devoted to, in fact, what I want to do is to show you how this kind of tool, lighted theta series, can be very fruitful for analyzing many communication systems and also designing some other ones as we will see. So, first topic that we will consider is the use of these theta functions. In fact, I will use the terms theta series and theta functions depending on what we are doing with. And, okay, I will show you the small difference, but we can consider these two objects as being the same, roughly speaking. So, first of all, these can be used to analyze performance of communication systems, in coding, shaping, secrecy, that means, for example, I mean, that means the physical layer security. And it can be very interesting in order to design some very good coding scheme or shaping, let's say, shaping scheme as well, et cetera. Okay, and then second part. So, I will not unveil too much of this because we are working on this area as well in one way, so it's something which is a little bit under secret, let's say, right now. But I will show you how theta functions can be also used as a waveforms in order to transmit information of a nonlinear integrable channels, as for example, the fiber optical communication channel. It can be. Okay, let's start with the analysis part. So, the analysis part is more related to coding, right? Okay, so let's start with a very simple function, which is the Jacobi theta function, and then we will see how we can construct all the family, I mean, the whole family of theta functions that we're interested in, okay? Okay, so we have here this function theta, depending on two variables, z and tau, and okay, it is exactly this series, okay? And I will do something, sorry, sometimes I will use the tau variable, in this, which is this one, yeah? And sometimes I will use the q variable instead of the tau variable, and the relationship between these two variables, q and tau, is given by this exponential of i pi tau, and the q variable is just the development in Fourier series of this function. And then the other variable is z, and which, in this case, is a scalar, but more generally, as we will see, it can be a vector. Okay, and so this is what we can call the elliptic variable, and the other one is the modular variable, okay? And in fact, what we will see is that in many cases, all the theta series that we will consider can be constructed from just this function, so just one function. So if we are able to make a table of this function, which can be sufficiently good, then we can derive all other theta functions of interest for us, let's say, of course, not all of them, but all theta functions of interest as a function of this single theta function, Jacobi theta function, okay? So the first connection that we can make is through the sum of Gaussian measures, which will be very important, for example, in physical layer security, but also in some other topics related to mainly multi-user communication using lattice. And so this is this famous sum of Gaussian measures, so it's just a sum of Gaussians, which are in fact shifted by K, which is an integer. So just develop this exponential, and then we get this relation between the sum of Gaussian measures and the Jacobi theta function, okay? So here is an example in two dimensions, because here it was in one dimension. That means that if X, instead of being a scalar, is a vector, a two-dimensional vector, we have this, okay? This is a sum of Gaussian measures when the sigma square equals 0.3, and then you can see when sigma square equals 0.6, it tends to be something almost flat. And of course, if the variance increases more, then it tends to something uniform, okay? Okay, then let's go to the theta series of lattice and let's start with something very simple first. So what is a lattice in general? So let's consider what we call an n-dimensional lattice. We consider full-ranked lattices. That means lattices that are, in fact, that are, let's say that are in the whole space, not just that live in just a subspace, okay? So it's just a discrete additive subgroup of Rn, yeah? And it can be defined, in fact, by a basis, which means it's n linearly independent vectors, v1, v2, vn, and we can define from this basis a generator matrix, so just the columns of g will be these vectors, right? And the lattice can be defined as g times any integer-valued vector in dimension n, okay? So now let's go to the theta series of the lattice lambda and we have many, many parameters of interest that can characterize a lattice. And one of them is this theta series. So we will distinguish the one variable and the two variable, okay? So the one variable theta series of lambda is just, in fact, the generator function of the Euclidean norms of the points x in the lattice lambda, okay? So as you see, I will use tau here for the variable, but so we have still the same relation between tau and q, which is q equals exponential i pi tau, okay? And then the two variable theta series, so we add now the vector-valued, the vector, sorry, z, the vector variable z, and we have this definition of the two variable theta series of lambda, which is just, so we just add this exponential two i pi times the inner product between z and x, and x is inside the lattice lambda, okay? So, and in fact, now in what we'll follow, we will only consider the one variable theta series. At the end, when we'll consider the transmission of a nonlinear channel, we will need the two variable theta series, okay? But I will remind it later. Okay, so in fact, we can see the theta series of z, I mean the one dimensional, the one dimensional series I mean the one dimensional, sorry, the one variable theta series of z, is just the Jacobi theta function evaluated at point z equals zero, okay? And so it is also called theta three of tau, okay?  So it is the theta series of z. So it is, so the first ingredient that we will need to construct all the other theta series that we will need afterwards. The second ingredient is the theta series of z plus one-half. So what is z plus one-half? Just add one-half to all integer in z, so, and you will have not a lattice, but a shifted lattice and what translated lattice. And then thanks to the Jacobi theta function we can express the one dimensional theta series of z plus one-half in this way. And it is called, generally this theta series is called theta two of tau, all right? So we have now two theta series, theta two and theta three. All the, I mean both these theta series are coming, in fact are deduced from the Jacobi theta function, all right? So this is for example, this is a very well-known example of a two-dimensional lattice. It is the A2 lattice or hexagonal lattice. So it is named hexagonal because, okay, so these are lattice points. This is a basis of the lattice. So one zero and one-half square root of three over two, which is the second vector. What we call the fundamental parallel top will be this kind of body, right? And then the Vorino region is the set of points which are closer to some given lattice point than to some other one. And in this case, it's a regular hexagon, okay? So this is the generator matrix of these A2 lattice coming from this basis because you can have, of course, infinitely many possible generator matrices for given lattice. And a theta series for A2, the one variable, can be computed by using only theta two and theta three. I will show you then why it is given by this expression. And if we develop it, I mean, if you make a Q series development of this theta series, then we obtain this, which means that we have one point of norm zero, which is the zero point, of course, then six point of norm one. For example, if this is the zero point, then, oops, sorry, I can't see very well. So this, this, this, this, this are the six points of norm one, et cetera. Six points of norm three, six points of norm four, et cetera. This is what it means, okay? And of course, it's an infinite series, okay? Now, we have seen some generalities. Let's go to the multidimensional case before going to the applications section, okay? So, first thing we will see is how to compute the theta series now for a multidimensional lattice because we need it just as a function of the Jacobi theta function, okay? Okay, so we need some basic rules to do that. In fact, it's like a lego, yeah? You just put, I mean, some elements on top of each other and then you can obtain what you need. So, we need just these three rules to construct our theta series. First of all, what is the theta series of the lattice, which is the direct sum of two lattices, okay? So, suppose that we know the theta series of lambda one and the theta series of lambda two and we have lambda, which is the direct sum of lambda one and lambda two, what is the theta series of this one? It's simply the product of the two theta series of theta series of lambda one by the theta series of lambda two, so this is very simple. Then, what is, we need another rule. It is the computation of the theta series of a scale lattice. So, if you multiply all points of lambda by some positive number alpha, what would be the theta series of alpha lambda? It is simply the theta series of lambda evaluated at point alpha squared tau. It's very simple. You can see it just from the expression of the theta series. And finally, from a very important, is the union of cosets. Suppose that, so lambda lattice is a group, yeah? So, you can define cosets. It's cosets coming from groups, from negative groups, yeah? So, what is the union of two cosets, C one, and suppose that lambda is the union of two cosets, C one and C two. And then, simply the theta series of lambda will be the theta series of the coset C one plus the theta series of the coset C two, yeah? So, let's see on one example what we have. A two, so the hexagonal lattice, we can, in fact, show that it is the union of two cosets. It is, in fact, the direct sum of Z and square root of three times Z. And you make the union of this lattice, because this is the lattice, with another coset, which is Z plus one-half, direct sum, square root of three, Z plus one-half, okay? And it will explain why we got, you know, this formula for this theta series, as we'll see. Just use these three rules. We have here some scaled version. We have a direct sum and we have union of cosets. So, we have everything. We can compute the theta series of A two, right? Same for another example, in the eighth dimension, it is E eight, the eighth lattice, the gosset lattice. This is the densest lattice in dimension eight. And it has been proven very, very recently, maybe some months ago, that this lattice was, in fact, could make, sorry, the best packing, sphere packing in eight dimension. Not, we knew that it was the best lattice packing, but we know now that it is the best packing in general, yeah? So, okay. So, how to evaluate, sorry. So, you understand now why from this formula for A two, we can obtain this, because it is, we have here the product of two theta series, corresponding to Z and to square root of three times Z. And then we have here the product of two theta series corresponding on to Z plus one half and square root of three times Z plus one half. And then the union of two coset, it means the sum of the two theta series, okay? So, everything is very simple here. A little bit more complex, it is this construction, okay? It is what we call binary construction A. So, how does it work? So, in general, binary construction A is this kind of