 Good afternoon, everyone, and today I will just start with a few, I think, useful information because some of you asked me by email about the exam, so I think I should spend a few words about the exam and also I will also give you a bit of a summary of what we have done so far and what it's left, okay? Like this you can maybe orient yourself a little bit better. I apologize for this because I mean this is really the first time that I give proper lectures to an audience that it's not neuroscientific, right? So normally you give either some like popular science very, you know, entertaining talks or you just give proper talks to a neuroscientific audience, so this for me this was a little bit new. So anyway, the exam, so what I will ask you to do it will be to, I will ask you to read a paper. I will select a few papers also that are basically similar to the studies that I presented during the lectures, so some of them would be human studies with fMRI, others would be electrophysiology in animals, so you can pick up one of these paper you have to read. The paper won't have an abstract and won't have a title and you have to basically provide title and abstract, you have to write the abstract of this work. So basically, because I think the aim of my course was really to give you a grasp into neuroscience research, right? So I really would like, so by of course talking about time and how time is investigated, what we knew about time, how time is implemented in the brain, really the purpose is just to make you familiar with the neuroscience research and the logic of it. So that's why when you read a paper and when in order to make an abstract, you really have to just focus on the following things, the things that you see listed in the slide. So you have to really try to understand what are the key questions that the authors want to address with the experimental work, what is the hypothesis or predictions if they make any predictions about how are the questions addressed, so what is really, what kind of experiment do they run, so what is the experimental manipulation they use, what are the results, so really the facts, what they show that the results and how these results are interpreted by the authors, right? And then as a last thing, what is the significance of these results, what do they add to the field? So really in order to I guess write an abstract, you really should try to answer in a very of course concise way because an abstract has a limited number of words, normally it's 250, 300 words, so you have to concisely try to have more or less all this information. Yeah, so I think my suggestion then is really to read papers, among you know the papers that listed in the references, also you can read according to your, to your, really to your taste as well, so to the research you are, you feel more or you can, you know, you can be driven by your curiosity about this subject rather than that one, this experiment rather than that one, right? And you know, you have to read not just to, not to remember the content, the content somehow it's less important but you have to rather focus on the logic, on the few stuff that are listed in the slide. I hope it's clear but we will have, with some of you I will have the chance to talk, especially with the diploma, with whom I have to apologize for today, for missing the meeting today but yeah, so we can meet tomorrow. Okay, so what we, we have done so far, I think in the first week we really focused on specifications and we, and on this, we talk about the internal clock, so we really said that time, so the focus was on, we focused on milliseconds to few seconds time range, we focus on duration perception and processing, we mentioned how it was difficult to study time because we don't have receptors for time because there is no specific pathway, neural pathway for time. We talk about the, the, the scalar property, so we, and the Weber's law, so we basically said that the capacity of perceiving time is the variance in perceiving time, the variability scales with the interval at hand, okay, so although then this is called scalar properties present in human, in animals, across also different tasks, although there are some violations and we talk about some of these violations that concern the use of interval that are below second or below 100 milliseconds and above two seconds. Then we briefly mentioned the internal clock which was the very, was a dominant way of thinking about the, how the brain process time, so imagining really a clock-like mechanism in the brain that was basically, was unique and universal, no, so the clock tells time, no matter the sensory modality of the input, no matter the task at hand, no matter the range at hand. And we, we, I brought as a proof of the existence of somehow this clock, the, all the words that show the, show a core of, a core of areas of brain regions that seem to be engaged in temporal computations again, no matter the sensory modality, no matter the task, no matter the range, right? And I mentioned this work, this, this FMRI experiment where Jenny Cool used, asked participants to discriminate duration or color, the color of a visual stimulus. And I talked a little bit of what we measure with FMRI, okay? Sorry, so is there a question? I heard a noise, a sound. You want to make, is there a question? No, okay. Oh, no question in the chat. Okay. Okay, so the second week we focus on the role of sensory features and sensory court, this is a sensory court activity in time perception, because one of the sort of counter argument against this universality of a temporal mechanism is the fact that there are sensory features that can influence the way you experience time, right? And we mentioned all those experiments that use space, so distance, or they manipulate the speed of a moving object, right? Or the contrast, the luminance