So I'm going to talk about random matrix theory, a particular part of random matrix theory. So random matrix theory, for those of you who know, is a very vast area of research with a lot of applications, many, many results, et cetera, et cetera. So try to give, to cover some of these topics in two weeks, would be very foolish for my part. So what I'm going to do instead, I'm going to be selfish, and I'm going to focus on the work I've done. And the work I've done essentially could be summarized in a title, which is the title of this lecture, which is a statistical mechanics of random matrices. By the way, I'm going to use the blackboard all the time. That's OK with you? So the title of this course is going to be statistical mechanics random matrices, even a particular type of random matrix at some point. But we'll see this thing later on. And what is the main goal of these lectures I'm going to give you? I'm going to try to give you some very, very cool tools to solve these problems. So I'm not going to focus on universal results, et cetera, et cetera. So what I'm going to do is, or the main goal of this series of lectures is the following. Let me put it here. So the main goal would be something like the following. And actually, this happens not only in random matrix theory. It happens also in other areas of science, like for instance, economy, ecology, et cetera, et cetera. So I'm interested in a problem in random matrix. Here, a problem of interest concerning random matrices. I don't know whatever. Maybe you come from different areas. You have various different interests. And what I'm going to do, I'm going to map exactly this problem into a problem in stack mech of disorder systems, also called for the people in the known spin glasses, the stack mech of disorder systems. Can you understand my writing? I hope so. And the people, the last part you can see, very well. So I'm going to do this mapping. This mapping, essentially, is exact from the beginning. So I have a very interesting problem in random matrix theory of random matrices. I map it exactly to a problem in a stack mech with a partition function, a free energy, et cetera, et cetera. And then what I do here, once I realize that my problem can be understood in the setup of physics, what I'm going to do is to apply all the machinery I know from physics to solve the problem. And what is this machinery? Well, this machinery would be, so number one, of course, concepts and ideas of the foundations of statistical mechanics, partition function, free energies, et cetera, et cetera. So I will be using things about a stack mech. And these are the idea of what is a partition function, what are free energies, et cetera, et cetera. So this part, I will not cover it, because I assume that everybody knows the basic of the statistical mechanics. Am I correct on thinking that? Very good. Then I will be using some tools of disorder systems. And again, disorder systems spin glass is a very vast area with many good results. The physics is very interesting. And that gave rise to the Nobel Prize in physics, one part, to Giorgio Parisi in 2000 and 21, if I recall correctly. So I'm not going to go into details of what are spin glasses, the physics behind them. What I'm interested here in these lectures, very short lecture, is to use the tools developed to understand spin glasses to solve problems of interest in random matrices. So which are those tools? Those tools is what is called replica method. I guess some of you have heard about it. Who knows the idea of replica method? Raise your hands. And the rest you don't know. That's very good. Have something to teach. New. The other method is called cavity method. And maybe for other very advanced results on random matrices, you would use other techniques. But I'm going to focus on those. Good so far? Good, and then I need some basic results from mathematics. Tools from mathematics. Let me see that. I'm not missing anything. Then I need some tools coming from mathematics. One tool is a very important tool that every student from physics should know, but sometimes you don't know, which is OK, which is the so-called side point method. This is a very cool method that is used, actually. It's a cornerstone in many, many results in condensed matter physics quantum field theory. So one tool I need to explain to you is the saddle point method. This is also called the Laplace method or the steepest descent method or the stationary phase approximation method. It depends on the context. But this method is also called Laplace method or the steepest descent method or the stationary phase approximation method, stationary phase approximation method. All these concepts are used synonymously, even though it is not true. For a specific type of mathematical problem, what you should call it is either steepest or Laplace, depending on the other problem is called either the saddle point method or the stationary phase approximation. Have you heard about this method? I hope so. Very good. Then we'll need some results of Gaussian integrals, multivariate Gaussian integrals, which again, there are many, many results very important in QFT or FT, you know what I'm speaking. Here, I'm worried about expressing the terminals in terms of multivariate Gaussian integrals, all right? And finally, I need some very simple results of expressing Dirac deltas, Dirac deltas and theta functions in a smart ways, OK? That's it. Questions so far? Nothing? OK, so how I'm going to, or how I thought I could structure these lectures? Let me see. The way to structure them is going to be the following. This is going to be the content. So first week, well, I have to say that I teach a lot, OK? But I never managed to follow my own schedule. It's impossible. I don't know why. I'll try to do that, OK? So first week, day one. So this is what I'll try to do. Day one, we are going to introduce the mathematical tools. This is today. Second day. Second and third day. This is one three, tools of spin glasses that would be replica and cavity methods. This is four and five. We'll do the mappings. We'll set up into deciding which problems we think they're interested in random matrices. And then we'll do the mappings, two problems in statistical mechanics, OK? So mappings. So in particular, I think I'm going to focus on, no, we'll do it generally, OK? General mappings, or as general as possible, OK? And then in week number two, second week, in days one and two, we'll focus on a spectral density of random graphs, directed and undirected random graphs. Of random graphs. Then days three and four, we will develop what is called LAR deviation theory for this type of problems. LAR deviation theory for this type of problems. And of course, day five is the exam. Questions. Now, the most important question is about the exam, I guess, right? What I'm going to put in the exam, I need to think about it, OK? But as Mateo mentioned, it's going to be very, very, very tough. All right? Very good, so shall we start? Yeah, excellent. So let's start with day one, which is today, which is mathematical tools. So OK, before, while I'm erasing, can somebody tell me something about the, what is known as the saddle point method? What is the idea behind the saddle point method? Somebody is a way of calculating integrals without having to do the integral, OK? That's very cool, because everybody knows how to do derivations, but nobody knows how to do integrals, right? So it's much, much more difficult to do integrals. So the idea of the saddle point method as, what's your name? Christopher? Christopher. Is to do integrals, OK? Actually do, we evaluate the integrals in a particular case. So let me see, some mathematical tools. We start with the saddle point method. Also known, as I told you, like the Laplace method or a steepest method or a stationary method approximation, all right? So the idea is the following. So suppose I have an integral of the following sort. I'm going to denote this integral as i sub n, and this is equal to the integral from, for instance, from a to b, the exponential of minus n f of x, OK? And what I want to study is what is called the asymptotic behavior of this integral when n goes to infinity. I'm not interested. If I could, that would be very cool. That would be much, much, much better. But sometimes you're interested in the asymptotic behavior of this, like this happens in statistical mechanics, where you're interested in the thermodynamic limit, right? So here, I want to study the asymptotic behavior. Let us put it here, behavior of this integral when n goes to infinity. So for those of you who know the Saal point method, you know that the result is that when n goes to infinity, or for n very, very large, the asymptotic behavior of this integral, and then the notation is like this, I'll explain what this thing means, precisely, is the exponential of minus n f of x0, where x0 is such that the derivative of f at x equal to x0 is 0, and the second derivative of f of x at x equal to x0 is positive. And what this symbol means, this means that, you know, physicists, we confuse the symbols, all the time, we use the, and I'm going to do that a lot, but at least this symbol means the following. What this symbol means means that, if I take the limit of I sub n, if I take the limit, sorry, of the 1 over n, the logarithm of I sub n, n going to infinity, let me put here a minus sign, this is equal to f of x0. This symbol, what it means is this limit. Good, so how do I prove that? Do you know Taylor's function? And if you know this method and you know properly the Taylor's function here, what appears is the starting point of a perturbation theory, Feynman diagrams, et cetera, et cetera, is simply a Taylor's function. So what I do is I do, let us do it for those people that do not know these methods. So this is a proof, it's an informal proof, it's not a mathematical proof. So I take the function f of x, I do a Taylor's function around x0. So since the first derivative is 0. And by the way, here I forgot something, you have to assume that x0, where you have the minimum, is between the integration interval. If it's outside the integration interval, then you have to generalize this result. And the result is called Watson theorem. We're going to assume that x0 is between a and b. So you have that f of x is equal to f of x0 plus 1 half of the second derivative of this function x minus x0 square plus the sum for n greater than or equal to 3 1 divided by n factorial, the nth derivative of f of x0, x minus x0. All right, so I put this thing apart because that's important. So then what I do is simply I put this result in the integral. What I have, I have that. I suppose n is equal to the integral from a to b in the x exponential of what? Of minus f of f of x0 minus n divided by 2, second derivative of f at x0 x minus x0 square minus sum for n greater than or equal to 3 capital n divided by n factorial, the nth derivative of the function of x0 x minus x0 to the power. Now, this term is a constant. It can get out. Can you follow my writing? Everything's OK? Yeah. So this guy, I can take it out. So then I'll have this equal to the exponential of minus n f of x0. And I have the integral from a to b dx. And then I have the rest, no? Exponential of minus n divided by 2, second derivative of the function evaluated at x0 x minus x0 square.  