chain length. Here, we test whether such measures can be generalized to capture
the effect of chain crosslinks on the folding rate. Crosslinks change the chain
connectivity and therefore also the localness of some of the the native
contacts. These changes in localness can be taken into account by the
graph-theoretical concept of effective contact order (ECO). The relative ECO,
however, the natural extension of the relative CO for proteins with crosslinks,
overestimates the changes in the folding rates caused by crosslinks. We suggest
here a novel measure of native-state topology, the relative logCO, and its
natural extension, the relative logECO. The relative logCO is the average value
for the logarithm of the CO of all contacts, divided by the logarithm of the
chain length. The relative log(E)CO reproduces the folding rates of a set of 26
two-state proteins without crosslinks with essentially the same high
correlation coefficient as the relative CO. In addition, it also captures the
folding rates of 8 two-state proteins with crosslinks.
|
Atutov and Shalagin (1988) proposed light-induced drift (LID) as a physically
well understandable mechanism to explain the formation of isotopic anomalies
observed in CP stars. We generalized the theory of LID and applied it to
diffusion of heavy elements and their isotopes in quiescent atmospheres of CP
stars. Diffusional segregation of isotopes of chemical elements is described by
the equations of continuity and diffusion velocity. Computations of the
evolutionary sequences for abundances of mercury isotopes in several model
atmospheres have been made using the Fortran 90 program SMART, composed by the
authors. Results confirm predominant role of LID in separation of isotopes.
|
We are concerned with the convergence of a numerical scheme for the
initial-boundary value problem associated to the Korteweg-de Vries- Kawahara
equation (in short Kawahara equation), which is a transport equation perturbed
by dispersive terms of 3rd and 5th order. This equation appears in several uid
dynamics problems. It describes the evolution of small but finite amplitude
long waves in various problems in uid dynamics. We prove here the convergence
of both semi-discrete as well as fully-discrete finite difference schemes for
the Kawahara equation. Finally, the convergence is illustratred by several
examples.
|
We describe a maximum-likelihood technique for the removal of contaminating
radio sources from interferometric observations of the Sunyaev-Zel'dovich (SZ)
effect. This technique, based on a simultaneous fit for the radio sources and
extended SZ emission, is also compared to techniques previously applied to Ryle
Telescope observations and is found to be robust. The technique is then applied
to new observations of the cluster Abell 611, and a decrement of -540 +/- 125
microJy/beam is found. This is combined with a ROSAT HRI image and a published
ASCA temperature to give an Hubble constant estimate of 52+24-16 km/s/Mpc.
|
In this work, we study a class of deception planning problems in which an
agent aims to alter a security monitoring system's sensor readings so as to
disguise its adversarial itinerary as an allowed itinerary in the environment.
The adversarial itinerary set and allowed itinerary set are captured by regular
languages. To deviate without being detected, we investigate whether there
exists a strategy for the agent to alter the sensor readings, with a minimal
cost, such that for any of those paths it takes, the system thinks the agent
took a path within the allowed itinerary. Our formulation assumes an offline
sensor alteration where the agent determines the sensor alteration strategy and
implement it, and then carry out any path in its deviation itinerary. We prove
that the problem of solving the optimal sensor alteration is NP-hard, by a
reduction from the directed multi-cut problem. Further, we present an exact
algorithm based on integer linear programming and demonstrate the correctness
and the efficacy of the algorithm in case studies.
|
This paper discusses the hardness of finding minimal good-for-games (GFG)
Buchi, Co-Buchi, and parity automata with state based acceptance. The problem
appears to sit between finding small deterministic and finding small
nondeterministic automata, where minimality is NP-complete and PSPACE-complete,
respectively. However, recent work of Radi and Kupferman has shown that
minimising Co-Buchi automata with transition based acceptance is tractable,
which suggests that the complexity of minimising GFG automata might be cheaper
than minimising deterministic automata.
We show for the standard state based acceptance that the minimality of a GFG
automaton is NP-complete for Buchi, Co-Buchi, and parity GFG automata. The
proofs are a surprisingly straight forward generalisation of the proofs from
deterministic Buchi automata: they use a similar reductions, and the same hard
class of languages.
|
Speech-driven 3D face animation aims to generate realistic facial expressions
that match the speech content and emotion. However, existing methods often
neglect emotional facial expressions or fail to disentangle them from speech
content. To address this issue, this paper proposes an end-to-end neural
network to disentangle different emotions in speech so as to generate rich 3D
facial expressions. Specifically, we introduce the emotion disentangling
encoder (EDE) to disentangle the emotion and content in the speech by
cross-reconstructed speech signals with different emotion labels. Then an
emotion-guided feature fusion decoder is employed to generate a 3D talking face
with enhanced emotion. The decoder is driven by the disentangled identity,
emotional, and content embeddings so as to generate controllable personal and
emotional styles. Finally, considering the scarcity of the 3D emotional talking
face data, we resort to the supervision of facial blendshapes, which enables
the reconstruction of plausible 3D faces from 2D emotional data, and contribute
a large-scale 3D emotional talking face dataset (3D-ETF) to train the network.
Our experiments and user studies demonstrate that our approach outperforms
state-of-the-art methods and exhibits more diverse facial movements. We
recommend watching the supplementary video:
https://ziqiaopeng.github.io/emotalk
|
Bregman divergences play a central role in the design and analysis of a range
of machine learning algorithms. This paper explores the use of Bregman
divergences to establish reductions between such algorithms and their analyses.
