Zdaj smo prišli svojo prišličnje spike, tako še je hodnje v sku, ne za vse, ali za prišličnje. Zdaj je Mateo Gatti, z EKOL Politeknika, v Franske. Kaj je prišličnje, nekaj nekaj detaj, nekaj nekaj potrebečnji teori, z vsej vsej, tako pa, Mateo. Čakaj, Davide. Dobro vse na RCTP. Det del je, da vse preddaveš, ali ja hamam tudi, kako prav tebe vse zej, a ki je tudi neko Lega, ti moj rebunje čudov, n prove svoje. Tako, nekaj možem tudi prijo, ki bomo neko, da bo ni bo, Or complain, you can use my e-mail here. So, the idea of Lodčilles Letcher was to make the bridge between what Pedro has just told you about made by Well agu N comptrionchuckles theory and the equations of rins mieg n shares theory and the applications. Any about spectroscopy, that you will start to static out from next lecture. Spotrofljenje pa z專adnjih vseh pavnoje obojevače je zaradi pobitno vsakro flaske, da se se udrije sprednje diskalitih. The last argument of these lectures is about what comes next, after you introduced all these formulas, what comes next. The answer, considering the point of view of the formula, Zato vzpoče, da je prejzupočno prejspoljeva, je to tudi tudi o petroskopu, še to je najbičaj zelo, vzpoče, da je začela, je to predikšnja, sej analizi, je to zvukovana spektra. Završenje spektra je zelo zelo zelo zelo zelo zelo zelo zelo zelo zelo zelo zelo zelo zelo. Tama tudi možno je nekaj materijali for solar energies, so new solar cells, new materials for memory devices, new materials for new colors for candies. So the applications of spectroscopies can be very, very different and these functions are made for calculation of electronic excitation spectra that are at the basis of spectroscopy. The first question we should ask whenever we start to use analytical formulas is why we do what we do. So this is the first question that I will try to address in the following. Why should we use these functions instead of, for instance, the may-body we function or the density. So what we are interested in when we want to do spectroscopy or in general when we solve quantum mechanics problem are observables. And we have learned from basic quantum mechanics that if you are at temperature zero and for a given number of particle n, is that observables are expectation values of some particular operators that are related to the specific observables. And expectation values are calculated as integrals with respect to the may-body we function of the given operator. If the system has n electrons, the final answer is maybe just a number, and at the end what we have to do is a very large integral with respect to many of the degrees of freedom in our system. So this is a very complicated object, but in principle, if you know the may-body we function, what is here is just a recipe that is telling you that if you give me the may-body we function, I can tell you which is the observable that you are interested in. You have just to perform this very complicated integral, but this is a functional that is in principle known. The only problem is that this is very complicated and you have to make a very large effort to calculate and to store this may-body we function, which in most cases of interest is impossible to do. And after all, after you have made this very huge effort, you are just interested in a number. So this is not a practical way to go. The alternative is density functional theory, and in density functional theory we have learned that instead of calculating observables using functionals for the may-body we function. We replace these functionals with other functionals. These functionals could be in principle functionals of the external potential that defines our system. And in density functional theory the idea is to calculate observables as functionals that in principle are different from the original functionals. And these functionals are functionals of the ground state density. And Oember and Kohn has told us that in principle we can calculate all the observables, not only the observables that can be explicitly calculated as observables in terms of these intervals of the density. So single particle operators, but we can calculate in principle any observable as expectation value in the ground state wave function in principle all the quantities that we are interested in. And this is in terms of functional of the density as I've just said. So instead of using the may-body we function as our descriptor of the system which is what very often we do in quantum chemistry when we do simulation for small molecules where the number of degrees of freedom is limited and this is called configuration interaction theory or in case of quantum Monte Carlo calculations where we make a stochastic estimation of this may function instead of using this as descriptor in density functional we use the density which is a more compact object as our descriptor. And density functional theory is telling us that we can calculate everything in principle as a function of the density. But the first question that we have to answer is where do we get the input that we have to insert in this functional which is the density. And the answer given by Konešan is the genius idea to build an auxiliary system which is the Konešan system that is just meant to give us the density that is again the input that we need to put in our functional to obtain the observable. It's an auxiliary system because as we have already discussed previously the Konešan system is just meant to give us the density but for instance the eigenvalues of these Konešan questions are not supposed to give us information about excitation energies. The only information that the Konešan system is supposed to give us is the density. And we know that we have to solve this system of equations that are the Konešan equations where we have the Hamiltonian that is an effective Hamiltonian where in addition to the external potential that describes our system we have the RT potential that is related to electrostatic interactions so classical electrostatic description of the system plus a correction that is the string correlation potential of Konešan that is a local potential, that is a function of the density that is formally defined as a functional derivative of the string correlation energy with respect to the density and this is the quantity that we have to approximate. So this is what Konešan gives us, it's the density but the second problem of DFT is that for most of the cases we do not know the functionals. So even if we have the density we are not able to express our quantity of interest as a function of the density. And the typical example is something that has to do with spectroscopy and excitation spectra. So this is what we are going to discuss in a moment. To summarize the exact Konešan system is designed as the good density. It's often used to calculate observables directly in the sense that we use the functionals that were in principle supposed to be used in terms of the many body wave function but we replace the many body wave function with the Konešan many body wave function and this is an approximation clearly and the problem is that for most of the cases we don't know the explicit function of the density. So the quantities of interest for us in principle are function of the density but we don't know them and if we use instead the original function in terms of the many body wave function but with the Konešan wave function then this is an approximation and it's not supposed to give us the good answer. This is because the Konešan system is an auxiliary system that is meant just to give us the density. And the first example where we discuss this is photomission spectroscopy. In photomission spectroscopy there is some light that is used to kick out one electron from the system. So typically you measure the kinetic energy of the photomitted electron and you can also measure if you do under-result photomission the angle of the emitted photoelectron. And if you combine this information related to the kinetic energy of the photoelectron in its direction, so its angle that you can associate to the k point inside the material what you can obtain is a collection of dots that you see on the right panel and for instance you can fix a given dot that corresponds to a pair of energy binding energy and k point that is associated to the kinetic energy and the angle of the photomitted electron and then you can scan the angles and the energies and what you obtain are these dots here that correspond to the non-structure of the material. This is what photomission spectroscopy is and if you combine direct photomission that measure the occupied states with inverse photomission that measure the unoccupied states and you can retrieve the structure of the material. So this is the experimental definition of a structure. Now in the independent particle picture what you would obtain in the description of this experiment is just the fact that you think that you are removing one electron from the material and this electron was occupying the single particle levels at different k points if you are in a solid and so the description is just a collection of very sharp peaks mathematically these are delta functions at the energies that were occupied by the electron before being emitted from the material. So this again is for direct photomission where you remove one electron from the system you go from n to n minus one and this would be for the unoccupied levels for inverse photomission where you put one electron to the system. So this is the independent particle picture just a collection of delta peaks at the energies of the single particle levels. And this is also what function DFT gives us and in particular this is a comparison between the LDA function, the structure on the left and the experimental results in the center right panel and you see that this is the band structure of bulk germanium and in particular you see here that in LDA you obtain a band structure that has a problem in particular around the band gap because LDA is giving a metallic one structure and this is the famous or the infamous Konsham band gap problem it's the fact that typically in Konsham LDA you get an underestimation of the band gap and this has two reasons first is that we are using LDA that is an approximation of