construction, okay? You take, in fact, a binary code of lengths, a binary linear code, sorry, of lengths n and dimension k, all right? So, and in fact, you consider one coset as being any even valued vector, n dimensional vector, right? So, it is to Zn. And you add to all these points one given code word from coming from this binary code. So, it is only one zeros. The values of this code words are just, the components are just ones and zeros, okay? And then you make the union over the entire code C of all these cosets, all right? And you obtain a new lattice, lambda. If C is linear, then it's very easy to prove that this union of cosets is a lattice, okay? So, now, let's go on. We know that two Z as theta series, theta three of four tau, why? Because theta three of tau is the theta series of Z and the two Z is just a scaled version of Z. And so we know by the second rule that the theta series of two Z is theta three of four tau, okay? Now, two Z plus one, because we will have something like two Z plus one coming from one component here, if you have one component of C which equals one, then of course the component of this, this component of this vector will be of the form two Z plus one, okay? So, two Z plus one is just two times Z plus one half. And of course, theta series of Z plus one half is theta two, okay? And theta series of two times Z plus one half is theta two of four tau, okay? So, now, by using the first rule, we know that two Z n as theta series, theta three of four tau to the power n. And finally, the coset two Z n plus C will have this theta series, which is the product of theta two to the power, the Hamming weight of C because the Hamming weight of C is the number of ones in the code word C and that's why in this case it will be, so theta two corresponds to a value of the component equals to one and theta series correspond to a value of the component equals to zero. So, you will have theta two to the power of wh of C, so the Hamming weight of C, times theta three to the power, the number of zero of the code word which is n minus the Hamming weight of C, okay? And so, to obtain the theta series of lambda, it's a union of all these cosets, so just add all these terms and we will obtain so the Hamming weight and emulator of the code, okay? So, the Hamming weight and emulator of binary code is just, it's a, sorry, it's a two variable polynomial and the power that you can find on X will be the number of zeros of a code word, of a given code word and the power of Y is the number of ones, so the Hamming weight of a given code word. So, just replace X by theta three of four tau and one by theta two of four tau and you obtain the theta series of the lattice lambda that we got by using this construction A, okay? So, let's go back to our example E eight, this famous lattice, okay? So, I recall you everything concerning theta three, theta two, okay? And so, this construction A, so now, of course, we get that by using the third rule, we get that the theta series of lambda is just the sum of all cosets, so two Z eight plus X of the theta series of this coset. This is, now, it is something that we saw on the former slide, okay? And we know that to construct, in fact, to construct E eight, we need this code which is the extended Hamming code of lengths eight and dimension four and the Hamming weight in the numerator of this code is this one, which means that we have a code word of weight zero coming from X to the power eight, so it is the zero code word, the whole zero code word. The code word of weight eight, which is the whole one code word, and finally, 14 code words of weight four, okay? And so, just replace X and Y by theta three or four tau and theta two or four tau, respectively, and you get these theta series and these are the first terms in the Q series enumeration, okay? The Q series development, sorry. And so, and it's possible to generalize it to a very large family of lattices, so we can compute efficiently theta series of lattices in most interesting cases, okay? In fact, this lattice is not exactly E eight, but it is a scaled version of E eight. It is square root of two E eight. And so, to have the theta series of E eight, just divide by two all exponents here and you will obtain so this theta series, all right? So, we have now, I mean, by using this trick, let's say, we have now a very nice way of computing theta series of, when for example, our lattice is obtained by using construction A, binary construction A. Of course, there are many, many other constructions and especially when the dimension of lattice increases, then binary of construction A is no more enough and in this case, we need to consider some other kinds of construction, but for which we have the same types of tools. So, I will not go, of course, deep into this direction because it's something which is very long to consider. Okay, another way of getting the theta series of E eight is in fact, in fact, what we have is that we can use, in fact, the theory of modular forms because the theta series of E eight is a very specific modular form and it is what we call, in fact, a modular form for the full modular group, SL two of these, so the group of matrices of two by two matrices, integer value matrices with determinant equals one, and so what we know is that the theta series of E eight is just the Eisenstein series E four and which is given in this way where sigma three of M is the sum of the cubes of the divisors of M and so we have another way of computing the theta series of E eight, okay? And we can check that we have exactly the same coefficients here for Q two, Q four, Q six exactly, et cetera, sorry. Yeah, okay, so now let's leave the constructions and the computations of theta series and let's go to the applications of these, okay? So let's start by maybe the application which is, which really needs a lot these theta series developments. It is to start with the Gaussian white hat channel. So suppose that you have Alice here which wants to transmit to Bob through a Gaussian channel, so a channel with additive Gaussian noise and we suppose that the variance of the noise here is N zero and there is an eavesdropper if, which has, which can eavesdrop the message I mean, let's say the signal transmitted by Alice and through another Gaussian channel with variance N one, then we know that by, I mean, information theory says that the secrecy capacity, that means the amount of information that Alice can transmit reliably, transmit to Bob, so that Eve, in fact, will have, I mean, no idea of what would be this information is in fact this difference between the capacities of the channel between Alice and Bob and the channel between Alice and Eve and of course this capacity, secrecy capacity will be non-zero if N zero is smaller than N one, okay? So if we have a channel advantage, if Bob has a channel advantage, compared to Eve and we know that by using lattice coset coding then this capacity can be achieved up to some gaps to some small gap of one half bit but I guess that this small gap is just a technical gap coming from some upper bound which is not very tight. Okay, so what is lattice coset coding? So let's say that we have, suppose that we have a lattice lambda b which is good for coding. This lattice maybe can be shifted that means just translated by some given constant vector. And we have a sub lattice of lambda b which is lambda e which is good for secrecy. We'll see what it means, good for secrecy. And in fact as you can see, then this is b and e means that lambda b will be the lattice for Bob, let's say and lambda e the lattice for Eve. So this is the confusing lattice, lambda e and lambda b is the good lattice for Bob, okay? Here is an example to dimension, okay? So we have, so all these points are lattice points from lambda b from what we call also the fine lattice. And for the sub lattice in fact we have, in fact what we have is not exactly a sub lattice of lambda b but a sub lattice of lambda b shifted. So either you consider that lambda b is shifted or lambda e is shifted but one of the two lattices here are shifted and the sub lattice is two z two while the lattice is z two, okay? So that means that if we quotient lambda b by lambda e we get quotient group with four elements because this is the index of lambda e related to lambda b and these four elements are just these ones that means star, circle, triangle and square, okay? So for example these squares are, these big squares are volumetric regions of lambda e and that means that in this case, you know, you can represent one given point of lambda b in this way we say that it is one point of lambda e and in this case it is just, we have just to say that it is one of those squares, right? Plus one point of lambda b over lambda e that means now we have to specify inside one of these squares if we have a star, a circle, a triangle or a square, okay? And in fact, the idea is to encode the data inside this quotient group, okay? So if we have, for example, we have here two bits that we want to encode and so if we want, sorry, for example, zero, zero will be encoded into a star, zero one into a circle, one zero into a triangle and one one into a small square, all right? So, and now what Eve can see? Eve will see some, I mean what has been transmitted plus some noise, but the problem is that because the data have been encoded inside this quotient group, all right? Then the problem is that what Eve will see if she's interested, of course, in decoding the data will be not the Gaussian noise, but let's say some folded Gaussian noise so with PDF, a sum of Gaussian measures and in fact what happens is that if the variance of the initial noise is not too big, then she can still know which point, I mean she can still decode in some way, but if the variance then becomes too big, then what she will see will be something almost flat and because it's almost flat, it means that she will have no way to decode, in fact, the information encoded in this quotient group, all right? And it can be illustrated in this way. For example, suppose that Eve, sorry, that Alice sense this point and suppose that all these points, yes, which are surrounded by pink areas, correspond to the same coset, all right? It means that all these points correspond to the same information, secret information, all right? And so now what we want to do is that because Eve sees a variable distributed as a sum of Gaussian measures and we want that Eve, I mean, that information leakage that comes to Eve is as close to zero as possible, then it means that Eve has to see something, I mean this kind of distribution that has to be as close as possible to the uniform law, okay? So it means that we have to define a distance between this distribution and the uniform distribution, yes? And it is what has been done. So here we have this sum of Gaussian measures, F lambda E, so it is related to the lattice lambda E and sigma and define what we call the flatness factor of lambda E, which is in fact, sorry, the infinite distance between this F of lambda E sigma of X and something uniform on the volumetric region of lambda E, so it means that it has pdf equals to one of the volume of lambda E. So the volume is just the determinant of, sorry, the absolute value of the determinant of the generator matrix, so which is also the volume of the Voronoi region of the lattice. And then it can be proved that this infinite distance is just, can be just computed in this way, so it is related