It moved to ICTB, before that he was a student of the French group, so today he will talk about face transitions in high-dimensional inference. So please, Jane. Thank you very much, Aydrun. Do you all see my slides and do you hear me properly? Yes. Okay, great. So hello everyone. Thanks for these great workshops and thanks for the speakers for all this new knowledge. So today I would like to discuss a recent work, which is a joint work together with my colleagues Nicolas Malkry and Clément Luneau from EPFL in Lausanne and Cynthia Roche, who is a mathematician in Columbia University in New York. So what I will discuss is a special type of face transition that is happening in very sparse high-dimensional inference and learning problem that has been coined the all or nothing phenomenon. And roughly what it means is that if you're trying to perform inference of very sparse signals, which means signals that have many zero components, or try to learn from high-dimensional data that has an effective low-dimensional, that is effectively of much lower dimension that lives, for example, in a lower-dimension manifold, what happens is that algorithms in the very sparse limit have a behavior where they are typically able to perform very good, as good as they can actually, or very bad, as bad as possible, essentially they lead to nothing. And this is why it's called the all or nothing phenomenon. So let me motivate a bit this high-dimensional data that has effectively a low-dimensional structure. So one example in signal processing is very known is the fact that if you take a natural image like this Lena picture and you represent it in the proper basis, in the wavelet basis, here I start from there, I apply the wavelet basis, and then if you try to threshold a large fraction of the wavelet coefficients, the ones that matter the least with the lowest amplitude, and you apply to this new signal that is effectively extremely sparse, the inverse wavelet transformer, what you realize is that the new picture is essentially exactly the same as the original one. What does it mean? This image, which actually leaves a priori in order of 10 to the 5 dimensions, which is the number of pixels, has an intrinsic dimension, which is much lower, which can be of the order of hundreds, which is the number of wavelet coefficients that actually matter. Another example that is the, for example, MNIST dataset in machine learning that has, so each vector that represents these images of numbers lives in 784 dimensions. Actually, there are many techniques, many authors have evaluated the intrinsic dimension of the manifold in which actually leave these numbers, and it is of the order of 10 to the 15, so much lower. And one very cheap way to convince yourself that this is the case is what I did here. I just wrote the simplest machine learning algorithm that you can think of, which is a simple linear classifier, Perceptron, using a logistic cost with a L2 penalization, and I run the plain stochastic gradient descent. And what I do is that I take two numbers, for example, let's say nine and one or three and five, whatever two numbers you want, this defines my two classes that I try to classify. Of course, a priori, there is no reason that this data is linearly separable, it has been generated in a very complex way by people. But if you try your stochastic gradient descent, here I use 5,000 training examples, 8,000 test examples, a bit of L2 penalization, and I try to classify the numbers one and two, sorry, one and nine, that defines my two classes. What appears is that your simple linear classifier is indeed able to obtain a very good test error, in this case, less than a percent of misclassification. And one clear reason behind this success of a linear classifier for this high-dimensional data is that these numbers actually live in a much lower dimensional space, and therefore you have many degrees of freedom to find a hyperplane that will separate these two classes. All right, so all that motivates the so-called bet on sparsity principle that says essentially that the intrinsic or effective low dimensionality is often a crucial ingredient for the interpretability of high-dimensional data. So in this work, we used a statistical physics approach that is of considering idealized models of high-dimensional data with the low intrinsic or effective dimension. We perform, thanks to statistical physics, an average case or ensemble analysis, which leads a typical behavior of algorithms, which is to put in contrast with the techniques from computer science that generally lead a worst case analysis. We are able to access the so-called information theoretic and algorithmic phase transitions, where information theoretic means the phase transition related to the Bayesian optimal algorithm, which does not, we do not take into consideration the computational constraint, while algorithmic phase transitions correspond to practical algorithms that are running in a polynomial time. And what we are able to obtain are, again in contrast with computer science that generally get bounds, we are able to obtain exact asymptotic thresholds and formulas in so-called high-dimensional regime. High-dimensional means here that essentially the number of parameters or components of the signal to infer or to learn are of the same order as the number of data points that you have access to. And this number is extremely large. And the type of quantities that we can access are free energies or mutual information. So this is the same thing, minimum mean square error, generalization errors, and so on. Okay, so the paradigmatic models that we have been considering are the following. So these are probably the most studied nowadays high-dimensional inference problems. They play the role of the easing model in physics if you want. So the first one is random linear estimation, which is also called compressive sensing, which corresponds to the following inference problem. You have some signal x, which can be sparse with many zero components. You have some random matrix phi, which is known, which allows to project the signal x. Some noise is added to this linear projection. The noise, of course, is unknown and is a standard Gaussian in this case. And what you obtain are these observation vector w, and the inference task is given w and the projection matrix phi. Are you able to recover the sparse vector x? Okay. This is a special case of a more generic model, which are called generalized linear models, where now instead of having a linear relationship between w and x, you can put here any function, which can be nonlinear, stochastic, it can be whatever you want. And also this model is very nice in the sense that you can also interpret it not only as an inference problem, but also as a learning problem. For example, if you take the activation function phi to be the sign, you recover the so-called perceptron neural network, which is the algorithm I used just before to classify amnesty. And you are in the so-called teacher-student scenario, which also corresponds to the so-called realizable rule setting in machine learning. So what does it mean? Imagine that you want to use a perceptron neural network as a model for data generation. This is a generative model. So what you do is that you generate data points, inputs to this neural network that you feed in this neural network from which you obtain labels. Okay. So this gives you kind of training data and underlying this training data. There is this rule. And if you take the weights of this neural network to