the exact Konsham system and second and most importantly it's the fact that the Konsham system is an auxiliary system that again is meant to give us just the density but it's not meant to give us the band structure and also the band gap and this is also the case in if you have the exact exchange of correlation potential for instance you can also think that you want to calculate the band structure of the homogenous electron gas so in this case the LDA would be exact of course the homogenous electron gas is a metal so there is no band gap but you can still compare the band structure with more advanced theories like Green's Function Theory and you would see that even the exact Konsham band structure because LDA is exact so it's known is not equal to the exact band structure you don't get the exact band structure of the material in the case of the gas this can be proved directly because you have the exact approximation and you can have very good approximation for this potential in materials and you would obtain also in that case that the band structure is not equal and the reason is that again I want to stress the fact that we don't get the exact band structure because we don't know how to express the band structure in terms of the functional of the ground state density so what we have to do is we have to change the descriptor again instead of using the made by me function and density or the density we have to use a different descriptor and in our case the proper descriptor would be green's functions green's functions have been already introduced by Pedro these are describing the propagation of additional particles in the system and in particular I will first of all discuss about the one body green's function and it's linked to spectroscopy so this has been already introduced and the one body green's function is a function of two points in space and time and one frequency and it's a function that can be expressed in this way with this fraction representation that is called the Lehmann representation and in particular for what is interesting for us is the fact that this function has a function of frequency as poles that correspond to the zeros of the denominator and poles correspond to the addition that we measure in spectroscopy and these are those that describe the structure of the material so we use and we define the green's function indeed because the poles of this function will be the exact quantities that we are interested in contrary to and in particular a quantity that is of interest for us is the imaginary part of the green's function and this imaginary part of the green's function is expressed in the reciprocal space so you have just taken a free transform of this quantity and you go to reciprocal space, so in case space and then you can see that you can express this imaginary part of the green's function and this expression here where you have peaks at the additional removal energies that were the poles of the green's function that are weighted by these amplitudes that are at the numerator of the green's function that are called the Lehmann amplitude and this quantity is of interest for us because it's called the spectral function and it's the quantity that we can compare with photoemission and in this way you see that we obtain quantities that we can compare with photoemission as simple functionals of the green's function in particular in this case these are very simple linear functional of the green's function we have just to take the imaginary part of the green's function, the absolute value and obtain the spectrum now you have seen that the Gaussian system is auxiliary system where you have an effective potential that is meant to give us the density in the framework of green's function and one body green's function in particular we have to generalize this idea of auxiliary system and instead of having this local and real potential that is the change correlation potential we introduce a more complicated potential effective potential that takes into account all these change correlation effects beyond the art description of the system as in the case of this change correlation potential of Gaussian but it has more features because this new effective potential is now no local space so it acts as an internal operator with respect to the wave functions and moreover it's frequency dependent because the green's function is describing a propagation in time so it is no local in time and if you take the Fourier transform it gives us a frequency dependence so the self energy is not only an operator it is no local space but it is also no local in time and it means that all the quantities become frequency dependent including the wave functions the effective wave functions the quasi particle wave functions and the energies so this is just a new auxiliary system that is meant to reproduce the single body in green's function so a more complicated object and this means that this more complicated object requires a more complicated effective potential that is the self energy you have seen that green's function can be calculated as a solution of the Dyson equation and this Dyson equation is just equivalent of this effective equation that I've just written here and the solution of this Dyson equation can be formally obtained as inversion of these operators where you have the self energy and the single particle non-interacting green's function and easily expressed in terms of the single particle energies the non-interacting energies so this is a quantity that we are readily able to obtain to calculate and the self energy is introducing all the effects related to exchange and correlation and from the imaginary part of the green's function we can calculate the spectral function this is the expression that is explicitly written in terms of the real and imaginary part of the self energy the self energy is a complex object contrary to the consham potential that is real the self energy has a real and imaginary part so both contribute to the imaginary part of the green's function and to the spectral function and the description of the spectral function in terms of this more complicated object is much richer than in the case of the non-interacting picture so in addition to these single particle levels you have other features that are described by the contribution coming from exchange and correlation that is encoded in the self energy and in particular the real part of the self energy is renormalizing the energy of the peaks so it's moving the position of the peaks and the imaginary part of the self energy is inducing a broadening of these peaks so each of them is moved the imaginary part of the self energy is also adding new feature in the spectral function so all in all instead of having a single peak that is very sharp you have a peak that is more broad which is still a prominent peak very often and this prominent peak that has a different energy and it is a different broadening it's called quasi particle peak it is a dominant contribution in the spectral function this is what still defines the bond structure in an interacting picture but in addition to this you also have other features that are called side bands or satellites that are a pure effect of exchange and correlation this has something to do with the fact that when you remove one electron in the material and this positive charge is perturbing the system and it can create additional excitation in the material and you see these additional excitation as satellites for instance this additional positive charge can induce the collective excitation of the charge that are called plasmons in the material and you see these additional excitation as in the spectral function and this would be plasmon satellites so these satellites are due to the coupling of the hole of the positive charge in the material and additional neutral excitation that has been created by the fact that this positive charge is the perturbation in the electronic system again this is a pure effect of correlation and it cannot be captured in a single particle picture so the description in terms of the Green's function requires a more complicated object because it has to describe a richer physics which is related to a normalization related to broadening of the peaks and to the creation of these additional satellites now all this is in principle exact for the one body Green's function and in the case of the one body Green's function in this more complicated auxiliary system we have the same problem as in the conscious system we need to make approximations for this self energy, this effective potential the advantage of the Green's function framework is that we can define effective particles and we can have an intuition of the physics that we want to describe instead DFT is a made body theory of collective variables which is collective variable which is the density in DFT we have Cauchon electrons but no one has ever met a Cauchon electron so it's not something that we can measure we cannot use our intuition in physics this is something that we can exploit in terms of Green's functions there are different ways to approximate this self energy one way of approximating the self energy is very similar to LDA and it's developed in the framework of dynamical material theory where we express self energy as a functional of the local Green's function where local means that we just take a particular part of the Green's function in a particular space in the orbital space and we are interested just in this reduced part of the Green's function and we express make an approximation of the self energy as a functional of just this reduced Green's function but this is not what we typically do in many body perturbation theory and in what you will discuss in the rest of the school instead what we do in many body perturbation theory we just follow the propagation of this additional particle that is what the Green's function describes and you have already seen that you can follow these different stories that have to do with the effects that are related to the propagation of this additional particle design drawing final diagrams so whenever you have an error this corresponds to the propagation of one additional atom in the system and then you can think about what this is causing