 This was basically where I think we ended last time. Yeah, exactly. I hope you all are aware that I posted also online that there is also not the syllabus with the references, but there is also a file with all the references that are more or less linked to what I present in each of the lectures. Bear in mind that if there are some new topics that emerge from the lectures because of the questions, like for example, in case of Weber's law, I might add, I might continuously update this file with new references that you might ask, OK? And also the reference of the internal clock model. I should warn you, because most of the models that I'm going to talk in my lectures are not very, are not mathematically so well formalized as you might expect, OK? So this is something just to, exactly, to be clear that most of those models are not so formally. So it's less, what matters most is not just the mathematical formalization rather than the biological possibility. So most of them refers to some physiological mechanism that is existing in the brain. Anyway, so we ended with this, which is basically a sort of summary picture that tells us that more or less in the brain, there are several areas that seem to be involved, seem to be associated with temporal tasks. Some of those tasks are perceptual. As we said, some are more motor, so involved motor components. Some refers to milliseconds range, and some refers to above seconds, OK? And what we know more or less is summarizing this picture. So it's a network that includes some subcortical brain structures like the cerebellum, the bisercanglia. Others are cortical areas. Some of these areas are like the frontal, so dorsal lateral prefrontal cortex, inferior frontal gyrus. Others are more posterior. And so most of these areas, like the supplementary motor area, but even the cerebellum, the bisercanglia. So most of the areas that you see depicted in these summary slides is areas that are involved in some motor circuits. They are important for motor coordination, for motor initiation, for motor planning. So there is motor, it's a key issue for time. I think changes, experience of change, it's a key feature for the way we acquire temporal knowledge, OK? But what I was saying is that the fact that most of these areas that you see in this picture are areas that are involved, are seen active in temporal tasks, these areas are active no matter also, so independently from the sensory channels from which you receive the information, not of the time that you have to judge. And so this is taken as a proof of the fact that you have so that in temporal circuits, sensory areas don't really play a role. And we do have more or less a clock that is a model, we say. So a clock that tells time independently from the sensory channel from which you receive information. And this is a proof. Now, what I also was anticipating last time, so there are a bunch of other empirical evidences that are against this idea of zero role of the sensory regions in temporal computations. And this empirical data comes from mainly psychophysics, OK? So it's from psychophysical studies. And psychophysical studies that basically wander. So there are all studies that wonder whether if I change the feature of the sensory stimulus that I have to judge in time, do I change my perception? My perception changes as a function of changing some physical properties of the stimulus. And of course, the answer is the answer to this question. So is yes. Yes, if we change sensory features, we change duration perception. And I'm showing data that supports this claim. And one comes from an interesting study that has been conducted by Daniel Casasanto and Lera Borodiski in Stanford. It's done for students, so not silly students, OK? But smart people that go to Stanford. But you will be surprised by what happened in this experiment. So basically, subjects were presented with lines on the screen of different lengths, like something similar to what I'm showing you now. Something moving, a line that grows in space. So you see that the end points and start points are different. But what matters here is in this start and end is varied randomly. So it's not something that the experimenters are interested in. What they're interested in is changing the length of the segments that they show. And so what they manipulate here is both the spatial displacement in pixel. So how much space is covered by the line. And also the time, so the duration, this line is presented for. And they basically have all possible combinations. And what you see is basically in these graphs, these plots are on the y-axis, the estimated displacement in pixel. And this is the target, sorry, on the y-axis, yes, you see the estimated. So the percent of the subject on the x-axis is the physical change. So the manipulation of the experimenter. And in case you basically care about space, as I said, they also manipulate the amount of time these lines are presented on the screen. And here you see the estimated duration as a function of target duration. So here you see that students can do this task very easily. So because there is basically a diagonal. So the longer, the greater the spatial displacement, the longer, so the judgment somehow is congruent. So the longer the duration, physical duration, the longer is the perceived duration. And it's in the same way for a spatial displacement. But when you look at how the estimated duration changes, as a function of target displacement, you see that there is a bias. So that basically subjects tend to judge that stuff that are displayed for greater space are also judged as if they were longer in time. So this is what this graph, this plot in A is telling us. So target displacement, this is the physical displacement. And this is the perceptual judgment in duration. And here is the other way around. So here you have the target duration. And here you