to the theta series of lambda E, all right? So it's very important now to know the theta series of lambda E because if you want to have an information leakage coming to EVE, which is as close as possible to zero, then we need to minimize this theta series among all lattices, we need to minimize it, okay? And so now we can show that the mutual information between the message transmitted by EVE, sorry, Alice, and what EVE sees can be up about by this value, which is in fact, an increasing function of epsilon lambda E, which is in fact, this flatness factor, yes, and so we have seen, we have shown that if this volume to noise ratio, so this gamma is larger than one, then there exists a family of lattices, lambda E, index, sorry, index by the dimension n such that this epsilon goes to zero when n goes to infinity, and this is in that way, this was the first step to prove that we had a family of lattices that could achieve the secrecy capacity and in the white-type Gaussian channel, okay? It is just something, it is very important to have the full, really the full theta series of the lattice and not only some terms, why? Look at this lattice, gamma 72, it's a 72-dimensional lattice, discovered recently. This lattice, in fact, is very special. It's the densest we know in dimension 72, and this is, it's a theta series, at least the first terms, so you see the number of points of Euclidean norm 8, of Euclidean weight 8 is very big and then of course these numbers increase a lot when the weights, we want to consider are bigger and bigger. So this is the flatness factor when you compute the rule theta series, okay? And of course when the SNR or the generalized SNR goes, I mean, becomes small, then this flatness factor goes to zero and quite quickly in this case because we have dimension 72, all right? And it is normal, it means that the, I mean, the distance between our distribution, the distribution seen by Eve and the uniform one goes to zero, okay? And this is the same flatness factor but computed by using just terms up toward the 20 and as you can see, then it has no meaning because the flatness factor is distance, so it can be negative, of course. So that's why it's very important to be able to compute the whole theta series and not only the first times, okay? Another example of the use of theta series just consider regular coding, lattice coding on a narrative white Gaussian nose channel. In this case, the error probability, yes, can be up about in this way, so still again we have the theta series of the lattice that comes to us again, okay? Another, let's say, application of theta series is what we call probabilistic shaping, okay? What we have even in a regular communication problem, what we have is that we can transmit a finite subset of a lattice and in general what we do is that we use the finite subset of a lattice with small Euclidean norm, that means with small energy or small power, right? And so there is another way of doing that. It is to use the full lattice but to weight each point of the lattice by this probability, okay? So it means that it is just a Maxwell-Boltzmann PDF, I mean for these lattice points. So it's just or discrete Gaussian probability, all right? So the problem is now what can we, how, sorry, can we define the power and the rate of such a signal set because these are the two most important things we have to know, parameters we have to know in order to transmit. So the power by dimension is just given by this. So it is the sum over all points of the lattice. In fact, the Euclidean norm, the square Euclidean norm of the point times its probability, which is given by this weight. And in fact, we can prove that it is just equal to the logarithmic derivative of the theta series of the lattice lambda. So it evaluated at point tau equals i divided by two pi sigma square, okay? So it is, so we have a very direct relation between the power of this constellation we are using and the theta series of the lattice. Now the rate, so how to define the rate of such a constellation, so just the entropy, all right? So of course we normalize by the dimension to have the rate per dimension. And so it is this, it's a definition of course and we can show in the same way that it is given by P over two sigma squares, so this P, plus one over N times the log of the theta series, okay? So still again we have a very, I mean, we have a very direct characterization of power and rate in this case if we want to use probabilistic shaping by using the theta series of the lattice. So it's a very, very important tool, even in this case. Okay, so there are many, many other ways of using theta series, but of course I will stop for the first part here, okay? And now let's go to the second part. So as I told you I will not unveil too many things for this second part, it is related to waveform design. And in this case we can show also that lattice theta series can be very important, but in this case we will be, I mean we will have to use the two variable, theta series is not the one variable as it was the case for analysis, okay? So first of all I just remind you some general points concerning communication of a nonlinear integrable channel, okay? And the one we have to consider in Huawei and in many companies, telecommunication companies is the nonlinear optical channel. Maybe in some years we have to consider some other more fancy channels, but for now it is the only one of interest for us. And so as you can see, this is, for example, what has been done up to now, so these are quite old results. The newest one comes from 2012, but they are some better, I mean some better results now of course, but okay. So this is optical communication, so we have the SNR here and we have the spectral efficiency we can achieve here. So this is the so-called channel limits which is the log of one plus SNR, let's say. If we were in a linear channel, right? But it's not the case. We are in a nonlinear channel and in this case, so if you consider the nonlinearities as, I mean the result of these nonlinearities just as noise, so this is what you have. So you will have a maximum here for the rate and then the nonlinearities will become too important and then it will be a mess and of course nothing will work correctly. So in the single mode fiber, light propagation is governed by this nonlinear Schrodinger equation. So it's an approximation, but it's a good, very good approximation for what we have to do. And so the commercial communication systems up to now operate in the quasi-linear regime and they consider the nonlinear effects as noise. It is just what I told you. But there is another way to solve this paradigm. It is in fact, so something that has been proposed very recently to consider nonlinear free transform in order to, not only to solve the nonlinear equation and in this case, the equation has to be integrable which is the case for the nonlinear Schrodinger equation. So I will not go into details for this integrable equation setting because I don't know too much about it, Nira. So that's, and so, but so in this case, if we use the nonlinear free transform, we will be able not only to solve this nonlinear equation but also we'll be able to design some communication system in the same way as it has been done for many years in wireless communications by using OFDM, all right? So we'll have a kind of nonlinear OFDM system, all right? So why? Because in the nonlinear free spectrum, what happens is that we have a nonlinear, sorry, we have a superposition principle. That means that we can add components which is not the case in the time domain, of course. And because the equation is nonlinear, okay? So just what we can do is just use the nonlinear free transform, superpose all signals we want to transmit and then go back to the time domain, okay? So this is an example of a nonlinear free transform for rectangular pulse. So we have two components for the nonlinear free transform. We have the continuous part, which is more or less equivalent to what we have by using the linear free transform. And which is, and it is continuous. That means that it can be defined on all real frequencies. And then we have a discrete part that corresponds to soliton solutions. And this discrete part appears when the nonlinear regime becomes, let's say, important, okay? For example, here we have, so the rectangular pulse and capital A is the amplitude of the rectangular pulse. And so if A, capital A is not too big, then we have the famous sync function in the continuous part because it's, if A is small, that is almost the regular free transform. And we have nothing in the discrete spectrum. Now, if A becomes bigger, then we have, of course, something here in the continuous spectrum, which becomes different from the sync function, yeah? And we have a component that appears in the discrete spectrum part, okay? Then if A becomes even bigger, then as you can see, even this peak almost disappears, the central peak. And then we have two components in the discrete spectrum which becomes bigger, et cetera, et cetera, okay? So, all right. So what we have behind the nonlinear free transform? So, first of all, the nonlinear free transform depends on the nonlinear equation. If we change the nonlinear equation, we have to change the nonlinear free transform. It's not the same one, okay? Then, as I told you, the nonlinear free transform, so the nonlinear spectrum contains a continuous part and the discrete part, okay? The nonlinear free transform diagonalize the nonlinear channel, okay? In which way, in fact, we can, by using the nonlinear free transform, we can write, in fact, the channel becomes diagonal in the same sense as when you consider OFDM in a linear channel, okay? Exactly in the same sense. But maybe, in this case, the channel gains, instead of being scalar, can be matrices. So, it's a little bit different, but it's the same kind of phenomenon that appears. So, we have a superposition principle, the nonlinear free domain. We can add the components, which is not the case, of course, in the time domain. And it has been extensively investigated in the context of water waves because we can get the same equation, okay? So, we have some waves, some ocean waves that, in fact, are governed by exactly the same equation as the propagation of light inside the fiber, which is the nonlinear Schrodinger equation. Just exchange the space and time component and you have exactly the same kind of equation, okay? Now, if, okay, I will not tend to detail this here, but if you consider, because in order to construct these solutions based on nonlinear free transform, we had to consider some boundaries, which were, in fact, the boundaries, the minus and plus infinity boundaries. But now, if you want to consider something which is, let's say, easier to implement, I mean, which is implementable, it's better to consider something equivalent to Fourier series instead of Fourier transform because everything is done digitally in our area, of course. And in this case, we have some thing equivalent here which are these generalized Fourier series and what are these generalized Fourier series? These are, in fact, the Riemann theta functions. So, still again, theta functions appearing, okay? So, just to finish, it's very short now. So, Riemann theta functions as waveforms. So, not only to analyze, but just signals to transmit. Okay, so these Riemann theta functions, so any finite bound solution, that means that, okay, in this