on the rest of the system and this can be expressed in terms of interactions so you have the coulomb interaction that is represented by the dash line and you can think that this additional particle is capturing with the density inside the material and this density in the language of final diagrams is represented by a circle like this so this corresponds to the artery potential the artery term in the Hamiltonian it's the scattering of the additional particle with the density you can have exchange diagram like this one that corresponds to the fork exchange in artery fork and you have more interesting diagrams where you have more interaction lines and in particular will be interested in this kind of diagram where the additional particle in the system is polarizing the medium and this polarization is represented here by this ring diagram also called the purple diagram where you have the propagation of one other particle and the propagation of a particle with the reverse sign because the error in this way has a reverse sign and this is corresponding to the propagation you can understand this diagram as the fact that this additional particle in the system is creating an additional electron in pair in the system and this is associated with the polarization of the material that is related to the fact is the consequence of the Coulomb interaction and it's the consequence of the fact that the system the medium is seeing the presence of an additional particle in the material and these polarization diagrams are those that are creating a screen a reaction of the material for the presence of this additional particle and all this is something that we have to take into account and these effects are all encoded in the self energy so the self energy is just the collection of all these possible stories that we have to keep track and there are consequences of the fact that we have an additional particle in the material and the spirit of making approximations in the Green's functional theory framework is just that we have to select the most important stories the most important physical effects that we have to take into account and in the physics in the GW approximation in particular we take into account in the self energy the exchange effects plus these polarization effects these screening effects and the GW approximation is called GW because the self energy turns out to be the product of the one body Green's function and the screen Coulomb interaction W and the screen Coulomb interaction W is screened by the inverse electric function and instead of adding this per Coulomb interaction P you have this screen Coulomb interaction W and the difference is given by this inverse electric function that is the scrubbing screening and this screen is related to this polarization this creation of additional electron pairs in the material so the GW approximation is describing the coupling of the additional electron or the additional Coulomb with electron pairs in the material that are screening the propagation of this additional particle in the material so you can understand we are reaching the question time so you have time for a few months ok, thank you so the GW approximation can be understood as the propagation of a boat on a surface on a sea, on a lake and this propagation of this boat is creating waves and these waves are those that are describing this polarization and this is in contrast to Artifox and Artifox can be understood as ice skating so you skate on ice and the ice is not reacting so it's completely frozen it's not able to polarize to react for this perturbation so in GW you take into account these additional waves in the propagation and GW is today the standard approximation to calculate one structure and it's in very good agreement with experiments so these lines we are calculating in the GW approximation by Rothing and Ljue and it's also correcting the Artifox estimation of the band gate now GW is not only able to calculate to give us the one structure but is also able to go beyond this quasi particle description and it's also able to give us satellites and this is a relatively fact that we can also calculate this frequency dependent object that is the self-range and here it's an example and then I will conclude with this it's the photo mission experiment of bulk aluminum in the middle panel and this is compared the calculation of the spectral function on the left that is calculated in GW plus cumulant, cumulant is just vertex correction to the GW approximation but let's say this is a calculation of the spectral function and you see that the main feature is this one that corresponds to the band structure of aluminum so you have just a parabolic band and in addition to this you have replicas that are satellites and if you measure the distance between the band and the satellites these are equal to the plasma energy of aluminum so we can understand them as plasma in satellites and you see that this GW plus cumulant calculation for the spectral function is able to capture the physics but it's not in quantitative agreement with the experiment if you want to be in quantitative agreement with the experiment you have to take into account all the phenomena that are related to the photo mission experiment in itself and if you do so then you can get a good agreement quantitative agreement with the experiment this is what we have done in this right panel and this photo mission spectroscopy will be the subject of the next lecture by Polina so you will get more details about this in the following I will skip the discussion about excitons we will have the occasion to discuss about excitons in the rest of the week and I will just go to the conclusion and the conclusions are the fact that we use Green's functions because of several we are interested in spectroscopies and the different spectroscopies are linear function of the Green's function so these are non functional of the Green's function if you calculate the Green's function and perturbation theory gives us a very powerful way to devise approximations because it's related to intuitive picture of propagation of additional particles in the system something we cannot do in Consum and in particular I have discussed the use of the one body Green's function for electron addition removal energy and you will see in the following we can use the two body Green's function for the calculation of electron excitations associated to absorption and other spectroscopies that are measuring neutral excitations like electron energy loss spectroscopy and elastic stress elastic stress scattering spectroscopy and the frequency dependence of the self energy and other kernels brings us information that is beyond the quasi particle picture and with this I would like to thank you for your attention if you want to know more information on our activities in particular on what Lucia is doing you can look at the website Lucia has also prepared an online kulsera mock on density fashion theory this is the address and there is also a book written by Lucia on body perturbation theory Green's functions and quantum of the car and this is the book and with this I would like to thank you for your attention and I wish you fun with Green's functions and the rest of the school so thank you very much Matteo and the session is open for questions if you have any or maybe Matteo I can start with one so of course in your group I would say the most expert group on satellites and you have shown this last example where there is this plasma satellite in the photo emission spectrum of bulk aluminium and as far as I understand you can have a plasma satellite because of correlation effects what you have described but you can also have some kind of plasma satellite because of all the effects which we do not account the fact that we compute the spectral function but then the electron is going out and exciting possibly other excitations so can you comment on that is there a way to disentangle when a satellite is correlation driven and when it's not? Ok, so first of all we are not the most expert group on this but we are one of the groups working on this aspect and the reason is that satellites are a qualitative feature of correlation so if there is no correlation you don't have satellites so this interesting because it's really a fingerprint of correlation Yes, then to answer your question, yes so in a calculation that is just a calculation of the spectral function there is no photon energy dependence so the spectral function doesn't depend on the photon energy instead experimental spectra do depend on the photon energy and there is always a contribution of the outgoing photomitted electron and this outgoing photomitted electron can also scatter on the way out from the material and it can also induce plasma satellites as the all that is left behind and then there is also interference effect between these two effects which contribute to plasma satellites and not only and this is a photon energy dependent so this is the step that we have to take into account when we go from panel A on the left to panel C on the right and this is very important if you want to reach quantitative agreement with the experiment indeed and very often we discuss about strong correlation effects so corrections to correlation because we find deficiencies in our description of photomission spectra but often I have to say that most important effects come from the fact that we are not calculating directly what is measured what is measured is the photomission spectrum and if we calculate the spectral function this is not exactly the same thing but there is a gap between the spectral function and the photomission experiment and indeed we have put a lot of effort to go beyond this spectral function description for photomission it's very important to try to work together with the experimentalist to bridge this kind of gap this is now clear maybe we can start with the questions online mukeš sing mukeš sing maybe he can do the question himself so can you try to unmute yourself because the name is mukeš sing if I spread it correctly ok maybe we can read the question so the question is sir how do we know that how do we know what term should one use for the calculating surfanage I guess that you are referring to this it's