of a certain visual stimulus. And they ask me, the task was always the same, was to discriminate time perception. And what all those studies showed is that really the sensory features impact your perception of time. And then we talk about the contribution of sensory court, of sensory cortex activity and perception. We mentioned the work, the electrophysiological work by Alessandro Toso and Matthew Diamond and Colombian colleagues, where basically we actually saw not only these behavioral effects, these behavioral biases, but we had the chance of seeing how the barrel cortex activity, which is basically a primary sensory cortex. So it's the cortex that is receiving information from the whiskers of the rat. So the activity in that in barrel cortex basically can be used to mimic the perceptual behavior of the rat. And linked to that, we also show by using a different perspective, so by making inferences about causality, so the importance, the necessity of the activity of a certain brain region in temporal discrimination, then I presented to you the studies in humans, they use transcranial magnetic stimulation, and they interfere with by inducing an electric field over in the cortex, they are able to sort of shut down the activity of these of the visual courtesies and this is an impairment in temporal perception. In the same line, we also show how this sensory, this visual cortex, how in visual cortex the temporal processing happens in the neural circuits that are also engaged in spatial processing. So we really try, we seem to see a link between temporal and spatial representation in visual courtesies and this was also a TMS experiment. Then I mentioned the SDN model, so the state-dependent network model by Dinguono Mano, where we actually saw behaviorally, we saw some data that seemed to meet the prediction of the model, so time is an object included in the context of previous events, so time is in the dynamic of a network and the network dynamics doesn't reset if it doesn't have enough time to go back to rest, so basically every temporal interval it's basically included as a unique object in the dynamic of the network at that point in time, so when information arrives into the system. So we saw the behavioral studies and we also saw the in vitro study, where basically in line with this SDN model we saw that it's possible to induce a temporal dynamic in a network, in a slice of a piece of cortex basically, so in a very local system let's say, that it's not a brain so you can train this tissue to express some time, although we said that of course it's very difficult to link this activity over time that is expressed in the network that is trained can be linked to perception, so that there is this big gap to be filled. And then this week basically I will try to focus on three different aspects which are basically, actually there are two aspects, one it's really time in the firing rate of neurons, so in two ways I will talk about this and so time is included in the slow ramping activity of neurons and this is what this ramping, what we call ramping models seem to suggest, so that is really this rapid, so sorry not slow ramping activity of neurons that we'll see today, or the time is encoded in the speed of the neural network, so in how quickly the network reach, the neural network reach a certain state and this we'll talk tomorrow and the last day I will focus on a slightly, on a new perspective in time studies, so people that start to investigate the existence in the brain of a form of tuning to duration, a form of selectivity, so duration is like color or like orientation, so for which we have tuning mechanism in the brain, so we want to see whether we have this similar tuning mechanism in the brain and how this tuning, this duration selectivity also can be topographically organized in the brain. Okay so let's start, so if there are no questions I will then start with this ramping idea and I will share something different, so stop share and I will share something here, yeah basically under this label of energy read out or ramping models are all these ideas, the time is really in this activity, it is in this neurons that basically ramp up in their activity, this ramping up activity is very common across the brain, so many brain regions can have, many neurons can show this slow ramping activity and I will show you a few experiments on that, in different brain areas, some are in parietal areas, ramping activity is also observed in pre-motor cortex, so in prefrontal, sorry cortex, so areas that are more frontal as well as posterior regions, so this of course this ramping activity you can observe only if you record, this is not quite sure but I will see if I have time to tell you more, but it's mostly possible to observe this type of ramping activity in neurons, right doing electrophysiological recordings in single cells, okay so you do in animals, so and in fact what I'm presenting today is this study by Giazairi and McShadlin and this is a study where they use monkeys, so they train two monkeys to perform the task, this task and I will tell you, so the task is the following, so the monkey stare at this red dot and then there is something that flashes here, okay this flash is just describes the the receptive field of the neurons from which they record, what does it mean, what is this receptive field, so they record from neurons that are my keynote was just closed, I don't know for some reason shuts down, okay share again, okay so this is the monkey brain, why it is quickly open to application again, why I'm experiencing this weird, okay let's see if it happens again, so it's this area here is the, so sorry this is the the the monkey brain, so this is the front, this is the back, so this is the cerebellum as we saw also in human brains and yeah the basically what you see represented here is as