case of, if you consider these, let's say, generalized Fourier series, then we only have a discrete spectrum components and it means that if we consider, I mean, finite bound solution is just equivalent to finite bandwidths, okay? So, they can be given in terms of Riemann theta functions which are these series, okay? So, we have gamma, which is a symmetric matrix with positive definite imaginary part so that this series can converge and then A is a vector in ZD, all right? And as you can see, if, in our case, if we choose gamma, okay, remove the real part of gamma, so suppose that the real part is zero. So, just consider that we have an imaginary part which is positive, definite, and then just, okay, if you consider only these ones and in this case, this gamma, because it is symmetric, is defined, it defines in fact, the gram matrix of a given lattice. Gram matrix, for those who don't know, is just, let's say, the product of the transpose of the generator matrix by the generator matrix itself, okay? So, this is the gram matrix of the lattice. And so, in this case, we can express this Riemann theta series as the two variable theta series of a given lattice, okay? And in this case, we know that the solution is given in this way. So, you have, so here it is the, so the Riemann theta function related to some gamma matrix here of this variable. So, theta minus and theta plus are just some shift vectors that depends on many things related to the propagation, et cetera, so I will not even go into details here as well, so just, it's just up to some easy term. It is just the ratio between the, let's say, if we can use some lattice here by using this trick, it's just the ratio between the two variable theta series of shifted lattice and the same lattice shifted in another way here, okay? So, still under exploration, let's say, and I will stop here, okay? Let's go to some conclusion. So, as we have seen the theta series, I mean theta series or theta functions, they are a powerful tool for analysis of lattice coding, all right? We know many results about theta series of unimodular lattices, so I didn't introduce you, what are unimodular lattices or n-modular lattices, but you have to know that these lattices are the, I mean, among the best ones, so they are the lattices of interest for us, and even when the dimension becomes very high, then we know many things about these theta series, especially we know some concentration results about theta series, so some, we know that lattices in the same genius, so it's a little bit long to define, but we have exactly the same way in terms of theta series when the dimension becomes high enough, okay? And it may provide an elegant solution to the problem of communication on the nonlinear channel, and I will stop here, my talk, my presentation. Thank you. So, are there questions concerning the talk? Very nice talk first. So, first question. So, you already did two expressions for the probability of error in the given dimension, can one reduce error of exponents in a lagal again for, from this type of presentation? Yes, there is a paper about it from Portiref in the 80s. Yes, he derived also exponents, yes. For, in general, for infinite, first for, let's say, infinite constellations in general, and then specialized to lattices, to lattices, yeah. And so, a second question is, so once you get your lattice, I mean, you can randomize the, in the alien space, you can randomize this recognition so as to make the thing as a stationary point process. Can this be leveraged to compute, to compute some of the characteristics, like mean number of points in the volume, or things like that, or variations on, yes, I know that there are some works about random lattices, but I don't know too much about it. It's, but yes, I know there are results about random lattices, yes. So, I thought that the most important thing about lattices is that it was structured, you don't want to randomize. For what we have to do, yes. You're right, yeah. Nobody, yeah, yeah, yeah. But yes, I mean, you stay inside the lattice, yeah, yeah. I mean, it's, in fact, when I say random lattice, it's the choice of the lattice, which is random. It's, maybe it's not exactly what you mean, yeah, okay. So, for your question, I don't know, I don't know. Other questions? So, I have two questions. One is related to, I would say, the engineering of the lattices. So, I mean, you get these numbers, which are 0.98, no, no, no, no, no. It turns out that when you implement things on a chip, you have resolution of 12 bits, basically. So, you'll get never those numbers. I mean, the question is how robust if we decide typically to implement lattices with the 8-bit resolution, yeah. How robust is finding such a nice number, but at the end, we just have 8 bits to implement it. Yes, it's the same problem as when you implement big constellations as, for example, 256 or more QM constellations, you have exactly the same problem, because in fact, QM is just a finite part of the Z2 lattice. And so, then when you have, of course, you can lose, but then it's, I mean, when you increase the size, and you have lattice implementation in new generation efforts, it means also that the resolutions, and the ADC resolution of the implementation should go higher and higher. Yes, but as I said, it's exactly the same problem with QM, exactly. I mean, the fact that you use lattice doesn't impact more than just regular QM constellation. You have exactly the same, because in fact, the lattices that we construct for a communication purpose, these lattices can be built from these Z2, I mean, these QM constellations. So, basically, let's say the problem of precision coming from these ADC, et cetera, will give you exactly the same impact if you use lattice codes, or if you use just QM plus bit interleaved correlation, which is the solution that is implemented right now. And the second question is about the application, so you showed the application in the optical, which is nonlinear. A lot of people are working on, I would say, molecular nanotechnologies to use molecules as a means to communicate, where you have diffusion, stuff like that. Do you think these techniques can be also used in this molecular nanotechnologies? The only thing you have to check is that the equation governing this diffusion, when you are in the nonlinear regime, of course, is integrable. If it is the case, then you can use, I mean, the same kind of tool, but you have to find first, I mean, you have to find many things. What is the Fourier transform in this case, et cetera. There is a lot of work to do, but maybe, I don't know. In general, if you want to be very precise on your model, then the equation is no more integrable. But I guess that there is always some integrable equation not too far away from the system you want to consider if you are in some nonlinear medium. There's a third thing I didn't ask, and I'll finish by that, and you have also a question. Yeah, then I'll just ask, and then I'll go. You didn't talk about the decoding aspects. Yes. No time to do that. Ha ha ha! Ha ha ha! Ha ha ha! The question is, of course, the big difficulty, except when you take off LDPC codes, but the difficulty is still, but the biggest difficulty when you code is the decoding part, where the complexity is crazy. So can you give us some hints on how difficult or the processing and the decoding end is? In fact, it's, let's say, recently a lot of progress. I mean, let's say that before, maybe a couple of years ago, we knew how to construct some low dimensional or medium dimensional lattices, and the decoding was really painful, because it was a problem. But recently, I mean, thanks to some high dimensional lattices or even medium dimensional lattices constructed by using what is called construction D. So it's a multi-level construction. We know that by just using multi-stage decoding, so the code for the first level, then remove the component coming from this, then go to the other one, et cetera. And in fact, it can be proved that you can achieve the capacity of the Gaussian channel by doing that. And I mean, even in practice, it works very well. And the complexity of decoding in this case is very reasonable. It's no more than the one you have by using, for example, this bit into lift combination. I mean, it's the same order, yeah. Okay, I think you only had a question. Yeah, generally when we use a data function, it's always because we are related to a modular phone or a tomography folder. And so we don't see if it's important for you or what you aim. So I would like to just, I'd like to know, and even for constructing a new object, the fact that there are tomographic forms where you can come to damage them, a set of tomographic forms can produce new objects. And there is a very theoretical part that can help to have new objects. And there are a lot of recent developments that we can say for integrable matrices. Yes. Okay, yes, we would be very happy to have some help from this point of view because this, I mean, first of all, I just know how to use on a software modular form, that's it. I'm not really a tomographic form, I mean. And so, but I think we could have some collaboration on that because we have some need, which I'm not fulfilled to know. And especially we can have also, I mean, for some other problems, for example, for MIMO communication, or probably, I mean, we need to understand, I mean, we need to understand the behavior of some coding we're using, coding skip, sorry, we are using. And in this case, some, for us, fancy objects appear that we cannot analyze. So for example, instead of having, let's say, a Xilaris, we can have, for example, in the MIMO case, we can have lattices defined on some non-commutative order. And in this case, instead of having this, just the, let's say the Euclidean weight, we have to consider some determinant. I mean, I don't remember exactly the expression, but the sum of determinants or to the power something I don't remember exactly. And I guess it probably, it should be related to some automorphic form, but I have no idea. So it's an object, I don't know how to manipulate it. So, yeah, maybe we could, sure. Yeah, other questions? I think we got everything, let's thank the speaker. Thank you.


