Federico Toschi: The Physics of Flowing Human Crowds (TSVP Talk at OIST)

Okay. So I think we can start. Thank you everyone from for joining today's TSBP seminar. It is my pleasure to introduce Professor Federki from Endovven University of Technology Department of Physics and Science Education. So Federico has been here for few weeks now and he's leaving tomorrow but he's supposed to come back again maybe in the next year and uh he has done many works in the past on many different topics and they the face that include dynamics soft matter biopysics and u this is also ex exemplified by the many reviews he has written and the latest one on the mulers but Today this is not what he's going to talk about. He will talk about the one he published in 2023 about the human crowds. And indeed his talk is the physics of flowing human crowds. Okay. Thank you very much Mar for the introduction and I welcome everybody. I hope you can hear me properly. Everything is is is functioning. Um what I'm going to do is really try to give you a little bit of of overview of what I've been doing over the last more than 10 years by now. Um on a topic that you could call active matter is a very special type of active matter uh humans. And as you will see my perspective from the beginning has been the one of a physicist trying to figure out uh the basic mathematical and physics type of modeling. So um I'll try to stay a little bit uh at a more uh general level but everybody that is interested in details uh welcome to contact me or you know to to read publications. I will give some reference where you can find additional material later on. So uh first of all um as I said I'm a physicist so I like to start from the very simple things and try to see if I can understand them and that's a little bit the route that I've been following and I'll give you a little bit more example later on and so also the menu for today is following this sort of you know historical development in my group we have been focusing first to try to see if we can replicate some of the feature of the dynamics of a single person moving alone And then moving to you know the next more complicated things two persons colliding with each other. So very low density and then more general more general kind of situation that um now we understand quite a bit but in the beginning really scared me from the modeling point of view and then if time permits I'll give a little bit more indication of um what this may be useful for. for example in terms of nudging trying to to to change the dynamics of crowds and you know some challenges ahead. So I already would like to highlight that if you want to see more you can find our web page here maybe not completely up to date but for sure you can find a lot of information. Now um this is a nice movie that I found on the web that immediately illustrate the fact that indeed if you think of person as active entities then of course some u large scale complexity and organized motion can can develop and you know already visually if you look at this recall some hydrodnamic patterns and um okay before proceeding let me try to answer the question why we may be interested in this kind of modeling and understanding. Well, uh mainly three reasons, maybe more but at least three reason. There are situation where we are interested in a personal comfort. If you go in a museum and you want to look at an exhibit, if there is a person in front of of you, that person is a person too much, right? Um if you go for example for groceries, uh well, what you probably want to do is to be as efficient as possible. want to buy what you what you're looking for and you know getting out and there are other situation where instead the concern is primarily in terms of safety and this relates but not only uh to situation where you have a very large densities. Now another things that I want of course to point out right from the beginning is that this is not um in general a problem that you solve only with math and physics because we are talking about humans. So of course there are important psychological aspects and of course ethical aspect involves. So I've been working over the year also in terms of education with colleagues from psychology and philosophy to try to put these things together. For example, in terms of physics and mathematics, you may understand numbers, you may understand densities. But why here there is a larger density than there maybe you need to look into web psychology and in order to do measurement or to apply nudging of course there are important ethical aspects. So this is something that I think is very nice because you can learn a lot and it's really multi-disiplinary and one of the key point is that this type of social system really requires putting these things together. So you cannot solve them just in terms of you know quantitative mathematical or physical modeling. Now another important things is of course usual modeling um triangle. So you start maybe with observation and uh you need to have good observation in order to be able to develop good models and that this model could be used for example to do something in terms of nudging for example and nudging maybe could be used to prevent formation of very large densities and possibly risky situation of these kind of things. Now uh from a a physical point of view um this is an active matter systems of course is out of equilibrium is a statistical system and you know very multiscale problem. So um very very few words only few words about historical developments. One maybe of um key point was the extension of molecular dynamics like approaches to the modeling of humans and this was um associated with Eling and collaborators. These were mostly qualitative works however have the advantage of showing that you can model some of the phenomenology that is observed. For example, if you have people that want to pass through through a door here and of course uh this type of modeling here requires the knowledge of the forces which are called social forces that let you interact with a wall or with another person. And this is something that of course depends on many parameters. I will comment