if you cut here, you oh god now why it is, sorry I seem to have problem with keynote, let me try to convert the keynote into PowerPoint, safest option let's see, oh very sorry, yes, I don't know, I really don't know, maybe let me try to quit keynote then I will reopen again and if it happens again I can convert in PowerPoint and see, okay let's try, okay so what you see is, no you see it's just okay let me try to to resolve to find a way around, but I don't see any option, well maybe, well maybe I think well let's try like this anyway, no it's very blurred, no Matteo how do you see, it's very, no it's worse, no because normally it's much nicer, okay I'll try it then to PDF as you search, so okay let's try to just let me guide through it because now I have to put all the info in the slide whereas before there was some animations, so let's just focus on this, okay, so I was telling you about where basically the where the experimenter did the cut, so like you have to imagine that they cut, this is a coronal section, so they cut here as if my face was just off, okay and so what you see is exactly this, so the lateral intra parietal sulcus is this red areas that is inside the intra parietal sulcus, this sulcus that you see here and here this is a coronal section, it's calling like this because it's like a crown, okay so it's like cutting here and this LIP area contains neurons that fires for if you present, if you have to make a saccade, so an eye movement towards a specific position in space, okay, so let's say if the monkey is so fixed is has to make a saccade to this gray zone, basically there is only a bunch of neurons in LIP that will fire if the monkey saccades here and that's called the receptive field of the neurons, so it's basically the piece of external space that elicit a neural response if stimulated, okay, so that's the receptive field of the neurons from which the guys, Giuseppe and Shardland recorded, okay and they basically this is the way they select the neurons so they have to want to make sure, so they select the neurons and they want to make sure which piece of the space these neurons respond to, of course they don't respond to the piece of space, the information that is presented in the space, they respond to a saccadic eye movement that is made towards that spatial location, this is the function of this LIP neurons, okay, and so basically what they do then, so the monkey keeps fixating, this is the external space towards which they have to make a saccade, but for the time being they just fixate, then there are two sequential flashes, one it's a ready signal, they call it ready, and then a second, these are in peripheral locations so they are not in the receptive field of the neurons from which they record, are somewhere else in the visual space of the monkey, okay, and those two visual flashes basically mark an interval, so it's what they call a sample interval, this is a duration for the monkey, okay, and the duration can range from 500 milliseconds up to a bit more than one second, okay, so this is the range of TS that they use, and then the monkey task is basically to hold the response, so to produce this interval, so to produce the interval between ready and set by holding a saccade and making a saccade only making a saccadism eye movement, they have to make a saccade in this spatial location, only when the time that they have, they have the experience before has lost, so they have really to reproduce time by holding the response, and basically they get reward, okay, if they wait in time is appropriate according to the duration, the TS they experienced, and here you see basically this is the plot of the sample interval over the production interval, and this is basically this green area tells you that when the monkey gets a reward, and even the reward timing is basically is given at a time that is scaled with the interval that the monkey basically experienced, so it's very short, so it's very close to the 529, but it could be the variance, the variability of the reward delivering, it's much higher for durations that are bigger, okay, so anyway this procedure, so they train two monkeys, and this procedure leads to this type of behavior in the monkey, so in the two colors, the two lines that you see here, the plots are the behavior of the two monkeys that they train, one it's dark and one it's with these white disks, and what you see is the production interval as a function of the truth, as a function of the sample interval that they use basically, the straight line, so this sorry this diagonal line, it's the expected behavior as if the monkey, if monkeys were perfect clocks, okay, but as you can see both monkeys show this show a little bias, so they in the first place you see that they can perform well, right, because you see that they can perform the task, so their reproduction is closer to 500, in when the duration is 500, it means closer to a thousand, when the duration was a thousand, okay, so somehow they perform the task, but they are not perfect clock, so they perception or better day production as a bias that basically this is something that we encountered before, so they tend to overestimate the longer duration, and they underestimate the shorter duration, as if basically they basically regress into the mean of the distribution, so their performance sort of merge becomes closer and closer to the mean of the distribution at hand, and also what you can I guess, this is basically the gray bars are basically the distribution, these are basically average behavior, right, this is the full distribution of the production times, and here you see that you see again the behavior, which are the little discs of the two monkeys, dark and white, and the line, the fitted line in between is a Bayesian model, so basically the Bayesian model that if you want to see the full detail