And what I do, I do this thing in many ways. Well, I can proceed in several ways. One way would be I do a change of variables. I denote y is equal to the square root of n x minus x0. So then I have that the same integral is equal to the exponential of minus n f of x0. And then in the change of variables, what do I have? I have a square root of n a minus x0, the square root of n b minus x0, half dy divided by the square root of n, exponential of minus 1 half of second derivative of f of x0 y square. And then let me put it like here. Here I have the exponential of r tilde of y. So r tilde of y is this when I do the change from x to y. Just work it out. And the next step you can do is the following. So this is equal to the exponential of minus n f of x0. And then, so let me see, this would be the integral, the same integral, square root of n a minus x0, the square root of n b minus x0, dy square root of n, exponential of minus 1 half second derivative of f of x0 y square. And here I do a particular expansion. It's equal to the sum of the series from n for n from 0 to infinity of 1 divided by n factorial. n factorial r tilde to the power n y. Good. Questions so far? So then what happens? So what happens if you look at the leading term? If you look at, thank you, if you look at the leading term in n, so the leading term, the one that is the important one in the limit of n goes to infinity comes from here. When n goes to infinity for very large n, the integral goes from minus infinity to infinity y, because x0 is between a and b. So this is negative. This is negative. And when n goes to infinity, it goes to minus infinity, and this to plus infinity. And you can look at the collections to n of this part, but they are not exponentially big. OK. So in field theories, you would call that this is, you can look at these results in the book of San Justan, for instance. So in field theory, when you do this case of derivations, this would be a Gaussian measure. Yeah, you have a Gaussian probability distribution. The Gaussian measure. And these are the terms that come from perturbation theory. So that means that the leading contribution, the one we are interested in, the leading term, would be the following one, would be the exponential of minus n f of x0. And then the integral from minus infinity to infinity, d dy squared of n exponential of minus second derivative divided by 2y squared times 1. You take the series of terms in this part. And this is a Gaussian integral. So therefore, you get that this is equal to exponential of minus n f of x0. And this is the square root of 2 pi second derivative of f of x0. Questions? Yeah, I assume that it's between a and b. I'll say it at the beginning. I just erased it. So if x0 has to be between a and b, in such a way that when you do this integral, this integral goes from minus infinity to infinity. If this would not be the case, if you have that x0 is not between a and b, then you can generalize this result. And the theorem is called Watson theorem. But for our cases, or the cases of interest, our x0 is always within a and b. Or as a physicist, you assume that it's between a and b, and you do the derivation. More questions? Which one? This sum here? So this sum here is like since I'm interested in the leading term in n. The one that contributes to the leading term is when n is equal to 0. The rest of the terms would be the corrections to the leading term, which is perturbation theory. Which if we would have time, I would tell you how to do a perturbation theory for random matrices. But we will not have time. More questions? Why? I'm doing the integral from minus infinity to infinity. It's not correct? It is correct, isn't it? This is a 1, sorry. If you don't understand my writing, this happens. Don't be shy. This presents to be a 1. Sorry. More questions? Very good. So now, sometimes it happens that instead of having a just the exponential of a real function, this function I didn't say, but it's supposed to be real. The argument is real, and the function is a mapping from the reals to the reals. You have a function in the complex plane. So suppose now that you have the following now. Suppose that f, the program is, sorry, once more here. So this function here, for the Laplace method, is a function from R to R. So suppose now that I have a function f, but in the complex plane. And I have the same type of integral. So I have the integral, which is the integral from a to b of this set, exponential of minus n of set. So I have in the complex plane a point a, a point b. And then this is a line integral in the complex plane. So I have to choose. Let me choose a path. Although if the function is analytical, the result of the integral is independent of the path. Choose a path gamma, that goes from a to b, the path gamma. And again, you're interested in the asymptotic behavior of this integral when n goes to infinity. So in this case, you can do the same trick, or something very similar. So what you do is you look for a point in the complex plane. Let's say, let's say, in this point, set 0. You look at point in the complex plane, such that the derivative of the function evaluated at set 0 is 0. Then if the function, if f is analytical, the exponential of minus nf is analytical function, that means that the result of the integral does not depend on the path. So that means I can modify the path as I please. So what I do is I modify the path to go through set 0. Go ahead. Sorry? Because I did a mistake. So it should be below. Thank you. Yes? Thank you. So what you do now in the case of the complex plane, you assume that there is a point set 0, such that the derivative of f at set 0 is 0. So you take the path, you deform it to go through this point, and then you move the path, and then you can do the Taylor expansion, et cetera, et cetera. And then when you do the Taylor expansion, there would be, and I'm going to leave this thing as an exercise, you'll have a Taylor expansion expression, which is the second derivative of the function evaluated at set 0 times set minus set 0 squared, and higher order terms. So then what you do is you move the path in such a way that the imaginary part of this expression is constant along the path in a small region. And then you apply the side point method to the real part.  So at the end of the day, you find that there's in total behavior of this integral is, again, the exponential of minus n f of set 0. This is a result from complex analysis. If you have a function which is analytical, an analytic function, the line integral in the complex plane does not depend on the path. So I'm assuming here that f of set is an analytic function. Therefore, the exponential of minus f of set is analytic function. So here, we're assuming that this function is analytic. I only care again about the asymptotics. And since I only care about the asymptotics, I only need to deform the path a little bit in such a way that the asymptotics cares just a bit about what happens around this point. More questions? Go ahead. Very good. If you have many points, this happens also in this case. That's a very good point. If you have many points, what you do, you apply this to the various points. So you can do this. And actually, in a stack phase, sometimes it happens that you have an equilibrium state, a metastable state. Metastable states appear when you take into account these different minimums. So let me delete here. So if it happens, the following is very interesting question. Thank you for that. Let's go back into the real case. Suppose I have a function like this, f of x. When I have one local minimum, let us call this thing x0, 0, x0, 1, to x0, n. So what you would do when you are integrating over the whole line for simplicity. So then I have, again, so I have the integral, i n is equal to the integral from minus infinity to infinity of dx exponential of minus n of x. So what would happen in this case is when n goes to infinity, again, it's asymptotic behavior, this would go like the following. This would go like the sum for i from 0 to a small n of the square root of 2 pi n, the second derivative of x0, n, the exponential of minus n of f x0, n. Now, sometimes you need to keep the contribution from all minima. But in other equations, the only one you're interested in is in the deepest minima. Suppose that, for instance, I'm going to exaggerate this picture, the deepest minima is this one here, x0, n. And then what is going to happen? Well, what is going to happen when n is very large? I can always write this thing as follows. Let me forget about this part.  So when n goes to infinity, this is very small. So the most important contribution is the contribution that comes precisely from the deepest minimum. If for some reason, and this happens, actually, Mateo has worked on this application, so inference problems. Sometimes you have to take into account contributions from other minima. And in physics, these are called metastable states. Good. More questions? Go ahead. So I repeat. How do I know? Due to the structure. Ah, there's a bleeding term. How do I know that they are not the leading behavior? Because they are subleading. They don't have the form of exponential of n. So you see, normally, this would be related to a partition function in a stackmate. I mean, I'm always interested in the logarithm of the partition function, which is free energy. So whatever which is not exponential in n, in the partition function, in the limit when n goes to infinity is subleading. And it goes to, say, the thermodynamic limit. So there might be some case where subleading terms can sum up to exponential contribution, but I don't think so. But I'm not sure. But you know, this term is subleading, in the sense like, if I take the logarithm of this expression, you divide it by n, this term would go to 0 when n goes to infinity. That was your question? Very good. More questions? Go ahead. This one here, again, if you don't understand my writing, please yell at me. I can rewrite it. So the argument is the following. So suppose you have various minima. If you generalize our derivation, you will get this. But of course, what happens is you have this sum of exponential of minus n. And it happens that if you look at the behavior when n goes to infinity, the deepest minima is the most important one in most of the cases of interest. So how can I see this? Well, let us forget about this part. This is not important when n goes to infinity. So let me focus on the deepest minima, which is this one here, which I denoted as x0n. And I'll write that expression here. Let me put it here as follows. This goes like the exponential of minus n f of x, 0n. I take it out. And I subtract the arguments of the other exponentials. So then I have 1, because it's the term that I take out, plus the exponential of minus n that multiplies f of x, 0, 0. That would be the first minima minus f of x, 0, n. Plus the exponential of minus n f of x, 0, 1 minus f x, 0, n, et cetera, et cetera. And then what happens? What happens, this is the deepest minima. So then any other minima minus that, or the value of that minima is positive. And you have a beautiful minus sign. So when n goes to infinity, the important term is the one just subtracted. More questions? No, I have to, you have to, OK. If you do this derivation, and that's very important, that you do the derivations, what happens when, instead of having a minimum, you have a maximum? What happens? So the integral diverges here, OK? So somehow what you are doing when you are doing this integral is the following. So you are splitting the integral around the parts where you have minimum, and you are forgetting where you have maximums. It would be the same. But the second derivative changes sign. And if you go to the derivation of the real case when the function was real, then you have the integral of a Gaussian weight. But where the sign is the other way around, so that the integral diverges. So it doesn't make any sense. So that's why, when I did the real case, and I'll leave it as an exercise for all of you to do derivation, it's very important, you have to. For the sign I put here, the second derivative of the function at x0, for real function, has to be positive. If it's negative, the integral is not well defined. More questions? No questions? Good? OK. So it's important that you do the derivation, because now, so to know the details of them, you have to choose a path such that the real part has the appropriate sign, and the path around the imaginary path is constant, because what you want to do is to apply the Laplace method in the complex case. Constant along the path, so it doesn't change. So then you take it out of the integral, and then you have the real part, and in the real part, you apply the Laplace method. More questions? No? OK. So of course, this Laplace method, or the steepest method, is very powerful technique. It's used a lot in stack mech. As you see the structure, it can be easily generalized. Suppose now that I have, again, something like the following, but now I have a multivariate integral. I have the integral. So I have a map from Rn to Rn. No, from Rn to answer, I'm doing here the integral over Rn. So I have the integral of dnx, the exponential of minus n, where my notation dnx is equal to the product of i from 1 to dxi. And again, I'm interested here in what? In asymptotic behavior when n goes to infinity. So if you do the derivation, for those of you who didn't know this method, so derivation is straightforward, the only thing that you have to be careful about that now you have a function of various variables. So suppose, so here, the result would be that this is equal, sorry, it goes like exponential of minus n f of x0, when x0, the vector, along it to Rn, is such that the gradient of f of x applied to x equal to x0 is 0. And when due to a Taylor expansion, in order for the integrals to be well-defined, the Hessian must be definite positive. So that means that the partial derivative with respect to i, with respect to j of f of x evaluated at x equal to x0 has to be definite positive. So this is the Hessian matrix. Good, go ahead. No, this time I'm mixing notation. Lovely, thank you.  