be sparse, you just generated data with a low effective dimension with respect to the ambient dimension of the data. Indeed, the dimension of the data is the number of input neurons here. While the effective dimension of the data you obtain, that means the labels here are only functions of few neurons. Okay. So the sparsity of the weights here allows to generate data with an effective low dimension. Okay. And the learning task is given this data that has been generated from this so-called teacher neural network. A student is given this data and tries to learn this neural network knowing the architecture. He doesn't know which features have been selected by this neural network. He doesn't know the value of the weights here, but he knows at least that such a neural network has been used. Okay. So this generalized linear model includes many applications and special cases such as compressive sensing that we already discussed, CDMA and superposition codes in communications, the so-called phase retrieval problem in signal processing. This perceptron with the sine function is also called one bit compressive sensing in signal processing. You have the rectified linear unit, which is a very important nonlinearity that is used in deep neural networks, or the classical sigmoid or logistic regression, which is a probabilistic model where the quality of the label is given by this logistic function where the weights appear here. And these are the data points. Okay. Another model class of model that we consider are the so-called low-rank matrix factorization, which is a simple probabilistic model for past principal component analysis. So in this inference problem, or you can also think of it as a learning problem, what you are given is a matrix W that is a, you can think of a matrix of data. And what you're trying to do is to find a low-rank representation of this matrix. So the generative model for this matrix in this setting is the following. There is a low-rank matrix X that is multiplied by itself, X, X transpose. You can even think of X as a vector. In this case, this is a rank one matrix plus a noise, which is unknown, of course. And the problem is given this W. Are you able to recover the low-rank structure that is hidden in this W? Namely, are you able to recover this rank one matrix, X, X transpose? Lambda here is the signal-to-noise ratio, which is the control parameter in physics terms. And N here is the dimensionality of this X, which is needed for the problem to be non-trivial, to have phase transitions. Okay, so before going in the regime of very sparse signals or data with an effective low dimension, let us consider the generic setting where the most specific setting where the variables are not sparse. In this case, let us consider binary entries for this vector X. The generic scenario in this high-dimensional inference problem is the one with a discontinuous phase transition and the appearance of a so-called computational gap. So what does it mean? It means that if you try to, if you plot the error of algorithms, you will observe discontinuous phase transitions and the appearance of a so-called impossible, hard, and easy regime. What does that mean? If you consider the Bayesian optimal algorithm, which leads to the so-called minimum mean square error, so the optimal algorithm is doing what? It's exploiting fully the posterior distribution given the data. And the minimum mean square error is defined here. If you plot this quantity as a function of the signal-to-noise ratio, the higher the SNR, the easier is the inference task. You see that up to some threshold, the MMS is very large and therefore you are in the impossible regime. Whatever algorithm you use, you cannot beat the optimal one and therefore you cannot reconstruct the signal. And then suddenly at this discontinuity, the Bayesian optimal estimator is able to perform. And you enter the so-called hard phase in the sense that even if the best algorithm, the optimal one, gives you something, practical algorithms in the sense that they do not need the age of the universe to run, such as a plain PCA, which just look at the principal eigenvector. You just do the eigen decomposition of this matrix and you look at the principal eigenvector or the so-called approximate message passing, which I won't discuss in detail, but essentially it's a version for dense factor graphs of the so-called belief propagation or some product algorithm, which is conjectured to be optimal in this problem, optimal among the class of polynomial time algorithms. You realize that you need a higher signal-to-noise ratio and therefore you have this hard phase because in this regime, we don't know any practical algorithm able to match the optimal performance. And suddenly these algorithms, in this case this AMP algorithm, has also a discontinuous phase transition and you enter the easy regime in the sense that this algorithm is able in a finite amount of time to match the optimal performances. Another example is in this perceptron problem. Now instead, I will use the learning interpretation and plot what actually matters in machine learning, which is the generalization error. So what is it? Here is the optimal estimation of a new label that has not been used in the training data. So the training data is this matrix phi. Each row of this matrix is a data point. These are the labels. I give you a new data point and I ask you to estimate the associated label. And this is the square deviation between the Bayesian optimal estimation of this label and the true one. And if you plot the generalization error for this perceptron model in the case where the weights that have been used by the teacher network to generate the data is binary, the picture looks like this, you also have this impossible hard easy regime. Impossible here in the sense that the optimal Bayesian optimal algorithm performs poorly and suddenly this discontinuous phase transition to perfect generalization. But if you use a practical algorithm, this AMP algorithm, you need more data and at some point you obtain a perfect generalization as well and you are in the easy regime. Here the x axis is the sampling rate that is the number of data points that you have access for in the training set divided by the number of parameters to learn, the dimensionality of the weights in the teacher neural network. So a very generic picture appears them. And the question that we wanted to answer in this work is does anything special happen in the very high sparsity regime that is when the effective dimension of the data is of much lower dimension, is much lower than the ambient dimension in which live the data points. Okay. So this question has been partially looked at by recent work by Gamman, Xadik, Rives, Zhu and Xadik. That first considered this compressive sensing problem that I discussed, that I recall here. They considered a sparse signal which is simply Bernoulli, okay, so made of zero and once and this parameter row controls the sparsity. So the higher is row, the more you have once, okay, the lower is row, the sparser is the signal. And what they did is that they took the known rigorous result in the in the literator that essentially gives you an exact formula that I will not describe for the minimum mean square. Okay. There is a so-called replica symmetric formula. This vocabulary comes from physics that allows to predict asymptotically in the high dimensional limit. What is the minimum mean square? And if you plot this quantity varying the sparsity level, this parameter row, what you observe is that if you rescale the x-axis, which is the sampling rate by a proper quantity that will depend on the sparsity level, when the sparsity level decreases, sorry, when the, so the sparsity increase, which means this quantity row decreases, you see that this curve tend when row is very small to a step function. Okay.  