The fourth lecture of Tania Sharpe, please. OK. Thank you. So as a, hello? Is the connection. Recording in progress. OK. OK. So today, the first week, we talked about information. We talked about entropy and we talked about information in the linear system with Gaussian inputs and Gaussian outputs. And then we started to talk about nonlinearities in neural responses. And today's topic will be maximally informative nonlinearities for multiple neurons and how they are coordinated with each other. And so we will continue with this topic today and also talk about how that leads to a theory of diversification in biology. We will compare this with properties of neurons in the retina and also talk about how this is related to a theory of phase transitions. How one can think of this diversification as a second order phase transition and how this theory can be used to predict large-scale properties of retinal arrays. So to sum up what we started last week, if we have an analog signal and one neuron, which has one threshold, then I will not have access to all of the underlying analog signal. But I will only know whether the values were below or above the threshold. And so if it was above the threshold, we will denote it as one. And if it is below the threshold for that neuron, it will be zero. But actually, my information will be even somewhat less than that because the effective threshold fluctuates. So even if we were to repeat the signal, then on some trials, there will be a spike. And then on the next trial, the neuron will not produce a spike. So that's set up for one neuron. And ideally, in order to maximize information, and it's similar to those games that we discussed with submarines and so on, if I have a range of possibilities, I would like to place the threshold ideally in the middle of the distribution such that I will have one bit of information. But maybe that will require me to produce spikes more frequently than the system can sustain. And so in that case, I will be as close as possible to this central point given the metabolic constraints on the neural firing rate. So in the case of one neuron, one binary neuron, the problem of maximally informative solution is, I mean, it doesn't have anything interesting, is fixed by metabolic constraint. But then it becomes more interesting once we have two neurons. So this is just how we can quantify for one neuron. We will compute the response entropy, meaning the variability in this direction and across trials, the overall variability, and subtract the variability across trials. So for a given value of time or x. So now when we have two neurons, then what is interesting now, of course, I will have more gradation, more information about the underlying analog signal. So I have now two thresholds. And if we know that if the value was very high, then both neurons will spike. And if the value is intermediate, then a blue neuron will produce a spike and the red neuron will not produce a spike. So let's see if we have any cases like this. So for example, here. So in that case, I know that the signal was somewhere in the intermediate range. So with two neurons, we now have more access to the underlying analog signal. But the question remains, what is the optimal separation between the thresholds of these two neurons? And so the parameters of the problem, there are only four parameters. The two thresholds, mu one and mu two, and the uncertainty or reliability of the two neurons, mu one and mu two. So we will consider that the solution will be at different levels separately for different values of noise because noise is also to reduce amount of noise. I also need to invest into metabolic resources. So the one and then the thresholds for two neurons, one can approach it differently. If we fix the maximum, so in this problem, we decided to fix the average spike rate across the two neurons. And in that case, the average spike rate is related to the total number of spikes that the system can produce as a whole, thinking that maybe that's limited by the blood supply and so on to the group of neurons. But one neuron can spike, produce more spikes than the other. So the difference between the thresholds of these two neurons is less weakly coupled to the metabolic cost than the average threshold. So that will be our key parameter to set what is the difference in thresholds for a given average threshold. So of the four parameters that are available, we will talk, there will be one free parameter to optimize. And this parameter is interesting because it will determine whether the two neurons are sometimes play equivalent role, meaning they have the same threshold and I have reached the result or they play different roles. So then this is the figure that I ended last lecture and now we will go over this figure one more time because I think it's important and then go inside the calculation and disassemble its parts to find out what is the driving force between the bifurcation that we see here. So what is shown in this three-dimensional graph is the information that these two neurons convey about underlying Gaussian signal as a function of the threshold difference between neurons. The average threshold is fixed for all of these curves and then noise is the same for these two neurons and then it changes from large values in red color to small values in low color. So one can see that when the noise decreases, the overall information that these neurons convey increases. That makes sense because once we have less noisy neurons, then we get more information. But what is interesting is that there is a bifurcation between having, for a given value of noise, if noise is large, then the peak of the information is at zero, means I would like to have identical thresholds and average the result. Or we can have slightly different thresholds and so we can look inside this information function and see what causes this bifurcation. So at this point we observe that the optimal threshold difference becomes non-zero and the further you go from the critical point, the larger is the optimal difference between these thresholds. So the less noisy are the neurons, the further I can separate them. The further is the optimal separation. And if we change parameters, so as I said, for a set of these curves, the average threshold is fixed, but if we move around, change the average threshold, then this picture will remain, but slightly the position of the critical point will change. So I thought that it might be interesting now to take a look inside this computation and we will examine together what is the driving force for this bifurcation. So I thought that we will have a little file in Mathematica and we can... First I would like to show the code is minimal, so I just defined the logistic nonlinearity here. Maybe the type is a little bit too small. Can you see the type? Let's see. So there is a way... is this Mathematica? Yes, I can do bigger... I think there is a way to change the font, right? Yes, yes, I will move things around. So what I was hoping... Let's see if I do a view or something now. Maybe in format. Okay, size. Let's do larger. I think there is an advice for me in the chat. On the right bottom corner you can change the font size, right bottom corner. Let's see. It's usually a slider and a light, yes. Oops, that's not what I meant. Well, I guess that's one way of solving the problem. So let's see, but there should be... It says style, input, format, size, 16 points. Like that. Is that better? Yeah, it's a bit better. It's a bit better, yes. We can make it better. It should be okay. All right, so... I mean, the code is not that... So I will remove parts that we don't need. So I will give you... That actually we don't need noise entropy. So the phenomenon is entirely based on response entropy. So this is... And so we define logistic nonlinearity. You can define a different nonlinearity. It doesn't matter so much. And this is... So now we have two neurons. So we have four response patterns. 1, 1, 0, 0, 0, 1, and 1, 0. So... And the response entropy... So P11 means... So this is a function of these four parameters, a threshold for one neuron, noise for the first neuron, threshold for second neuron, and noise for the second neuron. So we have a Gaussian distribution of signals. And we have logistic nonlinearity for the first neuron and logistic nonlinearity for the second neuron, and we integrate. So this is P11. So we need the probability that both neurons will spy. P00 is the same thing, but instead of logistic nonlinearity with respect to X, you get a logistic nonlinearity minus that. So instead of... So 1 minus... I do 1 minus this. Turns out it's the same thing as logistic nonlinearity with minus X. And then P01 is... You take 0, the opposite sign for the first neuron and the positive sign for the second neuron, and then switch around. So then our response entropy is a sum over the possible P00, log P00, P11, log P11, P01, log P01 and so on. So we just have four terms. And mutual information we don't need for now, because the main effect is already present in response entropy. So now if... Now we can disassemble and look. So if noise is large, so NN is noise in my case, so we will get... It takes a little bit of time because these are infinite integrals, and it takes a little bit of time to compute, but you can see that with 1 it will look like this. And when noise is small, the derivatives will have the opposite sign. So the critical point will be somewhere between 1 and 0, 2. So we can... What noise values would you like to try? That's a question for students. What value should we try? Maybe 0.7. 0.7. 0.7? 