so in principle the self energy is describing all these change correlation effects in the electronic system so if you have it you have the exact answer for the one body Green's function so you calculate it exactly in practice we have to make approximations and the approximations are related to the physics that you need to describe and the advantage of Green's function theory is that you can keep track of the physics because you have these effective particles that are interacting in the material and you have to as always in life you have to make a choice and the choice is related to the most important physics of your material and in the case of the GW approximation it's a specific case we make the choice of identifying the most important physical aspect that is screening that is this polarization of the system for this propagation of this additional particle in the material it's not the only choice there are different choices that can be made in particular in the Green's function formalism we can associate approximations with couplings in the case of the GW approximation we describe this screening physics in terms of couplings between quasi particle and neutral excitation of the charge so electron pairs associated to the charge and for instance we completely miss the coupling with spinning excitation which are the other kind of bonds and in your material your system of interest as this specificity that this coupling is important you should choose other type so the choice is related to the physics Thank you Matteo and I read another question from a student online so it's actually a double question so the first one is what does it mean to speak about non-locality in time and then the second question is why the name self energy so why do we call it self energy non-locality in time it's due to the fact if we can understand it from the fact that the Green's function is the propagation of a particle from a time t to a time t prime so this is giving us already one reason why we have no locality in time the second reason indeed is more subtle in the sense that the mini body Hamiltonian is static in our case it's not time dependent so we have a static problem and when we introduce the self energy we make a choice which is we want to avoid to take into account explicitly all the mini body possible excitations in the system that are two particle three particle, four particle excitations and we fold all these mini body excitations in a frequency dependent effective potential that is the self energy and this is like an embedding strategy and indeed self energy it's called in this way because it's a way to describe the effect of the other excitation on the particle itself so this is one of the reason why it was called self energy Ok, so I think we have time for one last question if there is any from the audience here otherwise we can pick up Hello, sir. Hello So my second question was that let's say if we put the self energy and we can improve the results Will improve, sorry Will improve the result maybe energy and band structure Ok Again it depends on what you are interested in if you are interested in the density the Konsham system is enough because the Konsham system is meant to give us the density if you are interested in band structure you cannot use the Konsham system because the Konsham system is an auxiliary system so it's a system of effective particles that are auxiliary particles that are just meant to give us the density and you have to introduce a different framework and in particular the Krins function framework where you have this effective more complicated object is the self energy it is effective more complicated and the auxiliary system is meant to give us for instance the band structure then the quality of the results of this more complicated framework depends on the quality of the approximation for this exchange correlation send energy so if you make a good approximation for the send energy you get good results if you make a bad approximation you still get bad results ok sir so one more thing is there any other thing apart from the density of state which can be calculated from Konsham equation exactly not the density of states the density yes sorry density ok in principle you could calculate from the density and you know that in principle you could calculate all the observables as functionals of the density this is what DFT tells us yes but we don't know the operator you told the problem is that for most of the cases we are interested in we don't know this functional ok so in some cases we have good approximations to the functional in particular for the total energy we know that we can have good approximation to this functional which is also implicitly unknown but we have good approximations the LDA, BBE these are the widely used functional so for the total energy we can obtain good estimates for quantities that are related to spectroscopy this is much more difficult so in particular for bad structures we don't have these functional we don't have ok so maybe how do we know that the we move to the last question from a person here in presence and then we have to move to the next so you can put the question on the chat and we will try to address it ok ok thank you ok so how do you build this greens function so if from the equation you are showing we basically compute this from the Komsom Eigen states but like so when computing this self energy we do some Dyson expansion so we have like for example higher order greens function terms when we do this expansion so how do you compute these things because this is like an independent particle level at an independent particle level but somehow you have to include some interactions between these things for example if you are computing the dielectric tensor for example in the when you are doing this thing we have to compute the dielectric tensor so the imaginary part of the dielectric tensor is somehow related to the we have to consider the interaction and are these when doing this thing because when you are doing the GW I guess we don't consider these effects so how important are these effects in the bandgap collecting the bandgap and the bands ok, many questions but I try to be synthetic so you calculate in this Dyson equation representation you can calculate the greens function by any approximation of the self-energy ok, because this G0 is something that you can obtain directly from the single particle energies all these change correlation effects beyond the single particle description are encoded in the self-energy so anything that is related to interaction is in the self-energy any approximation to the self-energy can be used to calculate the greens function in this in practice you will see when you do for instance GW calculation in practice with Yambo how this is important the effect of the self-energy is represented here on the spectral function so you go from this single particle picture where you have sharp peaks to this richer description where you have peaks that are broad and where you have additional features how this is important for the band gap I would say not only for the band gap but for the band structure in general and for effects beyond the band structure that are satellites an example is here for germanium so instead of having a metallic material as in LDA or a very large gap as in RTFOC you are in much better agreement with the experiment and the difference between GW and RTFOC is in the screening so you have to calculate this in screening and you will do this in practice so don't forget to come also in the next days to the school OK, so thank you again Matteo


Hey, everyone, this is Gabrielle with Oxfamata Group. We are here at Oxfamata Toyota today, and I have Chuck Schumann here with us once again. Now, he's going to be going over a 2018 Toyota Avalon. This is a touring. So there's some really neat features on this vehicle that Chuck is going to go over with that. Absolutely. If you want to talk about that, that'd be great. Yeah, 2018 Avalon, down here in Kentucky, we call it a Turin. But this is a touring edition. In the 2018 Avalons, in every trim level, you're going to get the Toyota Safety Sense piece. So you've got a multi-millimeter wave radar here in the front. An in-dash camera up there, that gives you pre-collision with pedestrian detection, lane departure, dynamic radar cruise control, auto high beams. All of those very cool, very safe safety features standard in every trim level of the Avalon. And like I mentioned before, this one's the Touring. So it's a really cool look, very sporty ride. It's got these great 19-inch gray alloy wheels that just look really cool. You can tell it's the Touring from far away. But just a really stylish, very cool look. And this thing is very, very nice and low to a safety feature. Let me show you this. If you look here on the side view mirror, this has blind spot monitoring. So that little orange symbol lights up when somebody's in your blind spot. If you have your turn signal on, it'll beep, or it flashes to alert you. It doesn't beep. It only beeps when you put the car in reverse. If a car's coming down the lane as you're trying to back up, it'll beep to alert you. It's called rear cross traffic alert. But you look inside this thing and it's got big leather seats. They're heated in the Touring. It has navigation, just a ton of space. You can actually program the driver's seat for two different settings.  He is, yeah. But very, very comfortable ride, dual air control so you and the passenger can have different, you know, temperature settings as well. And then you've got a ton of space back here. Your guests have their own air vents in the back. Avalon is just nice, comfortable. It's a luxury car with a Toyota badging on it. Yeah, it's absolutely beautiful. Well, thank you for going over some of those things with us. So if you guys have any questions, we'd like to stop in and take one of these for a test drive. Please let us know. You can always give us a call. Phone number you'll reach us on is<PHONE_NUMBER>. You can also visit our website at oxmertoyota.com. And I'll have a link to this one that we just spoke about in the comments below. And I'll have all the pricing and some other details in there. So thanks you guys for watching. Bye.