of the model is in the paper and the supplementary material, but basically they assume, I will tell you conceptually, I will try to describe, this is the Bayesian theorem basically, so they assume that the monkey is a Bayesian observer, so and a Bayesian observer that takes advantage basically of the knowledge of the prior knowledge of the distribution that they experience in the task to optimize, to reduce the variability of their behavior in condition of uncertainty, so basically what this formula is, is basically this is the, if you are familiar with the base rule, I mean this is the posterior, so this is really the perception of the monkey, and sorry, I pasted the wrong formula, this is not the one I wanted, okay, it's not this one, there was in the other, yeah, I deleted the wrong one and I kept, so I deleted the good one and I deleted the good one and I kept the wrong, this is basically just tells you is the likelihood basically, it tells you that the measurement, so T s, so T m, so the perception of the subject, this is the conditional probability of T m of the measurement over T s, which is the real duration, okay, so the likelihood is basically a process that has some noise in it, that they basically model as this noise, they model as a Gaussian that has a mean zero and the standard deviation scales with the T s, because the greater T s, the larger is the noise, so this process of perceiving the interval has some noise and is also influenced by Weber's law, so we see that the variability is function of scales with the interval at hand, and what I wanted to show with a different equation is that basically the posterior probability, so which is basically the perception, is a function of the likelihood, so this incoming sensory information, this process of encoding the information that has noise and follows the Weber law and the prior, which is basically the probabilistic knowledge of experiencing different intervals, so is the knowledge of the sample interval that the monkey basically experiences in the experiment, and basically what they, and the prior, the model, the model they use for the prior, is just a uniform distribution, okay, so it's a static prior, it's something that it's like that the monkey acquired at once, so and this uniform distribution ranges basically the range that the monkey experienced, so from 500 to a bit more than a second. Okay, so this is just to tell you that this bias in performance, this regression to the mean is explained in Bayesian terms, okay, assuming that perception follows, perception of time follows also this Bayesian rule, and this is basically what you see depicted here, is basically, so they record from these neurons in LIP, and this is the behavior of a cell, they record that 58 neurons from LIP, and this is just the depiction of the response of a single cell during overtime in the experiment, so you see that basically there is the, so if there is the target, so basically the sample interval is the distance between ready and set, okay, so the larger this difference, so the neurons fire at the target, at the presentation of the target, this is the really the interval that they are supposed to time, and the longer the interval the later the circuit, okay, I hope it's clear, so whereas here if the time is, here is that the target appears ready set, so it means that the interval to time is short is 500 milliseconds, so here you see the firing of this cell that it's immediately, so it's shorter than here, for example, because this means basically that the cells express the behavior of the subject of the monkey that can perform the task, and even at the cell level you see that there is different behavior according to the duration that the monkey is experiencing, so this is an example of a single cell, but then let's see what happens if we look at the on average the behavior of the cells on average during this period, no, from target to second, okay, so and this is again the average of this 58 cells, and what you see these are the, so every epoch of the trial, so every, so here the basically the signal is aligned with the silent interval, with the silent event, sorry, of the of that epoch, so here everything is aligned to the ready signal, remember the ready is here is the first flash, ready set is the interval to be timed, so ready set from ready exactly to set, and this set to second, okay, and they look at the specific temporal windows, so they basically, you see that there is this discontinuity in the plots because they focus, they zoom into temporal windows of interest, and what you see is the firing rate of spikes per second of the average of this 58, and color coded are basically, is the activity sorted according to the different, so is the activity sorted according to the activity, the temporal interval that the monkey has to produce, so shorter durations are in blue and colder color, longer duration are warmer color, and so here you see there is a after a mission deep, so this is would like to stress the fact that ready set is really the time of the duration encoding, okay, so it's when basically the monkey just experience time indeed, so there is no motor preparation because the monkey doesn't know until the end when, for how long the circuits needs to be old, okay, so here there is no expectation of reward, no motor preparation, and this is the initial state, so the first 500 milliseconds what they observed is just a deep in the neural activity that doesn't seem to be different for the different durations, whereas here they see something very interesting, so in the last 200 milliseconds of this ready to set period, so before actually the set, before the offset of the interval, they observe this increase, this modulation, so the activity of this neurons is different according to the type of interval that they have to, that they