Thank you. I'll try to be brief. One the first question is to the question about India. The ethnic fragmentation of India was mentioned and I can quite understand that it's a convenient way to handle this kind of research but it seems to me on the other hand that it also perpetuates the fragmentation of Indian society because of this approach connected with that however ethnic fragmentation in India might be a blessing in disguise because if the Hindus were all united then the other minorities in India would suffer a great deal such as the Christians and the Muslims and so on so perhaps it's a God's blessing that you know fragmentation in India actually does exist which by the way will perpetuate it also by the British colonial power. Then I come to Guatemala and that is that what will be the consequence of this research on the future prospects for the indigenous people of Guatemala and also for the indigenous people in other parts of Latin America because the genocide has already more or less finished but the discrimination still goes on against the Amerindian population in practically all the Latin American countries. Secondly what is the reason for the discrimination against indigenous people in Guatemala and Latin America. Thank you. So I'm gonna collect a few more questions but please try to rapid-fire questions here. Miguel. Okay just very briefly I just want to raise two points in relation to what Francis was saying and in relation to the last presentation especially in the in the sense of the selection of your sample so I was quite surprised and concerned about the selection simply because the the characteristics of your students seems to me that don't really don't represent the distribution of preferences and views. So you most likely have lower bounds as a means of actually the views and perceptions of women in Pakistan but your response about how to deal that was really surprising to me the language. So I really encourage you to to do something about it. Thanks. This is Joe Barthi on the question on India and also related to what Francis was saying because your unit of analysis is at the district but we know that the publichood provision is tied to the constituency levels because and that's where the reservation and all those things happens like either the MLA or the MP members of parliament or members of legislative assembly constituencies. So if you move from a district level to a constituency level measure maybe things would change because reservation policies are all implemented at that level and which might be which might also give us some results on political influence in the publichood provision. Thanks. One more question here in the front. So also trying to be very very quickly and again on the same study on India. So one of the things that I know this is picking up on something that Francis said is how much of the saliency of the boundaries is actually what's causing this relation to fractionalization and lack of access of unequal access to the public services. And just to also reinforce something that you suggested and I think it would be a very good idea intersecting economic classes let's go back that quantiles in income with those identities and see whether that affects access to those services. So I'll ask a final question just picking up on Ricardo's last question. So I was also wondering about intersecting identities and if any of you have looked at that I know several of you have but if there's anything you want to comment on intersections between different types of identities in the work. So we are at time but I want to give each of you one minute to answer your favorite question. And then please continue the conversation over the break. Carla why don't you start. Thanks for the questions very quickly. So the reasons for our discriminations to indigenous people in Latin America they started at the colonial period right so they have been quite persistent mostly economic reasons. So during colonial period they were basically slaves in Latin America until the 50s or 70s indigenous peoples were sold with the land right that they were working on. We have the commodities of coffee plantations cacao plantations banana plantations indigenous people are chip hand labor. So it has been like that since colonial time until today they mostly work in agricultural sector and the consequence of the research for the indigenous population in Latin America in general is that you see is the point we wanted to make is we treat them as one homogeneous group and that's not the case. So if we are having a when pollution education for instance the fact that in the average we see that there are no difference anymore between the indigenous populations and the non-indigenous when it doesn't mean it's true for all the others. It's the same for the labor market right. Somehow we need to know why certain groups are falling behind compared with the others. So I'll answer the first question which asked about fragmentation can does not necessarily have to be a bad thing especially for the case of India. So there is some work which suggests that this negative impact of fragmentation is much less if there are cross-cutting identities. If the identity of caste cuts across the other identity of maybe language or maybe religion. So in the case of India for example Prayena Singh has found out that in Kerala where the identity of caste cuts with the identity of language this negative impact does not exist then. However in India in other states caste as an identity still remains important and does not cut across other identities in fact it is the other way around. The caste has very significant overlap with economic attainment of economic outcomes. So because of these overlapping identities between class and caste, caste again has a very important influence on provision of public goods and other economic outcomes. Second question regarding public goods provision we're not trying to explain variation in public goods provisions so that is not our concern we're just saying if public goods are there their impact they will help in reducing inequality that was our concern. Thirdly regarding the salience of boundaries we do find overlapping identities we do find an overlap between caste and class using a measure of cross-cuttingness and then in other paper we find that this because of this a disadvantaged groups particular scheduled tribes have participated because of their disadvantage have participated in Maoist insurgency in armed rebellious movements to address their grievances. So yes this cross-cutting identities have impact as extreme as participation in armed rebellious movements. So on the intersecting identities part so our context was very homogenous in terms of ethnicity but what we are trying to do is look across the 23 countries and that in that meningitis belt to see if the effect is generalizable and one of the things that comes up is that a lot of them you know you look at the anthropological data on on bride price practices much of that's what of the region does practice bride price. So there could be differences in the intensity there's definitely differences in the kind of amounts that are paid based on the education of the woman and the region of the country so maybe less in urban educated areas bride prices less of an issue in urban education areas and in poorer rural areas. So one of the things that that becomes a concern for us is trying to understand kind of differences by wealth and and basically trying to understand how poorer households basically view daughters as these tradable assets right which is a which is a big problem so if you view your daughters I say selling daughters which is the I'm an economist but anyway it's it's that's what the most direct way to describe really what's happening but if you view your daughter as a tradable asset what does that do as a what does that mean as a coping mechanism especially you know I mentioned that we've done some work on trying to understand how climate change will affect disease going forward basically the consensus is that it will worsen these epidemics in the future so so what does that mean in terms of already poor or inequality by wealth and already poor households that already view their daughters as this kind of because of cultural practices as these tradable assets for bright price so these are the kind of things that we are trying to think about in terms of intersecting issues and and identities. Yes on sample selection so languages it's it's much more difficult than you'd imagine we have a very sort of segregated system of education I went to a convent school because of my family background English is the only language I speak properly effectively I you know I can't communicate in I can communicate but you know not very in a very sophisticated manner and that is the problem with with so if I if you go to lumps most people will speak perfect English they'll have immense trouble with with Urdu which is the national language if you go to Punjab University most people will speak beautiful Urdu but they would have a lot of trouble with with English the problem then becomes that the measure of sexism is not really coming from economics it's coming from social psychology and we are not psychologists who we are worried about how the language of the statement is going to to you know so how do we actually translate so we need a translator that that is fluent both understands the context in which the statement was made in the sexism measure and then can translate it in Urdu and we really haven't been able to find some but it's certainly at the back of our mind we do realize the problem professors to which is already raised the issue of internal consist external consistency which is here is you know a little sample from an elite university in a little bubble can you really extrapolate to the population and and we really can't and it's just that we've actually tried several times to run experiments in other universities and it's been remarkably difficult and we can talk about that over the break intersectionality yeah that's the next


Hi, everyone. Welcome back to the Inclusive Theatre Festival 2023. I am so excited to be starting the event with our third presenter for the day. Just let everyone in. So we had two amazing presentations this morning from Simone Brasini and from Mooma Holt. And this next presenter is someone I'm very excited about. CSUN Theatre has been pursuing this group for a long time and I'm so glad we finally got to bring them to ITF. Our next presenter is Sinsen Valid. Sinsen Valid is a disability justice based performance project that incubates and celebrates artists with disabilities, centralizing artists of color and LGBTQ gender variant artists as communities who have been historically marginalized. Led by disabled people of color, Sinsen Valid's performance work explores the themes of sexuality, embodiment and the disabled body. Developing provocative work where paradigms of normal and sexy are challenged, offering instead a vision of beauty and sexuality inclusive of all bodies and communities. Maria Palacios is a performer with Sinsen Valid as well as the Spanish language community's outreach specialist. Also known as the Goddess on Wheels, Maria is a poet, author, spoken word performer and a workshop facilitator. Nomi Lam is a creative director of Sinsen Valid. They are a musician, illustrator, creative coach and Koheneth Hebrew Priestess who creates earth based Jewish ritual tools including the Omer or Oracle deck and the Dreaming the World to Come planner. We are so excited to have you here with us, Nomi and Maria and please take it away. Thanks Ashna. Thank you so much. Maria, do you want to introduce yourself. Sure, I'm sorry I was like. I thought you would go first hello hello hello everybody we are super thrilled to be here. We were so excited when you invited us because we love it when people love us so. Yay. Again, my name is Maria Palacios, I am a pronounce or she her.  And I, I am currently existing in Houston, Texas, also known as the Acoquiza land of the Acoquiza peoples with Sinsen Valid like you already heard I am spoken word artists and I've been performing with Sinsen for sins since 2007. So I feel like I'm, you know, yeah I've been doing this for a while with sins and valid so super excited. Currently as a staff. I serve as the bilingual Spanish speaking community I reached coordinator. And recently we've committed to language justice by offering our material performances and everything else not only in English and ASL but also in Spanish so we're super pumped up I'm going to pass it to Nomi so she can introduce herself. Thanks so much Maria. I'm Nomi lamb. I use she and they pronouns and I live in Olympia Washington, which is squawks and land. Because there are a lot of peoples around here the Nisqually, the Shehalis, the Puyallup and other medicine Creek Treaty tribes. And yeah, I'm a I'm a musician and performance artists and also do like illustration and other things like that I'm the creative director of sins and valid I've been working with sins. And I think I came in the year after you Maria so I'm like 2008 was my first since a valid show. And yeah, I think that's that's what I have to say oh visual description. I'm wearing a black dress.  