ask a subject to judge the displacement, so the length of the segments. And here you see that there is no effect. So as if basically the spatial displacement influences time, but the time does not influence the spatial displacement. And basically, they interpret this data with the fact that often, so you basically use some spatial concept to tell time. So you use space to tell time. And these guys are linguists, they're interested in language. And basically, they believe that there is nothing rooted in the brain that enables you to do so, to use the space to tell time. For them, it's something more conceptual. In fact, that you conceptualize the notion of time, it's really driven by space. And that's why you have this asymmetry. And but something indeed, for example, if you think about the way when we talk about time, we often use spatial terms. We use this, this was a long, not talk. It was a short, so we really use a special metaphor to refer to time. We use often space. But this can be something that is more fundamental. I don't think it's only conceptual. It can be even more fundamental in our way we experience time. And now I will show you some more. There is a question in the chat. OK, sorry. I don't see the chat. OK, yeah. If you touch now the actual temporal duration. So this means that the duration is the same for different displacements. Or vice versa. Yeah, basically, they use, so is the question so this you see here, OK, here, that the target displacement is different. And also the duration can be different or can be the same. And when it's the same for the same physical duration, if the spatial displacement changes, you see a change in perception of the duration. But you will see it clearly also in another experiment that I'm sure have more data for that. It probably is more clear. I showed the full range of the stimuli that they use. But they cross everything. They only analyze here the data where one is constant and the other varies. The other dimension varies. OK, so another experiment of the same sort that tells that so there was a spatial displacement here is also spatial displacement. And it's a different task. So here you have a stimuli of just a square that moves. Here what changes is the speed at which basically it's the velocity. It's not the amount of space covered by the stimulus. It's just the speed at which it moves. And so you have a fixation. You have these little black dots on the screen that starts moving from left to right at different speeds. The speeds tested I think range from just the static, so 0 degrees per second. This is the references, so the way they calculate, they express the speed to 32 degrees per second. So how many degrees of visual angle it's covered when this thing is moving. And here the subject is asked so it sees across and is queued to start to reproduce. So this is a motor task. So they have to press the key old and release to reproduce the experience duration. So they don't have to judge the speed. They have to judge time. Because they have to reproduce time. And here you see basically the reproduction, the overestimation. 0 means perfect. Negative values is under estimation and positive overestimation of time as a function of the velocity at which this square moves. And as you can see basically there is and sorry in the different symbols indicates different base duration. Because exactly so the dots moves at certain speed but is displayed for a certain amount of time that could be different. The range is from 200 to 1,000 from 200 milliseconds to a second. And here you see for each of these base duration how changes the reproduction as a function of the velocity at which this square moves. So the faster it moves, the longer the subject keep press the key. So there is an overestimation as a function of the speed. The faster the longer if you want. Same thing in a different here. Actually the experiment is even simpler. So on the screen there is just one target, one object in the screen, a shape. There's a geometrical shape, either three targets or five targets. And these are displayed as a stationary object or they move basically. Here they even don't use, they don't manipulate speed but just they compare the performance, the error. Here you see the mean constant error as a function of the fact that the objects were stationary or they were moving. And here you see that the moving object, it leads to basically more errors and in judging the duration. And then it comes so it's not just the speed, just moving. It's also another feature. So here I'm talking about an experiment that a student, a PhD student of mine conducted. And here you basically don't change there's any speed any special displacement. You just change the luminance of the visual object. So the brightness, okay? So you change the contrast. As you can see here, okay? So here you see this is exactly the stimulus she used. She's a grating, a Gabor patch that is displayed for different durations but what we manipulate. So here there are two things that are manipulated, not the duration. So and the stimulus could be, the range could be from 400 milliseconds to 1.2 seconds. So this Gabor is displayed for different length but it also appears on the screen with different degrees of contrast, so of luminance. Sometimes the contrast is very sharp. Sometimes it's barely visible. And we measure this contrast in each individual. So for each individual subject, we identify the minimum contrast to be perceived. So that leads to really a clear perception in every subject. And then we move in steps. So we start from really the minimum threshold. So 2% of this threshold value. So this is the minimum contrast level for each individual participants and to the 90% of these values because of course you don't know but this contrast sensitivity, so the sensitivity of the contrast is something that varies. Like any perception of