And here, this line means as bad as it can be. And suddenly you jump to a regime where you can perfectly reconstruct the signal. So in order to study this model, what they did is to allow all the control parameters in the problem, which are the signatures ratio, the sparsity level, the measurement rate to be sequences of N. They are now allowed to depend on the system size, which is in contrast with the usual statistical mechanics techniques where usually you consider all the control parameters to be fixed. Okay. They do not depend on the number of spins in physics language. And what they show is this so-called all or nothing phenomenon, the name is very appropriate. They show that when the sparsity goes to zero, if the measurement rate, the number of accessible data is less than some threshold that depends on the sparsity on the signal transfer ratio, then weak recovery is impossible, which means essentially that you cannot say anything even using the Bayesian optimal estimator about the signal. The MMSE is one where one here means the maximum value. While above this threshold, strong recovery is possible, which means that you are perfectly able to reconstruct the signal. So I was very curious when I've seen this result and I wondered how generic it is. So what I did is to take one of my favorite model, which is this sparse principal component analysis and develop a kind of analysis which is similar in spirit, but which is technically extremely different, where again allow all the control parameters in the problem to be sequences of N. But before analyzing this quite complicated model, what we did is the first to take the known results in the literature as they did for compressive sensing to plot the minimum mean square error for the spike, that is this rank one matrix, and therefore to scan to see what happens when we let the sparsity of this vector X or equivalently the sparsity of this rank one matrix, this spike, sorry, increase so that it's made of more and more zeros. We are zooming on the corner of this phase diagram. This phase diagram tell you where reconstruction is possible, where is the art phase, which is this yellow region, where is the information theoretic phase transition, algorithmic transition as a function of the SNR and the sparsity level. And we are trying to zoom on this corner to see what happens. And surprisingly, the very same phenomenon appears. So if you rescale properly the signature notes ratio by some information theoretic transition that was derived erystically in papers by Flora and Lenka, what you see is the same phenomenon you see a curve that tends when the sparsity level, so when rho goes to zero when there are more and more zeros to a step function. Okay. And so what we did is to prove a very fine result on this model, which I won't parse the result and this is not really the point here, but essentially this result tells you that if you take any sparse signal where the sparsity is really allowed to depend on n, you can really have very, very sparse signals. This is the truly sparse regime where the number of non-zero components, sorry, the number of zero, yeah, the number of non-zero components scales sub-linearly with the size of the system. We have a very precise control on the mutual information where the mutual information is in physics term the free energy, which is the fundamental object you want to compute. And it tells you how close you are from a simple scalar formula that you can plug in your computer and evaluate. And it tells you how far you are, what is the deviation. And importantly, from this theorem, which is on the mutual information, you can obtain as a corollary one object that interests you probably the most in order to compute, in order to predict the performance of the optimal algorithm, which is the minimum in square. And you have two bounds that you can precisely evaluate. And you see from these bounds that this MMSE indeed verifies this all or nothing phenomenon, that is this quantity when the sparsity goes to zero and in the large system limit in the high dimensional regime, you see that indeed there is a threshold above which this function is below which it's one here and above which it becomes zero. So the all or nothing is really there. And now we have a theorem for that. But we wanted to go beyond the information theoretic analysis and also study what happens for algorithms, which was not done before. And so what we studied is this AMP algorithm, which I recall is a version of belief propagation for dense graphs originally introduced for compressive sensing by Yoshiyuki Kabashima and rediscovered later by Ondra Montanari, by Dono and Maliki, which is a very simple recursion, but extremely powerful. And this algorithm enjoys two very special properties. The first one is an exact characterization in a proper asymptotic limit thanks to a so-called state evolution, which is a simple scalar recursion that tells you what is the mean square error, the error that will lead the algorithm in the large size limit without even running it. You can predict the behavior of the algorithm. And moreover, this algorithm is conjectured to be optimal among all polynomial time algorithms. And so what we did is first, we needed to essentially say that we still have the right to use this state evolution analysis in this new regime, where now all the parameters depend on n when the sparsity is extremely high and so on and so forth, which are not a priori state evolution does not apply in this case. But what we prove is that essentially we have the right to use the state evolution analysis in this extremely sparse regime. Informally, we prove that state evolution that allows to track AMP and therefore the curves that I will discuss right now are valid in the very sparse regime. And by very sparse here, we mean that the sparsity parameter can go as one over log n to any power. So what we observe is that there is also an algorithmic transition at which if you collapse the curves, if you rescale them by this threshold that depends on the sparsity level, you see that also the algorithm, this AMP, when the sparsity parameter goes to zero, experience this all or nothing transition. But what is also interesting is that this transition is at a totally different scaling. So the AMP transition goes as one over rho square. So the SNR increase much faster than the one required from the information theory point of view that essentially scales as one over rho. So if you plot the AMP and MMSC behavior, the optimal algorithm and the practical one on the scale of the information theory transition, you see that when the sparsity is very small, you have a large computational gap here, the x axis is on a log scale, that appears. So the problem becomes extremely difficult from a computational point of view. So then what we wanted to know is how generic is this transition. So we wanted to even go beyond this sparse PCA problem and to see what happened in this extremely generic generalized linear model. And essentially, you do not have to read the theorem here. This is not really the point, but this theorem tells you, gives you guarantees again on how far is the fundamental object, which is the mutual information between the data and