Hello and welcome to the CrossBPO add-ons video. This video will be going over how to install and use the CrossBPO add-ons. To install the CrossBPO add-ons, simply go to the Knowledge Base. Navigate to the Knowledge Base from the application. Go to the top left where it says Help. Go to User Guide. And from User Guide, you can go to the top right and click on Add-ons. Navigate to the CrossBPO tab. Scroll down to where it says Install the CrossBPO add-on here. Once you've clicked on it and installed it, go back into Bookmap. Go to the top left. Configure add-ons. Go to Add add-on. Add the CrossBPO indicator here. And you should be greeted with a screen showing all your active instruments. Now to use the CrossBPO add-on, there are numerous use cases. The primary use case would be to look at different market spreads on a single ticker. For instance, right now I'm looking at the multi-book perp for Bitcoin USGT. At the same time, I've got the last trades for Hoby, Binance Futures, OKX, Coinbase Pro, and the BestBit and Offer for Bybit enabled. Now let's have a look at this recent sort of pump. If I look at this, I can see this orange line trades much longer, much higher. And what I can see from this is Binance Futures had a steady incline. The trades took a while and executed much later than the trades from Bybit, Hoby, and OKX. As you can see, these came in much earlier. This tells me that the moves were happening on different exchanges, but HarbourShash slowly caught up and finally Binance Futures got the information. Now you could be saying that on Binance, there were no walls here and we can look at the Binance ticker for this time and see if the walls were hit all the way back. And on here, you can see that this is where everything happened. This is where Binance happened. And it took a very long time for Binance to finally come in to affect and you can see the volume sort of happens, the hunting of crosses. It's a very large sort of spread here and finally hitting the wall here. So though you'd have got the information much later, you could have sort of seen that you're expecting a push up and a slow decline. But that's something that you could have captured on with this cross-PBO add-on is the fact that prices were looking to wick into this and decline. You zoom out and see price continues to go down and everything sort of appears as normal. But always as a constant, you can see the Coinbase Pro is always higher than Binance's price. This tells me that people on Coinbase Pro like to trade short more and the market makers or the powers that be at that time always like to take the shortstop and have to be more aggressive with the shortstop much higher. Price versus also true for the buy-bit trigger. As you can see, this one's always an inch lower. And if we just go into our add-ons again and hone into just both the Coinbase Pro and the Will-Be and uncheck the Will-Be one to look at the buy-bit and Coinbase by itself and then go into chart visible components and turn off the ask-a-bit for Binance and just look at it overlaid within the Binance or price. So we can see the pink and the lilac are the asks whereas yellow and the orange are the bids. Orange being for Coinbase Pro and yellow being for buy-bit in my case. You can see that though the spread's a different price will look like the same and again this is information you can only sort of get from tick sort of data and this is what I mean by spread. Spread is just the difference between the best ask and best bid. Spread from exchange to exchange differs as different people trade on different exchanges so the behaviors are different. The behaviors on buy-bit are more lower-focused because they're trying to take out more longs than they are to end to take out more shorts. And for Coinbase Pro they're trying to take out shorts and it's much easier to take out shorts if they go higher to take them out here. You can see they have to hang around for much longer because they know that they're not in fear of introducing new shorts in the market if they go up higher. But at the same time they know if they stay up a bit higher they can always get people suckers bets as I like to call them enter in at this price then liquidate them at a lower price. This is one instance where you can use cross BBO to glean an advantage. I go back to this credentials and we go back into this add-ons page and we look at this options and just turn off the buy-bit and just look at last trades. You can see that often the green line in this case buy-bit will always trade lower than any other exchange. Price of cross-biz exchanges will appear the same on the ticker but that is when they finalize the price at close because they like to keep closes to the same sort of price. In terms of stop hunts and last price because you get stopped out based off of the last mark price depending on how you enter your thoughts. You'll be stopped out if you enter some stops here on Coinbase Pro and maybe not on buy-bit. As you can see there are some differentials between the exchanges. This can also help you try to identify which exchange you may or may not want to use just purely based on spread data as well as trying to identify where to place your stops and if you need to actually force yourself out of a position. For instance, if we go back to the case we have on here you can see that Binance finally does all the movement here and if we re-add the Binance asking bit, Binance does its move here but to you it might be so scary on Binance saying they're still taking the time in doing this so you may already be in the shore or enter the shore at say this wall and then said oh no price continue to go up, do I do or do I do not want to take my position off out of fear of price going higher and looking at other exchanges you can see that you in fact want to keep your shore in place at least for meanwhile as you can see you would have been profitable in that shore for a while to come but you may have as they call it paper handed it because you are scared of what was showing on Binance and how the spread was moving as you can see this is what we call spread, spread widens and arbitrage takes you into effect as all the exchanges are done with collecting orders but Binance is not done because Binance has more traders than most other exchanges so maybe they needed the extra time to get these people into long or take the stops so prices on multiple exchanges go down, Binance stays up and arbitrage takes you into effect then there you go Binance snaps back and trades with everything else it's using these sort of and exploiting these behaviors that can give you an advantage using the cross BBO indicator that has been one of the use cases you can use cross BBO indicator if you find more use cases leave a comment in the video description below and share it with everyone else I hope you enjoyed this video if you found use case and found it helpful for you if you have, leave a like subscribe to this channel for more and I'll catch you guys on the next one peace


The Narcissist will leave you for dead.  The Narcissist will use up everything that you have to offer. They will take up all of your time, energy and money until you have nothing left for yourself. When we are given to people, it should always be part of what we have reserved for them. What we have kept specially for them, we should not be going into our own reserves for the Narcissist. That's meant for us. That's supposed to keep us alive, but these Narcissists are so demanding. They will make you work very hard to meet their standards. But nothing will ever be enough. They cannot be satisfied. Nothing is good enough for them, because they don't feel good enough for themselves. Which is why they expect more from you than they expect from themselves. They depend on you for their survival, often at the expense of your own survival. They will demand so much, until you haven't got enough to look after yourself. You haven't got the time or energy to attend to yourself, because the Narcissist needs all of your attention. You haven't got the money to look after yourself, because the Narcissist needs to live a lavish lifestyle, so you find yourself making sacrifices. You find yourself being coerced to go into your own reserves, your own life support, to then give that to the Narcissist. And even then, it doesn't change anything. It doesn't put an end to the demands. It doesn't satisfy them. They will always want more. They're like buckets with a leak at the bottom. They can never be filled. And the more you try to help them, you will just end up running yourself into the ground. Because it will never be enough. You will be forever running on this endless hamster wheel. Trying to please them. It will never stop, because they have these insatiable desires. They cannot be satisfied. As soon as you give them your time, energy or money, they don't even take the time to appreciate it. They're not grateful for anything you've done for them. A quick way to test this is just to say no to them. Say no the next time they ask you for something. The Narcissist will often respond by saying that you never do anything for them. Regardless of what you may have done for them, up until that point. You could have gone into your own reserves and sacrificed the things that you need to please the Narcissist. But they will still see it as though you never did anything for them.  The Narcissist will put you under incredible amount of pressure. They will make unrealistic demands. But you find yourself constantly given into them. Constantly giving them whatever they want, whenever they want it. Because if you were to say no, it would cause a Narcissist injury. Which would then be followed by the silent treatment. Or Narcissistic rage. They would become very bitter and resentful towards you. And they may even smear your name. And tell people that you don't look after them. Because of this, you find yourself constantly given into them. Due to the fear of how they will react. Or the fear of what they may say to people about you. You just want to keep the peace. You just want to avoid any arguments or disagreements. So you let them have what they want. Even at the expense of your own health and well-being. You may find yourself given away things that you need. Just to please the Narcissist. And they always want more and more from you. It's never enough for them. They take more from you. Than what you are able to provide. Until you have nothing left to give to yourself. And eventually, you have nothing left to even give to them. Because they've used it all up. You end up in a state where you feel numb and desensitized. They've overexposed you to abuse. To the point where you become less likely to feel shock or distress. At scenes of cruelty or suffering. You don't feel anything anymore. You've become emotionless. You're lacking emotion, sympathy and sensitivity. You're not financially productive. You're missing that energy and aura. That you used to have.  They gradually caused your health to deteriorate. Until you ended up in this condition. They knew what was happening to you.  But they just didn't care. Their needs were more important. So they sat back and watched you run yourself into the ground. Trying to please them. Trying to make them happy. Knowing fully well what they were doing to you. And when you've given everything you've got to give. You're broken down. And you've got nothing left to sustain yourself. Nothing left to get back up out of the pit they've left you in. They don't take responsibility for what they've done to you. Now they're pointing the finger at you. They're bullying you. Marking you.  Telling you you're not good enough. Because now you've got nothing. You just gave everything you had to them. And they used it all up. But if you were to ask them. They would tell you you never did anything for them.  They will make you feel so small. As though you're completely worthless. And then they will just leave you for dead. They will leave you to deal with the consequences of their actions. The consequences of everything they did to you. But it doesn't stop there. The narcissist isn't just going to leave you for dead. No. That would be too nice. That would be too pleasant. Even after the narcissist has taken everything from you. And left you in their pit of misery and destruction. They will then make accusations about you. They will spread rumors about you. They will ruin your reputation.  You would only be met with other people. Who are also trying to destroy you. Because now they've made everyone think.  The narcissist cannot just leave you for dead. In their minds. You are deserving of a punishment that is far more severe. They want to put you through hell. They want you to experience daily suffering for the rest of your life. Where you will wish that you were dead. If this video has caused any distress to you. You can email me for support. At coachingatnarksurvivor.co.uk I hope that this video resonated with you. Thank you for watching. And I'll talk to you soon.