0.7 is okay? Yeah, I mean everything. But between this regime, we know that our critical point is somewhere in between these two regimes, right? So 0.7 is too big. That's the 0.5. You know how to find... The algorithm for finding is zero of a function. So we're looking for the zero change in sign of this non-linearity. And notice that 0.5, but now the scale, I guess it's getting a little bit smaller, the range. So we can do maybe plot range all if I can do that. We did 0.5 and we know 0.2 is too big, so we will do something in between. You know this method of finding is zero. You take the interval and you divide it by half. So between 0.2 and 0.5, 0.7, around 0.3 will be our next value. So it might be also 0.3 is already on the other side. And so what is... Maybe what would be interesting is to see how these various terms behave. So we can discuss how... So initially, when, for example, it can be a homework exercise, if the threshold is the same, and as you notice, I'm plotting the threshold difference. So one can expand this expression. So for example, P01 and P10 will be the same term approximately. And then how these four probabilities, how they change this behavior. So the symmetry breaking, so the noise is only placed into account but only by affecting the probabilities of response. So the noise entropy doesn't affect... It's not the driving force. So I even think that if we expand, we find something that is a product P00, P11 over P01, P10, this ratio as a critical variable. So any questions so far? Say it again. Just a moment, we need the mic. Sorry, could you just tell one more time what were the four states? So let's... Four states. The four probabilities. Yes, so this one is... The first state is P00. We can plot them. Maybe that's... So this is the probability that no spike has occurred. So this is P00. And then when both neurons are spiking, then the next one is... And then when one of them is spiking and the other one is not. And the other one, we can maybe even plot them together to save screen. Maybe I can try to write it on the blackboard. So essentially you have the signal, then the threshold, and then... So this is the X that is going to go to this nonlinear function, which in this case is the logit, which is, say, 1 divided by 1 plus e to the minus X is a function of X. And so this is the probability of firing. Tanya, correct me if I'm wrong. Yes, that's right. So firing an X is this signal that in this case is a Gaussian with a certain mean, which is mu. So this is the threshold tau. And this is the mean mu. And it has a certain variance, which I think is B, right? So the signal... So let's set the mean of the signal to zero because we will count everything relative to the mean. And so the threshold tau is what I call mu. And then the variance of the signal will be 1 because everything will be counted in units of the variance. So then the noise nu is in units of signal variance. Okay, so this is, let's call this a phi of X. So essentially what... So the probability that the neuron fires is phi of X. This is X of T, right? Yes. X of T minus mu. And then it's divided by B, no? Which is the noise... Of the neuron. Yes. Okay, so this B is essentially related to the slope of this line, right? Yes. Okay, so this is the probability that neuron 1 fires. Yes. And this is the probability that... So this is B1. The neuron 2 fires. Okay, so this is B11. It depends on mu1 and B1, mu2 and B2. Okay? Is this clear? Then you have four possibilities. Zero, zero, zero, one, one, zero, zero, one, one. So you compute the entropy. Yes. I think it might be useful to write it down the probability of no spike as one minus this and then to show that it is the opposite sign. X is equal to, say, 1 minus 1 over 1 plus e to the minus x. So this is equal to... If you do the calculation, this is e to the minus x. Well, 1 plus e to the minus x. You multiply by e to the x. This is 1 divided by e to the x plus 1, which is phi of minus x. Okay? Thank you. So this is the probability of not firing, right? And it's e to the minus x. Okay? Yes, so now if we look at this, we can plot these probabilities as a function of the threshold difference. We set the average threshold to, say, 1 in units of the standard deviation of the noise. And the noise, I think, is set to 1 also. Let's see. Oh, I guess noise. So this is the value of the noise 0.35. And the probability of not firing when symmetric probabilities are smoothly behaving. So if we plot them separately, there will be little peaks like this. But when plotted jointly, they're essentially constant. And then the cross terms, when one neuron is firing and the other is not, are more affected by the threshold difference. Okay? So in that case, there is something interesting to look at. And now we can change from this probability to log p times log p. So in this case, let's see how this one will behave. We do log of this quantity and multiply by itself. And then we have p11 minus, I think it's okay. Okay. So they're already looking more interesting. And you see that the balance between them can, they already have different signs because they are on the opposite side of large values. So in general, I think it's also useful to know this property. How does the log of p log p depends as a function of p. So if we say x, okay, so this is a useful function to know. So this is the entropy of a binary process that goes between 0 and 1. And because it's a kind of natural log, it doesn't go to 1, but it goes between 0 and 1. So in our case, p00 was, and p11 were on the opposite side of this function. So they have the opposite second derivative. And then we can take a look at the cross terms. Okay. So these ones behave as they are. And so if we take noise to be very large, so now maybe the sum of these two terms. Okay. So the sum of the cross terms between the neurons that are firing, one of them firing and not the other will make it, will drive the system towards the same threshold. And then the, these terms here, the one that 00 and 10 can drive the system towards different threshold. So this analysis here says that the driving force behind this transition is this transition between kind of the interplay between not when neither neurons are firing and the neurons and both neurons are firing and whichever term wins is determines the transition. So in other words, if we plot these two terms separately here, so the term that is most important is this term p00. We need that term to be large in order to have a positive derivative at the kind of, and the way we, so this is the fact at the tails of the distribution was 00. So if we go above the critical point, so we know that already I think 0.7 was above the critical point. And so then these two terms are, there's, well maybe get closer to the, okay. So the conclusion is that the, the interplay between these terms 00 and 11 is the one that, so this term has to, the key term is the absence of spikes in both neurons. So information from silence is the one that will be driving the transition towards diversification. Any questions so far? Okay, so then maybe we can go, I'll go back to the main PowerPoint and I can upload this mathematical file to Slack and then you can examine in more detail what's going on in the, in the calculation. Okay, so this is the excitement that comes from diversification and a few more questions for the audience. So what do you think will happen when instead of a Gaussian distribution we change to a sparser distribution or change the mean, the average threshold between neurons? Any insight? So I have a general question. So essentially in this exercise what you are doing is you are taking the, the response function of the neurons fixed, right? Yes. Okay, so it seems to me that this specialization occurs because the noise, the variation of the noise is too, it becomes smaller than the dynamic range of the neurons and then it is convenient to have neurons with two different thresholds to essentially reproduce a larger dynamic range of the two neurons at all. I don't know if that makes sense. Yes, so the nonlinearities are fixed but the parameters vary along this axis and along that axis. So when the neurons have smaller noise then you can kind of tile the underlying analog signal and assign them different parts of the dynamic range to these two neurons. Yes, exactly, yes. Okay, and then remember last lecture we talked about how the neuronal nonlinearity has to be has to be the cumulative distribution of the input distribution. So at the end of today's lecture so what we will discuss if you have more neurons than two then you will continue this pathway, this splitting of the thresholds and ultimately, I mean maybe I will show this figure now, you will end up with a distribution of threshold that matches the probability, well I will take this slide maybe now and show. So what happens if you have more than two neurons? So this is this slide here. They have a different problem but the same kind of result holds, they have a different definition of noise but this is the threshold and as they kind of number of, in the case they are adding the number of neurons but you can think of this as transition between high noise and small noise for a large in a population of say 1,000 neurons. So what happens is they all start with the same threshold and then they split into two subgroups, maybe not equally but let's say equally but in reality could be in different proportions. So 500 neurons take this threshold and 500 neurons take this threshold and then you can take this part of the dynamic range and consider it separately. So because the input variance is smaller so the effective noise is larger so you will have to go a little bit further until you reach the critical point for that part of the dynamic range and then they will split. And so the splitting will continue and then ultimately if we are allowed to make the noise in the individual neurons very small then each of these thresholds will be a separate neuron. And the distribution of these thresholds will be the input probability distribution and when we sum the activity of this neuron, of this population, it will be the cumulative distribution of input signals and so we are arriving back at the Laughlin's result in the weak noise limit through this idea that what Laughlin's result represented was one neuron but it was a summed activity, you can think of it as a summed activity of many little neurons that are packed inside with individual channels. So it... I just wanted to understand whether this is clear, whether they are okay. Yeah, so there is a lot of information here because we are... and then we can go back and forth so this was kind of one of the concluding slides but I'm showing you where we are going and then maybe we will trace the path. So the idea is that you start with one neuron and what people say is that the neuron has a spike rate and it represents this summed activity of various compartments and these compartments can... they have different thresholds. So it's a way of maybe not fully developed, this theory not fully developed is to coarse grain a neuronal population and represent it as one effective neuron and it now has multiple response rates but in this way we can unite this picture with thousand neurons and each neuron is binary and then what should their thresholds be and arrive back at the results from last lecture on... if I can draw maybe... I cannot quite annotate here so if Mateo can you reproduce this result where neuronal non-linearity will be like a sigmoidal function or here and it is a cumulative distribution of the input thresholds. So if you have say this... this is the distribution of inputs, right? Then... and so this will be like the... this will be p of x this will be the integral minus infinity to x of p of x x prime okay and the optimal response function should exactly be equal to this, right? Yes, and now I can think of... if I put this threshold density similar according to the input distribution such that more thresholds in the middle and fewer thresholds on the edges then the joint activity of these neurons so will be the activity of that low noise neuron so now instead of... if all neurons have some fixed amount of noise but the thresholds are distributed according to... So essentially the low noise limit is where the