And yeah, so you already heard sins and valid submission statement, just to reiterate were a disability justice based performance project and movement or movement building organization that centers black indigenous and people of color queer trans and non binary people with disabilities. And we've been around since 2006 we the first show was basically an idea of our founders Patty burn and Lee Roy Moore and people wanted wanted more. It was a show about disability and sexuality and people were like, Okay, what when do I get to be in the next one and so now it's however many years later 1516 years later. 1717 years. Wow. It's November. Yeah. Oh, wow. Cool. Yeah, amazing. So Maria is going to share more about why sins exists. Yeah, so this is kind of like unreal almost unreal to when you start thinking about it you know when you have lived through the evolutionary process of a movement and when you get to be as old as I am I'm 57 right now turn 58 in January. So it's kind of like you're able to, to look back and realize you know how much things have changed. So, since invalid exists, I think in part because of that evolution that that social evolution that justice evolution the recognition that despite the movement you know because the disability rights movement started, you know, earlier. And despite the movement we, we recognize that there were communities that have been marginalized and have been left out of this movement you know, and it just kind of like boggles my mind for me personally being who I am an activist somebody who was there because I'm one of those disability people from back then, I'm one of the capital crawlers, you know the help us the ADA, you know, so I was there I know that brown people were part of the movement I know that we are there in the trenches we had been there working, giving and forming and doing the work kind of like behind the scenes you know while being left out of every movement.  So, when, by the time that since invalid started in 2006, the birth of disability justice had already sprouted in conversation in communities of color and queer communities of color. Since invalid exists because because it's absolutely necessary to have a space like this because until since invalid. I think in the arts in the world of performance in the world of of movement building. Again, I like to remind people we were left out. You know, so when since invalid happened what I love about it is like. How something as big as what we have become started as something so small like a tiny seed you know, and when Patty burn and Leroy more got together and made sense and valid happen. And the reason that they even like realized it right away how big, you know the importance of significance of of of how we were going to evolve and it's the same way. When I was 23 years old, doing activism to pass the ADA back then I did not realize how important those moments were to me you know it's kind of like when you're doing the work when you're putting your body in the line when it's your advocacy, you don't you're just doing the work you know you're not stopping to think wow well I wonder what someday I'm going to become historic you know. But it just happened and I think the sense and valid. It gave a platform for expressing disabled arts, you know because that's how we started we started as disabled arts we started as performance art as you know we weren't we did not immediately come in and saying oh we are disability justice on theater.  It was just meant to be it was going to happen either way you know, I think that everyone have not been since invalid. The movement would have happened anyway because you know, when a body gets pregnant. Eventually the baby is born, no matter what you know so the movement happened and then just kick a birth to what is now known as since invalid. So, yeah, do you think I covered it pretty well know me or do you know add something to that part. No, that's great I just want to say not all pregnancies come to term, but, but I get your point what you're saying. Yeah, so we wanted to share some about what we've been working on in the past few years and make some time for questions and we have some videos of different performances to show folks. And the first one that I want to share with you all is. It's an example it's something that I edited together from the last big stage performance that we did which will, I think we'll share more about that after we watch the clip but the clip is kind of to highlight different ways that we bring access into our work so maybe like. Try to notice how many different types of access you see in this video and also know that this is edited together from many different versions so people wouldn't necessarily be watching. Something that has like every access accommodation in in one video if that makes sense I think you'll you'll see what I mean when I share it so just give me a sec to get that set up. We love like barnacles, Crip lives and climate chaos. Lights up on a scary white dominatrix supervillain wearing a black leather corset and headdress made of red inhalers. I am Mistress Asma and I want to scare you make you think you're dying maybe you will. What kind of attack are you hoping for my sweet? The kind that will land you in the emergency room at a moment's notice? Or does the slow terror of breathlessness building to a sharp crescendo of parric turn you on? We clutch clumps of the land between our fingers and toes as if we can squeeze the blueprints and toxins from every speck. He uses his right hand to push buttons to play the next line. As the blazes erupt in the hills who will come and get me? Another black man, Sean enters the stage. He has mid-length locks and wears a black version of the same outfit as Latif. He extends his arm palm up as if asking a question and Latif moves his arms in consent. Sean begins to remove the adaptive talker and other equipment from Latif's tray. He sets them on the floor next to the wheelchair. He removes the tray from Latif's chair as Latif guides the process. Sean unbuckles Latif. Latif extends his feet reaching for the ground. Sean lifts him under his armpits. When my building starts burning will the firefighters listen to me? That I need my AAC device when they are rescuing me from the flames. Sean supports Latif as he takes steps forwards. Will my electronic voice be saved or will it disintegrate in the ash?  The stage is red and the backdrop is purple. He wears a corduroy jacket and no shirt and jeans. He walks forward. He leans forward at the waist, brings his hand up, crossing his mouth, his ear, fluttering out to the side, leaning as if the wind is blowing him. He turns, slowly around, and then jumps, landing back in his original position and backing up. He repeats the sequence.  We are the future. The powers that be choose to not hear us when we say, the land is ours, the planet is hurting, wear a mask, protect the water, black lives matter. Nobody is disposable. And then I turn to my community and they too are selective of which black lives matter to them. They don't think black disabled lives matter. Their ableism allows them to exclude us because they fear becoming us. Y'all may not want to hear this though. We know that we listen with more than our ears. We listen with our entire bodies. We listen with our core. So I'm wondering if folks want to share observations. What did you see in terms of access in this video? What types of access did you see or experience for those who don't see? I mean for me there was just so much going on and it was wonderful to see. I love the visual descriptions before every performance. I thought the sign language that was happening simultaneously so you could look at both together was really cool. I don't know if anybody else wants to bring anything else that I may have missed. That's great. So, ASL and audio description. Yeah, Millie. I was just going to say that even beyond the things that were done, like in giving the performance to an audience built into the performance was this piece of that there was always movement and sound there was always both. So if one was inaccessible, the other can be experienced. And just realizing, I understand I know that there are people that are both deaf and blind but like trying to encapsulate as many senses as possible. So that there can be an experience of something was really cool. Yeah. Thank you. Claudia, do you mind sharing what you were saying in the chat? I'm not sure I understand. Oh, sure. Oh, sorry. That's my hands being bad at typing because that's not what I meant to type. Um, literally it being online. I don't know why it typed so strangely literally being online being a film. That's what that word was supposed to be. It's supposed to be film literally it being a film that we can access together now is just a beautiful piece of the access design. Yeah, thank you. Amanda. I really appreciate it how there was this audio in the background describing it was happening. And it felt very natural. Thank you. I think I'm going to just reiterate what I think I heard you say because there's some background noise, but you are saying that the audio describing what was happening was helpful. And then just Sonia. Yes, thank you. Um, this moved me to tears. This was my first experience having accessible theater. I am going to be 40 next year and I really I'm going to be late to theater in general because of lack of access due to extreme poverty. So this was not only as you know as an indigenous Latino woman but as a disabled person to be able to experience all of those different types of access was amazing. Thank you so much to Sonia and Terry. For me, a major piece of the access here was that it was not just for us and about us it was by us. And I think that being able to see disabled bodies performing is extremely powerful and extremely necessary because it is something that we can do. And I think that we are often treated as audience members only, and that we, you know that a lot of entities make big, big efforts to get us in the audiences but then there's no pathway for us to get on their stages, or to be recognized that we can be artists and we can be just, we should have the right to witness it which of course we should, but we should have the right to make it and we should have the right, we should have pathways cleared for our access to make it. And so just that all of that wrapped up together is creating access because it's showing us that this is something we can do. I've been wanting to act since I was eight years old and I saw one disabled actor before I was 18 years old. And the disabled actors I saw never looked like me they were always skinny white people is the other thing. So, yeah, it's, it's the, it's the fact that we're there and that we're doing it. And I do think that that is creating access. Thank you so much. I really appreciate