experience, okay, and we will see here that if you zoom in, if you look at the this set activity here, so here this again set the average of the 58 neurons in the set activity as a function of the sample interval, so you see that there is almost linear increase in the firing rate as a function of the length of the interval, okay, here in the, so in the set you see the distribution of the slopes of this ramping activity in the different neurons because they basically calculate a slope for each of the 58 neurons, and in black are the neurons where this slope is significantly different from zero, so you see that there is this linear this ramping here, and this is I think the most interesting bit of the story that they tell, because it's this activity can be due to time, nothing else, no expectation of reward, no planning of a motor of a saccade, whereas the activity that they see here, so from set to saccade, so once the monkey know the interval, he knows for how long he has to hold the saccade, and so he knows also when to expect the reward, so which is very, you know, it's crucial for the monkey, and basically what they see is just this initial deep and very fast ramping up, what is important is that before making, so from 500 to 200 before making a saccade, there is this again ramping activity, that this time has an inverse relationship with the interval, so you see that there is a steep ramp for shorter duration, and a much flatter, so sustained, I would say, ramping response for longer duration, okay, and you see depicted the same, so it's a summary of what I just said here, this built up rate that scales, so that changes as a function of the interval, and this activity of course, it's more related, you know, we know that LIP neurons, the job is to fire in preparation of an eye movement towards a specific spatial location, so it's pretty normal that they show this type of behavior. The novelty here is the fact that this ramping activity is modulated, has a temporal precision, let's say, so he's modulated by the interval the monkey has to produce, and again here we go back to the concept of the possibility of isolating a circuit that does just time, I mean I think what is, as I said many times now in my lectures, is that I think it's more likely that rather than having something that just does time, we have a time behavior in each circuit that needs time, so this is a circuit that needs a temporal precision, and it's a circuit that is specific for making eye movements, and these eye movements needs to be produced with high temporal precision, that's why time matters here, so time is in this ramping activity, because we need ramping activity in this task, so and I think this is this modulation of time, it's very very interesting. Anyway, so another similar behavior, okay this is just to tell you, because now it's already four o'clock and I want to show something in you once, but just to tell you that this type of behavior, this ramping activity is not a peculiarity, as I said before, of LIP, of Parallel area, even for example primary visual cortex can express this ramping activity, and this is here, it's shown here, I'm sorry I have to go quickly through this, but this is a study that has been published in Science now quite some time ago, and this is primary visual cortex, so I think they record in rats in primary visual cortex, and what they do, they train rats to expect a reward when they stimulate different eyes of the rat, so in one case they just stimulate, they know that the stimulation of the left eye, so if the stimulation is with the beam light basically, they stimulate one eye, and then the rat knows that if it receives a stimulation on the left eye, the reward will come immediately, so very shortly, so after, I don't remember, I think the durations were in the range of a few seconds, half a second, and a second and a half or something like that, whereas if the stimulation was on the right eye, so they receive this light on the right eye, they're going to get the reward twice the time of the left stimulation, okay, I think, so they basically expect a reward at a given point in time, and what they see in neurons that are responds to the stimulation of the left eye or the right eye, here are colored coded, okay, left eye, it's the neurons that respond to left eye stimulation is in blue, the neurons that are responding to the right eye stimulation are in pink, and as you see, so here it's basically in this basically under this bar, this is the moment where basically the stimulation is given to the eye, and here you see how basically the firing rate of these neurons, this is a single neurons, here they plot single neurons, single cells, these are, and here you see that they ramp up at different time according to the expected reward, this ramps up quickly and just goes down quickly, this has a more sustained response because this is when the reward is delivered, okay, but ramping up is not the only behavior electrophysiologists found, there is also a sustained decrease, so there is also behavior in the opposite direction, okay, so this is when the time when the stimulation is given, and this is this deep in the activity, so inhibition in the activity that then so this deep is different according to the two different durations, okay, also here this is another type of behavior in the firing rate of the neurons, they are neuron steps rather than sustained decrease, they peak, they peak at the expected time of the interval of the sorry the expected time of the reward, okay, so they have here they peak, so when the duration is expected early and this peaks a bit early but when it's expected late, and these are basically when you observe the behavior of the neurons that are sensitive to the stimulation of left eye, right eye, these are the response of neurons that are not sensitive to that