yours, it's subjective, right? You might have different, your sensory system might have a different sensitivity compared to your colleagues, right? And even in your, can change in the single individuals depending on the physiological state, depending on the fatigue during the day. So for this, you need a very precise measure of this contrast sensitivity and you use this sort of references of what is the minimum contrast sensitivity value and you use to choose the steps of your manipulations. So these are logarithmically steps, this level of contrast, and you have minimum and maximum arbitrarily in the sense that you decide based on this threshold measure. And then you ask participants, so you show this stimulus that varies in contrast and in duration and you basically ask the participants to reproduce it. And she ran two experiments. In this case, basically, she uses this type of stimulus. And this is another experiment in which the stimulus is likely different. This is something is a very small detail in vision psychophysics. It's just this stimulus, the average luminosity, the average luminance of the patch is equal, but it's very dynamically within each of these little squares. And this is made, so you have to imagine this stimulus as a flickering patch where all these little square changes in luminance over time. And this is made with the purpose of not causing adaptation in your retina, okay? So it's a sort of sophistication that you use to make sure that the effects that you see are not due to this adaptation of the receptorial level. But it's not so important for the purpose of my talk today. But just to say that she did this task in two different conditions. And here again, the same logic. So she used different contrast level and different durations. And here the task is just to reproduce the duration. But she did the same manipulation of the contrast in a more perceptual task. So she, in this case, it's a duration discrimination where basically she asked the participants to discriminate the duration of this stimulus, which is a standard. So he has a fixed duration, which is half a second to discriminate this duration compared to this other stimulus, which is a comparison that could be in duration longer or shorter than this standard, okay? So this is a stimulus that varies in duration. And the range varies from 200 to almost a second, 900 milliseconds. So the subject task is decide which one of the two was longer in time. As here, so here the task is temporal. There is no judgment of the contrast that you ask to the participants. But nevertheless, the stimulus that is fixed in duration varies in contrast. And again, we vary the contrast level by setting a minimum. This is the minimum perceived contrast, 2% above this minimum value. And this is 90% of this value. And these are intermediate steps that are decided arbitrarily. And basically, as you might guess, the expectation is to find a difference of the perception of the same physical duration as a function of the contrast level that you use. So what you expect is that the greater the contrast level the longer the perceived duration, okay? If duration happens through an integration mechanism of the energy of the sensory input, okay? The more energy, the longer the duration. This is more or less the idea. The hypothesis that we tested because this is more or less what we believe also it happens with frequency, with the speed or with velocity, or with also spatial displacement. And basically, this is here, you see the results of her. Let's just focus on this column here where you basically have on the y-axis, you have as always, as always my plots. This is the percept. So the reproduced duration in the first experiment with the Gabor, with the grating. And this is the reproduced duration when the stimulus is this patchy, this is dynamically changing stimulus, but still a reproduction as a function of the target duration, now 500 to 1.2 seconds, okay? And here you see that this is the reproduction of the subject as a function of the different intervals. And the different colors are the different contrast level that we used. So the more the pinkier curve it's refers to the brightest stimulus. So the stimulus where the contrast was the greatest. And as you see, there is this effect, there is this expected effect. So there is the brightest, the stimulus longer is the reproduced duration. I hope it's clear. And this is just, it's exactly the same plot, but here is the bias. This is the average across the different durations. Basically just pull the performance across the different durations. And here you just plot as a function of the contrast level. So you see the greatest the contrast, the graded estimated bias, okay? So this is true for the two reproduction. Here things are slightly different. So because this is the results are the same, but the way I represented the results are different because this is a discrimination task where on the y-axis you have the comparison. So your judgment longer. So there are the number of times you judge the stimulus as the second stimulus as longer as a function of the different durations. And you have psychometric curves, okay? For each of the different. So you know that in this experiment the standard duration is 500 milliseconds. You have to compare these 500 durations to durations that are shorter, 200, 400 or longer, 800 in a second. And here what you see, you appreciate, so you see that the steepness of the curves is the same. So meaning that the sensitivity, the precision is the same no matter the contrast. The contrast just creates a shift in these psychometric curves. So it makes you judging something. So for example, it makes you judging. I'm now looking at the 90% contrast. So this very pinky curve. So this means that in this condition something that last, let's say 500 milliseconds. So a little bit more, maybe it's 