hearing all your voices. Okay, yes. One more, and then we have lots more to share with you. I work with children kindergarten through fifth grade. I have a group of kids that are on the spectrum, using those the voice devices and such. I have them use them when we're doing little scenes or stuff or they're talking to me. I was totally blown away and moved how it was used and the emotion was clear. It gave me like a new sense of wanting to explore that more with these kids who are going to eventually hopefully one day be able to use those and express their emotion so thank you very much for that. Oh, wow, I'm really moved by what everyone shared. Thank you so much. So something about this performance that you can't necessarily tell from looking is another whole layer of access was that we created this whole performance during lockdown of coven and so this was never on the stage live as one whole performance. We rented theaters in four different states and had people with no more than six people in a space at the same time we were observing strict coven protocol and then had you know patty on zoom directing and filmmakers in each location and then it was edited together and presented online so we got to experience it all kind of together online. And hopefully, you know, we are planning an in person show again that we plan to be a hybrid event but this was a real experiment and how to perform is accessible in this time still you know patty was very attached to being a print and like theater and so I feel like we she had a vision and really did it and I would love to hear Maria do you want to share more about your experience of working on this show. Sure, I echo everything that you've said know me. I think that often blows people's minds to realize and recognize that access is possible that inclusion is not a dirty war that scares people. You know, unfortunately because of ableism and just I always like to say that ableism is at the root of all evil that oppresses disabled people and it's true. You know so even as someone who is part of the show. And who's already used to the practices of inclusion that since invalid, you know, just, you know, we kind of created this. And then for me, it's mind blowing, you know, like, like, viewing the film that you'll just saw. I know me share it with me last night, or Friday night whenever it wasn't. And it just kind of blew me away like the part where, and one big I mean the voice that speaks in Spanish you made me realize holy cow.  I can totally understand and I really appreciate you know everybody's feedback and recognizing and seeing those various types of access because it is possible and we are demonstrating it through to this and you know, know me and when you said yeah we did it all during I almost forgotten that you know that imagine all this different in person as a whole different animal. So it's because a whole different production. But I think, like the level let me our efforts you know the things that we commit to doing for to make sure that we are inclusive demonstrates to the theater world to the performing arts world that it's possible. It's doable.  And did you. I do. One of the things about the show is that you did flamenco dance. Oh my God. You guys. Yeah, yeah, it's. It's not a but anyway, it's not quite available in the world in this moment, but there's actually a documentary about it that I can send you links to but but Maria will you talk about what it was like to do like asynchronous flamenco. Yeah. So the wild thing is that I had, I'm not a dancer by any stretch of the imagination movement is not my forte. Right. I was like I was joking I was telling me the other day that usually with sins is like Patty as director she's so influential that she'll say Maria do you want to dance and I'm like, sure, you know. So the joke that I say is like Patty says jump and I just say how high because Patty has that level of faith in us and recognizes where we are able to do incapable of doing. She'll like put it out there on the table you want to try this so flamenco Patty loves flamenco and we love flamenco it's just gorgeous, but having to learn it through zoom was was difficult you know it was scary for me it was like the challenge for me as a performer for the show was that you had to do a step outside of my comfort zone which my comfort zone is spoken word, you know, it's you know lifting my poetry from the page and giving it life and performing it. But dancing dancing is not my forte you know I don't feel that that movement comes natural to me it comes with a lot of effort it comes with with a lot of second thought intentional you know, action. So yeah, it was like very scary. But it worked out it worked out beautifully the way that we did it was we, the instructor recorded herself sitting down doing the movements, you know, after we had a session and you know the wildest thing is we only had a lot for sessions. Something like for sessions I learned how to dance flamenco online and for freaking sessions. You know, but the most amazing part for me was knowing that that piece of flamenco piece that I was doing was going to be accompanied by know me who was doing percussion on her on her leg know me talk a little bit just about that I know that that we're kind of touring a little bit but this is just so badass. Yeah, well, so we have one of the performers Seema ball is a flamenco singer she lives in Seattle. And so she and a guitarist were in Seattle singing the song, and then Maria was in Houston dancing flamenco from a wheelchair, like using her arms so beautifully and so you know a lot of flamenco is the percussion so we're like okay where do we get the percussion.  And Patty was, I'm like, I'm not a percussionist and, and Seema is like, you know, she's a flamenco singer so she's like it has to be exact like it, you know I was like pretty nervous about it but it was, you know, like Maria says Patty is like you can do it you're going to be amazing just go ahead and do it.  You know, but, but we did it and in the way that that it came together. It's some at moments you even think that we're in person. That's how you know it felt. So usually it's possible. And it's, it makes me think you know what Terry was talking about just never being never having a place. We're seeing examples never like having opportunities to perform.  So, should I show, I was going to show an excerpt from your one of your pieces from that show Maria. I also wanted to share. You can watch our documentary about creating this performance which includes a lot of video clips. It's free on YouTube if you are an institution that wants to show it and contact us because there's another way we would want you to do it for that but just for your own enjoyment. Please feel welcome to watch it on YouTube and it's, there's many different versions so there's an ASL version. There's I believe an ASL with also signed description like visual descriptions. There's an audio described version there's a Spanish version and I think there's a Spanish version with audio description as well so enjoy, and I'm going to just show Maria I'm sorry this isn't a longer clip of your piece it's what I was able to find. And I don't know if there's somebody doing live captions but I sent a transcript for these pieces because it doesn't have captions on it. Okay. Myself. Poetry begins in the darkness. Prepared. Prepared is a word that weighs a ton when you think of disasters. Maria a Latina woman wheels into the frame. Being prepared means having access to resources. Access to the necessary extras reserved for the privileged who don't think are privileged. They stand in front of us in their three piece suits asking if we are ready. Do we have an extra wheelchair. Do we have non perishable goods stored away. Do we have a way to get out if we get hit by mother nature's anger. She's right to be angry you know. She's tired of being raped by human greed. The rain started around midnight. I don't know what it is about hurricanes but they seem to like that midnight to 3am slot when people have fallen asleep. We get awakened by the wind and the rain hitting the windows. Lightning brings glimpses of daylight. Trees are shaken. The wind roars destruction. Mother nature cries and weeps and howls and we huddle and pray and cry with her because there's nothing else we can do. Houston we have a problem. Houston we have disabled people waiting in high water. Houston we have people who had to abandon everything.  Equipment spent years waiting for equipment. Crips can't afford to replace. We had to leave accessible vehicles. We had to leave accessible homes and place our trust in the very world that wishes Crips did not exist. I want to talk more about this piece and about the Crips Survival Network. Yeah absolutely. So thank you Nomi for sharing that excerpt. That is actually a 10 minute piece. And for me that piece was very emotional. It was difficult to write. It was difficult to memorize. It was difficult to perform. And it's difficult to watch for me. It was difficult to be able to share and represent the truths of disabled people who face ableism to the max who face being abandoned being forgotten. It's a no necessary, but it doesn't make it any less painful to recognize that our disabled lives are in so much danger of being left out of being abandoned of. It's dangerous because of ableism. And with climate change and climate chaos. Things can only get worse for disabled people. I'm going to talk about the Crips Survival Network in a second but I just feel like the urge to say that, because since invalid started back then with like crib bodies and sensuality and sexuality and performance art and our movement is something that kind of like happened, you know, like us just recognizing all the shit that's hitting us constantly being aware of the oppression and feeling the huge responsibility to move forward saving each other's lives. So our energy and the flow of what we do has shifted over the last few years. We have moved beyond our physical existence and our access needs as far as being central and and being human. I think that we have moved from from protecting disability rights to basic human rights. You know, disability justice is about that. So the Crips Survival Network is an initiative that Patty Byrne and myself started a year ago. Shortly after I came on board as staff, we, we were, we had the opportunity to talk to other Crips really and we, we met some disabled people in New York who had been literally been abandoned during COVID, and they were nursing home residents who were who actually lived in the nursing home, you know, people exist in all areas of society. And just because the nursing home is not the most ideal place for anybody, it doesn't mean disabled people don't exist in those, in those situations.  All of a sudden, watch on the news that the governor was the governor was sending COVID positive people to their facility and saying that it was empty. You know, and, and we're like, oh my gosh, sorry, I have dogs. We already know that disabled people get abandoned, you know, but when it becomes kind of like on your face. And that realization stares at you and you're like, oh my God, we have to keep each other alive, you know, so this is kind of like what we already knew that disabled lives are in danger we already knew that we need to save one another we already knew. But this was kind of like for me and Patty was started talking after this after being part of this conversation. And we thought at first, we thought we need to do something we need to do something that is related to could survival something that can help disabled people during the disaster something that can reach out and let them know they're not alone.  