response function is still like this okay but the noise now is much more picked okay and this is the threshold mu okay so that essentially you want to place different neurons with different thresholds at different say mu 1, mu 2, mu 3, etc. in such a way that the density of thresholds in any interval matches the density... matches the say the derivative of this response function okay is this clear? So we said so the optimal transfer function so the optimal g of x should be equal to the cumulative distribution, okay, times are constant so essentially now we are in a situation where the noise... so the transfer function is fixed okay and this is not satisfied because essentially the noise is very low variance it has a very low say low noise limit okay so the distribution of the signal is very picked but you have many neurons okay so what you want to do is to have the... you want still to have the population of neurons as a whole response in a way to mimic this relation here okay so what you want is that say the number of neurons which have a threshold in this interval should be proportional to the derivative so if you take the derivative of g g' of x this should be essentially a constant times the probability of having stimulus x okay so you want that the fraction of neurons which have a threshold in an interval should be proportional to the derivative of the response function is it okay, Tanya? yes, yes, thank you yeah so we... yeah so it's also... if we go back to the case of two neurons if the nonlinearity is very stretched I can't really cut this distribution in two so it's only when the distribution is more... the response function is sufficiently sharp then it makes sense to cut the input distribution in two so that's another kind of intuition behind the result okay so now I can maybe compare this with data so we will talk about neuroscience so there was a question in the chat about looks like supercritical bitch work by frication so this is more ideas from dynamics so what we will be discussing that it is more I mean it is similar but the connection that I'm making is more closely with second order phase transition not in terms of dynamics so that we will analyze parameters of this by frication in a few moments so now in the retinal case so if you background on the retina so this is a famous recording from the retinal cells done by Kufler in 1953 and he shines light at different positions A, B, C or D and records with a spike with an electrode the number of spikes so one can see that in the central position neuron produces lots of spikes and in the surrounding region fewer spikes so that led to the concept known as the receptive field for a neuron so in that case the receptive field will be somewhere bigger than region B but A and D and C will be already the edges of the response field for that neuron so this is one neuron and now there are many neurons in the retina because it's a detector array and there are different kinds of cells but within each cell type they tend to tile the space and potentially if there is interest I can separate lectures we can talk about variability in this array and how coordination in the shapes of these arrays they are not perfect circles and so on but for the purposes of today's presentation you can ignore the fact that they are not pure you can think of them as approximately circular regions and the retina has been a very good testing ground for theory because it's fairly close to the sensory input and we can test these ideas about information maximization and there are also different cell types so we can think about coordination across different channels and why these cell types the way they are so the canonical theory and a lot of the cell types were defined in this way whether they are responding to lights on so in this case this is on parasol cells in primate or off cells which disposed to light decrements and whether these are more of smaller cells they are called midges that have higher accuracy and often color red and green cells and this would be blue and yellow cells so that's one type of cell type specialization but in addition today we are talking about the cells that they were discovered in the retina that are more that whose experimental observation by Kasner and Bakus have led to this theory of cell type specialization so you have the stimulus and these cells filter it with a very similar temporal kernel but then once you filter it you get different kind of stimulus after that you plot that on the x-axis and in agreement with our theoretical framework they turn out to have different thresholds so here is an example of cells that the blue and red neurons that encode the same aspect of the light intensity in the visual world but do this with different thresholds and that was surprising at the time because usually the cell types in the retina were defined by differences in how they filter the incoming signal and in the retina you can tell that there are actually two different cell types because they form overlapping mosaic here so the idea is that the analysis that we did, the theoretical analysis should be applicable everywhere in the brain but in the brain when we are far from the retina when we do not have arrays of cells it's harder to detect that cells form separate classes than in the retina so another observation is that in addition to these two cell types of cells so they're both need to light decrements so on the previous side you can see they're called off cells because they primarily integrate whether the light intensity went down so when the light intensity goes down this is when we get the large projection onto the X axis so that's why they're called off cells and then there's an on cell would be the one that has a kernel that comes up and then comes down so in the case of the on cell here is an example of nonlinearity and you notice that it is less steep than both of the off cell types and so that's a hint that these on cells in our language of the theoretical model they will have larger noise so by fitting these nonlinearity we can estimate the average amount of noise for the two off cell types and for the on cell type so this one is around 0.3 and the other one is around for the on cells 0.45 and if you recall in our simulation our critical point was around 0.3 something so that's where the critical value would lie so then the critical value depends so each neuron when each pair of neurons when they're recorded they have slightly different for each pair they will have different average threshold so the average threshold is different the position of the critical point will be different so this range here is the range how much this critical point changes when we change the average spike the average threshold for the two neurons so in other words when in the experiment they measure the filters they measure the nonlinearity and then we fit them and we get our four parameters mu one mu two mu one and mu two and after that we can say whether the theory predicts the optimal mu one minus mu two consistent with the measurement of the three other parameters okay so any questions about this so this comparison has essentially no three parameters and it asks why or it you know attempts to explain why we have two off cell types in the off channel and only one cell type in the on channel and the explanation is that for on neurons the noise is larger and therefore these cells are in this regime and in the off channel for light decrements the noise is less and so they are in this regime where it's optimal to have slightly different thresholds is it clear any questions yes Carlos for curiosity the threshold level for neurons experimentally have you found if they are time dependent or signal dependent or a certain neuron has a certain threshold his all life no they are all dependent and they all adapt so in fact this data so remember we said in the kind of in the theory we said that I'm measuring all these units here in units of the standard deviation of the input signal so as the contrast changes the nonlinearities shift so there will be a moment or some period of time when if you change the input signal the nonlinearity will not be optimal and then it will converge to the optimal value as the neuron progress adapts so I actually have additional figures to this to this extent so here this slide here so in this case you have different contrast in the in the input signal and so the thresholds are slightly you know differ as a function of the contrast and noise doesn't scale perfectly with contrast but the thresholds remain separate across the range of contrast and yes so that's the answer so the nonlinearities change and to this model we assume that they have adapted fully to the input probability distribution but in reality they will be only partly adapted and also another thing is another I would say not fully understood phenomenon or the one that I would like to understand better is that these neurons in addition to having different thresholds they also have different dynamics upon changes in the contrast so the high threshold neuron so they are also named adapting and sensitizing based on difference dynamics of how they behave when the input probability distribution changes so one neuron I think approaches the its final threshold value from the top, from large values down and the other neuron jumps to the very low values and then increases so they approach the optimal values from the sides and that theory is partly developed I think in the Bacchus and Cassner's papers but I think more can be done from the theoretical side there is it okay Carlos? Thank you I was asking mostly to see if there was a separation of time between the shift on the non-linearities shift and the shift of the threshold maybe one of them is lower so in order to correct it the brain uses this other strategy to reverse a slate Yes, so I I will prepare some slides for next lecture so we had a recent paper where we followed up on this result and roughly speaking is that turns out that the difference between these two thresholds is what you can think of as a theoretical approximation that these two neurons are actually the same but one neuron gets an extra inhibitory input from another cell and in the case of the retina it's an emigrant cell so what happens is it's possible that two neurons have identical properties but one gets extra inhibitory input and as a result its threshold gets higher and then the whole circuit adapts to the extent to which that intermediate neuron adapts so this intermediate neuron then coordinates the difference between these thresholds and then there are other interesting ideas so it turns out that there is a connection with a form of stochastic resonance so that but in this system with two neurons and then a third one neuron is coming in so you might think that I'm deviating a little bit but basically it turns out that it's every time I make a connection in neural circuits I fact I introduce noise so the