Thank you for the point. Where does this condition come from? Do you know? That's right. So the matrix must be positive, definite in such a way that when you do the Taylor expansion, the quadratic term has a positive definite matrix, so the integral is well-defined. If not, the integral is not well-defined. It blows up. Good, in this area, when you do this type of derivations, this set of this condition for x0 to be an extremum, or sometimes it's called critical point, these are called saddle point equations. These are so-called saddle questions. Now, be careful, because now it's a function from a higher dimensional space to r. So when you have a critical point or the extremum, you have to classify what type of extremum you have. You can have minimum, maximum, or saddle points. So to apply this method, the extremum you have to take into account must be minimum. Because if there is a saddle point again in the direction where you have the maximum, the integral is going to blow up. So x0, let me put it here more explicitly. x0 has to be a minimum. Very good, more questions? So sometimes when we do this type of derivations, what we do, what we say is the following. So let us assume that it's a minimum and then you carry on. Because sometimes to check these things, depending on what you are doing, sometimes to check this thing is very difficult. And normally what happens is like since you are starting from a well-defined problem, what you would happen is like this has to be a minimum. Because otherwise, the problem will not be well-defined from the beginning. So essentially, nobody checks those conditions unless you need those conditions for something else, like for instance, perturbation theory. Go ahead. Yeah, yeah, this one here. Yes. The Hessian matrix, so that means, so this is a matrix now, because it depends on these two indices. This is a Hessian matrix. So when you put that a matrix is greater than zero, that means that what you are saying is that the matrix is definitely positive. So that means that, OK, the easiest way to say these things like all the eigenvalues are positive. Or another condition is like all the minus are positive. All the minus are positive, definitely. But this is easier to think about this condition with respect to the eigenvalues of the matrix. Yeah? You de-analyze, and if the eigenvalues are all positive, the positive is definite. The matrix, sorry, is positive definite, yeah? More questions? So, OK, so there are no more questions about saddle point methods, saddle point equations, et cetera, et cetera, that I will use a lot. So let us now go to another part, which is multidimensional Gaussian integrals. So again, if you take the book of San Justan, for instance, you find a lot of information in there. It's this very thick book that has like 2,000 pages. This is the black book of Converse Matter Physics. I forgot the title. So what I'm interested in here is the following. So I want to relate. So I suppose I have a matrix, A. It's N times N matrix. This N has nothing to do with the other N. And for some reason, in some problem I'm interested in, the determinant of A appears. And what I want to do is to write the determinant of the matrix in terms of integrals. So I want to find a way. You'll see why this is useful. I want to find a way to express the thing in terms of Gaussian integrals. So let's start them with the simplest case. The simplest case is suppose that the matrix A is symmetric, definite, positive. I suppose that A is real. So N is real. It's real, symmetric, and definite, positive. Yeah? So one can show that one divided by the square root of the determinant of A is equal to the integral of dnx. Sorry, the integral of dnx divided by 2 pi to the power N divided by 2 of the exponential of minus 1 half x A x. Sure? I guess you have seen this, at least the one-dimensional case. Well, and how do you prove this? There are many ways to prove it. There are very good tricks and very weird tricks. Like, for instance, suppose that the matrix can be divided into the product of the square root of matrices and do a very weird transformation. Or there is another simpler one. How do you prove this? Sorry? This is a multivariate Gaussian distribution. Suppose that you want to prove this. So by the way, good point. This is what is called multivariate Gaussian distribution, of course. It's missing the mean values, vector mean values, but this is the multivariate Gaussian distribution. You can diagonalize it. Very good. So the way you diagonalize it is the following. We know that since A is a real and symmetric matrix, so that means that it can be diagonalized by an orthogonal transformation. Suppose that O is a matrix, which is the orthogonal transformation that they diagonalize is A, so that the O transpose A O is equal to lambda. Where lambda is the matrix diagonal with the eigenvalues of A. Of course, since the matrix A is symmetric, that means that the eigenvalues are real. And since I am taking that is definite positive, the eigenvalues are positive. There are no zeros or negative eigenvalues. Right. And then what do I do next? What do I do next? I do a change of variables. So I say, so what can I say? I say that O, so x is equal to O x prime. So I go from x to x prime, where this O is precisely the orthogonal transformation that diagonalizes the matrix. And once I've done that, I do the change of variables. I do the change of variables. And now, so I have. So let's do it step by step, OK? Because then I'll put an exercise, which is a bit a deviation of this. So I have this expression here, x transpose A x. I do the change of variables. So the change of variables is that x vector x is O x prime. So that means that this is x vector prime transpose O transpose A O x vector prime. But this is the diagonal matrix, all right? So this implies that this is equal to, what I just said, x prime transpose diagonal matrix x prime. But this is equal, let me put it explicitly. This is equal to the sum of i from 1 to n lambda i x i prime prime square. I have not done anything, but I need to at least to go through this for those people that have not seen this. And then since I'm doing an integral, I have to do the change of variables in the integration variables. So that means that dx, sorry, dx is equal to the terminal of the Jacobian transformation that is normally denoted like this, partial of x with respect to partial x prime, the determinant dn x prime. This is the determinant of the Jacobian of the transformation. But the transformation is an orthogonal transformation. And the determinant is equal to, no, plus minus 1. Because orthogonal transformation can be the standard one, or the orthogonal transformation can be a reflection. Sorry, it can be rotation and rotation and reflection. Reflection has the determinant minus 1. The problem is like here, in this transformation, you have the absolute value. It's the determinant and the absolute value. Since I know that the determinant of O is plus minus 1, so that means 1 is also an absolute value. So the measure doesn't change. So that means that this integral here, the integral of dn x divided by 2 pa pi to the power n divided by 2 of exponential of minus 1 half this is equal to what? It's equal to the integral dn x prime of 2 pi to the power n divided by 2 of the exponential of minus 1 half. I'm going to put it like this. Sum i from 1 to n lambda xi square. And now the integral has decoupled into one dimensional Gaussian integrals. Because this is equal to the following. I can write this thing as the product of i from 1 to n of the integral. I'm not putting the limits of the integral. I'm assuming this from minus infinity to infinity. Sorry about that. Of d xi divided by square root of 2 pi exponential of minus lambda i xi square divided by 2. And this is equal to what? The result of the one dimensional Gaussian integral everybody knows. Unless you do a mistake as I did before. This would be 1 over the square root of lambda i. Which is equal to 1 over the square root of the product of i from 1 to n of the lambda i. But the product of the lambda i is the determinant of lambda. And the determinant of lambda is equal to the determinant of a. So one more step. I'm being very explicit with the steps. Just for those of you who have not seen this. So let me continue here. So this is equal to 1 divided by the square root of the determinant of lambda. Because the lambda is a diagonal matrix. The determinant is simply the product of the elements of the diagonal. And now the determinant of lambda is equal to the determinant of a. Because the determinants of matrices are called, well, the determinant of a matrix is what is called, is one of the invariants of a matrix. It doesn't change by a similarity transformation. And this is a similarity transformation. So therefore, this is equal to 1 over the square root of the determinant of a. Good. So then I've proven what I wanted to prove. That 1 over the square root of the determinant of a matrix a can be written in this way. Exponential of minus 1 half x a. Good. I guess you have seen this thing for the people who have seen this thing. I apologize. People who have not seen this thing. You will see why we need this. Very good. Questions? Go ahead. This is a determinant. No, no. This would be without these straight lines. Is the Jacobian of the transformation which is a matrix? Yeah, so this notation is a weird notation that sometimes we introduce. Well, it's a compact notation. So what this thing means is the following. So this is actually a matrix. So I have the partial derivative of x with respect to x prime. So this is a matrix that if I take the entry ij of this matrix, what it means is this. It means the partial derivative of xi with respect to xj prime. Since the transformation is the linear transformation I mentioned before, this is precisely the matrix of the linear transformation. The matrix is O, and the determinant of O is plus minus 1. More questions about notation or any other thing? OK, very good. So exercise now. If you with an exercise, which is the following one, suppose now I have the following object. I have the internal and dimensional integral dnx divided by 2 pi to the power n divided by 2 of the exponential of minus 1 half x transpose A s x plus B times x, where B is simply a vector, B is a vector in. And we will use this in at some point. So it's useful to write it down. So in condensed matter physics or field theory, this B is what is called a generating field. It's called a generating field. Or in probability theory, this would be a measure, which is a measure, it's a Gaussian measure. So this is the moment generating function. It's as simple as that. And the logarithm of this would be the cumulon generating function. So this, from one point of view, is simply from physics generating field. In probability, this would be the field or the variable that generates moments. Variable that generates, let's say, a moment of a distribution. In this case, a distribution is Gaussian. Right. Also, for some weird reason, because these things sometimes happen, for some weird reason, this has another name, which is called the Habard-Stratonovic transformation. Very useful also in condensed matter physics. Very, very useful for other reasons. This is also called, but the result is called the Habard-Stratonovic transformation. That may tell you why it