We present a new scaled isodistortion theorem involving Bregman divergences
(scaled Bregman theorem for short) which shows that certain "Bregman
distortions'" (employing a potentially non-convex generator) may be exactly
re-written as a scaled Bregman divergence computed over transformed data.
Admissible distortions include geodesic distances on curved manifolds and
projections or gauge-normalisation, while admissible data include scalars,
vectors and matrices.
Our theorem allows one to leverage to the wealth and convenience of Bregman
divergences when analysing algorithms relying on the aforementioned Bregman
distortions. We illustrate this with three novel applications of our theorem: a
reduction from multi-class density ratio to class-probability estimation, a new
adaptive projection free yet norm-enforcing dual norm mirror descent algorithm,
and a reduction from clustering on flat manifolds to clustering on curved
manifolds. Experiments on each of these domains validate the analyses and
suggest that the scaled Bregman theorem might be a worthy addition to the
popular handful of Bregman divergence properties that have been pervasive in
machine learning.
|
We carry out a delay stability analysis (i.e., determine conditions under
which expected steady-state delays at a queue are finite) for a simple 3-queue
system operated under the Max-Weight scheduling policy, for the case where one
of the queues is fed by heavy-tailed traffic (i.e, when the number of arrivals
at each time slot has infinite second moment). This particular system
exemplifies an intricate phenomenon whereby heavy-tailed traffic at one queue
may or may not result in the delay instability of another queue, depending on
the arrival rates.
While the ordinary stability region (in the sense of convergence to a
steady-state distribution) is straightforward to determine, the determination
of the delay stability region is more involved: (i) we use "fluid-type" sample
path arguments, combined with renewal theory, to prove delay instability
outside a certain region; (ii) we use a piecewise linear Lyapunov function to
prove delay stability in the interior of that same region; (iii) as an
intermediate step in establishing delay stability, we show that the expected
workload of a stable M/GI/1 queue scales with time as
$\mathcal{O}(t^{1/(1+\gamma)})$, assuming that service times have a finite
$1+\gamma$ moment, where $\gamma \in (0,1)$.
|
New physics close to the electroweak scale is well motivated by a number of
theoretical arguments. However, colliders, most notably the Large Hadron
Collider (LHC), have failed to deliver evidence for physics beyond the Standard
Model. One possibility for how new electroweak-scale particles could have
evaded detection so far is if they carry only electroweak charge, i.e. are
color neutral. Future $e^+e^-$ colliders are prime tools to study such new
physics. Here, we investigate the sensitivity of $e^+e^-$ colliders to scalar
partners of the charged leptons, known as sleptons in supersymmetric extensions
of the Standard Model. In order to allow such scalar lepton partners to decay,
we consider models with an additional neutral fermion, which in supersymmetric
models corresponds to a neutralino. We demonstrate that future $e^+e^-$
colliders would be able to probe most of the kinematically accessible parameter
space, i.e. where the mass of the scalar lepton partner is less than half of
the collider's center-of-mass energy, with only a few days of data. Besides
constraining more general models, this would allow to probe some well motivated
dark matter scenarios in the Minimal Supersymmetric Standard Model, in
particular the incredible bulk and stau co-annihilation scenarios.
|
A new matrix representation for low-energy limit of heterotic string theory
reduced to three dimensions is considered. The pair of matrix Ernst Potentials
uniquely connected with the coset matrix is derived. The action of the symmetry
group on the Ernst potentials is established.
|
We study some consequences of dimensionally reducing systems with massless
fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider
fermions in the presence of an external Abelian gauge field. In the reduced
theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein,
magnetic flux strings are mapped into domain wall defects. Fermionic zero
modes, localized around the flux strings of the 3+1 dimensional theory, become
also zero modes in the reduced theory, via the Callan and Harvey mechanism, and
are concentrated around the domain wall defects. We also study a dynamical
model: massless $QED_4$, with fermions confined to a plane, deriving the
effective action that describes the `planar' system.
|
We relate the cardinality of the $p$-primary part of the Bloch-Kato Selmer
group over $\mathbb{Q}$ attached to a modular form at a non-ordinary prime $p$
to the constant term of the characteristic power series of the signed Selmer
groups over the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$. This
generalizes a result of Vigni and Longo in the ordinary case. In the case of
elliptic curves, such results follow from earlier works by Greenberg, Kim, the
second author, and Ahmed-Lim, covering both the ordinary and most of the
supersingular case.
|
Quantum mechanics can speed up a range of search applications over unsorted
data. For example imagine a phone directory containing N names arranged in
completely random order. To find someone's phone number with a probability of
50%, any classical algorithm (whether deterministic or probabilistic) will need
to access the database a minimum of O(N) times. Quantum mechanical systems can
be in a superposition of states and simultaneously examine multiple names. By
properly adjusting the phases of various operations, successful computations
reinforce each other while others interfere randomly. As a result, the desired
phone number can be obtained in only O(sqrt(N)) accesses to the database.
|
In this paper, we present a global complexity analysis of the classical BFGS
method with inexact line search, as applied to minimizing a strongly convex
function with Lipschitz continuous gradient and Hessian. We consider a variety
of standard line search strategies including the backtracking line search based
on the Armijo condition, Armijo-Goldstein and Wolfe-Powell line searches. Our
analysis suggests that the convergence of the algorithm proceeds in several
different stages before the fast superlinear convergence actually begins.
Furthermore, once the initial point is far away from the minimizer, the
starting moment of superlinear convergence may be quite large. We show,
however, that this drawback can be easily rectified by using a simple
restarting procedure.
|
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