best way of having zero noise is not to have a connection so it turns out in this case I could have send one signal to one neuron and another signal to another neuron but then I would have noise in both neurons so it turns out that these neurons that have larger noise and they have larger threshold is because they get extra input and that input the difference in the noise between these cells is because they get this extra inhibitory input so the the extra input can explain both the increase in the noise and increase in the threshold well I hope yes so and now we are back to our we can talk about various phase transitions so actually that was my second slide but so across various contrast so these are the thresholds are maintained and the difference between the cell types what we think in the retina can be disassembled is that one set of cell gets an extra input from another inhibitory neuron so then here is an example of prediction so we say this is two neurons and we know their thresholds and we know their noise and then you vary the threshold difference between the and you know the average threshold but you vary the threshold difference and compare it with experimental points so very often the theoretical peak of the curve corresponds with the actual measurement of the two neurons so now how can we think of this analysis with two neurons how can we make predictions for larger arrays okay so now we can talk about bifurcations and approximate this mutual information and I didn't tell you that somehow in the slide but basically the figure that I showed here was for the case where neurons have the same noise but they also can have different noise levels so in this case so this is the slide somehow skipped over so as you as you noticed in the experimental case the neurons both of neurons had smaller noise than the on neurons but their noise in them was also different so if you make the plot of information versus average noise for two neurons and the threshold difference but now neurons have slightly different noise levels then you get the same picture as before now the surface is shifted so it becomes optimal to put a neuron that has smaller noise closer to the center of the probability distribution alright so we have a question in the chat what are the assumptions behind this nonlinear information model so the some assumptions as we will discuss in a moment matter in a quantitative way but not qualitative and some assumptions are maybe more critical so the assumption was that the input distribution is Gaussian so that's not a critical assumption you can change the probability distribution we the nonlinearity doesn't have to be a logistic function it can be some approximately that but the critical assumptions are that neuron is binary each neuron is binary such that we have four states and another assumption is that the noise their responses are independent given the input although that's also not will not affect the results so Colin did I is that okay I'm not sure whether the chat is from a student who is online or in the class online we do not see the question alright so Colin asked what are the assumptions behind the nonlinear information model yeah so the assumptions are that the neurons are binary and then we have four response patterns and so this is the main assumption and so then this is you know this is the case when this is the picture that you get if you ignore the difference in the noise for these two neurons neuron types and if we take this small difference in the noise into account then the picture shifts such that the two maxima are no longer equivalent and one of the predictions here is that positive threshold I think have to go with positive differences in the noise just like in this experimental situation so in other words if the neuron has smaller noise then it should have smaller threshold and so it will be encoding signals that are closer to the mean of the distribution so the symmetry is broken so the first picture is what we can say is a spontaneous symmetry breaking I have two identical neurons here in this picture I have two identical neurons and both spontaneously one of them will go and take over a smaller signals of a smaller range and the other one will take over signals with larger magnitude but when the noise between them is not equal then there is a bias and the signals that are smaller should be coded by a neuron with a smaller noise and that's this picture right here where in the experimental case the thresholds for the neuron that has higher threshold also has a higher noise value and we now think that the difference between these both phenomenon is that they get an extra inhibitory input and then we talked about this and now we can model this the neighborhood of the critical point in the spirit of mean field theory of kind of Landau mean field theory and so this is our information function it will have a quadratic term which is in terms of threshold differences and it will have a coefficient in front of the quadratic term that depends on the noise and it changes sign at the critical value then information cannot increase indefinitely so we have a force order term and it has to be negative because the information will go down for large threshold differences and then there is a linear term which is absent if there is no difference between neurons but if you have difference in the noise between neurons then it will have this linear term and break the symmetry so you might notice that this is identical description to magnetization we have I even chosen variables such that they will correspond so what is magnetization is a threshold difference magnetic field plays the role of the noise difference between neurons noise plays the role of temperature and then we are maximizing information instead of minimizing free energy so therefore there is a mapping from this expansion to the theory of phase transitions and using this theory and predictions for large arrays we can use it to make predictions for large arrays so do you have any questions about this expansion? so I have a question about the sign of the first term so when the noise is large you should have that the emission information is maximal at zero so the coefficient should be negative of m squared yes that's right so I can get out of it with a being negative okay so what's important is that there will be a critical value and it changes sign here and it should be then once we have this expansion I mean this is one of the simplest thing that can happen to a maximum so a maximum will change sign and becomes to maximum so once you have this expansion you have full predictions for how the threshold differences between neurons should behave as a function of the noise so we know that it just like magnetization as a function of temperature so when noise is less than the critical value then we will have a positive threshold difference and because it's a linear term multiplying kind of a quadratic thing we know that the optimal threshold difference will go as a square root so now you can analyze these numerically and it's almost you know it's now surprised that if numerics we take a mutual information and find the position of the optimal threshold difference as a function of noise it has to behave as the absolute value to the one half power then another one and this is a prediction in terms of in the simulation you can take it very close to a critical point to find the to find the exponent so then the next prediction is how does the threshold difference should depend on the difference in the slopes of the neurons and according to the Landau-Mienfeld theory it should be as to the power of one third and that's what you get here in addition for example this is a proper second order phase transition so we can take a look at the second order derivative of information with respect to this equivalent of magnetic field or the slope difference and at this critical point the derivative will diverge so that will be an analog of susceptibility and if you fit the simulation points then indeed you will get the scaling exponent of minus one that is predicted for mean field theory and you can even have another second order derivative that changes as a function of the second derivative of the noise and it jumps discontinuously between two constant levels with discrete jumps so just like in the mean field theory for magnetization so now we can compare this and maybe it also partly is related to the Collins question about which parts are which assumptions of the models are critical so now imagine that this picture which I that we talked about on the previous slide that was for a given average spike rate given average threshold for the two neurons now if that parameter changes then this threshold difference is a function of noise will always behave in this square root like way but the coefficient that multiplies how fast the square in front of the square root will depend on the average firing way so once you know this numerically this constant and how it changes as a spike rate you can rescale and therefore you can put the data from different neurons even though they have different spike rates into unified coordinates and so then this will be one example so this is a normalized threshold difference between neurons as a function of the noise and this is the optimal prediction of the theory of the mean field theory square root and the actual data lies below this square root or some other exponent and then we can compare the data so it turns out that the scaling exponent in the retina with respect to mu is slightly different from the optimal prediction so it's about 0.4 instead of 0.5 and the scaling exponent with respect to change in the noise difference it should be 1 over 3 but it is more like 1 over 7 so it's larger and then you can ask how does this compare to various physical systems so the mean field which is these exponents are known in physics so for the mean field the prediction is 0.5 instead of 0.4 that we observe here and this function is delta we should be 3 instead of 7 and we can compare to various other dimensional systems for example 2D ison model will have these exponents 3D ison models will have closer values to what we observed in experimentally and also that matches experiments in physical systems so we know that in order to go from mean field to the physical systems we have to take into account fluctuations in neural responses but it's interesting that our retinal array and its scaling exponents actually deviate from the mean field predictions but they deviate in the same directions in the experimental physical system so it gives us at least a hint that if we take into account fluctuations across the array then we will be able to explain these exponents better any questions so far? I think it's ok so I think we are close to being out of time but I will just end by saying that we observed that the scaling exponents match the 3D ison model and we can talk about the retina is a 2D