is a cool trick. And what is the result of this? The result of this is simply the following. So this is equal to the exponential of 1 half B transpose the inverse of A B divided by the square root of the determinant of A. This is a 1, and this transpose, I apologize. So this is the inverse of A, which is the matrix that appears here. So this is 1 half the scalar product of B with A inverse of B inverse of A with B. Yeah? So how do you prove this? I'll leave it as an exercise. Do you know why this is a cool trick? You see it in reverse. That's why this Habard-Stratonovic transformation is a very cool trick. That's right, that's right. Because sometimes it happens that you have something quadratic, and you don't know what to do with it. If you do the transformation the other way around, what is quadratic becomes linear. Very good. Let me see. OK, final case that we will need for the case of spectral density of non-ermitian matrices is the following one. Now suppose that I'm using the same letters, I apologize. Yeah, suppose that now A is a matrix, n times n matrix, matrix, actually complex matrix. And the only thing you ask for it is the determinant of A is different from 0. OK, it's the only condition. Suppose that the determinant of A is different from 0. It can have real eigenvalues, complex eigenvalues, mixed up with n2, just this condition. Now you can prove that 1 divided by the determinant of A can be written as follows. As the integral as the product i from 1 to capital N of the set i, this set i complex 2 pi i of the exponential of minus the sum of i and j from 1 to N of set i bar Aij set j. Where set i and set i bar are complex numbers. And if, let me see, if I do a slight modification of this, I'm going to do it here. If I introduce now a couple of complex vectors, bi, bi bar, bunch of them, I have, I can write that. Let me see, the exponential of the sum, that's right, the sum for i and j of pi bar A minus 1 ij Bj divided by the determinant of A is equal to the integral of the product of i from 1 to N, this set i, this set i bar divided by 2 pi i. This exponential thing here, the sum of i and j from 1 to N, set i bar Aij set j, I can put this thing below. Plus the sum for i from 1 to N of bi bar set i plus bi set j. And again, in this case, this is the equivalent of the hardest to noise transformation the other way around. Or this would be, or this B's, you have a pair of them. These, again, are generating fields. Of course, this has no meaning of measure because it might be complex. But sometimes you call it measure. So this would be, again, generating fields. Good, so I'm going to let you as an exercise to prove this. So please do it because I might ask it in the exam. I'll leave this thing as an exercise. Yes, it's without the square root. So in some cases, instead of having the square root of the terminus, you have the terminus, you would use this trick to represent that in terms of an integral. Even you have a representation, an integral representation of using grass-mount variables, but I'm not going to use that, that's too much. More questions? It's not, it's in the whole. So you have to understand, I'll let you to work it out. Because you have to understand what this thing means. So it's better to take the real to put that set i is equal to x i plus real imaginary part. So what this thing means is you are integrating over the real part from an infinity to infinity, the imaginary part, sorry, from an infinity to infinity, et cetera, et cetera. This is what it means. It's 2 pi i, yes. You put it in such a way that when you go to the real and the imaginary part, the i disappears. And the square root of 2 pi i goes to the real part, and the other one goes to the imaginary part. So you have the factors of the corresponding complex, sorry, grass-mount intervals. Good. Questions? In this case, yes. In this case, still a, a symmetric, a symmetric matrix. In this case, that's a half to b. But when you do the derivations, you have to pay attention of the conditions you need to find this expression. And you will realize that must be symmetric in this case. More questions? OK, what time is it? You tired? It's the first day. You're going to say that you are tired. Yeah, a couple of more things. I think we finish for today. And maybe we do some exercises. I don't know. We'll see. So useful tricks now regarding Dirac deltas and Heavisite step functions that we are going to use a lot. So these would be useful expressions in our case, or Dirac deltas and Heavisite functions. And I'll never hear to Heavisite functions. It's just a step function. It's not the theta functions. Theta Heavisite functions, so OK. So the only expressions, the only results we are going to need, I think, are the following ones. This one is the following. Suppose you have the following expression. You have the limit when eta goes to 0 plus or 1 divided by x minus i eta. So I claim that this is equal in the sense of distributions to the principal Cauchy part or 1 divided by x plus i pi Dirac deltas. So what means this equal with a d? It means equality in sense of distribution. So that means you take well-behaved functions. I'm not going to do the details of the theory. So what this thing means is you take well-behaved functions. Suppose that this is a well-behaved function, whatever that is, that means. And then you calculate the limit when n goes to 0 plus of the integral of dx, this function phi of x divided by x minus i eta. This symbol equal in the sense of distributions means that you have to have equality for integrals. This operation apply to integrals. So if this expression, if this function is well-behaved, you can show that this is equal to the principal Cauchy part of pi of x divided by x plus i pi pi of 0. Well, this is the Cauchy principal part. What this thing means is the following. This means it's equal to the limit of epsilon going to 0 of something like this. So you take, what can I put this, like this limit of, sorry? P means Cauchy principal part, which I'm going to explain what it means in notation. So the Cauchy principal part of an integral means the following. Again, this integral is from minus infinity to infinity, for instance. So what you do is simply you regularize and you take out the part where the integral diverges, which is in x equal to 0. So you make the limit when epsilon goes to 0 of the integral from minus infinity to minus epsilon pi of x x, I'm using r dx, plus the integral from epsilon to infinity pi of x x dx. This is what this symbol means. This theorem that goes under the name Sokowski-Lemel theorem. And actually it's not very difficult to prove. I'll let you to prove it. Good? What? What this notation means? This is what is called Cauchy principal part. Sometimes you have that integral of an integral diverges, but these diverges can be removed. So suppose that you have an integral. Let me do it here. Let's do it for simplicity like from minus infinity to infinity. Suppose you have a definite integral f of x. And sometimes it happens that the integral diverges. And sometimes even though the integral diverges, the integral can be finite. So suppose that the limit when x goes to x 0 of f of x is equal to infinity, for instance. So then what you do with this integral, sometimes what the best thing to do is to do the following. You define a new integral that is you integrate around the singularity. For instance, you do the integral from minus infinity to x 0 minus epsilon 1 of f of x x plus the integral from x 0 plus epsilon 2 of infinity of f of x x. So you remove the singularity of the integral. And the way you remove it might be different from the left and from the right. Then you take the limit when epsilon 1 and epsilon 2 go to 0 of this object. And then you see what happens. In the case where epsilon 1 is equal to epsilon 2, that means you approach the singularity at the same rate. This is called Cauchy principle part or Cauchy principle value. When epsilon 1 is equal to epsilon 2, because there are ways, different ways to remove this singularity, when these two guys are the same thing, the result of this integral is called Cauchy principle value or Cauchy principle part. More questions. In this case, since I said that phi of x is a very well-behaved function, that means essentially that this c infinity doesn't have singularities. So the other singularity that can come is from the denominator. So since I'm applying the principle Cauchy part of this, the singularity is at x equal to 0. You go to your supervisor and you tell him what you ask me to do, diverges. What can I do both? So but again, if you start with a problem which is well-defined, unless you scroll up in the derivation, this singularity has to mean something. Remove it or understand it. More questions. For the problems we are going to do, Chris, this will not happen. But maybe in the future, it might happen that you find infinity somewhere. More questions? Yeah, yeah, yeah. This appears, for instance, when you do, for instance, it depends on the context, but I know what you mean. So what happens in that case is that, suppose that you have an integral that goes from minus infinity to infinity to this one, and you have in the denominator this, or the thing you have before, you have x minus i epsilon or i eta, then you can do this integral going to the complex plane. You know these tricks, right? You go to the integral, go to the complex plane, so you complexify the integral, and there is a theorem or a lemma, it's called Jordan's lemma, that tells you that depending on where the singularity, the pole is, and how you close, the contribution that comes from a semicircle, when the semicircle goes to infinity, is 0. So you know what I mean? No, normally that comes from another part. And actually, this theorem, you can prove it this way. You can complexify, use residue theorem, et cetera, et cetera. But one thing I need to point out, because sometimes when students, they do this, the way they close, is for the integral to give you something different from 0. And you don't do this, right? So what you are mentioning, I don't think we are going to find this thing, but maybe it's worth to mention. So suppose you have an integral the following, right? So you have an integral from minus infinity to infinity of phi of x, x minus i eta, right? So you are doing an integral in the real line of this function, phi of x. But in the complex plane, and this is a very well behaved function, but in the complex plane, you have a pole, a single pole at here, right? Actually, let us do it, let us do it more fancy. So you have a pole here, x0, and you want to resolve this integral. So what you do is you say, ah, OK, so what I'm going to do, I'm going to first consider a finite integral from minus r to r, and the integral goes from minus r to r. So what I do is I take the integral from minus r to r of phi of x, s minus x0 minus eta. I want to do the limit r going to infinity, because the integral that I'm interested in is this one. But first I do it finite. And then what you do, you complexify the integral. So you say, ah, so this is related to, I'm going to do the integral in the complex plane. I'm missing dx all the time. z, z minus x0. And what is the, and I choose a closed path, right? What is the closed path I choose? No, that's not true, all right? So you don't choose the path that encloses the pole. You choose the path that makes that the integral of the semicircle goes to 0, OK? And that depends on the integral. So you never choose a path so to, you know? You say, ah, if the pole is above, I'm going to choose this one, because I want to apply a residue theorem. It doesn't work that way. Because in the limit when r goes to infinity, you want to this integral to go to 0, because this is the integral you're interested in. So the way you close the path is such that then, when you go to the semicircle, you can apply Jordan's lemma, and that integral would go to 0 when r goes to infinity. More questions? Depends on the function. OK, five more minutes. OK, one more useful expression in this case for the Heavisite function. Here's the following. Suppose that you have the complex plane, and I think about the logarithm of set. You know, this function has a branch cut at 0, branch cut. And you can put it to go to 0 in the