the labels and the weights in this neural network. And you have a simple scalar expression for it and you can control very precisely the deviation. And all that is valid precisely in the regime, actually in a broader regime, but at least in the regime where you observe this all or nothing phase transition. From this very fine theorem, which gives you finite size fluctuations of the mutual information of the free energy, you can also derive an exact analytic expression for the generalization error. And also let me just mention that you can precisely get a limit when the sparsity really goes to one, when the signal is almost only made of zeros, the true limit. You can also get an asymptotic expression for this potential and it becomes extremely simple for this concept. Anyway, all that to say that from these results, what you can do is also plot the generalization error for this learning model. So here is the Percepton that I already discussed. This is the Relu-Rilou neural network, which is again used a lot as nonlinearity in deep neural networks. And you also observe that when the sparsity goes with n to zero, to small value, you observe again a collapse of this curve at a threshold which is explicit, the measurement rate threshold, the x-axis is the number of data points that you have access in the training set. And you see that when the sparsity of the underlying weights of the teacher neural network, which just means the effective dimension of the data is much lower than its ambient dimension, you see again this all or nothing behavior that appears in these different models. And again, we have an explicit formula for the threshold. So let me summarize quickly what I said. So statistical physics predictions allow to rigorously validate what happens in the corners of the phase diagram. And by corners, here I really mean when the control parameters are depending on the system size and can go to zero or diverge with the number of variables in the system. This all or nothing phenomenon seems extremely universal, at least in the models that we considered, universal in the reconstruction of very sparse information, that is information with an effective low dimension with respect to the dimension, the ambient dimension of the data. How generic it is, I think it's an extremely interesting question. We don't really know. There is this very recent paper that seems to indicate that in a very large class of additive Gaussian model, which does not include this generalized linear models, but at least includes the sparse PCA that I discussed, but other type of model, here X can be anything, it can be a tensor. In a large class of Gaussian model like this, it seems that from these results this all or nothing is actually happening for all sublinar sparsity or very wide regime of sparsity. I also discussed this all or nothing in algorithms, in particular in this AMP algorithms. It happens at least in sparse PCA and we proved it. A very interesting question is what about other algorithms like MCMC or gradient based? Is it specific to algorithms that are conjectured to be Bayesian optimal or at least in some regions like AMP or is it a more generic phenomenon from an algorithmic point of view? Another question is what happens in more complex models? Here I've discussed a single-layer learning problem. What happens when you have multi-layer, for example? Is it still the case or things smooth out? I have no idea. Of course, the most fundamental question is why this phenomenon happens. I don't have an answer right now. I don't have a real understanding of why this thing is going on. Now we know it happens in wide generality. I think it's very important to understand why is it the case. I will stop there. Thank you very much. Thank you, Jean. Questions and comments? Okay. Let's start from me. This signal-to-noise ratio also could be interpreted as a lambo for measurements versus the dimension of the dataset? So here there were two main control parameters that I've been discussing. In the in-front setting in this sparse PCI problem, I was considering the signal-to-noise ratio, which controls the signal strength with respect to the noise. But in the per-step tone, for example, in this simple neural network that I've been discussing, a more natural control parameter is instead the number of data points that you have access in your training data. In this case, this is the sampling rate. But crucially, fundamentally, if you want this signal-to-noise ratio and the sampling rate, they play a similar role. They are just control parameters that allow to control the difficulty of the inference or learning tasks. So they play a similar role, essentially. Yes, there is a question from Haiping Fan. He asks, can deep neural networks be approximated by multiple layers of generalized linear models? Yes. So deep neural networks are multi-layer generalized linear models. So if you concatenate multiple generalized linear models, you exactly obtain a deep neural network. Then the learning task in deep neural networks is you have this concatenated GLM. The task is to learn, appropriate weight matrices in this GLM in order to fit the training data and hopefully to generalize from there. The answer is yes. We have papers where so one can look at my papers and also other papers by Faw and Lenka, where we start from our theory that is under control for the single-layer GLM. And we concatenate these GLMs in order to say something about deep neural networks. Yes. And also this analysis you presented is quite similar to this finite-sized scanning analysis in combination. Yes. Can you repeat? So this analysis is quite similar to the finite-sized scanning analysis in such cases. Yes. So in order to obtain all this result, what we do is essentially a finite-sized analysis. So instead of getting directly asymptotic results for the free energy or mutual information, we place ourselves at finite size and in this case, all the parameters in the problem can naturally be functions of this size. And what we do is to precisely control what happens for a finite end. Yes. So this is a result, is a finite-sized result. Exactly. And from there, you can essentially zoom out in the corners of the phase diagrams. Yes. Okay. So are there other questions? Okay. If no, let's thank again all the speakers of this session. So this morning or this afternoon's session closes. Metal.


Unlike physical health conditions, diagnosing mental health conditions is more difficult because in many cases some symptoms that belong to one disorder are also symptoms of other disorders. Let's take the example of depression and anxiety. This is a symptom network in age-year-olds of depression and anxiety. And just to help us see the symptoms of the two disorders more clearly, we have the symptoms of depression in red and anxiety in blue and they're really intermingled suggesting that there probably aren't separate disorders at least at this age. So this approach called Network Analysis that we're trying in this project, if it helps us better understand how symptoms are related to each other and also how they develop through childhood, this really helps us think about how psychiatric classification is currently done and how it can be improved, which will eventually lead to us being able to help individuals suffering from these disorders better. The thing that drives me and gets me excited about the research is curiosity because we understand so little about mental health that the sort of possibilities for trying to understand these things is just endless.