array but this matches in terms of scaling exponents so it turns out there are papers and results which say that a 3D ison model with nearest neighbor interactions which is this one is equivalent to a 2D ison model with long range interactions so one can turn this result around and saying that because we observe a match in the exponents then it makes a prediction for how the scaling of the fluctuations across the array will change as a function of the distance along the retina to this power so I think I will stop here and I think we are out of time but I will leave you with this parallels between neuroscience and physical systems where we have a theory of how information maximization drives symmetry breaking and biodiversity and instead of free energy you can think about information maximization, temperature is equivalent to noise magnetization is the difference between cells and various exponents so that's my slide for today ok thank you very much so any final question or comment? so if not I would ask your patient once again because unfortunately we had some problem with the group photo so we have to I'm going to ask to all online participants to switch on their camera please we take another photo please switch on your camera so that we can do this quickly thank you hello can you switch on your camera hello can you hear me Colin are you there ok of course if you don't want to be in the picture it's perfectly fine but yes ok so when you want I think we can take the picture ok can you switch on the camera ok thank you great ok very good I will fast anyone else wants to switch on the camera I think we are ok so should we go ahead with the picture ok ok smile cheers ok just one moment are we done ok perfect thank you see you tomorrow have a nice evening


So this is my Elgato Stream Deck. I just got it for live streaming. I've been playing with it, I've been loading up some stuff. This is the uh it's got 15 buttons but you can also press it over so it's got two pages of buttons and uh turn it on and off uh and you can do just about anything you put any sounds on there you want you can have it automatically change camera angles and stuff like that uh you could have it go to websites you could have it uh do voiceovers you could have it go open up files you can you can have it do a whole bunch of stuff with a push of a button rather than having to go to your computer and and search for stuff you just one button uh if I want to say hey cash register you know uh and that's the Elgato stream deck involve your content I haven't even touched the surface of what this thing can do and I'm already blown away and I'm just loving it loving it loving it um it says right on it involve your content takes you to the next level Elgato stream deck get it today


Good morning. I'm Mary Ellen from the channel Mary Ellen after 60 and today I'm gonna talk about my favorites and my fails for the month of May and I don't have any new makeup in here at all. So most of the things are experiences but I'm gonna go ahead and talk about the things that I purchased first and most of them aren't new purchases. If I look shiny that's because I don't have on any makeup. I am trying a new tinted moisturizer with a SPF and I've just been trying it the last few days and I want to see how it works with makeup. So when I get done I'm gonna put some makeup on and and I'll let you know. I'm gonna do a review video soon and when I have a better idea of what I think about a couple of items and I have yet to make an appointment with my hairstylist so I will share with you what I've been using to temporarily cover my silver hair but I want to talk about this isn't in any particular order. I purchased this last year and it is called a chaffle maker and the only I only purchased it for one reason and it's because Dolores the baking diva did a video on chaffles and I eat low carb. I don't that's how I feel the best and I have really good cholesterol and vessels so that's how I like to eat and I have used it and enjoyed it but I wanted to share with you a video of hers and I did this recipe that she made on cheesy garlic breadsticks and I'm gonna link that below and oh my gosh they were delicious it was eggs and cheese and seasonings. It made me absolutely love it. Now this makes one I don't have a waffle maker. I think if you had a waffle maker you might be able to adjust the amount to make one. Jim doesn't care for these he likes regular bread and things like that but I love it and it's so easy and quick and it's delicious and there are tons of chaffle recipes. I think that's so waffle chaffle that's how I think you would pronounce it but this has been one of my favorites during the month of May and I'm gonna probably get my months mixed up. Now I really can't give you a review on these because they've never been in a fire but Jim and I were talking and we thought we needed to have something that we could keep a little bit of money our titles to our vehicles and just a few other things just to be on the safe side and I ordered two and I think I have a favorite and I'll put the links below for you to go check it out to see what you think and one of my viewers and friends on here is a former fire inspector so I'm hoping that she will let me know what she thinks of these but here is this huge envelope and it's like I said it's supposed to be fire proof it has Velcro you open the Velcro and there are two large areas to store items it's double. So so far we've been replaced with this and here's the other one it's smaller and I don't I think it was not I mean this was less expensive but I think I prefer the silver and it's supposed to be fire proof I hope I never find out if they're fire proof or not but we feel good having them and we both told our children where we keep them in case something would happen to us when we're together but I have felt good about these and I look forward to hearing from my friend to see what she thinks. The next item I bought in February because of L and L is the channel L is for living and this may be a strange time to talk about it but I really we've really enjoyed it and I just brought one in here and it is what it is a flickering flameless candle and it has a remote control and I'll tell you why I like it. I don't know if you'll see that flickering or not I'm not really sure if you will or not but it is so nice to have candles and no heat and we don't burn a lot of candles or don't have a lot of scent in our home so in the winter I will burn one candle in the whole house and it can't be a strong scent just because I don't really think it's real healthy but that's just my personal opinion but I'm really enjoying this and this is the largest one and I'll put a picture of the three of them up there but I've really been enjoying this and so has Jim we always look better in candlelight. You know I live in the state of Illinois and I think we're going to be required to wear masks for some time and I really wanted to get some decent masks and my cool friend and I named her the Queen of Cool. Her channel name is the O'Carroll Show and I ordered these from her. I got two leopard, three piece signs, three camo, two black and two blue and they are so soft. The first thing I did when I got them was wash them that's what the instruction said they're triple they are very very comfortable and if you have to wear masks I think that you want to have something comfortable. I know it's going to be difficult this summer but with my age and Jim's age and he's ten years older than I am I know masks are supposed to protect the other person but I think they kind of protect us too. Just my humble opinion but I'm going to link a video of Carol's below so if you're interested in these masks they're they're they're super nice. They really couldn't be nicer if you have to wear a mask so I wanted to tell you about those. On March 3rd I ordered some new tops from Amazon. I was watching a video of Susan Little Poet and I really liked the sleeve of the blouse she was wearing so I clicked on her link and I'm going to go ahead and put some photos in here of the tops that I ordered. I think I ordered four and two of them are in the same fabric and I wore one of them when I did my update on derma rolling and I'll put that up there and I'll put that in the cards and I'll link it below but I ordered four, got them in, I wash everything before I wear it, washed them, hung them up and they did beautifully. The first thing I do is I inspect it. I want to make sure the stitching is good, that it's not going to rattle, that the seams are flat. I like this. This has just kind of a tiny little pucker in the sleeves and what I did I think they have plus sizes. I ordered the extra, extra large and I usually wear a 14-16 top if I'm buying a woman size. They fit fine. They're not long and I don't really like a real long top but they're really comfortable and I haven't gotten to wear any of them out except for today I am going to go to the grocery store and I'm gonna wear this. So just looking at them in my closet made me happy in the month of May just like looking at my winter pajamas made me sad in the month of May. Last year I got several items I was really pleased with in the clothing and if you click on, I'll show you what it looks like, if you click on my Amazon page I have three different categories. One of them is called influencer which I don't think I am but it's just a bunch of different things that I use that I buy. I usually put everything I buy in my Amazon store and I try to remove something if it doesn't work for me and then I have another one that's beauty and one that is clothing but if you'll look there's a little box in the upper right hand corner and if there's lines in it you just click on it. If there's something I want to add or information about it or to size up or size down I'll put that information there but when I order anything from Amazon I go to one of my friend's Amazon pages and that's where I place my order. When I edited my video from last week I couldn't believe how bad my hair looked and it wasn't dirty it just looked horrible. Well so I washed my hair the day before yesterday and I filled in the silver and filled in the roots up in here. I used the color wow temporary root cover up. I looked back and I'm going to put a video up here and below. I bought these in May they're over they're over six years old and of course I don't have a ton of roots but I use this one which is the dark blonde and this one which is the blonde and I can put streaks in my hair like I said I did this a day before yesterday and it will stay in until I wash my hair which will be tomorrow so I have not been a slacker on my roots like I was last week. I use the brush that comes with it and you know me I go around the edges because I don't want to hit pan and I just bounce it in and put it in there just bring it in and if you want to get to your right in through here I just use an old elf eyebrow brush and I just run