real axis, the negative real axis, to minus infinity, in such a way that if I approach the logarithm from one side or the other, there is a jump of 2 pi i. So if I take the logarithm, suppose that this is x plus i eta, and I compare the logarithm of x plus i eta with the one below, x of minus i eta, and I apply the logarithm to these two things, I make eta going to 0, and I notice that there is a jump of 2 pi i. But only if eta is in the negative part. Sorry, if x is in the negative part, if it's in the positive part, this is not true, because here there is no jump. So therefore, I can say that the theta function of the step function of eta minus x is equal to the limit of eta going to 0 plus of the logarithm of x plus i eta minus the logarithm of x minus i eta. I think I put it correct. Did I put correct designs? Work it out. And this is the heavy side theta function. It's 0 when the argument is negative, and 1 when the argument is positive. And when x is equal to 1, flip a coin on the side. Doesn't matter for most cases. You see this equality here? If x is negative, what happens if you are taking this x, which is in the negative part, and then comparing x above and below the branch cut? And if I take the logarithm, there is a jump of 2 pi i. Ah, sorry, I forgot. I know what you are. We're confused. This is the limit of eta going to 0 plus 1 divided by 2 pi i. Now, there is a jump of 2 pi i between the values of the logarithm above and below. If I divide it by 2 pi i, this goes to 1 when x is negative. And on the other side, there is no jump. So this is 0. Good. Questions? In the definition of the logarithm, the complex plane is not has a special singularity at 0. This is called a branch cut, right? It's called a branch singularity. And it has a cut that goes from the singularity at 0 to the infinity. So that means that in this line, the logarithm is not well defined. And if you compare the logarithm above and below, there is a difference. Yeah, so no, what happens is the following. And this is another thing. So if you now take one of what is called a Riemann sheet. So what happens, you can define what is called the principal value of the logarithm, which is not the same as the principal value of Cauchy before. And what happens is that you take multiple sheets in the complex plane. And when you go around, here, if you stay in the same sheet, there is a jump of 2 pi i. But you glue this sheet with another copy in the complex plane. And it happens that this function, which is not defined in one copy of the complex plane, is well-defined in infinite copies of the complex plane. But if you stay in the same sheet with, I think this is called a Riemann sheet, there is a jump. The same happens with other singularities. For instance, when you have a square root, more questions. OK, so that's it. I'll see you tomorrow. Thank you. See you at 7 PM for the head together, here.


Coming up on DTNS the robots can't help Apple, but the AI may Facebook lets you push a button to send your photos over to Google and what tech companies will do about the pressure to change their business with law. This is the Daily Tech News for Thursday, June 4th, 2020 in Los Angeles. I'm Tom Merritt. And from Studio Redwood. I'm Sarah Lane from Oakland, California. I'm Justin Robert Young. And I'm the shows producer Roger Chang. Hey, we're just having a discussion about who we think the quintessential interviewer was. Maybe you have an opinion? Go listen to our expanded show, Good Day Internet, by becoming a member at patreon.com slash DTNS. Let's start with a few tech things you should know. Fitbit obtained emergency use authorization from the US FDA for its Fitbit Flow Emergency Ventilator. The lower cost design is based on the MIT event system and is the automated resuscitator style design replicating the function of manual resuscitation bags used by EMTs. With the FDA authorization Fitbit can now use its existing manufacturing partners to build these in large volumes. Messaging app signal announced its next update on iOS and Android will offer a dedicated face blurring option in its image editor. The feature can automatically scan for faces using an on-device system library and users can also trace over faces if it fails to detect one. Signal says all image processing will be done on device. Huawei launched the 6.81 inch Honor Play 4 5G. A lot of numbers there, but it's the Play 4. The Honor Play 4 and this one is 5G. Also a 6.51 inch model called the Play 4 Pro 5G. These are launched in China. A version of the Play 4 Pro will be offered with an infrared temperature sensor. The Play 4 5G costs $1,799 yuan, that's about $150 US, and the Play 4 Pro costs $2,899 yuan, that's about $400 US. And the version with the temperature checking costs you an extra hundred yuan. Some musical chairs going on at Google. Google announced Ben Gomez will leave his role as head of search to go to oversee Google for Education, Google Scholar and Education Search, as well as Google Arts and Culture. Gomez will remain a technical advisor to search, however. Prabhakar Raghavan will replace Gomez as the head of search and assistant, which encompasses news, discover, podcasts, and also Google assistant. Jen Fitzpatrick will now run Google's central engineering team. That's not a hard job, which has 8,000 employees and is responsible for the company's core technical systems and infrastructure. Corporate IT, UX, design, Google accounts, and privacy. But that's it? Yeah. Yeah, it'll be fine. Small little job. Facebook is rolling out labels that identify media that is either state-owned or state-controlled. Those outlets will no longer be allowed to buy advertisements on Facebook in the US starting this summer, and advertisements they run outside of the US will contain labels as well. Facebook used outside experts to classify the state-controlled media based on multiple factors, and outlets can appeal that label if they feel it was applied by a mistake. Alright, let's talk a little bit about all the streaming. People are starting to come out of their houses again, Justin. Are they still watching the streaming? Oh, heck yeah, Tom. Nielsen estimates that streaming is staying higher than it was pre-lockdown despite lifting of restrictions across the country. Connected TV includes game consoles, smokers, and the like. March 2, Nielsen estimated 2.7 billion hours of viewing on connected devices. That peaked at 3.9 billion for two weeks from March 23 to April 5. As lockdowns were eased, the hours fell, but not by much. The week ending May 10 still had 3.5 billion hours viewed. Nielsen said traditional live TV usage in early May was only marginally higher than 2019. Yeah, it's still probably too early to draw too many conclusions. That 3.5 billion might settle back down closer to 2.7 billion by the time everybody's really back to going outside all the time. But it does show that people turned to streaming more than traditional and have kept using it. So I mean, I guess you could conclude if this holds that we have accelerated the adoption of streaming among a large number of people.   Certain things will continue to stick even after life goes back to quote normal, whatever that means. And I think for a lot of people, it's like, I like that show. I'm going to keep watching that show where I'm going to, you know, I'm going to use the streaming service that maybe I hadn't used before.  Yeah, and not to mention, these streaming services are optimized for retention in a way that traditional television is not. Former Foxconn executive David Bourne tells the information that back in 2012, Apple executives, including Tim Cook, were reportedly in China to see the results of an experimental iPad production line that wanted to replace humans with robots. Terry Guo, Foxconn's chairman at the time, reportedly told Apple that Foxconn's assembly lines would contain one million robots within two years. Well, 2014 came along and that didn't happen. But last year, Foxconn was using 100,000 robots across all of its manufacturing and the information sources say that's based on dissatisfaction of the finished product of the robots by Apple. Apple launched its own stealth robotics lab in 2012 to try this out themselves, which housed a team of automation specialists and robotics engineers who initially tried mimicking that Foxconn iPad automatic production line. Apple reportedly wanted to cut 15,000 workers from the production line, but machinery couldn't handle Apple's precision methods. Apple also tried an automated production line for the 2015 MacBook, which was not only abandoned, but that MacBook itself was postponed by some months because the experiment didn't work. The information article also goes on to talk about how the adaptability of human run production lines is better because humans can be just told to do something a different way. Whereas machines have to be reprogrammed at this point. So if you want to change something midstream or increase capacity to lines that didn't have the robots, it's not as flexible as the humans. Not that the world needs any darker thought that isn't already populated, but the first thing I thought of was specifically with Foxconn, if the idea was to move to automated lines to remember their suicide epidemic that happened. And indeed, that was through 2010. So if they were introducing and touring Tim Cook through that, I wonder whether or not there was an element of like, hey, we know that this has become a scandal worldwide. It certainly was here in the United States, the uncomfortable nature of how happy these Foxconn employees were. Maybe this is a way that we can go forward and continue to keep your business. I wonder whether or not that had anything to do with it. You know, also, just the idea of the, okay, so there was an experimental, let's see how iPads get assembled, you know, using robots instead of humans. Come on over Tim Cook and various Apple executives at the time. And this is a few years ago, back in 2012, so eight years ago now.  I understand that the, the concept of needing human hands to be more precise when you're talking about tiny little parts of, you know, of very expensive gadgets. But, but the fact that it didn't really work out that well for Apple, you know, Apple kind of going, well, maybe we can do this ourselves and it'll be closer to home. You know, that the, the experimental lab they had was reportedly just a few miles from Apple's main campus in Silicon Valley. And that didn't really work out either, to the point where we're still, we're still kind of using the assembly line with all of its problems, as you mentioned, Justin, as we have for many decades. Yeah, this reminds me of 1830 and the, the race between the Tom Thumb steam engine and the horse drawn rail cart over a 13 mile stretch of track. The horse was supposed to lose. This was going to demonstrate the superiority of the steam engine, but the horse kept taking an early lead. It could adapt to the steam engine. Steam engine could just hit its top speed and go. The horse could like give itself a rest. And when the steam engine caught up, it could put out a burst of speed and eventually Tom Thumb, the steam engine broke down and the horse won. But less than a year after that race on July 31st, 1831, all horse drawn carts were replaced by steam engines on the rail line, BNO, that sponsored this race. So I just throw that out there as a sort of like, yeah, stuff doesn't work until it works. And this is how you get there.  