Hey guys, welcome back to come again. I'm Shannon and this week on your pop review I'm going to be doing the newly released pop Disney number 296 Darkwing duck vinyl figure. So stay tuned As I said, this is the pop Disney 296 darkwing duck Vinyl figure from Funko Pop. I ordered this way back in April and It wasn't yet released. It didn't actually get officially released until July I think it was like July 7th. I pre-ordered it on Amazon and then I got it I think I got it on like the fifth or six something like that But in stores it was released on the seventh. I believe So as you can see here, so as you can see here, you got pop Disney 296 Darkwing duck vinyl figure. You got a little picture display picture of Darkwing DW right there very nice You got the standard window packaging with the slight clamshell inside On the back you got number 296 is Darkwing duck 297 is Launchpad McQuack and 298 is Dozzlin Mallard DW's adopted daughter and then on the side here We got the display side nice image of Darkwing duck and cityscape behind him So let's go ahead and open this guy up and take a look inside There he is. Let me move the camera down a little bit So we can scoot him a little bit closer and get a better look at him So there he is you got his wide brimmed hat there Got it kind of just like with the old cartoon.  Guess that would be violet because purple would be this color back here Some people say it looks pink. It's purple a lot of what people say is purple is actually violet if you look at the color wheel so as you can see you got his light blue slash teal Turtle neck shirt underneath his jacket with the four buttons cape He's in his crime fighting pose and for those of you who don't know who were maybe born a little Little later in life Darkwing duck is a cult classic icon The spin-off of the original duck tails in the 1990s that was on the Disney Channel It usually aired like right after kids started getting home from school around 3 3 30 somewhere around there on there on Disney Channel's afternoon block and Saturday mornings Darkwing duck Is one of those characters that I Stood the test of time You know it was is a goofy Superhero type cartoon Span off from the duck tails and I say it's spanoff because One of the other stars of it Launch pad mcquack. Yeah, launch pad mcquack Got his start on duck tails, and then they crossed him over into Darkwing duck he Darkwing duck has a huge fan bases to this day along with duck tails I I don't really understand why Disney felt it necessary to change the Art style of duck tails to what it is now. I myself Love the old the 90s art style, and I hope that if they do end up bringing back Darkwing duck I hope They don't go with that new art style that new art direction that Disney is doing with all their All their cartoons is just I Don't like it at all. I mean I may be old-fashioned But apparently I'm not too old-fashioned because it seems more like they're going back to the 60s and 70s art style Drawing like the duck tails Mickey Mouse goofy and all them. I don't want to see that happen with DW I really didn't want to see that happen with duck tails Just two classic cartoons from my childhood. I really loved I introduced my kids to duck tails and They love it the original series not the new Disney series But the original along with the animated movie Lost lamp or something like that.  We're all in the same Animated Disney universe type deal. I think there were occasionally crossovers or whatever I don't think Mickey Mouse had his own cartoon at the time He would usually appear in the movie. They would save Mickey for the movies So let's go ahead and spin him around Take a look at the back playing back. You know, you can see his collar. You can see his feet his cape The cape is very reminiscent of Batman dark wing duck has always been kind of that Disney's version of Batman, I guess he'd call him And as with all pops his head does turn all the way around. I Was really excited to get this guys John just told me the other day that he had a pre-order nega deck I was thinking about making this my last pop because my collection is just getting too big for where we live and I don't know. I may have to purchase nega duck just to Say I have them both. It's the exact same figure.  I'm sure you'll be able to find him He might even be sold out. You never know But I don't think nega duck has been released yet So you might have better chances with him if you pre-order So there you have it guys the pop disney number 296 dark wing duck vinyl figure from Funko pop This has been another pop review by your friends at com again Have fun and go out and hunt you down some pops


Hubble's contentious constant, presented by Science at NASA. Thanks to astronomer Edwin Hubble and others, scientists have known since 1929 that our universe is expanding. Its current rate of expansion is called Hubble's constant or H-naught. There are two leading ways to measure H-naught, and for 15 years they more or less agreed with one another. Not anymore, and that's a big deal. Here's why. In the Standard Model of Cosmology, H-naught is a crucial ingredient, right up there with the speed of light. H-naught factors into everything we know about the universe, how old it is, how big it is, what it's made of. If H-naught is tweaked, we get a different age of the universe, different relative amounts of matter, dark matter, dark energy, and so on. Unlike the speed of light, however, scientists can't measure H-naught in the laboratory. Instead, H-naught has to be inferred from observations of the universe. One way scientists have measured H-naught is to use observations of type 1A supernovae combined with their host galaxy's red shifts. Each 1A supernova releases roughly the same amount of light when it explodes. Measuring the amount of light we receive from a 1A supernova tells us its distance. Using an object's red shift, or its increase in wavelength, tells us how fast that object is moving away from Earth. Researchers use many 1A supernovae as distance markers, measuring objects in our local universe, then moving out to get a measurement of the universe's rate of expansion. The other H-naught measurement technique looks at the Cosmic Microwave Background, or CMB, the afterglow from the Big Bang itself. The early universe was hot and dense. Light couldn't travel freely through space. As the universe cooled, the photons were released. This radiation left an imprint, providing insights into the composition of the universe at that time. The CMB can be used to make measurements from the early universe, such as the density of dark matter and dark energy. Those measurements can be combined with the model of the evolution of the universe, allowing researchers to infer the rate of expansion of the universe, or Hubble's constant. As these two camps have improved their abilities to measure H-naught, it has become clear that they disagree. A recent study using the first method yielded an 8% greater expansion rate than the second method's result. Now scientists are asking, are we missing something? Wendy Friedman, Sullivan Professor of Astronomy and Astrophysics at the University of Chicago says, it could be that we don't understand the uncertainties well enough to know why these two methods differ. Friedman led a 2001 study using the Hubble Space Telescope to measure H-naught via the first method, and is leading a new project to measure it more accurately. Another intriguing question, is it incorrect to expect agreement in these measurements of H-naught? Maybe the standard model of cosmology, which predicts agreement, is wrong. That would send researchers on an exciting search for a new model of the cosmos. Do we really know what makes up all of the radiation in the Big Bang, wonders Friedman? Is there a new kind of particle we aren't accounting for? Or are dark energies or dark matters properties changing over time? Over the next few years, researchers like Friedman will be trying to poke holes in how each method conducts its analysis, before possibly invoking a revised model of cosmology. For more mind-expanding news about the cosmos, stay tuned to science.nasa.gov.