this along here and then I'll just go right there and put it in but it really is easy there are a ton of different root cover ups and I've never tried the spray but I do have several of the powder root cover ups and and they're just my favorite and they're easy and that's what I like. Something I've done and I talked about it last month but I've taken it to another level and it is freezer organization. I have a chest freezer in my laundry room so one day I just took one bag out at a time and I think I have everything about in four bags. I just turned on my video on my cell phone and I just as I took something out of the bag I just said what it was so after and I kind of reorganized everything so after I was done I went to my computer and I'm tapped out a list. The first one is bag with black straps then bag with red straps then Walmart bag and and zippered vegetable bag so I've got this pinned on my refrigerator and then I have like what's on the side and what's underneath all of all of the bags and Jim has appreciated this so much because a lot of times after I've gone to bed he'll think well I think I'll fix a pork chop or something like that and he really appreciates knowing exactly what bag to go to to get what he wants because I what I do is when I get meat I freeze it individually and then and that way whatever we want we can just get out but I've been really happy with that and it works so well. Something I'm really excited about is Instacart but I've gone one step further now I know and you have to have a smartphone to do this you have to have the Instacart app and you have to have stores in your area that you can order from Instacart. When I place my order I always try to make sure I do it at so my delivery is between 10 and 12 so the last two times I've done it I have clicked on my the app and I can watch them as they put things in my cart and make it and I can communicate if they make a suggestion I can say no I don't really want to do that or you know and then also in the app when you order it you can mark if you don't want any anything to be substituted but that has been so helpful the first time I did it I got half my items the second time it did better and last time I was right I said a timer so I would start looking at 9 o'clock every 15 minutes I set my timer to see when they started and they started about 9 15 so I really like that and I think the Instacart shopper appreciated it too because we were able to substitute we were able to substitute things or not this is a cup that I've been drinking out of since Jim has known me and it says the difficulty in life is the choice and I do find that to be true so every morning I put about two tablespoons of half and half and I've used half and half for years and I microwave it for about 20 seconds and then I take my frother and I froth it up and I bring the frother up and it makes the froth higher well I had some of these freeze-dried coffee tubes in my I was going through my travel stuff since we haven't traveled and I had some in there and I thought you know what I'm gonna do I'm just gonna put a little bit in my half and half before I froth it so every day I've been adding some instant coffee in fact I'm just about out of the tubes so I bought I like Colombian coffee so Juan Valdez and I are gonna have coffee together every morning and what I do I just put a one heaping baby spoon into my half and half after it comes out of the microwave and I've froth that up and it is so delicious and it doesn't add any carbs or calories and it's just made me very very happy something else it's made me happy are these Parmesan crisps and I do know how to make crisps and I've done a video on it before and I don't think I could find it but if I do I'll link it below these are jalapeno and even though this is a small bag it says two ounces and I think this was around three dollars one bag will last probably five different servings let's see how many servings are in here well it says three there's three servings and it's 12 crisps so that means there's 36 in here I would say I usually get about five or six when I'm really kind of wanting something to bite into to crunch and and I really do like them and I got these at Aldi and I talked about on May 6th I changed my eating habits because I didn't want to start having any problems with my blood sugar well I'm happy to announce as a reward for doing that I have lost 10 pounds so now I am at my lightest normal weight you know there's a five pounds one way or five pounds the other and I really think the older we get the slower we need to lose weight so that was March 6th that's been so by doing it slowly I've lost 10 pounds and that makes me happy and I've had some questions on how I do my moderate low carb and I will link a couple of videos below and I'll tell you at what part to look for it to see if it's healthy for you I know what makes me feel good and I'm sure you do too I'm saving my very favorite to last I have one more thing through the month of May I truly enjoyed watching the voice number one I really enjoy the voice and I usually will start American Idol when they're down to about 10 and I enjoy watching that too but not near as much as the voice so I've really enjoyed that I can't get into watching series recently I'm not a huge television watcher I have watched some really good series in the past but I just haven't gotten interested I like I like something that is fast-moving so if you have any suggestions or you want to tell me what series you have been enjoying I don't I don't like movies that much because it's hard to sit still although we can now pause them so if you have any series that you've enjoyed just share that with me below and the biggest thing I am the most excited about is my oldest grandson graduated from the University and of course the graduation was canceled and I did have him over we sat on the bat patio and I got to visit with him for about an hour and it was wonderful and I'm hoping that we'll be able to do more visiting soon I do miss my family he is not going on to his masters at this time he's going to look for a for work in his field and he has a major in accounting and a minor in finance but it was so wonderful that he graduated and he'll be moving his things home soon even though we took classes online he has his apartment in Evansville Indiana I can say that that's where he went to school in Evansville and he has his apartment until I think the end of July and he also was on the Dean's List every semester so I'm really really proud of him and now I want to talk about my fails and one of them I had recommended to you and it makes me feel really really bad they're generic erasable ink pens retractable erasable ink pens they come with a little they have a little piece of plastic on the tip which I thought wow this is really great it's gonna keep that gel ink flowing we took it off and it did really well for maybe a week and then it just quits every one of them have been that way so I was gonna order my favorites which are the pilot friction and I placed an order and I thought for sure that I ordered them and I got a box of 60 big ink pens 60 for $5 this is just half of them I'm gonna give these to my daughter she works and she does a lot of after hours things where they have to give out pens but did you know you can get this is half of them did you know you can get 60 ink pens for $5 and they they work I just don't like pens that have a cap on them at all so then I did order my friction erasable gel pens and I don't use these for any documents to write checks or anything but I use it for everything else because I'm always making a mistake and if you're still here this is gonna be a giveaway and I'm gonna have one winner and I want to share with you what I'm gonna give away the first thing I'm gonna give away are two of my masks and I hope you enjoy them I'm not even gonna open this up this is the gold going coconuts I shadow palette from color pop I bought all these things I'll put a picture of them up here someplace and the Laura Geller flower district I ordered this from QVC and I'll put a picture of it because I'm not even gonna open them and then this is my last lip flushing faves it's from it cosmetics they're hydrating color awakening lip trio and the eco tools brush set that I know I've purchased 20 of I took them from the case they've never been used so since this is a giveaway I will not be able to reply to comments on this video but you can go to any video and you know I'll get back to you this is international this giveaway will be closed in three days you just have to be subscribed to my channel and be 18 years older older which I think I'm pretty well sat on that so if you want to be in the giveaway just in the comment section just tell me something you enjoyed during the month of May it is all good I want to thank you all for watching for commenting for giving me the thumbs up for sharing me with your friends it's very much appreciated and I will see you in my next video you take care and I do have a one of my her channel's net her channel and I just turned on my I just turned on my and if you want to know how almost two months in March and I've said I do know some so and he's that he may may norm


Good morning. Good morning Francesco. Good morning everybody who's thinking in with us today. It's great that we can do this conversation. This is I think the first in the program of live interventions as part of Me Family, which is a new digital project that's been developed by Moudam Luxembourg, the Musée d'Art Moderne conduction, and which was launched last week. And I'm delighted. My name is Suzanne Cotter, and I'm the director of Moudam Luxembourg, and I'm delighted to be able to have this brief exchange with Francesco Bonami, who is in fact the curator of Me Family, the project, which I'll explain in a moment, together with Immanuela Monsonis and with the participation of Luigi Alberto Cipini. The project Me Family actually began as an exhibition, an exhibition conceived from Moudam, for the spaces of Moudam, and Francesco, you were invited to develop this exhibition based on an idea that you yourself had, which related to the iconic exhibition of Edward Stysian, called The Family of Man. It's an exhibition that was actually presented at the Museum of Bononate in New York in 1955, and then subsequently traveled to 150 museums around the world. It involved 503 photographs by 273 artists from 68 countries, and the sweep of Stysian's curatorial thesis was a kind of universalised view of humanity through the cycles of life from birth until death. That exhibition in its exhibition form is preserved and on this permanent display here in Luxembourg, in the north of the country, in the town of Clairville. So it's an archive, it's kind of a living archive, and it was this archive that was the point of departure for you. I'd like to think, ask you to talk a little bit more about that beforehand. I would just like to