50. Yeah, something that it's slightly bigger than 500 as if it was 500, okay? So you tend to overestimate the duration. And here this is the same is the point of subjective equality, which is what I said, this measure of the bias as a function of the contrast level. Okay, so these results are interesting for this idea that if you change some sensory feature, you change the perception. So they're interesting for this purpose to indicate that something that it's low level affect your perception. And it's interesting because it might suggest, it might shed some lights into the the mechanism that leads to duration perception. Which is this integration mechanism, integration of some sort. And this is actually the, again, the hypothesis that is tested by looking even at the brain in this work by Matthew Diamond and his group. So Matthew works, is a PI at CISA and the cognitive neuroscience PhD. And this is something that you did with together with his PhD student, Alessandro Doso. I speech this to him. Yeah. So Roman is asking what does energy means in this context? Yeah, energy, it's a good question. It's basically the amount of sensory information that is, that reaches your sectors. So how much information is entering the system? This can be, yeah, I can define energy in this way. So how much your receptors are active and how much information is decoded from your neurons, okay? Exactly. So I hope I answered the question. So this is, it's going in deep into this. The concept is the same, the framework is the same. So here what they did, they manipulate, again, the energy of the stimuli, but here the energy is the intensive, the speed at which a vibration is given. Here the subjects are not just human beings, they use humans. So here you see this is the device they use. So they stimulate the fingertip of the participants with this device that moves, so the vibrates. It delivers vibration to the fingertips of the subjects, okay? And here they use also rats. And here what they manipulate is the intensity of the stimulation of the vibration of the rats, okay? So which is where basically in the vibrates are there are all the receptors of the rats, okay? Receptors that translates this sensory information, this vibration into, so it translates the vibration into action potential. So they basically leads to neurons to fire, okay? And here you see that the representation of, so you see a stimulus that has high speed or lower speed, okay? So this is the speed is expressed as millimeter per second. And here what they do, they just present a first stimulus that they call T1 that has a certain speed as a stimulus. Speed S1 and a certain T, a certain duration. And after an inter-stimulus delay, they present a second stimulus that has a certain speed S2 and a certain T, T2, okay? And what they do in their experiments, they manipulate the, they have all possible combinations of S and T. So and here you see a nice representation of all possible combinations. What they do, okay, in order to, since duration and speed are in different units, they just use, they normalize these values, the values that they use in order to make it comparable. So they have an NTD, which is an index, a normalize duration, which is basically the difference between T2 and T1 divided by the sum of the two. And the same they do for speed, okay? This S2 minus, and so you go from minus three, which so from positive values, sorry, positive values means that the in speed, for example, if we go this, if you look at this, this bar, the color bar, that it's time. So the positive value, the positive values means that the T2 is greater than T1 in duration and the same for speed, the red bars. So positive is the greatest, the second stimulus is greater in speed compared to the first stimulus. And here you have, you know, to sample, here you see that there is, in this case, you have a very, the second, when in time, this is a case where you have a negative value for time. So it means that the second stimulus is shorter in duration, but is longer, it's higher in speed. And here you have this sample here, you see? So here you see the case where the second stimulus is longer in duration, but has a lower value in speed. And they have all these possible combination, okay? And they ask, in some case, they ask, okay, in humans, they have blocks in which they ask subjects to pay it to judge duration. So the stimuli are manipulated orthogonally. So it means that the subject experience always the same stimulus that varies in duration and speed. But in different blocks of trials, they have been asked to judge the duration of the vibrations or the speed, the intensity of those vibrations. So what it changes is just the requirement to the subjects. For rats is different, rats, there are a group of rats. So they haven't tried to train rats to do two things. They just have group of rats that they discriminate speeds and group of rats that discriminate time. Okay, and so here is the plot of the psychometric, the performance of this task of human and rats for the, this is NTD, so this is physical duration, okay? And this is the judgment of T2 greater than T1 as a function and the different colors are the different basically the different speeds that they use. In order again to generate these psychometric curves, this is we call psychometric curves, they use only the trials. So they have the full range of possible combination of duration and speed. But in order to generate these plots, they only use in time the trials where the time is fixed, okay? And the speed varies, okay? And in here, they use the trials where the speed is fixed and the duration varies, okay? But they need, they test the full range of possibilities, but they just use a limited number of these observations to generate the psychometrics. And here, what you really, again, you see that the, there is a shift so that somehow the shape of