actually are 5G radios which we're building. And then this is a kind of Wi-Fi 6 and small cell solutions. We have some of the fiber optics. Some of those are built for data that will be required. The whole premise is from three or four angles. One we believe 5G will be probably next four to five years a massive amount of network investment that will be required by telecom operators but also with data center players and others to kind of build this network. And we see a real opportunity here. So while STR has been historically been known on the optic fiber side and that's probably still where we have a very strong global presence we are in that top three or top five in the world. We also felt that especially in a 5G environment there will be a convergence of both the fixed network like the optic fiber but also the wireless network. And so to that extent over the last few years we've also started building out our own wireless solutions where on such kind of products on the radio part we would actually compete with Huawei, Ericsson or Nokia. And we're also very proud that essentially what we are pioneering is a new technology which is called OpenRAN, Open Radio Access Network. And that's something that we have more than now 350 network engineers, software engineers who are building out the software they're required for the 5G network. And then we are looking at Indian partners who can then manufacture the radio physically. So we have partners like VVDN and Sankya Labs etc. So very proud also that it's truly a full India stack that we have made in India 5G solution. So I think look you know if you look at some of the data points today India deploys one tenth of the fiber every year that China does. Right and if you look at it largely both the economies of both the countries have you know the same population. So they clearly a tremendous amount of just fiber infrastructure would need to be deployed as we go from 4G to 5G. So I think that's the first part. Our own estimate is that probably four to five times more fiber will be required to deploy a high quality 5G network. And by that I mean you know probably we would need to showcase at least about 200 to 300 Mbps download and about 50 to 60 Mbps upload. That's when we look at 5G that's what you know the network we need to build out. So to make that happen one I think certainly as he said the fiber network needs to get built out at probably four to five X of what has been built so far. We also need a lot of both towers small cells both for outdoor and indoor coverage because I think that's something very important. Data about 80% of the data will be consumed indoors. So while we talk of large macro towers and cell sites you will need also a lot of small cells and indoor small cells like the solutions we have launched. Our solution is called Garuda and so such kind of solutions will be very important to also be deployed at scale and so that as you go from outdoor environment to indoor environment you're able to get seamless 5G connectivity. From one perspective there's probably already north of 70 countries that have deployed 5G and more than 200 or even 300 operators around these countries are deployed. So it's really important again that we don't go into a lot of debate of what will 5G be used for to be really every time we go from 3G to 4G and then now 5G probably we have some of these questions. So I think fundamentally I do see that commitment from the government and from the operators to get 5G to happen as fast as possible. I think the other part we should be mindful of is that we still see 5G devices probably in the 15,000 rupee range which has to start coming down very quickly to 10,000 into 5,000 so that we can also have larger scale adoptions. So I think that's something probably more from the chip and the mobile side that needs to happen. I think from the recommendations to PR I think without going into specifics I think the overarching theme has been two things. One is to provide it at you know when you look at global benchmarks you have some extreme cases like in China where they are given free of cost and you have other countries which have looked at it and provided very, very and certainly in the mid-band spectrum have provided the spectrum at a very reasonable cost. The second part is also to look at ways that the government can provide up to 100 megahertz of chunks of spectrum because having contiguous spectrum is also a critical part of how the operators can then provide high quality. So these have been largely the areas of where we have recommended and plus obviously you know there's still a lot of challenges in India in terms of right of way for deploying the fiber network. So that's where the government both center and state need to really find ways to make a single window authority, give more empowerment to the operators and to players like us to deploy it and self-certify that the network is being built in the right way without harming the environment or without you know destroying the ground or anything else. I think the way we're looking at it is three or four areas. One certainly in the core business on the optic fiber and cable, there's a lot of innovations not only on how do we provide ultra high capacity but also in a very, very low form factor. So just to share with you as an example, if you see this, this is one of the cables we have innovated and we're further working on. This is the world's highest capacity fiber cable and this is deployed into you know the leading data centers in the world, currently going into a data center in the US. So these are kind of innovations as you see more and more data centers come up globally and also in India. They are looking at such kind of innovations where typically for this amount of fiber, this has 7,000 strands of fiber in it, you would typically need this size of a cable and our innovations on the glass, on the fiber and cable have been able to reduce it to such a you know small form factor so that it becomes much easier for the data centers to deploy this and then transmit massive amounts of you know multi terabytes of data across the data centers. So these are very critical because also in a 5G environment and with AI and ML, Web 3.0 coming up and also the metaverse, these solutions will be very important to provide the infrastructure, the digital infrastructure to enable these kind of applications. So this is one area, the second area I think is clearly on the 5G part that we were touching on earlier. We will continue to innovate and build a lot of the radios that are required on both dual band as well as tri-band because again the 5G will be deployed across multiple bands of spectrum. So our innovation will be how to create the smallest form factor with the least energy requirement which is also environmentally friendly and then is able to still provide both dual band and tri-band solutions to for the telecom operators. We have set ourselves you know three very very important targets on the sustainability side and in many ways we are industry leading or probably global leading in our field for all of those. Number one we have decided and agreed on a target of net zero carbon emission by 2030. Second is we have targeted net water positivity by 2030 and especially given we are very intensive on the manufacturing side we have set a target of net zero waste to landfill across our manufacturing sites globally by 2030 as well and this is important because we have manufacturing sites across India, China, Brazil, Italy as well as we have manufacturing sites in the US that is coming up as well as the UK. So it's very important for us to have these sustainability practices across and so far through our sustainability effort we have impacted more than two million lives already.