explain that the exhibition that you did develop for us was subsequently transformed in the wake of the COVID-19 pandemic, and quite early on, I think as early as March, when the pandemic began to really unfurl here in Europe, and we realised that the movement of artists and of people that were needed to realise the exhibition was becoming more and more difficult. You, in fact, I remember an email saying, maybe in light of the content of the show and what the show was about, it should just all be digital anyway. We spent a couple of months thinking about that during lockdown, looking at scenarios, and then really exploring whether it really would be a viable thing for us to do, and if we could do it, how could we do it in a way that was substantial and somehow maintain some of the integrity or the integrity of the original curatorial project. So that we did do, and we were able to collaborate with Bass Design, who have studios in Brussels and also in New York, as well as with you and Emmanuel Luigi Alberto and our curatorial and communications and technical teams here at the museum. We also were able to bring on board the collaboration of all of the artists whose work is shown, who really are at the centre of this entire project, but to create something that we don't really talk about as an exhibition as such, but it's a platform for engagement, it's a platform for visibility for their work, and for users or viewers to be able to interact with it to some degree. So it's become another project. It's really been quite radical for us to be able to do it. Very exciting. We didn't know what to expect at the beginning. We also produced a publication, which exists alongside this platform, and that's something that also is available to purchase online. But back to the project, Francesco, can you tell us something about the way you developed the original curatorial concept and how that's morphed into this project that we're really engaging with now online? Well, good morning. I'm Francesco Monami, and together with Demanduella Mazzonis, we start thinking about this exhibition, The Family of Men, 1955, and it's a very important year because I was born there. So I'm not joking. But the show by Heggro Steghin at Noma was very radical, and I started looking into this exhibition and how it developed in that year. We were talking 65 years ago, and at that time Steghin did something that today, from a curatorial point of view, is almost impossible. He took many, many, it was a show based on photography. There was no other medium, but it was about photography. And it took the work of famous photographer of different nature and knowledge and vision and reassemble it into this exhibition, changing scale, changing cropping. It was something that some of the photographers in the exhibition didn't even like the approach of Steghin, but went along with it. And the exhibition became a real experiment in museum exhibitions. And one thing that caught my attention and that the show was produced in a few editions and could travel simultaneously around the world. I think it traveled in 80 venues in 1955 all around the world, sometimes simultaneously. And again, it's something that today we could not do it. Not because, of course, a painting cannot be shown simultaneously in 80 places or even two places. A sculpture cannot be shown. But to me, it was a reflection on the nature of art in an age that many artists work digitally through photography, through video, through film, medium that can be actually shared simultaneously. I reflect on the idea that artists become more protective on their uniqueness of the authorship. So sometimes if you ask an artist, can we show this video here and there? They say, oh, no, unfortunately not because the video is in two editions. And the one is there and the other one is there and it cannot be shown again unless you... And I found on interesting, not in a negative way, but interesting in the fact that in an age that allowed to share things, some artists have become more, you know, they like to share less. And that was an interesting idea that makes me think. I mean, our dream would have been to do something like Stuyken, to do a show, a multiple show that could be shown everywhere. Then COVID came and we didn't even went into this idea that would have been almost impossible to do it. But COVID came and I think I'm not a digital person at all. I'm not someone obsessed with online things and things of that. But with my surprise, you, Suzanne, came along and start reflecting on the possibility of transforming something very physical in, as you call it, not digital, but a platform. We didn't transform the exhibition in a digital version of the exhibition. We utterly transformed the nature of the idea into something completely different, which is becoming a platform. And I hope that people will enjoy this format of talking about something. We cannot stay showing about something. And I think that I'm not here praising Moodham because they... First, I praise them because we present to Suzanne the Idea with Emmanuela. I want to just do a little note. Stuyken was originally from Luxembourg. And there is a museum of the family of men near Luxembourg, which is fantastic. And I encourage everybody, even during lockdown, if it's open, to go to visit the museum of the family of men because it's a fascinating place with some original pieces of the original exhibition at MoMA. So it's really an amazing experience. So I will encourage. But the link with Stuyken and Luxembourg was very strong. And Suzanne liked the idea for the exhibition. And after, she was able to push this other idea of the platform, which it could sound normal, but it's not. A lot of institution during COVID postponed indefinitely or bluntly canceled the exhibition. And I understandably. And Moodham instead wanted to go along with the exhibition on another dimension. And we succeeded with all the help of everybody. I mean, this effort would not have been possible without the involvement of everybody, you know. All the curators, the marketing, the everybody in the museum, Emmanuela Mazzone's, Luigel Betoshipini, all the artists that have been involved. I mean, it sounds idealistic, but I don't see anything wrong in a moment like this to be a little bit idealistic. I think it was a very collective effort where, in a way, you know, we all joined forces to produce something quite experimental and quite fascinating. If it will work, if it will be a success, well, that part of the experiments are beautiful because allow the possibility of exploring new venue and exploring new way of failing, new way of succeeding and things like that. So I think that what we're doing now is also one of the little fragments of this experiment. And I think we prove that in a moment of crisis we can still do something which is propositional. We can propose something and we don't sit back and wait the crisis to finish. I mean, we use this banality where you never waste a crisis, you know? And I think that we can say that we didn't waste a crisis. I mean, Francesca, for a couple of points. I mean, one is, I mean, thanks for your really kind words about us, the team, but, you know, part of the process of reflection about what we would do was sort of, we didn't want to go through a period of mourning, let's say we did go through a little period of mourning about the exhibition where we realised we had to take the decision not to go ahead with the physical exhibition. But I, as a director, was really bolstered, actually, by many of the younger members of the team at Muldang who we were during one of our weekly Zoom afternoon teas during the lockdown here in Luxembourg. We talked about it and I said, this is what we're going to do, you know, we're thinking about and a number of the, a number of colleagues, young, the younger colleagues, you know, in different services said, but we're doing all this work, we're thinking about the digital, you know, it would be wonderful if we could do it. So they were really, I think I was encouraged by them because they sort of really saw the potential. So I think that, you know, knowing that there was a dispersed energy and will to sort of take it through. But I also, you know, other things I think what's interesting about the platform and I've spent time going through it all is how, I mean, I've been so impressed really myself by how much the work that is on the platform engages you and the ideas of the artists and at times I felt very moved watching it. And I noticed one of my colleagues here, Eve Hoffman, talked about how many people that he knows who sit outside of the art world who are not regular museum visitors have because of the communication around the platform had been engaging with it and were very, very comfortable with it because people, I used to sitting in front of a computer screen and they're more comfortable watching a lot of the durational work because a lot of the work on the platform is film and animations and it's durational. They're much more comfortable engaging with it on the screen than they might be in going into a museum and into a big spatial installation. So that, you know, that's, I think that's an interesting feedback. But I wanted to also pick up on your point when you were talking about Stysian's exhibition itself. And I remember when we went to Clairville to visit it together, it must be two years ago now, and although you knew about it, you've not actually visited it where it is held here in Luxembourg. And I remember you being struck by the fact that Stysian had worked with photojournalists. And, you know, you mentioned the radicality of the exhibition, but the fact that Stysian himself was a photographer associated with pictorialism and the 291 Gallery and Modernity and, you know, photography, photography's history and its evolution in being recognized as a fine art medium to be doing this exhibition where he's working with photojournalists. So there was a kind of promiscuity that's embodied in this particular exhibition. And it struck me when looking through going through the platform and engaging with the many different works that you and Amanda Manuela sort of selected for me family, that there is a similar kind of promiscuity, even though we can engage with all of this by way of digital technology, we're looking at very different forms. So we have this more pure, let's call it video in the work of Doug Aitken, which is amazing on screen. I mean, we think of Doug Aitken's work experiencing it really in this immersive, very physical, corporeal way. But actually, it's still incredibly compelling when you view it on screen. But then you have other artists who are working with game technology. I'm thinking of Garam Kim's amazing videos. Harun Faraki, who's kind of a forensic drilling down into the history of visualization with the development of technology that contains within it certain, I think, critical reflections or it encourages you to have them. So