And then you go back to the drawing board and you try again. So I think this, I would look at this story and say, huh, we're probably getting closer to robots being able to do this because we've figured out where they fail and people are working on fixing that problem. Well, sort of pretty related, but sort of on the flip side of this whole story, a California based startup called Instrumental Inc., perhaps you've heard of it, perhaps you haven't created by formal Apple engineers, has created a system that could help current Apple engineers during the coronavirus crisis, which has been rumored to be contributing to the delay of the upcoming iPhone 12, possibly anyway, particularly because travel to China has been restricted. Engineers who have to go and make sure everything's going well and make sure everything's up to speed can't go. They can't do it. They can't do their jobs. Instrumental system equips manufacturing lines with cameras and then analyzes those images using AI software so that the engineers can have more flexibility and not always have to be at any physical location to make sure that things are running smoothly. Cameras and artificial intelligence are designed to spot things like missing screws or bent springs or damaged batteries all in real time. So yeah, this is an example of something that people, you know, the idea of putting cameras on the assembly line so you could look and see what was happening. That's not new. But this company finally made it work. This is the one that said, oh, we can make this so that it is a replacement for you having to be here in person. To the to the point that Motorola and FLIR were using this before the virus to monitor lines like this isn't like, hey, maybe it'll work now. This is again kind of like the streaming thing and acceleration of an existing trend. I was once on a flight with one of these Apple quality assurance engineers and she told me a great story about how she was very, very aware of her favorite hotel bar in Shanghai and how she would take her little day trip and tear down a few products that she was set there to tear down and make sure everything was okay and then make sure she got right back to that hotel bar because she was going to be on a flight out as soon as her tour of duty had ended. And that could last as long as a few months. Sometimes she was there for a significant period of time, nor at least at this retelling on this flight was she particularly happy about it. So I could imagine that this is something that Apple could use. And you're right, Tom, this is just forcing the issue like now. Okay, now you can't go to China, even if it's just, you know, a company that has infinite money, and it's just, all right, go literally put this woman in a hotel so she can drink and look at tear torn down iPads for three months. Now you can't do that. What's the best way to do it? And this seems like a an effective and more drill down version of quality control. Well, and she was probably really good at her job.  You know, maybe some people enjoy it probably a lot of people don't but who else is going to do it. This is your job. So, to be an engineer who has a lot of skills that can be put to different uses. Because some of that just kind of like, how's it going on the assembly line type stuff can be sent to you remotely just it seems like such a no brainer. I know there's more to it than just like why didn't I think of it before. Obviously, people have but but it's a good solution. Yeah, because before the angles weren't right. You didn't see the things you needed the system couldn't spot the stuff you wanted to and it looks like maybe this instrumental ink has figured it out. The Facebook photo transfer tool that launched in Ireland at the end of 2019 is now available globally. The feature lets users directly copy Facebook photos to Google photos with an encrypted transfer rather than having to download and re upload them yourself. The option transfer a copy of your photos and videos is found in the settings menu under your Facebook information. Facebook support for other services beyond Google photos is indeed being built now. The feature is part of the open source data transfer project. Yeah, and that's that's the big thing you should be aware of if you weren't. I mean, we've had this in the US, Canada, Europe for a while. I think it came along around April earlier this year. But now it's everywhere. It's super simple. I did it. You press a button, it tells you okay, it's in process and your photos show up over there. It's so much easier than having to download. Where is it? What folder? And the data transfer project is an effort by these companies to stay ahead of antitrust legislation, at least in one sector that might have forced them to do stuff like this and say, hey, we're making it open so you can take your data with you. Granted, right now it's just Facebook and Google. It's just photos. But this is the beginning of the ability to move your data around between services. And that's something I want to keep an eye on. Yeah, you know, I'm curious to see obviously this happened because Facebook was under pressure, but I think it's a fairly, I mean, it obviously took a lot to build, but it's a low calorie give for them. And it shows you the evolving market of what these walled gardens really required to thrive. Google's threat analysis group announced it had recently identified phishing attacks against personal email accounts from staffers on both President Trump's and Vice President Biden's campaigns. Google sent a warning to the targeted campaign staffers on both campaigns, as well as alerting federal law enforcement officials about the attempted attack. The attacks against the Biden campaign staffers appear to have originated in China and the attacks against the Trump campaign staffers appear to have originated in Iran. Those are best estimates. It's easy for someone in another part of the world to make it appear like their attacks coming from somewhere else. But the threat analysis group is pretty good at those kinds of forensics. What's the significance of this host of politics, politics, politics? Well, it certainly was something that became a major issue after the DNC got hacked and the Hillary Clinton campaign got hacked specifically after one of the higher ups there, John Podesta, clicked on a spear phishing link. So if this is something that was being attempted on both the Biden and the Trump campaigns, it is certainly no surprise. To me, this is the new normal. Everybody has to deal with spear phishing attacks. You can only imagine that the prize is that much richer when you are looking at a heightened media environment. And remember how much of a chaos bomb those Podesta emails were and those DNC emails were the DNC emails were released the day or sorry, two days before the Democratic National Convention last year. So you could only imagine even if these were successful, I mean, these have been detected. If they are successful from somebody else that clicked on some of these links, then you never know when these kind of treasure troves of information will pop up. Yeah. All right, folks, if you want to get all the tech headlines each day in about five minutes, be sure to subscribe to DailyTechHeadlines.com. Tech companies are under fire for the tech they sell to law enforcement right now. I don't think you need me to explain to you why there's a lot of opinions about law enforcement right now. Amazon sells hundreds of law enforcement agencies a facial recognition tool called recognition with a K. We've talked about that a lot on DTNS. Among the interesting things about recognition, AI researchers at the University of Toronto and MIT did a study that found that recognition misidentified people with darker skin more often than those with lighter skin, particularly females, but also males. Amazon says that that research is flawed. They denied that claim, said you don't have the most current version of the algorithm. Amazon has also been criticized for its Ring Doorbell video sharing partnerships with police departments. They've also modified those to change it to be under the control of the ring person very clearly whether you would hand over video to the police department rather than just on an ongoing basis being able to improve it on a case-by-case basis. That's not just Amazon. Google has been criticized for working with geofencing warrants. These are warrants that permit the police to request anonymous information for phones in an area surrounding a crime. So you say, give me this boundary line, any information, anonymous information on activity there. And then if the police with that information can narrow down to suspects, they can get a warrant to get user names and location data for specific devices. Geofencing warrants are criticized for sometimes being overly broad in the area allowed. Then again, Google says we just comply with warrants. So if there's a problem with geofencing warrants, then we should work on reforming geofencing warrants. Google also pulled out of a contract to help the Department of Defense develop machine vision technology for drones. So Google has bowed to pressure in the past. Who else? Microsoft partners with the New York Police Department on a system that aggregates data from a network of cameras delivering license plates and other database-driven devices. IBM sells machine learning tools for predictive policing in an attempt to predict future crime spots and sometimes actual future criminals. But again, what kind of biases are in these data sets that these machine learning algorithms are trained on? IBM has also partnered with the NYPD to use images of New Yorkers to train AI tools. Well, not necessarily getting the permission of everybody in those images. And Nextdoor has been criticized for tolerating racial profiling by its users. Nextdoor has taken action, told Wired that it has seen profiling decline since it began requiring more detailed information before reporting someone as suspicious. So if you just try to type something on Nextdoor, sometimes it'll pop up and be like, hey, it sounds like you're trying to say this. Have you thought about that? Can you add these more details? There's also problems with Salesforce and other companies out there. Microsoft and Amazon are sponsoring the International Association of Chiefs of Police Conference in New Orleans later this year. Microsoft also has been an advocate for having legislation about facial recognition and how it should be used. They have leverage. They have lobbying. They have relationships. Should they all just stop selling this technology? Jeffrey Albert, a criminology professor at the University of South Carolina who serves as a member of the International Association of Chiefs of Police Research Council, told Protocol that if these companies step back from providing technology, law enforcement agencies would find other vendors. He said, quote, someone's going to sell it to the police to make money. So it might be principled for Microsoft or Google or Amazon to stop providing their technology, but that would not necessarily stop law enforcement from using that technology because they might be able to find and probably would be able to find another vendor. So the question is, what do you want them to do? You know, I think the biggest thing here is transparency and specifically pushing for that when you are dealing with law enforcement or governmental contracts. Let's also remember that Google sold Boston Dynamics and part of at least the rumored reason why was because Boston Dynamics was inherently going to move more into a defense contractor model. And Google did not or Alphabet did not want that to be necessarily such a gigantic part of their portfolio. The reason why people do this is because the money is big and it's good and it never goes away. You can you can continue to cash that check if a system is built on. And this is government in general law enforcement is no exception. Do not change systems all that often. They don't nimbly go from one thing to another. So if you can get a law enforcement contract that is a lot of long term money and you know specifically looking at the people who are sponsoring the association of the chief of police chiefs of police Microsoft and Amazon both sell AWS and Azure. And they want people to be on those platforms and they build products specifically for law enforcement so they can secure those contracts including some of the AI stuff. So all I would ask and all I've ever asked and by the way this is only going to become more of a problem up front as up front and detailed as you possibly can within the agreements and should the agreements become too opaque. Then I do believe it is our consumer right to hold them accountable for that. Well and in a situation like recognition and Amazon saying well our software is not recognizing certain people over other people. That's just not happening. But there's a study that says it is happening. It's on Amazon to say OK well maybe the people who are making the software you know we have to rethink that. Maybe we need you know another group of folks who are making sure that the people making the software are not introducing biases that are going to become problematic later on. I don't think a lot of this technology is inherently bad. I mean it's all about you know get the bad guys protect the good people. But it is rife with issues and so it kind of just falls on the people at the end of the day of like who's making this why are they making this and what are they thinking. But Amazon would answer you Sarah to say no we've done all that. It's these researchers we're looking at an old version of the algorithm. Well OK I mean that's so so I mean but but instead OK I think I think my point is instead of Amazon being like well that's wrong.  