What's up everyone, takedown here, welcome back to another video. I honestly wish I was able to record a different video right now, I wish I did not have to record this video, but for me it is important to share my personal life here on my channel because for me that gives a closer connection to my viewers, my subscribers, and anybody else that is interested in my content. So as you guys could probably tell because the title of this video I ended up getting laid off of my job due to the coronavirus outbreak and this week has been a crazy week for me, not only because I live here in Canada and everything is shutting down due to the coronavirus, but I also have been laid off which is kind of depressing for me. In one hand I do understand in the other hand I work security at a casino. They should need security personnel at the casino because there's still money at the casino, but we're going to be talking about that a little bit more, but as for the coronavirus everything's shutting down, museums, malls, any gatherings that originally it was any gatherings that are more than 250 people, right now it's announced 50 people, but there's talks that it's going to be reduced down to 10 people where meaning that they don't want anybody being in groups more than 10 people, which it's starting to get really crazy. The grocery stores are becoming empty, all the produce aisles are empty, toilet paper, hand sanitizer, soap, that sort of things in stores is getting cleared out. It is very apocalyptic scenes right now. People are posting these items online trying to get a hell of a profit from it, so everything over here right now is going crazy. As you guys know, I do work in Ottawa, Ontario, but I do live an hour away from my work, so once we got the call basically them announcing that we are officially laid off, everybody was concerned. Nobody knew what was happening for the first little bit for us as employees because it got announced to the news first, but not us. Took them a little bit while to update us, we checked our emails, HR at our location was one email would say one thing and then half an hour later they'd reverse it and say this is what's happening, then they'd send us another one saying this is what happening, so we did not know a thing until we got the official call from our supervisors saying all staff as of right now are laid off, they are sending out our record of employment, which we should receive in two days and we can go and apply for EI, which after this video I plan on doing. I'm going to start my EI, basically my unemployment application, that way I can hopefully get a little bit money while I'm waiting to hear about what's going to happen next, because everything is shutting down right now here in Ontario. Those that are infected are climbing, I don't know what the death rate here is in Canada, but worldwide it's increasing as well, so the infected rate is increasing right now as well, Ottawa started with one person getting it, within 24 hours a second person, then went up to five and 24 hours later went up to 10, it's been steadily increasing and that's just in Ottawa, Canada's capital, which is really close to the casino. I knew for work, us at the casino, it was going to happen, it was just a matter of when they were going to close it, but for us in security there's been closures at our casino in the past, not while I was working there this past year, but in the past there has been where they end up having to lay off all departments, so any of the restaurant workers, the cleaners, the slot techs, slot assistants, anybody that's in the back for the money, the count team or anything like that, all get laid off because there's literally no work for them, but security stays there for security, it's the same routine as always, you go in for your regular shifts, there's nobody there, nothing's open, you still have to do your patrols, making sure everything's locked up, making sure everything is secured, there's still money in the casino, so whenever we heard about these layoffs, we did not think we were going to be affected by it because we are security, right now there is still security at the casino, but it is only our security manager and our security supervisors that are there, no security employees are there, our full-time and part-time and nobody is there, so in total the casino laid off 800 people, which on one hand I understand is pretty crazy, it's chaotic right now, everything that's going on with the coronavirus, but as of right now there's no word on when I'm going to be back to work, which is depressing, first day I was all upset, angry, not knowing what to do, but I'm trying to think of the positives, right now some people are thinking in two weeks everything's going to go back to normal, I just don't see that happening in two weeks, I'm sorry if you do, but I have to think at it realistically and what I'm thinking right now is since everything is increasing, the number of people infected, the number of deaths that are happening, the fact that we can't or we're not supposed to go in crowds more than 10 people, it's going to get worse before it gets better and I don't think anything is going to go back to normal until it at least starts to level off for the cases and it's not increasing because right now it's doubling by the day most things, so I don't see it doing it in two weeks, I think it will be at least a month or more before everything starts to reopen and things start going back to normal. Without being said I'm trying to keep positive, I have been working on more videos, I have a lot more time on my hands, I'm able to go and see my girlfriend more which she lives in Ottawa, but for me I can literally drive from my house to her house and we're not going outside, we're not going to be in large gatherings or anything like that, there's nothing open anyways, so just go spend the weekend with her or spend I think in a couple days I'm going to be there for about five days or maybe a week or whatever, we'll see what happens but I have a lot more time on my hands for that, so that's a positive for me of course gaming but gaming can get dull, I have a lot of projects I'm working on, a lot of videos I'm trying to plan out, a lot of videos I'm trying to record, edit, get ready and my channel will hopefully not be affected by this but since I have a lot more time on my hands hopefully I can get a lot more things done before everything goes back to normal, so I'm trying to think of the positive while I have this time off, I am going to be applying for EI so unemployment and hopefully I can get some source of money coming in while I'm waiting to hear an update on work, so I just wanted to give you guys an update on everything that's happening right now in my life due to the coronavirus and share with you the facts that I have officially been laid off due to the casino closing because of the coronavirus, I hope everybody stays safe wherever you live in the world, I do know people that live in Ireland, the US so I'm hoping everybody is safe everybody just continues to wash their hands use hand sanitizers don't go outside unless you need to and don't travel outside of your country unless you absolutely need to so hope you guys enjoyed I just wanted to share you a little update with you guys and to check and just tell you guys to be safe because I hope you guys are so I'll see you guys in the next video please take care peace