stimulation as you see this is basically a flat, and this is just the differences between dominant and undominant responses, this is just a different way to see those three plots, but here you see as a difference between those two type of plots, so again this is not purely time in visual cortex, this is the rat is expecting to get a reward a different time, and he learned to expect this reward by a visual stimulation, okay, so we know to associate a certain visual stimulation with a certain duration, and again the visual circuit that receives this visual stimulation, it's modulated according to time because this is a visual task and it needs temporal precision, and you see that there is some trace of time in this activity here, so similar thing you can see, so at the beginning I said oh in order to see this modulation of time in neural activity you need to record from single cells, in reality this is not entirely true, you can even do with humans, this is what we did in an fMRI study, this is quite an old study of mine, where basically this task is very simple, so the the subject gets this blue target, this blue stimulus, and after a certain amount of time the blue annulus, this blue stimulus, change color gets, becomes yellow, and what we manipulate here was the time between the blue and the yellow, okay, so and in one case the blue, so the yellow, so the in one case the the the timing follow a unimodal distribution where the the probability of change was around, was maximum around eight seconds, and in other blocks of trials the the the probability of the change was either early, around four seconds or late, so here if you want, subject is expecting something interesting to happen, which is the color change, at the specific point in time, okay, so there is a an expectation, there is a temporal expectation, okay, and okay I don't know maybe I should just then I think it's only a few minutes left, so basically at behavioral level what you expect, if the subject can really use time to make this prediction, you expect the subjects to be very fast in responding when he highly expects this to happen, so around here, so and then if I present, because I have some tails here, if I present the stimulus here or here in the distribution then subject would be slow because the the change happens unexpectedly, same thing I can I can say here, so the change happens with high probability here and here but I can, you have tails here, so I can, if I show, so subject would be very fast if the the change happens when it's, when the subject has learned to be highly provable and it would be very very slow if things happen unexpectedly, and this is basically what we observe behaviorally, so this is how fast the subject responds as a function of really the the occurrence of the stimulus, and here you see that there is basically the, in this unimodal schedule the subject it's faster and faster by with time because if, if something is not happened it will happen for sure because this is what they learn, so here we also use the conditional probability but I don't want to go into that, and in the bimodal schedule it happens what I just said, so that here it's the most likely point in time where the stimulus happened and the subject is very, and the subject is very fast, and here again you see that the subject is fast when it's expecting and it's slow when it's expecting, it's the change up unexpectedly. This is an individual subject, this is the group, but what I think I want to show you a brain level, it's let's focus only on this piece of the information that resembles what we saw in monkey's brain, so basically this is the activity in primary visual cortex, when the subject is expecting something to happen around 10 seconds, and you see that also visual cortex, this is what I plot is the the percentage of signal change, how the hemodynamic response function change in time, so this is the time, time from target onset, and basically you see that the visual cortex is modulated by time, so it rises when something is likely to happen in time, and this happens also in the bimodal condition where basically something is likely to happen either early or late, and you see that there is this shape that resembles the conditional probability in reality, but what I want to point out here is basically this is the activity in primary visual cortex, when the change physically happens only late, so we just took only the trials where the color change happened later, but the subject, since the subject is in this bimodal schedule, is also expecting something to happen early, and so you see even if there is no physical change in the stimulus, your visual cortex lights up, so reacts, the signal rises in primary visual cortex when you are expecting something to happen with a certain temporal precision, okay, so even visual cortex activity can be modulated by time, and I'm basically ending by saying that this modulation is not only in visual cortex, we actually observe it also in a wide network of brain regions that includes the cerebellum, the parietal cortex, like the monkey eyes, the supplementary motor area, and the mid-frontal cortex, an area which is even more frontal is more or less here, so basically here you see also the advantages disadvantages of the technique that we use, so if you use single unit recordings you're able to see this behavior in single units, beautiful, because to see spiking neurons is very exciting, but of course you are constrained into a specific brain region, okay, or two brain areas maximum, whereas with fMRI of course you have a microscopic view on the process, but you can still appreciate something that is similar to what you see at a neural level, but here you observe across a wider range of regions, and I conclude, so thank you for your attention and I'm looking forward to your questions if you have.