It's it's more of like no here's why you might have thought this here's why we really care that that wouldn't happen. And here's what we're doing to make sure that that doesn't happen in the future. I mean one answer to this could be don't worry about it companies sell your products law enforcement needs them and and and don't listen to the folks complaining. I don't know that that's a tenable situation for companies to do right now. They are on immense pressure inside and out to take this seriously and pay attention so they will possibly lose customers and employees. You know we're seeing petitions and walkouts. So companies are probably wise to pay attention to this and not just ignore it. The other side would be to say just stop selling all together. Don't sell the law enforcement. But again it's not a flimsy excuse to say well but does that solve the problem if someone else just steps in and sells them. Is it better if these companies take their privileged position and use it to have better rules. That's what I would like to see is Microsoft and Amazon and Google and Salesforce saying you know what we're going to improve. Amazon is going to say we're not just going to tell you it's better. We're going to do what Justin said we're going to affect transparency. We're going to tell you how it's better. We're going to admit where it's not better. We want to push for legislation that will put limits on how it can be used which is what Microsoft is doing. It's pushing for legislation because private companies just not selling isn't really an effective tool in a marketplace as open as this where law enforcement can just go buy it somewhere else.  Let's come to a reasonable accommodation that helps law enforcement do their jobs properly and accountability. And look they're going to get they're going to get a vendor and that vendor if Amazon came out and said we are absolutely not doing this. Then the team that would develop it could spin out create their own company hook into AWS because they already know exactly how to take best advantage of it. And AWS would still get the money for whatever their server costs but it would be another company that would come out and do it. Like this is the genies out of the bottle on this particular issue. It's just a matter of how you can do it the most effectively and the most ethically. And I think a really good a really good statement from Thrumwalled in our chat is this tech is so new. How do we even know all the things that could be wrong with it and that's important to take into account which is there are things you know it can do. And those are the things you should allow there are things that it might be able to do and those are the things you have to be really careful about. You need to try them and test them responsibly to improve them. And then there's things you know aren't ready yet and those should be kept in the lab and not used in public. Well thanks everybody who participates in our subreddit. A lot of security stories end up there every day and you help us learn what matters to you submit your own stories. Vote on others at dailytechnewshow.reddit.com. All right let's check out the mailbag. Oh let's so on GDI yesterday we were talking about this this sort of like fun fantasy idea that some of us have on the show of having like a coffee shop but also where the podcast happens.  And somebody wrote in and unfortunately I did not get his name. But he said we had something like that in Pittsburgh in fact real real place. It was a restaurant that served waffles but was also a talk show. It's called the waffle shop. That's what we're going to do. Pack your bags everybody we're moving into the waffle shop was Brian. Thank you Brian. Yes the waffle shop a reality show was a performance art project and restaurant in the East Liberty neighborhood of Pittsburgh operated by Carnegie Mellon University students. That's awesome. That's so great. That is now the long term plan of the Daily Tech Show. Right. Yeah it turns out we all have to live close by but we can hang out in our coffee shop. Like everybody on France. It's going to be great. Hey shout out to patrons at our master and grand master levels including Reed Fishler Paul Reese and Mark Gibson.  Oh man you know a very serious episode yesterday kind of went out of our format and did kind of more of a breakdown of our relationship with the police specifically in a reaction to everything that's going on right now in the murder of George Floyd. But we are back to our regular format tomorrow we got a great interview about the the epidemics of 1957 and 1968 why they're different. And we got some great little tidbits in there including where social distancing our modern idea of social distancing came into the public health playbook. Hey thank you everybody for continuing to stick by us and support us. Patreon it means the world. I put up an editor's desk today for everyone. Usually the editor's desk just goes to folks at the associate producer level and above. But this one went out to the whole batch if you're wondering why you got it. It's because it's me talking about some of my feelings and the situations around that Monday show that we did this week. And thanks again to those guys and lady who participated in that show as well. And thank you all for being willing to listen and you can continue to support us daily tech news show dot com slash Patreon. You can also continue to give us feedback which we love our email addresses feedback at daily tech news show dot com. 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Hawaii, the state of clean energy on Think Tech Hawaii. I'm your host, Mitch Ewan, and today on our show, we'll be discussing the Association of Energy Engineers for Hawaii with our guest, Russ Kohler, who's the president of AEE Hawaii. So welcome, Russ. And let's turn it off. Okay. Aloha, Mitch. Aloha, y'all. It's nice to be with you. Nice to have you. And let's just start, I just wanted to start off a little bit with your background of how you became an energy engineer in the first place. Well, I graduated from a Merchant Marine Academy, Maine Marathon Academy, studying marine engineering. And I've always said and very clear to me that a ship is the most efficient cogeneration combined energy system in the world. That got me into energy. While I was at the Academy, my father in California at the time started an energy management company called American Energy Save. By the time I became a senior, I was very interested in getting into energy management and energy efficiency. And so when I graduated and got my Coast Guard third assistant engineer license, I moved to California, did not get on the ship, decided to stay on land, and get into energy management and become an energy management expert. So that's what I did. That's how I did it. My first position was at a hospital, where I, within a couple of years, became chief engineer. And it was arguably the most energy efficient hospital in the state of California. My dad was a director at the time, and I was the one who was putting all the projects together for the chiller plants and boiler plants and all the different energy management control system stuff we were doing in the hospital. So that was mid-70s. I took over the company with my brother in 1980. And from 1980, for the next 25 years, that was my life. Quite a bit of alternative energy, cogeneration, energy efficiency projects. So that's where I was cutting my team. So that was a consulting company. So you had a wide range of various systems that you were able to look at and become smart on, right? That's correct. That's correct. Everything from lighting retrofits to cogeneration. Well, that serves you very well in your current job, I'm sure. It sure does. When I tell people that I was actually involved with renewable energy in the early 80s, they look at me with disbelief. But believe it or not, that is when the solar industry started to cut its teeth and the wind turbines and things that started out as tax shelters and got their wings. Now it's about AEE. What is it and why should we be interested in it? Well, AEE was founded in 1977. So a couple of years before I joined, I joined in 1980. I got to know the founder of AEE quite well, name of Albert Tuman. I developed AEE to essentially be a teaching and educational society so that you could bring the knowledge to all energy engineers and be early adapters to college universities, to engineering students with the goal of always to make the world more energy official. Combat carbon, carbon to carbon footprint around the world. It was all being done at early stages. His goal was to take this internationally. It's the only international energy engineering society in the world. We're in 100 countries. There's over 18,000 members worldwide. And as I say, I joined in 1980. So do the math. I've been a member for 41 years. I became a certified energy manager in the mid-90s, shortly after the program was developed. The certified energy manager program within AEE is the gold standard for the organization. There's 13,000 or 14,000 certified energy managers worldwide. And again, it was to develop younger engineers and students and bring them into the field. A lot of the talk today is about how many of these energy engineers are going to be retiring, and do we have enough energy engineers coming up through the ranks to take those positions? Is the CEM recognized generally across the industry? He said it's the gold standard. Is that a certificate that the industry recognizes? Yes. It's internationally recognized by ANSI. And I can't quote off the top of my head. I didn't write it down here. But one of the European organizations is the CEM. One of the European organizations is also recognized as worldwide. In many cases, and I did put this down on a slide, and I'm not reading from the slides, but many positions worldwide, you have to have a CEM or you have to be capable of getting a CEM. I've seen many cases where someone will get a position with the stipulation that within a certain amount of years, within two years, let's say, you will achieve your CEM. And I've seen, too, where if someone didn't achieve it, they were looking for another job. What goes into getting a CEM certification? I mean, is there a course that you have?  