these curves, it's very, it's similar, it's very similar. So there is no really change in the precision of this duration in this duration judgment, but they seem to be a shift of the psychometric curve that is a function of the difference in, here, the difference in speed of the intensity, sorry, see the speed of the vibration. And here, it's the difference in function of the duration of the vibration. And basically here, what it happens that you are more likely when SP2 is greater than SP1, you are more often likely to say that T2 was greater than T1. So basically, the faster, the longer. The more intense, the longer. You can rephrase it like this. And when T2 is greater than T1, you are more likely to say that SP2 is greater than SP1. And again, the longer, the stronger. The longer, sorry, the longer in duration, the stronger is the feeling, the faster is the perceived speed in the vibration. So compared to the first work that we saw where we talked where we saw the spatial displacement here, the manipulation is perfectly symmetrical. So you see that speed affects time and time affects speed. And what is interesting here is also, I like this paper because of the logic. This is a very recent publication. I just, I think it was online a few weeks ago. And what is interesting is this is also the logic that the experimenter follows, okay? So here what they wonder, okay, where does, so is this effect, where does it happen, this bias in perception in the first place? Because you see that as I repeat because I said in previous lectures. So in these tasks, there are several cognitive components. Several things happen from the cognitive point of view. You have the encoding of the sensory stimulus. You encode the duration of S1. Then you store this information in working memory. Then you basically, then you have a second stimulus to encode, you have to retrieve information for your memory, the memory of the previous stimulus. You have to compare. You have to take a decision and respond. So the authors here, they just, so they check this behavior when the constant stimulus was the first and when it was the second. And again, if what this bias is something that happens only at the decision stage of the task, you should see the effect only when this manipulation is applied to the second stimulus because remember that the second stimulus is where the decision has to be made because it's when you compare two things and you decide which one was longer. And so basically they sort of claim that this, since this effect happens no matter whether you apply the manipulation to the first or to the second stimulus. So it means that basically this effect should be at the encoding stage, should be when, because it happens when you just extract information and there is no decision to make because still you have to wait the second stimulus before making a decision. But then they run a second experiment where basically they just get rid of all this very complicated extracting cell. So they get rid of the second stimulus basically. They just use a single stimulus and they ask the subjects to do, to just decided to have a reference. You remember at the really beginning I was telling you about this single interval task where you just get rid of the two stimuli, just use one and the subject builds up a long-term reference and just uses this long-term references for comparison but it receives in each single trial a single interval. And here the subject has to respond. So it sees, it sees, sorry, it feels the manipulation, the, it feels the tactile stimulus and then he has to rate with a ruler that appears on the screen. He has to rate his sensation, okay, his perception when it was zero was less, not much intense, so very short to really very strong sensation, very long duration. And basically they use more or less the same procedure and this I want to make this, I want to cut this story short. They see exactly the same thing. So if you plot the duration estimation as a function of intensity of the speed of the stimuli, you see the same bias and the same for intensity. So the stronger, the longer, the longer the stronger. Interestingly then, and this comes the brain. So they have this idea, which is something not new because so they believe that basically this duration perception happens through this duration. So this encoding, this information is encoded through an integration process. And they hypothesize that there is a leak integrator that does this job. So this integration is not linear, but it's just, it saturates at a certain point. It leaks information over time, okay? It's not a perfect linear integration. And this is basically what describes this leaking integrator where basically what is important is gamma is the percept, is what the subject experience. Lambda is the leak rate. So the amount of information you lose over time. And this is basically the input of the, is the sensory input that you receive basically, okay? And so this, the ratio of, and so this basically, this is basically how your perception changes over time, okay? And the ratio of this constant integration as a function of the leak is the time constant of this integration. Excuse me. Yeah. Sorry, I have a question. Can it be, okay, this is just a wild guess, but can it be that a stronger stimulus just leaves a wider trace in activated neurons that takes longer to seize completely? Like with the longer stimulus I activate more neurons and it takes longer to extinguish all the activity. So I perceive the stimulus for a longer time. Yes, but indeed it is more or less so like this. So here are, yeah, it is like this somehow in the sense that a stronger stimulus has elicits greater activation in the signal, okay? And this greater activation is somehow read out has longer to last longer in time, okay? So, and I think it's more or less what the model assumes if I interpret correctly. Well, I