At first it was like a conversation about about a backpack a backpack containing a stuff that can help disabled people and stuff that usually the non disabled world wouldn't let us have, you know, everybody and their mama is doing life saving for disaster, you know, prevention. And so part of our initiative was, was having a backpack that will contain things that are often denied to disabled people expensive items or whatever. But then the conversation shifted. It shifted to more like beyond just offering emergency water or battery operated radio or a flashlight or the things that those backpacks please stop that those backpacks would have in them you know, we realized that one of the most valuable things needed to keep disabled people alive is each other, each other surviving and each other knowing that we are here for one another. It is that the constant reminder that our lives are worth saving, because that is the message that society sense to the world is that we are discardable disposable we are the throwaways of society. We can be forgotten and we're often forgotten, more often than not, you know, so to us surviving means reminding each other constantly that we were saving that we are not alone, that our survival saves other disabled people there are lives are disabled lives have meaning. During covert, you know, and it is an example that I always bring up when I talk about how disabled people are left and forgotten during covers 11 texts as I mentioned. He was a man a quadriplegic man who could contracted covert ended up in the hospital, and the state of Texas starved him to death. They decided that his life was not worth living that his quality of life was not enough to keep him alive and they denied him food. Even though he was a man with a wife and children and community, and everything that non disabled people think that we don't have. Right. And that's why disabled people disabled lives become so at risk of being thrown away because the non disabled world sees us as broken. They don't recognize our value, you know, so the crypto viable network is an effort is as an initiative to come together as disabled people and save each other's lives. So, since about 14 months ago almost a year and a half Wow, we about 20 organizations, more the majority of them are led by brown disabled people. And a couple of them are actually not even disabled led, you know, but they're doing justice work so we have become a community a family of right now 20 organizations we've been getting together. Once a month to formulate dream and envision how to save each other how to stay alive, how to save each other's communities. And through this conversation. We are about to launch ourselves into hubs. You know this 20 organizations are going to be survival hubs script survival network hubs for their communities and as part of this initiative since and valid will be dispersing funds for each of these organizations. So we can help save each other, not only from natural disasters but from the disasters of ableism and political threats you know, I always like to remind people that that disabled people don't need to wait unfortunately for a hurricane to hit us or for an earthquake to happen or for a pandemic to do to take place for us to be in danger. You know we live in danger from ableism every single days of our lives no matter where we are. So that's in a nutshell, the crypto revival network. And I wish and hope that disabled people around the world will continue holding on to one another for dear lives because doing so saves us. It saves us we have to, we have to continually continually fight for our survival, and I'm not exaggerating. That's a little bit about the perfect timing because my dogs are bonking. Thank you so much, Maria. Yeah, and I think, you know, I'm guessing a lot of us are are thinking about this with climate chaos and everything that we're experiencing and I also, I think it's useful to see the ways that like there are 10 principles of disability justice. Which we didn't really include in this program, but a lot of times we'll kind of base our trainings around that and you can look it up 10 principles of disability justice, but you know, these principles of like wholeness like we are all whole people. That we like cross disability solidarity like we weave that into the performance, and then that also becomes a part of what we're actually doing in our lives not just on on stage and so that's why we named the this event like disability justice or performance as movement building because they're really intertwined in our work. I want to give some space for questions and reflections and then we have one more video before we close out. Sorry I had to mute because I was coughing I'm a little sick. Yeah, does anyone have any questions. Terry, did you want to say something came on. Thank you I'm trying to figure out how to raise my hand and I'm on my iPad and it ate that option. Thank you for calling on me. How does someone get involved with you or are you a closed collective do you work with people who aren't necessarily local to all of you it sounds like you at least did during coven. Yeah, we were kind of all over the place. And it's very relationship based. So, and Patty burn is the, is the director so there's not a clear. I would love nothing more than to have a artists and residents program we've done this once many years ago, but to help develop people's art and then help them become a part of since invalid stage productions and that just has never quite taken off so it's, you know, based in on what Patty forms relationships with. And also, we would love to know you and love to know your work and apologize that we don't have like an audition process or anything like that like work. We're kind of an ensemble, like Patty works with kind of the same people over and over and then we'll bring in like one or two people. We want to learn about what people are doing in the world so please do reach out to us. Social media. You know, we do have Instagram and Facebook page and Facebook page is right now in Spanish dedicated to Spanish speaking audiences but do follow follow us because we often have events that you could be part of on on social media so, and we also have a newsletter. Yeah, and we actually like, we've been working on doing this crit bed life. Instagram campaign, which it's looking like it's going to be sorry my dog is like eating my couch now stop it. I mean, like, it's going to be about ways that people are taking action for Palestine from bed. So that's going to be the focus of it that wasn't it was going to be more like, here's how I live my life from bed but in this moment that feels like where we want to really put our energy and attention. And that's also a way like if you want to participate when we do calls like that that you can, you know, make a little video and post it on our social media and stuff like that. Thank you. Thank you. Does anyone else have any questions or reflections. It seems like not Maria do you want to talk some more do you have anything else that's on your heart to share. Oh, I think that want us to move to your beautiful video. Great. So, um, this is from the same show. And this piece was I feel very connected to bees. And these are definitely having a hard time. And you know what I'm not feeling super articulate right now. So I think I'm going to just like let you watch the video. We can talk about it afterwards if you have questions. Let me find it one moment.  She sits on a platform which is wheeled onto stage while she flutters her hands as if they were wings. She smiles as if pleased with herself and moves her hands through multiple fluttering positions. The cameras capture her from different angles, including overhead. She has one leg and two wings and a fancy hat with a jewel that drips like honey over the curls of her bangs. She strikes glamorous poses. She head bangs and shimmies to the music. She raises it and smears it on her body and her face.  Yeah, so that piece, one of the things that's really fun for me with sins is kind of inventing like a whole vision of what the piece is. So where Maria is very content oriented of like, here's the poem I'm going to write. I usually start with an image and then kind of build out from there. So I've done things where I'm a baby bird in a nest made out of legs or I'm a mermaid interacting with these huge puppets or I've got a skirt that covers most of the stage with people dancing under it. And with this one, I had heard a description of a queen bee that had a lot of the same language that is used to describe fat people's bodies. Like talking about, I don't want to say, it was just like, you know, saying that it was gross or something like a queen bee is like so big and gross and I was like, well, that sounds awesome and beautiful to me.  I'm like, we have to love being alive in the bodies that we are alive in. And so that's, that's where part of what I was working with in that also just about like the modification of beauty and yeah, lots of ideas in there. Thank you for watching and thank you for the responses in the chat. Does anyone else have any questions or thoughts before we wrap up? My dog has things to say. She's a puppy. Okay. Maria, anything else you want to say before we close out? I just want to say that you are such a badass. I absolutely love that piece and the power that it represents giving, you know, bodies, beautiful representation.  I adore that piece. And I love that the show closes with that piece, you know, and that we're closing with that piece because, Nomi, you are glorious. You are, you're first of all the queen of costumes. You know, you do everyone in the show with your costumes and that piece is like one of my ultimate, ultimate favorite ones because you not only look stunning and gorgeous but the power that you represent and that you share is just so, you're amazing. Thank you, Maria, and back at you.  So blessed to be on this planet with you. Yeah, thank you so much, Ashna, for bringing us here and to everyone. I hope that you've had a really great weekend. Thank you so much, Nomi and Maria. We've learned so much in the past hour from the performances and from everything we saw. I'm just so fascinated by all the work that you do and I'm so glad we finally got a chance to introduce you to the Northwestern and the Evanston community and everybody, all our seesaw friends online here today. I'm sure there's so much we're going to take back from these performances and honestly as Maria was saying just how badass everything that you guys do is. It's so true. And I hope we can all move around in life with that kind of like confidence and love and innovation, which you guys embody so well. Thank you for being here and thank you to all our audience members for being here and for interacting with us. We're going to take a 15-minute break before our very last presentation of this year's Inclusive Theater Festival at 3.45pm from the brilliant Claudia Alec of Calling of Justice. So feel free to stay on the call and just keep your camera on or off as you need to and we'll reconvene in about 15 minutes. Thank you all for being here. Thank you so so much. Thank you.