Welcome to Access a Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey guys, good evening everybody. Welcome to another edition of the AccessaTrader.com Nightly Wrap-Up Show. Hope everybody is doing well. So let's talk about the market, right? Let's talk about the technical views of the market, what's happening now, what we could expect, at least going into tomorrow. Okay, number one, really nice rally here in the cues from the macro side. I think what has been lost in translation with everything that's been going on with all the headlines, nauseating headlines ready to the point of like no return, you kind of have to like what the bulls are doing, right? Same news, day in, day out, ridiculous amounts of new cases. I heard just like in New Jersey, there was like a spike of like 50% overnight, okay? Where I live, where I live the case has been very, very small, like very, very small. But from the county that I live, you know, north of 250 cases and as the state, well or, you know, it was like 6,000 cases like doubled overnight. So there's a lot of worry, okay? There's a lot of worry, but what's lost in translation is actually the technical side of what the bulls are doing. And although again, I don't see that this is being the generational bottom that a lot of people are kind of hoping and praying it is, but I do like at least what we're seeing from the point of stocks going from supply to supply and demand to demand.  And we believe that the house will vote and everything will be good. We'll get additional stimulus and everything's fantastic. The bear case is obviously, well, this is a dead cat bounce. There's a lot of downside that is going to still come. We still don't know what it is, blah, blah, blah. But again, the scoreboard is the scoreboard and our job as professional traders kind of trade around that scoreboard. Although the scoreboard is not going to define your day, it is going to give you some clues. Today was a very hot day for that. We'll get to that in a second. So here's kind of where we are. So we talked about a couple of days ago that we started building over this 185 level. And I believe the market, I said back then, I think if nothing comes out materialistically, we could get a run to 192. So we get that run to 192 today, actually 192, 72. So we get that run. As you can tell here, market stopped right at supply. The problem with this move today was it was very, very odd. If you guys, especially for all you guys who traded in the intraday ranks and trade beta, you kind of know what I'm talking about. So the data was up today, a thousand points, pretty much most of the day. And most of it was to do with Apple, Boeing, Boeing has just been absolute, just a rocket, right? Absolute rocket. You know, obviously I have some other names as well, Microsoft. Semis have been very, very strong. But again, if you look at today's tape, it was very, very peculiar. What I mean by that was when you look at one point before, and we'll talk about the spike into the close, you look at the NASDAQ 100, the NASDAQ composite was up 300 points. And if you looked at the action intraday, right, all I kept on seeing was weakness, like literally everything that I traded, for the exception of NVIDIA. And I think it was NVIDIA and Apple at that time, right? If you look at all the stocks that I look at, intraday, right? This is the intraday chart. Forget about the close, right? So everything gaps up and started to fading. Netflix gaps up, right? Forget about this. This is the last five minutes of the day, right? Netflix gaps up, right? Cells off seven. What else was there? Beyond, there was a nice pivot today in the room. We'll talk about that a second. You know, gaps up, gets downgraded. Cells off about five, six points off the highs. And you started seeing that over and over again. Alibaba, right? Alibaba gaps up, right? Gaps up to 94. There was a nice pivot towards end of the day. All goes all the way down to 90. So you started seeing that all in Amazon really, really good today. And at one point, right? So Amazon gaps up and goes all the way down to 905. So gaps up to, Amazon gapped up to, jeez, I think it was like 99, it was up like 50 at one point pre-market and went all the way down to 905. And I'm sitting there and I'm like, what about my stocks, right? Like, what the hell's going on? What about my stocks? So I turned around in the webinar and I said, I don't want to buy anything. I don't want to buy anything, okay? Everything is selling off. They're putting in lower highs. I think these things are going to fade. I think they're going to fade. I don't want to buy a single thing. And slowly but surely, everything started playing out that way, at least on the beta side. And you started seeing kind of move by move, pivot by pivot, little by little, things are getting weaker and weaker and weaker and weaker. And I'm thinking myself, all right, we're going to roll over here, right? We're going to roll over here. It's obvious. Everything is all good. And you started seeing like pivot by pivot. And I'll show you this in a second. This is kind of why this is such a weird day. So we talked about 457 to the upside just in case the market rally. This is in the morning. And goes 457, goes to 460. That obviously becomes the second entry. It never, right? It never even comes close back to the 460 level. So we're waiting for, excuse me, 560. So we're waiting for the confirmation that never comes. And so I started putting in pivots into the room because I started seeing weakness, right? I started seeing weakness, started seeing strength at the same time. So I said, you know what? Let's see what confirms. So weird stocks started confirming. So, you know, crone, I mean, great move. There was nothing wrong with crone. 584 needs to build. Again, I screwed this trade up because I just don't, I just don't trade these small caps anymore. But this thing starts building 6, 585 confirms 6 and goes all the way to 665. For those of you guys who didn't screw up the trade, great job. BYND, 68 for builds below can flush out. BYND, right? So here was BYND. It took out the lows, took out the 68, went all the way down to 6640s. Again, nothing wrong with that as well.  Okay, Roku's not rallying. This is going to be a good trade. I think the stock has a shot, you know, to get below 90. Excuse me, I put in the wrong pivot. I put in the wrong pivot. Did I put in the wrong pivot here? It was 91. It wasn't 90. Did I put in the wrong pivot here? I put in the wrong pivot, guys. For all you guys on the Twitter feed, you guys probably caught the trade. I messed up. I shorted Roku at 91, okay? I shorted Roku at 91. It went down, it was like 91 in teens. It went down like 70 cents or so, right? 70 cents or so so quickly. I couldn't get any size. So I wound up not covering anything and wound up taking an 80 cent loss and watched it later confirm the right pivot. I think I screwed up, guys.  I put in the wrong price. It went from 90 and it went all the way down to 87.  There you go.  Now I know why the stock held those levels.  It wasn't a proper level. But more of the stories, more of the stories, I started watching all these stocks getting weaker and weaker and I couldn't understand how the market was holding up and I personally had a very odd day, okay? I caught a Tesla short, made some money and then I didn't enter the Tesla short. That went down 30, okay? I got caught and now I see I got caught in the wrong price macro on Roku. So I understand at least why I lost some money. But the most amazing part of the day, if you really think about it, right, is how the good the bulls, how really good the bulls played things out, okay? And again, I firmly believe that you can do whatever you want in this market as far as as long as your process is being highlighted, okay? But I do believe this as well. I think that everybody has a really good, really good save zone, right? And everybody trades the stocks they feel comfortable with and at a certain point today when I saw the stocks rallying that were in beta, I kind of mentally checked out, okay? And this is kind of what we talked about yesterday on the video, kind of like being completely laser focused and I kind of checked out and I wanted to get some rest and I started putting in pivots towards the end of the day, right? I started putting in pivots into the day because for me, myself, I had...  