What is required, I'm sorry, no, wrong word.   Woo-hoo-hoo! Good question, isn't it? Is it mother nature? Is that worthy of you worshiping? Is it your mom, your dad, your family life? Is it some celebrity, some YouTuber that you watch? Is it a band? Do you worship a band or music?  What do you worship? And what is worthy of your worship? Is it a higher power?  Now, let's all take a firm stance together of what is not worthy of worship in our lives. That is our own mind. Yeah. To worship ourselves, and I don't mean this in a way to put yourself down and think less of yourself, there's a difference between thinking less of yourself and thinking of yourself less. Okay, so if we worship the mind and we worship our thoughts, what does this mean? This means that everything that pops into our heads is worthy of our attention and praise and admiration and we believe it to be true. Wrong. We know this. You know this and I know this. And sometimes it's hard to decipher what's true and what's not about ourselves. But what we do know about our thoughts is that we don't know where they come from. That's one thing we know. The second thing we know is that based on your past experience in mind, a lot of what comes up in here isn't true, isn't useful at all. And it's not worthy of our admiration and attention and worship.  Let's see what you're trying to tell me. Let's see what you're all about. Hey, here's another thought. Come on in. We got leftovers. Come sit at my table and dine with all of the other thoughts. Let's see what you have to tell me about myself and the world and the reality in which I live. Sit down, have a glass of wine. We got dessert. We got tiramisu coming out. Take a seat. So many of our thoughts, everyone, do not require worship, which is why the mind doesn't require us to worship it. I fall into that trap. Of course I do. Of course I do. When one thought comes in and it's like something self-critical, right? Some worry that I'm worrying about the future, that I don't know where I'm supposed to be or I said that thing. Maybe I said the wrong thing. Maybe they looked at me differently and I made them feel, but all of this stuff comes in and makes me question certain things. And if I were to be one to always worship every thought, I'd be stuck in my mind all day overanalyzing, overthinking, believing that every thought is true and every thought is not true. You do not have to believe everything you think. One more time for the kids. You do not have to believe everything you think. Everything you think. What is it, 30,000 thoughts a day? You think all of those are true? No, no, they might seem true. Sure, okay? And there's all these kind of things we can do with cognitive behavioral therapy to see if any of those thoughts hold any water if you wanna have fun with them. See if they really exist in reality. See if they're really true and you can play that game with yourself. Just ask yourself, is that really true based on what I've done in my past experience? Probably not, okay? And is this a useful thought? So when we say worshiping the mind, you don't have to. I don't think it's worthy of your worship. I think we can learn to be objective about our thinking through meditation, which we'll do in a moment, and to be a witness to what's happening, which is all about mindfulness and meditation, right? Be a witness to the thought and what's going on and choose to engage. Choose to engage in some of these things and have the awareness and have the discipline to not engage sometimes. And be the parent. Be the parent of your life. And this is something I've had to come to terms with sometimes where, Scott, I love thinking. I love thinking. I can think all day. You could meet me in 10 years, okay? 10 years. And you'd be like, Scott, what have you been up to? New jobs? New this? No, I've just been thinking. It's been the best 10 years ever though. I've thought about so much stuff, right? My mind can be so entertaining and I can have so much fun in there and imagine and all of this. And we have to realize, and I have to realize that sometimes we have to be a parent and say, one enough is enough for ourselves. That's enough of thinking. Let's go do things. That's enough of looking into that scenario. You've had enough there. You've dug deep enough. Let's get out of there, okay? So this is about being a witness to what's happening, not worshiping what's happening in the mind and being a bit of a parent to ourselves, all right? So with all of that being said, I hope you take a bit from that and know that, you know what, maybe Scott, maybe a smidge of that I notice in my own life, in my own mind, where I get caught up in a story. I get caught up in some kind of scenario build about the future. And I believe all that to be true and I believe all that to be useful. It's not worthy of your worship most of the time, okay? So wherever you are in the world, thanks for tuning in and wherever you are in a room, come into the space a bit. Let's just sit with each other, sit with yourself. And when you're ready, you can just softly close your eyes.  What do you see? Nothing, Scott, my eyes are closed. I know, I know, chill, chill, chill. Are any images popping up in your mind? Just as you sit there.  Those kind of glass slides where you have a specimen on them, right? And you're just looking objectively at what's happening. As a scientist, it's just you don't have a bias.  So just watch the mind and see what pops up. And when you have an image or a thought, you can say out loud, oh, I'm thinking. Oh, I'm imagining, that's all. Just be a watcher for just a few moments in silence. Now, if you need a place to come back to, just come back to your breathing. Simple as that. Nothing extra, nothing more, nothing less. And if thoughts come up, you just say thinking.  And just see it for what it is. No need to judge, no need to be hard on yourself. Just say, oh, okay, I'm thinking. And come back to breathing. And when you're ready, you can just open your eyes slowly, gently, softly, coming on back. You don't have to look at the screen if you don't want, and if you're on the podcast, hey, no screen necessary. Now, what a lot of you may have noticed in that simple little exercise is that maybe you weren't having a lot of thoughts and images. Yes, I think some of you might be not in your head because I gave an intention and expectation to be the watcher, to be the watcher. So you're already in a state of alertness and awareness, you're kind of waiting for the thought, waiting for it. And when there's a really cool exercise where if you're really overthinking and come to a seated position and ask yourself, I wonder what my next thought will be.  Nothing's coming because you're waiting for it and you're like, where is this thought creation mechanism starting, when's it gonna actually pop up? And you're experiencing this state of awareness of your own mind. So a lot of you may have in that exercise, maybe not a lot was coming up. And when it did, if it did, you said, okay, that's just thinking and I come back. My friends, let's not complicate the meditation thing. It's been complicated. You see all of these apps, you see all of this science coming out about it, you see all of these different techniques too. If you're a beginner here, even if you're not, just sit with yourself for a few minutes and just watch the mind. That's it. You don't need an app, you don't need me guiding you, just sit with yourself if you can, even 30 seconds at a time. And this is the practice. This is the practice, okay? So a few things there. No more worshiping the mind. I don't think it's worthy of your worship. Don't believe everything you think, okay? Be an objective observer. Be the scientist with the glass slide and a specimen. Those are your thoughts, just watch it. Just watch it with no bias, right? No good or bad, it's just, yeah, it's thinking. Yes, I'm imagining. Another tool is to be in that little state of observation. Ask yourself, I wonder what my next thought will be and you wait for it and you just wait and see, okay? I hope you enjoyed this episode. If you did, you know, some of these techniques, and there's a whole lot more with the anxiety course I put together, which is in the description, it's not on scotsaintmarie.com anymore. It's just in the YouTube description. So I'll put the link in the podcast description. There's free videos if you just want some extra tools for your mental health toolbox. And if anxiety is something that you experience, as I do, as every human does, some more, some less, some more frequent, some less frequent, we don't need to put you on a scale, okay? Your experience is your own. If you want some extra tools, there's a free, what did I even call it? Free six-part series and it's just free videos and it's a mini course. And if you find that would be useful, and go do it, I guess. Okay, now I wonder what the next, I wonder what you're doing today. I hope you have a great day. I hope this was a bit centering for you. I hope this was useful for you. And I hope you have a wonderful day, my friend. And keep being you, take it easy, enjoy life the best you can and enjoy the day the best you can, all right? We'll talk to you soon.  All right, bye-bye.