Is there a normal program? Yeah, there is a formal five-day course with an exam on the fifth day. But backing up from that, if you don't have any formal education in electrical engineering, mechanical engineering, or some form of environmental sciences engineering, the test is very difficult. It's not something that you can just take the five-day course and expect to achieve a passing grade. In fact, you have to be able to qualify to be able to take that course. You have to either have a college degree, be a professional engineer, or be in the business for X amount of years just to qualify to sit for the training. And then think. How is the training actually given? I mean, maybe pre-COVID, was it an in-face, in-person kind of training program? Or was it online? Or was it, I mean, how do they deliver the program? Prior to COVID, it was all face-to-face training. You either, for instance, with the chapter, I've looked at bringing instructors over to Hawaii to do the training. They'd be training along with us as a chapter. The chapters, in a lot of cases, will act as tutors for the students because there's quite a bit of math involved with the test. It's a pretty intense program for five days. I can tell you, one of my colleagues at Amgen who was an electrical PE, I talked them into going through the training, and he did not too well on the test. And the reason is because it's a diverse background. It's not just electrical. It's HVAC. It's generators. It's all types of things put in together, water efficiency, lighting, all these different things. So does AEE have a textbook that people can study all these various disciplines? AEE has quite an extensive, I won't call it a library because you've got to buy the books, but it's a very extensive list of books that you can buy and start getting yourself acquainted with a lot of that stuff. The training program itself comes with a binder. It's very extensive. Lots and lots of information, and it's not just a day training. You've got to go home and do homework and study. So it's a pretty intense five days. There's been quite a few trainings here on Hawaii, on Oahu. There was one on just before, and I mean just before COVID, or I should say to shut down, in March last year there was, of course, an exam on the big island. In fact, my vice president of the big island was in that training, and she passed the test. But there again, she had 15 years' experience with ECO or Helco on the big island. So she had a background, she had a background in some renewable and some alternative energy. Is the exam open book or closed book, or how rigorous is it? You know, that's a good question. It's very rigorous, and it is open book. But yet it's still, if you don't have the background in a lot of these subject matters, you're not going to do well without a lot of studying. And I certainly recommend the tutorials that are offered. So how long does it take for your president to, your vice president, to re-qualify to take the test again if he didn't do that well? Oh, no, that's not my vice president. I was a colleague of mine at Amgen. Oh, OK. He was an electrical engineer that I worked with at Amgen, the biotech company.  It is pretty critical to these days because there's such energy hugs. Everyone that's on my board of directors has a certification. OK. I had mentioned in a slide that I was just talking about 80 Hawaii for a minute. Board of directors, pretty diverse group of people. My vice president of Kauai is, she works at Kaua on Kauai. My vice president of Oahu is a VP of engineering with Bank of Hawaii. My treasurer is president of a consulting, energy consulting firm. There's a lot of work utilities on the mainland. Vicki, whom you've met, she is actually a resource energy manager for the Army National Guard. Again, I mentioned earlier, I mean, she couldn't have gotten that position without having a CEM. Myles is stopping. You know, he's the energy manager at the University of Hawaii. Yeah, no, not miles well. He's an interesting one because he had to take his first exam was the certified energy auditor, the CNA. It's listed on, I think the second slide is where it's listed. And when I interviewed almost all these people I'm talking about except for Vicki and Ray, my treasurer, and recruited them into the chapter. Myles was interesting because he didn't feel like he had enough experience. And I convinced him finally that you have enough experience to take your CEM. And he did. He took it. He took it out here in Oahu a year ago. And actually, it was 2019. And he passed the CEM. And that was great. So each one of these guys, my director of scholarships, he's got his CEM, CDA, he's a solar PV expert. He's one of the foremost solar guys here in the state. Oh, really? Oh, yeah, yeah, yeah. Tell us a little bit about the scholarship program. This is something I hadn't heard about. So young upcoming students here, is this something for them? Or is this for people who have already graduated? But anyway, tell us about it. Well, it would be for either one. If you wanted to go back to school and you were doing your graduate studies, we actually had a young lady who worked for her. His name is Fred Brooks. My solar guy, my director of scholarship. And we nominated her for scholarship. She's at the University of Hawaii. She's an electrical engineer. She takes most of her classes out of the same building you're in. And she lives in, I believe, the state of Washington, Milana. And we nominated her for her scholarship. It really just depends on where they are in their studies and in their interests. Here she is, an electrical engineer. She's working for a solar PV maintenance company. And she, to me, was a perfect candidate for a scholarship. So yes, we're trying. The student side of our chapter is fairly new. We're trying to build it up. COVID didn't help. We had plans to get with the dean of engineering, miles being down there, setting up meetings. But this was kind of a dead year for that. So it's something that we plan to do for the future. Well, I'm hoping this interview will be helpful to your outreach program for the young engineers or want to be engineers that are coming up the line. Well, I do, too. In my position over at the Marine Corps base of Hawaii, as you know, I get involved in a lot of teaching. I'm presently teaching a young, what we call, energy NCO. The Marine Corps, in fact, the Marine Corps base of Hawaii is the only base in the entire world that has an energy NCO. And my job is to teach them and get them up to speed. And primarily AMI metering, which is advanced metering infrastructure that we have. But reading meters is one of the main things. But I get involved in a lot of different things. She's new as of November. She's my third energy NCO. And I enjoy teaching. We're starting to learn about teaching and about energy auditing. We've got her involved in a very interesting subject future project yesterday. I was called by the environmental group over at the base. And of all things, if you read through this, it was about sea turtle hatchlings. Sea turtle hatchlings, mama sea turtles, there's more sea turtle hatchlings in Oahu than they ever have historically recorded this past year, which is amazing. And they've never had them over at the base. And the reason that they called me is because what's happening is these hatchlings are hatching and they're looking for the moon to direct them to the ocean. And what are they seeing? But light pollution from the housing. Street lights, house lights, walkway lights, and they're walking into the backyards of base housing. I think if I'm not mistaken, they've recovered. They've saved about 50. Unfortunately, some didn't make it in Paris. They get into the streets. And I went out there and I looked at all this yesterday with environmental. And I brought my energy NCO and my energy engineer colleague, Yako, who I think you bet. And now she wants to get into the training with environmental so that she can actually work with environmental with the whole sea turtle program. And I was thrilled. It's like, if I never brought you here, you never would have known this. And just in that meeting, environmental basically invited her to a training later this month, which great, everything she can learn is great. A couple of years ago, my colleague, well, the energy NCOs that I was working with, the elementary school on base contacted our public works officer. She asked me if we could put a program together. We put a program together. And we wound up teaching 400 elementary school students from third grade to fifth grade. Obviously, the third and fourth graders, we taught more basic. The fifth and sixth, they said sixth. It was third to sixth. We taught a much more advanced. I put a curriculum together on renewable energy. My slides about your program is there. Hydrogen, hydrogen station, wave energy technology, which is another HNEI technology that's been out at the base for quite some years. Geothermal, which is another thing we're studying with the University of Hawaii. All the different aspects of renewable energy is what we taught. And then, as you know, I invited you and Pat to come and teach the fifth and sixth grade gifted students on some renewable, on hydrogen technology and on wave energy technology. And I know that we all enjoyed it because we were asked very interesting questions. And I got to tell a story, a quick story. I have the right to do that. Those kids were so smart, and they asked such great questions, like really good questions. And I have to compare them to this group of students I had from Stanford who came to my system, you see over the shoulder for a tour. And there were 20 of them, and I didn't get one question. They were totally disinterested. And you compare that to the gifted student. I couldn't believe it. I asked, what the heck are you guys even doing over here?  Vacation, spring break. Do you remember the best question this young lady asked you about fuel cells? She said, well, if everybody in the world starts using fuel cells and the byproduct of fuel cells is water, what are we going to do with all that water? Isn't that going to raise the level of the oceans? No, that was a pretty amazing question. That's a pretty good question that she's thinking through the problem. She's already looking at it as a system and saying, well, it's producing water. What do we do with the water? So that's a great logical thinking. So we're getting close to the end. So first of all, another question is, how can all these actually engineers out there become members of AEE? How do they do that, Russ? Well, they can contact me or they can go onto our website, aehawaii.org. There's a tremendous amount of information in there. All of our board members are in there. They can contact any one of us. Any one of the board members would be happy to help them get involved. We have what I feel is a great blog. They can see all the different things that we've been working on talking about from a hydrogen fuel station. It's a great website. It's still evolving. That's how they can get involved easily. They can call me at any time. So what's the fee structure? So AEE National, the main AEE is $300 a year. As you know, you don't have to be an AEE National member to join a YA chapter. To join a YA chapter by itself is $50. But you can join a national, including the chapter, of the $350 a year. Students are different. We were only charging $10. Oh, well, that's a no-brainer, really. We're only charging $10 at this point. You know, we want to get as many students involved as we can. What can I say? In fact, I got a call yesterday from the AEE National vice president for region five, which were part of region five. And she was talking to me about doing an online training course for high school students. It would not be great. Training is training in seminars and conferences. Education is really what AEE is about. You know, I have pretty much the same goal as you to help the state of Hawaii to reach its goal. But we want to reach a goal with zero-emission technology. And that's a whole other show. And I know you do those shows all the time. But OK, so we're almost out of time. But I'd just like to give you an opportunity to give one final pitch to our viewers and to the engineers who are not members yet. So here's your chance to give your quick elevator speech, Russ. Well, please go to our website. Check it out. If you like it, contact me. Contact any of the board members that you might know that are in there. I'm happy to talk to you about any subject and energy management that you would like to talk to, talk about. And we get involved in some really, really great things. I mean, just some of the trainings that we're working on is our HVAC, how energy projects are affected by maintenance. And that was widely praised when we did that. We were working with you, Mitch, on a hydrogen program seminar. Now working with Nicole Loutz on a geothermal seminar. And so some of the tours that we're looking at doing is going down and seeing the new OE-35, wave energy technology, WEC, wave energy converter, it's down in Hollywood Harbor. And again, COVID has kind of stymied us from all this. OK. Please go to our website. You have any questions? Thanks so much for us, so. You're welcome. OK, we'll have to leave it there. You've been watching Hawaii, the state of clean energy on Think Tech Hawaii. Today we've been discussing the Association of Energy Engineers, AEE Hawaii with Russ Kohler. Thanks very much for participating, Russ. I really appreciate it. You're welcome, Mitch. Take care. Aloha, everyone. Aloha.