Nothing to do with getting killed, anything like that. But it was the point of, like, I felt the market was going to roll over. It started to roll over. They gave you opportunities to roll over and then they just didn't execute it to the point that where I wanted to. And I missed a lot of plays. I really did. I missed a lot of plays. And I think the best way of saying it is I kind of needed a mental break, okay? Subconsciously, I think the market told me I needed a mental break and I kind of gave it to myself, which kind of sucked because if you look at the end of the day of the pivots that I put in towards the afternoon, really got hit. I mean, really, really did very, very well. Again, congratulations to all you guys on Netflix 354, 354, 75, 355 Needs to Build. Here was Netflix, right? Netflix exploded, right? Exploded off that 55 level, went as high as to 63. Again, this has kind of got me agitated as we're looking at charts. Crone, nice move there. Tesla, again, congratulations all you guys that took the Tesla short at 532, went all the way down to like 512. Big, big move there as well. So yeah, you know, I had a very odd day today. And the question kind of going forward, right? And you could tell by even the way I'm speaking right now, like I was like literally all over the place mentally today, trying to figure things out, trying to rationalize everything. And some days, you just have to take into the consideration that you know what, it's just not going to be your day. You know what I mean?   I think that's what happened to me today is I drew so much energy and this is the worst part. I drew so much energy trying to figure out why my stocks weren't participating that I kind of mentally just gave up and missed the ride towards the afternoon. You know, again, I think sometimes that we have to put ourselves in a position that you know what, save your mental equity. Okay, you'll always get better value. And like I say every single day, you know, as much as I think I could walk on water and every single day is going to be perfect and logical and everything I'm going to put on is going to be great. Just doesn't work that way. You know what I mean? Just doesn't work that way. I, you know, I figured that out a long time ago. I don't dwell on it.  Okay?  And it just, again, I knew no matter if I would have kept on pressing the button towards, you know, towards the day, I would have really taken a day that, again, monetary was absolutely nothing to even talk about. But I think I would have taken really a paper cut and just sliced my throat. And at days like this, you really have to be kind of a bigger adult. You know what I mean? Like when you're not feeling it and you're not in rhythm with the market, okay, just don't trade. You know what I mean? Just don't trade. I made a conscious decision today to kind of stop trading, okay?  I'm okay with that, okay? I'm okay with that. I did the prudent thing to do. I did the adult thing to do. And as much as, you know, you turn around, you see some of these candles, $8 here. Also, there was also a 94 pivot. I believe it was a 194 in Alibaba as well that I put in the channel as well. 194. Where was it? Where was it? It was a 194 pivot for, also 194 pivot on Alibaba. I don't know what happened. Maybe I didn't put it in. But that was fine as well. So again, going into tomorrow, here's kind of what I'm watching, okay? I think a lot of people are looking forward to the weekend just because, you know, just because of how mentally intense this week is. What I'm looking for tomorrow, for the cues, okay? For the cues, just a macro. I want to see what happens here if they can reclaim the 193 level, okay? If they can reclaim the 193 level, I do believe the bulls can complete the sweep, right? Amazon was a complete a five-day sweep of running into the close. And if you look at charts, you look at some charts going in tomorrow, there's some great opportunities tomorrow if the market behaves. Look at Amazon. If Amazon starts claiming, it's gotten rejected at the 50-day moving average. One, two, three, four, five times. If Amazon can reclaim the 50-day moving average, this thing's going to see a 2,000 level. It's going to see a 2,000 handle. Also, I like Tesla. I thought the stock was going to be a short today. It was a short. I scouted some short. I missed a big move, but you can see how tight this area is getting here. You can see the bottom of the channel is right here. The top of the channel is right here. Something has to give. Netflix also looks pretty good. Netflix, again, if it could start confirming today's prices, you've got a lot of upside coming in. 373 as well. Boeing continues to be good. Alibaba is very, very close. Very, very close to confirming this whole downward channel if it can start building above this linear regression line. So that looks really, really good. Roku, I think, goes lower. Roku, I think, goes lower. This is the worst part of it. I knew it was going to go lower. I just mistreated it. I completely mistreated it. To watch it go down, I looked at the prices after the close, to watch this thing go down $4, that kind of was like the cherry on top of my mental recharge for the rest of the day. So I think going into tomorrow, we have to be flexible. If the queues get rejected, if the queues get rejected back at $193, do I think we're going to roll over? Absolutely. But we have to watch early strength for the stocks that didn't rally until the end of the day. And again, if you see where the rally came from towards a lot of the beta names, in the last five minutes, when I saw the queues putting up a $4 candle in the last five minutes, yeah, that would do it. So again, how many people were putting on trades in the last five minutes? So it looks pretty good on paper with the Nasdaq 100 did, but now the bulls have to make sure that they could prove to us, right? They could prove to us after a really, really good aggressive Ford they run that they could live with prosperity into the weekend. Guys, have a great night everybody. God bless. Again, as I always say, some days you're the pigeon, some days you're the windshield. Today I was the windshield. Tomorrow I'll be the pigeon. Guys, God bless. Stay safe. I wish you the best. Congratulations for putting in the time to take control of your trading. You're one step closer to owning your future and achieving the success you desire. Want daily trade ideas directly from Dan? Straight off his personal watch list? Unlock our free PS60 vault where you'll get nightly updates on pivot opportunities we're watching for the next day's session. Click the link in the description to get started today.


Well, Guido Capuano, who I referred to, he was a mature student, I mean he had, I think he had escaped from Italy right after the war or something like that, came to Canada. And he was a big gruff guy, and he had many ideas, many ideas, many good, many good chemical ideas. In fact, he was the, at least that year, he had what I would call the best dissertation of anyone when he graduated, but unfortunately he was also interested in money, and so he was always worried about trying to sell this, and I just couldn't quite agree with him on that. So he was an exceptional student, you know, a second one was Matt King, who was now in Perth Australia, and we worked together on sulfuric acid.  But nobody really knew how the process worked, and so Matt and I developed, let's say, a matrix, a matrix held as their approach to it, and equilibrium approached to it, and worked all that out, and eventually we could tell the industry how they should arrange their processes, and I'm really quite proud of that, I don't know, and Matt was a wonderful student too, he was another best, he had the best, what we call preliminary exam, but the year he was doing that, so he was a very good author.