mean, for example, to stimuli have the same direction. Okay, but this is, okay, no, maybe not because I think you're assuming that it takes longer for the system to encode a stronger stimulus. But this is physiologically incorrect. It's not like this. So because a stronger activity, so a more intense stimulus doesn't change the time in the time the neurons take to encode the stimulus. What we know is that, what we know is what you see is what you see in this plot. So that basically a stronger stimulus, sorry, yeah, a stronger stimulus elicits a greater activation, a greater response in the neurons. This is the modulation that you see a brain level. You don't see that the stronger the stimulus, the longer is the delay in neural activity. Okay. You see? So this is exactly, this is firing rate. This is spikes per second in a population. Okay, this is, okay, let's start from the beginning. These are neurons, okay? This is the spikes of neurons from which these guys are recording. When they present a stimulus that has different intensities. If what you're saying is correct, you should see different latencies here. So you see that the response is prolonged in time for stimuli that are at higher speeds, the yellow trace. Professor? Yeah? If I can ask, if I can just kind of ask something related. So the way I understood it, the question was, if I put more energy into a signal and more energy enters the system, the brain, then maybe when the signal is traveling across the brain, more activation, more neuronal activation thresholds are surpassed and so more neurons activate. And so for each population, a larger fraction of the neurons activate and it takes them longer to extinguish. And if this characteristic time of extinguishing is related to time perception, then maybe a larger energy, it has to- Okay, yes, and okay, you made me, okay, this was the previous some interpretation that I had with the question. And this is exactly what is, oh, sorry, I'll let you finish and then I will- No, no, that's the way that I interpreted my colleague's question. Yeah, and this is basically what the state-dependent network models assume. So what they believe is that the, it's not exactly the time, the network. So I don't know if it's, so yeah, it's exactly the time it takes to reach a certain state in the network that tells time. In some neurons reaches a certain state faster. So in other case, it's slower. And according to them is the fact, so it's exactly that it's the how fast the dynamic of a population of cells. So time is encoded in how slow or fast the population reaches a certain stage. Yeah, yes, yes, yes. It's exactly that. And I will present some papers that show that, that shows that the different durations, so different durations are encoded in different temporal dynamics of the population state. So it's really the speed of the dynamic in the population activity that my translates the time, my tells the time. But even in that case, even if this is the correct mechanism, you still need a stage that recognizes the different patterns, the different temporal, the different temporal dynamics of the population. You need a layer in your network, in your layer in the network that it's able to reach that this is the faster dynamic. So means shorter time. Okay, so that would mean that you would still kind of need a variation of the pacemaker aggregator model, right? Exactly. In a certain way, not exactly, but in a certain way you would have to, so you would have one system that oscillates in a certain way, and then you've got another that reads it out. Exactly. Even those models that assume that really it's the temporal dynamics of the network that tells time, in the end to explain the fact that, because if you just rely, so you have to take into account the fact that you learn and your perception is stable over time, and the dynamic of a population over time can change. So cannot be so volatile. So you need really to recognize this pattern because this pattern it's somehow rewarded because you recognize that this is shorter compared to that it's longer. So that's why all these models even assuming that, so really time is just in this dynamics, in the temporal dynamics of the brain, but you still need to recognize these dynamics. But in order to decide to make a decision. All these models, okay? Yeah, but does, so if we take a neuronal like population, and it has an output, probably there are many micro states that give out the same output, right? So the only thing that will be kind of rewarded would be a macro state, not a particular micro state. Yeah. But then again, that also, that again leaves the problem of the reading out. That creates the problem of the reading out. Yeah, exactly. Exactly. But that's why, so you can see this chronologically in the story of these interesting models that talks about population that in the beginning they were really excited and say, no, you don't need a clock. But here it's matter of labeling things. So the clock can be the readout. It's just moving the problem from one points to another. But anyway, you somehow need stuff that reads this pattern. Otherwise you won't explain the stability of your perception. And now you make decision based on that. But okay, what I wanted to show here in the first place is the fact that basically what they do, they record from barrel cortex, which is basically the first cortical stage of, and then the first cortical stage of tactile perception in rats. And they record from neurons that they are sensitive to speed, which are those, and here you see the behavior. So they have this on off somehow. They have this, yeah, and they really are sensitive to different speeds, but also they record also from, so, and they also see that there are no coding speed neurons. So neurons that basically don't care about the speed, they don't respond to speed. So they just have these two