I wonder if you could just say something about the selection of artists who are actually participating in this project? Well, again, we didn't want to do a remake of The Family of Man. But we reflected on the nature of the exhibition. And as you talk about the work from Isquiti between more art, photography and photojournalism. And I think we have been more, we became more, more sectorial in terms of selection of works in the proceeding in the last 65 years before there was photography. And within photography, I think there was a photojournalist, there was a fine art photography, but the boundaries were not so clear and divided. I think that, I don't know, but I don't think that Steichen was looking down to photojournalists when he was including Isquiti, was he looking at a little bit like a painter who can look at abstraction of figurative or photojournalism, not looking down, but as part of the same language, but with variation. It's like music. And today we are a little bit more sectorial, and so we were trying to look at an exhibition that was experiential. It was more up to time with the real world that we live now. I mean, a lot of young people see reality through digital media, through digital tools, through computer media, telephones. And so we are thinking maybe the way to pay an homage to the family of men was to look at through these mediums. So we limited actually almost excluded completely classical tool, medium like a sculpture or painting or something. Because we thought that that would be interesting to create an exhibition where the viewer was experiencing. And with the help of Luigio Matici Pini for the installation, we had conceived a show where you could go and simultaneously even listen to the sound of different videos and then be able to focus on each of them individually. But at the same time, we were stressing the cacophony of the exhibition as the reflection of the cacophony of the world. So that's the way we approached the show and the selection of the work. And we have to say that most of the artists really went along with that and was a refreshing way to see a show. And then, you know, because of the nature of the show, I think that that's why we are even into the circle of senses. We are able to be here because I want to stress it. What we did with the platform is not a replacement of the exhibition. Going to a museum as it will be, and I really am adamant about it, will always be a unique experience. Crossing the threshold of the museum, this symbolic space, like crossing the threshold of a theater, crossing the threshold of a movie theater, will never be replaced by any digital thing, you know? I think that comes across too in the platform because, for example, there are certain artists who participated, but whose work was actually physical, such as I'm thinking of Simon Fujiwara or the installation we're planning with Rudolph Stingel. So on the platform, you can see stills of different installation views of these works as they've been presented in different places. And I find it interesting because you could say they're a kind of document, they're not, they're a representation, but they don't pretend to be, this is the work. And in some ways, I like the fact that they say, well, you really would have to experience this in the place, in physically and in real time. So it's not trying to translate work into the digital medium, say, yes, you too can experience it. So I think it speaks to that point. We hope to enhance also the desire, you know, to see things. I think it's something that we all have experienced in our life to see an image of a famous work of art and having this desire to go to see it in real life. And so we hope that this will, even for the work, that cannot be really given the whole, not even the taste of what it is in real life, but give only the, as you say, it's not a documentation, just an hint of what the work could be in real life. We hope that the people will want, will increase the desire to go into the physical museum to see certain things that in the platform are just, let's say mentioned, but it cannot be really offered in the fair capacity of an experience, like Rudolf Stingel and Fujiyara. So I think that the platform becomes also a kind of a teaser for the real experience of those works or maybe other works. And now there is the permanent collection on Woodham that would have been part of the family, me family exhibition that can be seen and visited. And so I think that that, and what is told with the idea by the Chippini studio, installation. So I think that's also there with people can see, have a taste of what can be done within the real space of a museum in an innovative way, and to this full credit to the Woodham, to you and also to your team that came along. As you know, I've worked in museum and I've worked in institution, as a freelancer, and I have to admit that I always found certain resistance in changing the rules and the pattern of exhibition making. And in this case, I mean, I found a total porosity, porous environment willing to accept the, not my idea, but the circumstances and shape them into something that we hope is going to be strong enough to sustain the idea. I think this idea of porosity is, I'm seeing exactly the same word actually, I think it's really important that we think of that project of me family as being tremendously porous. I mean, I think we have five minutes to go before we're going to close off, but I did also want to just highlight the fact that in terms of the work that people can access on the platform, you know, among the many artists whose work is there, and projects such as the display, the permit collection display here in the museum. We have works by artists such as Sophia Almaria, who is this sort of incredible almost abstract work, but based on her and her sister walking through a Dubai mall, and Lara Baladi's amazing work, which is based on her archives of the Egyptian Revolution and its aftermath, and for which as an accompaniment to a kind of representation of that work, where there's also a portal into the archives, she's been developing since 2011, more of the revolutionary protests in Terrier Square in Cairo is very, very beautiful animation called a lesson in history. So the platform is also, you know, there's this porosity in that there are things that are presented, it gives you desire, there's things you can engage with, and there are works that have been made especially for it. And I think as a result of this sort of program, eight and a half as well, there'll be other content such as our content, but conversations with some of the artists that will continue to feed it. I mean, perhaps just a final point, we have three minutes, but maybe to hear from you Francesco, you know, to go back to Stysian's project, which I think is recognized as a was a universalizing portrait or an attempt to offer a universal portrait of humanity in the post-war nuclear age. I mean, this project, Me Family, it's less affirming in that way. You mentioned earlier this fact that it was really about the reality of now. And that reality of now is anything from certain. We cannot sort of, we cannot sort of place all of humanity and their desires, loves needs, disappointments all within the same compartment. I think, you know, and again, I think in relation to the idea of the digital or technology that it's not a panacea. It's not the answer. It's not the solution to everything, but it's part of a bigger set of possibilities. I just would like to hear from you on that before we say goodbye. Absolutely. I mean, it's not the panacea. It's not the cure. It's not the solution. It's not the replacement. And it's in a way more realistic way to look at the world with all those ups and downs. Nothing is taken for granted. While I think Steichen was more, in a way, idealistic, romancing, and also a little bit paternalistic. I mean, if we look at the show of Steichen today with the cynical eye, we could say that that was a little bit something like someone, I don't remember who call it, like National Geographic Photography in the sense that we look at the world as this, you know, where poverty become folkloristic, you know, stress and pain become kind of visually interesting. It was more the kind of, you know, kind of photography. Today, we are much more aware of the pain and inequality and injustice of the world. So, we cannot look with the same eyes that Steichen look at those things. We have to be very aware of that, very realistic, very respectful, and we cannot just take the world and turn it into our, as I say, National Geographic curatorial experience. I think that was a good good experiment and good experience for us, curator, and I hope for the mudam, to see how you look at the world. The name is Me Family, because today we look at the world from our own individual point of view, to the social media, Instagram, Facebook, and all this Twitter, but to stress the idea of the platform is that the platform is allowed in a way the viewer to have entered the idea of the former exhibition as more, more intimately and we, the viewer can embrace the show and put his voice or her voice or their voices into something quite new. That is something that in a museum cannot really do. People cannot, they're not allowed, but they're not, they don't feel comfortable to start voicing their enthusiasm or their protest against the work of art. They feel intimidated. The platform is, I hope, less intimidating and we hope that the viewer feel that way respecting the platform. That's the message to the viewer. We respect the viewer, the viewer should respect the platform and not find it a way where they can voice any possible. That's, I think, I look at things positively, let's say the great positivity of today's world, of the Mi family, as the social media are very dangerous, but at the same time they, for who can use it, develop a great sense of responsibility. What we say is our responsibility. So we can be angry, we can be happy, we can be, but it's our responsibility. What we say as curator, as viewers, as director of museum, is our responsibility. There is no safety net. We say something on the platform, you say it is there and you have to take full responsibility of what to do. So I think it's an encouragement to the viewer to participate it, but to participate in a responsible way as, you know, as responsible. We are all responsible. I think it's the show, if we can stress the last message of the exhibition, the Mi family should be an attempt to stress responsibilities. In any form and shape we can envision responsibilities. Art is curator, everything. So I really look, I hope that people will enjoy this way of understanding the art and the responsibility toward art and of art toward the people. Francesco, thank you so much. It's been fantastic speaking with you and thank you for this amazing project. Thank you for challenging us to go ahead. Have a great day. Thanks to everybody