So, welcome. I am Vidal Ajax from the IOTA Foundation and today I will present you the work that we have done with Luigi Vignelli and Basil Dimitrov about Implementation Study of Variable Delay Functions. So, one big question about blockchain research is how can we prove that time has been spent? And this is a big question that has many applications in consensus right control and distributed random generator, but not only blockchain, like it is also a question about security and like anti-spamming. So, one of the most use current solutions is what we call a proof of work that anyone should be aware of. So, the quick idea is that using a publicly known hashing function across the network, we have to find an input and such as the hash of this input is lower than a certain threshold, which determines the time if we look for them randomly because there is no other way than just doing it randomly. So, the problem is that it is very fast to verify it's only one hash, so like typically maybe one microsecond and it's lightweight to implement and we don't have a big overhead on the network. It's just like a few hundred bits, but it has a huge parallelization potential and because like if you get 1,000 machines, then you can have 1,000 more hashing power than like just one machine. So, this is the major challenge in blockchain area, like especially for Bitcoin for example, how to overcome this raise to mining that we can see. So, very recently, like two years ago, there had been an alternative that arose which is called verifiable delay function. And what is exactly verifiable delay function? It is a set of three algorithms. One is the setup which is a step that we process at the very beginning of the network and initialize the environment. It is very general, for example, it can be an RSE group or like an LFT curves. It is very general. Then there is the evaluation. When one of the participants of the network needs to evaluate a VDF, it takes an input from a very general input space which is determined by the network and the protocol characteristics and a challenge tool. And it returns a solution in the Y and eventually what we call a proof by which is used to speed up the verification. And finally, we have the verification which is performed by anyone in the network that wishes to actually check that the pair Y pi that the evaluator sent on the network is actually a solution of the input X tau. So, I saw inside about what is a video. So, the evaluation must run in two sequential steps which means that it is not parallelizable. This is the main difference with proof of work. It is that if you have 100 color like inside of the code and here we really care. Vidal, I don't know if you can hear me, but you seem to have a bad connection. We can't hear you very well. Maybe if you can turn down your camera, that could help your transmission, maybe okay, I know nothing about this, but maybe it could help. Okay, so we'll just wait like a few seconds to see if Vidal connects again. And if he does not, then we'll move to the second presentation, but I suggest that we still wait for one minute maybe. So, Vidal, are you back? I see you back among the participants. So, maybe you can keep your camera off. Just turn on your mic and share your slides. You can hear me? Yes. Okay. I saw that I was muted, but I don't understand what happened. Well, you were disconnected. We just lost the connection. It seems that you have a pretty bad connection. Yeah, it was very bad today. I don't know why. I'm pretty discreet. I will try to keep going with that, but I honestly don't know why it is so bad. Okay. So, the evaluation of the RSA-based... Share your slides again. Yeah, sorry. The evaluation for RSA-based VDF is for taking an input x and a change tau to compute y equal to x per tube per tau, which is actually screwing tau times x and getting back the value. You don't see the slides? No. It's not going well. Now we see them. Yeah, I don't know why it was disconnected actually. Okay, sorry. I'm very sorry. So, the evaluation consists in squaring tau times a number in the RSA group, and this is the underlying assumption of RSA-based VDF, but this operation can only be done sequentially and it doesn't have any way of parallelizing it. And actually, if someone were to know the private key of this RSA, which is like the factorization of n, then he can compute it in a constant time, like very, very fast because of modular properties of RSA groups. Okay, so here is the difference between the two VDFs. In the Piatrach VDF, we split the exponentiation that we just computed in log tau small pieces using APR-Chamy heuristic for the security, and then it is reconstructed during the verification. And in the Wysolowski one, we compute a sprue, which is a subexponentiation in which we take the exponent and we divide it by L with L is a small prime of typically like 200 bits. And this prime is also selected using a Fiat-Chamy heuristic. And then the verification is done by computing, by reconstructing by computing the power of pi for L times the remaining of 2 power tau over L. And so the major difference between both in like a high level is that the proof is composed of log tau elements for the Piatrach and a single one element for the RSA group. And that can be a huge difference in networks because one element can be about 2,000 or 4,000 bits. So log tau and we'll see the value of tau. So what is the contribution of our paper? So far we have a formal framework proposed by Dan Bonnet for a VDF to work on that. And we have two major proposals by Piatrach and Wysolowski. And we also have a theoretical survey by Dan Bonnet and his PhD students in which he gives some insights about why these good, why are the two major proposals good VDF in theory. But we have absolutely no idea, like no values of how VDF can be used in industry, in industrial environment and especially for critical timing. For example at the IOTA foundation we want to use VDF as a rate control mechanism because provovor can be very easily spammed. And so verification must be performed very, very quickly. And we had no idea how it was. And there is no implementation values, would it be academia or industry? So what we do is that we give experimental results of VDF and we suggest some improvements by using state-of-the-art algorithms and we make a viability comparison between proof of work and VDF. So what our experimental setup is, we run the simulations on a Intel Core i7 of 8th generation. So like three years old and we have done it using GMP library in C++ for multi-precision computation so that you can have like an idea of how powerful the implementation was. And to say also that we didn't implement using assembly. So concerning the evaluation, in this plot and the exercise, we have the value of tau ranging for 2.20 to 2.25. And here is the computation time. Unfortunately the time is not inserted when it is millisecond. But what is interesting is the trend. We actually find a linear and pretty predictable evaluation time as the theory was predicting. And something interesting are the different lines. In red we took the RSA modular size of 500, 1,000 and 2,000 for blue. And so we see that the modular size has a clear impact on the performances which should be taken into account when building, when using VDF for industrial purposes. Concerning the verification, we have a very nice property. It is that the verification is constant time for the regular speed one. And here I have an issue but the Weizsorowski is the dotted line whereas the Piotrk is the solid line. And we can see that it can be perfect under one millisecond. So this means that the VDF should not be a bottleneck for like transaction verification. And the constant time of the application is something very important because it means that you can increase or decrease the difficulty in the network without having to worry about the impact on like your bottleneck of transactions. And here we have a plot in which we plotted the verification time for the Weizsorowski VDF with a varying size of the L that we talked before which is the prime number by which you divide the challenge when you build the proof. And it is also important to take into account that this brings a trade-off between security and the performances because like just doubling the size of the L number just doubles the time it takes to compute the verification. And so to stick to the Weizsorowski one because it is the one we went for due to the shortness of the proof and the better performance that we found, we found out that the main part of the computation of the verification was spent on rebuilding Y by making a double exponentiation. And this spans between 30% to 90% of the verification part. So it is a very critical part of the verification to optimize for critical purposes where you have to verify a lot of VDF in the same time. So one solution is to use what we call multi-exponentiation algorithm. A multi-exponentiation algorithm consists in computing a product of exponentiation modular one same modulus faster than just the separate exponentiation and then taking the product of them. And in our paper, we have studied the Dimitrov's algorithm, but it is a bit outdated. And so the work that we are doing now is that we are studying also the simultaneous 2W area method, which consists in taking a window of side W of the exponent and then using a kind of a square multiply method. Then there is the Yen-Li and Lens-Tra simultaneous sliding window algorithm, which is an optimization in which you have a sliding window instead of a predetermined window. There is a binary GCD-based multi-exponentiation algorithm that is actually tolerant to what we call side attack channels. And there is modern solutions that we are investigating, which use parallelization. It is very recent, like two or five years recent. And so in the paper, we only talk about Dimitrov's algorithm, but as I said, it is a bit outdated. So one big issue when it comes to VDF used for blockchain is how can we generate the setup in a decentralized way? Because as we said, if someone knows the private key of the RSA group, then he can cheat and compute VDF instantly. And this is a major problem in VDF now. And it has been served as the subject of four papers published in the Stanford Blockchain Comparance this year. And one of the main papers is by Ligero, Tim, who created a fully decentralized way to generate a safe modules, everything modules. And because it is absolutely not a trivial problem. And finally, we have a discussion about VDF viability. For example, here we have a plot on the S-axis, we have the price in United States dollar that one can invest into like spamming the network with evaluating VDF and proof of work. And on the Y-axis, we have the speedup in throughput, which means the amount of VDF and proof of work that he can validate in a unit of time. The V dot are the proof of work evaluations and square are VDF. And so we have different colors for different kind of hardware. So what we can see is that globally, when you change hardware, you get a slower, like a lower speedup when you use VDF, then you will get for a proof of work, which is good because it means that investing in a very powerful hardware doesn't yield you that much more power, mainly because of the non parallelizable part of VDF, I explained, that you can make a lot of inner parallelization in the FPG axis. But what is more interesting is about the plane and NT dots that we have. The plane means the person only have one machine and the NT is that the attacker has one third and matching. And if the, and what we can see is that multiplying the amount of matching just gives you absolutely no incentive to know more power in the network. And then you have no incentive to make a race for hashing power or VDF power. What is important to understand in this is that here we only consider having to run iteratively VDF. I mean, you cannot start a VDF before you finished the previous one because you use the output of one VDF as the input of the next. Because of course, if you invest one third in one second machine, then you can run one third and VDF for different inputs. So it is up to the network and the protocol to manage this and propose a iteratively sequential VDF computation. And in a paper that we published at GLOBCOM conference this year, we proposed a rate control for like spamming prevention algorithm that we envision to use in the IOTA for which explicitly use this property of VDF. And a final word about research collaboration. If you want more information about VDF, there is an association which is called the VDF Alliance. It is a consortium of interest trial and research partners such as SEPRANational, SEPRANational Ethereum, Tegos, and more and more academic laboratories. And they have the website which is with VDFresearch.org and it is a useful way to find information about VDF. So this is the end of my presentation. If you have any questions, feel free to ask them.