different populations. And what they try to do, they try to basically simulate the psychometric curve. So this is the behavior of the rat, okay? And they try to build a neurometric curve. So by using this neural activity that they record from barrel cortex, and they basically decide to change the parameters of the model to tune the parameters of the model in order to approximate the psychometric curve. So the perception. So they want to create a neurometric curve that it's as close as possible to the psychometric curve. So they want to mimic with neural activity the percept or the behavior of the rat, okay? And they manipulate three parameters. One, it's the basically the constant of the integration. Okay, so how fast or slow this leak integrato integrates, okay? One, the other parameter that they change is the ratio, the contribution to this neurometric to the speed coding neurons and non-speed coding neurons. And the third parameter is the level of noise, the background noise that there is in the system, okay? And basically what, so the parameters that seem to work best in order to have a psychometric, a temporal psychometric that approximate, so a neurometric that approximate the psychometric is in time is this tau. So it's a very long somehow, 600 milliseconds integration rate, okay? So in integration time, the ratio it's like 60, 40. So 60% of the neurons are speed coding neurons. The 40% are non-speed neurons. And the noise level, I think it's an arbitrary unit, it's four point something, okay? It's not relevant for us. What is relevant is the fact that you have an integration window long. And I think this makes sense because you need time to integrate time. And what is interesting is the fact that you don't have to have all speed neurons, speed sensitive neurons to get this neurometric. On the other hand, the parameters are different for getting a neurometric in speed, a neurometric that approximate the psychometric for speed. Because in this case, the integration window is much shorter. So it's 90, the tau is 90 milliseconds. The noise level is a bit less, but again, it's less important for today's purpose. But what is interesting is that 90% of the signal to get this neurometric comes from speed sensitive neurons. So basically the authors claims that, so you definitely need different parameters in order to get those two different percept. So you have here the same source, the sensory source is unique. It's just this vibration in the vibration. Then you have two distinct percept. They're probably, so they are due to this, they are probably the results of this integration that happens with different parameters, okay? In order to get this distinct percept. Then they wonder whether we have two integrators, whether we have two distinct integrators or just a single integrator, okay? That just tunes according to the fact that you are telling time or speed, okay? So they adjust the parameters according to the type of judgments that you have to make. And to answer this question, they devise a nice experiment. So here again, I like the flow of the logic in the experiments. So here in order to answer this question, so you see tactile drive, a single leak integrator that is responsible to do this distinct percept. And here you have the single tactile drive and you have dual integrators for two distinct percept. To answer this question, they have an experiment where in one case, they ask participants, so to perform exactly the task of judging the intensity or the duration of this vibration. But in one case, they ask participants in advance. So the participants know in advance whether it has to judge the intensity or the duration. And if you have a single integrator that just can be tuned to generate different percept, you expect a different performance according so to whether you know ahead of time, whether you have to pay attention to duration or intensity. And in the second experiment, you are cute just afterwards, okay? So you see, sorry, you feel the vibration and only later on, you know whether you have to judge duration or intensity, okay? So if you have two distinct, if you have a single integrator, you expect a different performance when you are cute, because you expect to see a bias only in, you don't see, so only in one condition, but not in the other. You don't expect a bias in duration because you know that you have to tune with duration. And if you know that you are judging speed, you are just tuned to speed, that you don't get a bias by the duration and the speed. But indeed, what happens is that you, no matter those two condition, you still have a bias. So that you have a bias, so duration bias intensity and intensity bias duration. So the authors in this results are suggesting that the fact that you have two distinct integrators and not a single one, one for duration and one for speed. I hope it's clear. Well, Professor, does that mean that like when the signal enters the system of the brain, it's kind of dispersed in multiple, let's say analysis mechanisms, analysis circuits, and then you can retrieve the information from their outputs depending on what's asked of you. And it's not that you've got one like machine that, am I, is that correct or is the correct? Yeah, because if you have a machine that is able to reset a single machine that is able to reset according to what's your goal, you shouldn't see any bias in this condition, right? Because if you judge duration, you are able to judge duration, you tuned to duration and you don't care about speed, you ignore the speed, and it's the same for time. But so it means that you have two machineries a mile for this integration, although the input is single. So many guys think our time is over. See, time is over, sorry, I just went, but I wanted to finish this in order to tomorrow to start for something different. Okay. Okay, thanks. I'm sorry if I've been late.