a little bit about that later on. So in order to make things more quantitatively of course you need to have experiment and experiments are hard. Some of experiments, for example, this from the group in Ulik [clears throat] were done indoor. So you call some friends, you typically pay them. Um and um you see here that the white hat and this white hat of course simplifies the computer vision problem for tracking individuals and so extract the position and the trajectory of every single person in a quite dense crowd here. Now one of the key disadvantages here is that of course you cannot reproduce very large statistics. you can run it maybe a few times, 10 times and um and also people will do what you ask them and this is something that of course doesn't happen in a real life uh situation. So when I started to work uh on this topic which is as I said more than 10 years ago uh indeed I had these three points that I wanted you know to to to focus on first of all real life settings. So I didn't want to do artificial lab experiments and this is very important because of psychological factor but also because of the richness and variability of of behavior that you observe. Then good quality data that means a very high space and time resolution. So it means that I localize a person with very high frequency and then I can compute the trajectory and from the trajectory I can compute the velocity acceleration and you know I can do all sort of molecular like or hydrodnamic like analysis and then the statistical aspect. So I want to have very high statistics in such a way that I'm not able only to measure average quantity but also extreme events you know fair tales. So in order to do that of course I cannot do uh just one experiment and that's it. I may want to have an installation in a place where every day more or less the situation repeats over and over again like for example a train station or you know some other urban facility. Okay. So that it is a little bit what what I had in mind right from the beginning. H but when I started working with this which was not long ago but you know technology and uh you know software development particularly for what concerns computer vision um you know made a major breakthrough over the years but when I started more than 10 years ago it was not so easy to do what I what I just described because you wanted to have with a good accuracy position of a person. Now if you think about what is a position of a person that it is already something that it is not well defined because we are not a rigid body. So um what we decide to do well we tried few things they didn't work and so we rapidly understood they didn't work and then I sent um a student at the time now my collaborator Alexandro Corbetta um to media market to to buy this connect sensor that I don't know how many of you remember but this was something developed by Microsoft for gaming so you put it on top of your television and then you could play tennis or things like that So basically it's a depth field camera. So it's a camera that doesn't look at the color the illumination but look at the distance of the pixel from the from the camera itself. And so this type of sensor here um if you put it top down greatly simplifies the analysis because you are able to see the head of a person. And so the head of a person is probably a good proxy for what is a position of a person. As I said we are not free rigid bodies. So if I see a bed of a person I'm staying here and maybe I'm moving my head. Actually with our sensor you can see that there is an oscillation of few cm even if a person don't move. So um that's how that's how it works. So this type of technology we have been using in a number of different settings. Here is in some open space at a university. Here is a museum in the Netherlands. Here a city events. And I want to show you a little bit more uh of how things look like. So this was one of our first experiment in a train station. So you see that there were four of this connect at the entrance of under way under passage that takes you to the different tracks and these are persons passing by. Now maybe it's a bit hard to notice the difference in the intensity of gray but a darker gray means higher and so you can put a threshold here and decide that you compute the center of mass of the pixel which are you know enough gray and that will give you the center of the head. Actually you see the different tracks here and they computed a change in the level of gray. So maybe you can take the center of mass of the head or maybe including the shoulder and these can help you. No being a little bit more um accurate or estimating. Okay, so that's about uh the technology back then. Um you see here there is a a school with small kids waiting to enter in a museum. So just to illustrate the fact that even if you are very close to each other um we are able to disentangle the individuals. So it's a it's a very nice um way of um getting the data. Um and of course if you have good quality localization data with high frequency typically 15 Hz 30 Hz then it's quite simple to reconstruct the trajectories because people don't tend to disappear or reappear if there is somebody that is very close to where the other person was is the same person. All right so as I said as a physicist we like to start with simple things. So these things I'm showing you here was also a proof of concept of the technology that we were starting to use. So this is an small experiment that we run in a landing in in a in a building at the university campus. And you see here is a landing. So there are there is a ramp of stairs and other rampo stairs there. Here was our sensor looking uh down and this is how a person passing by was seen. This is the wall from one side, the wall from the other side. And this is not a very crowded place. So typically there was only one person in this corridor. As you see um the typical trajectory as sketched here are not exactly straight because nobody likes to turn 90 degrees. So, so and so well but in any case there is a sort of main longitudinal and um small transversal motion that now I'm going to discuss a little bit more and if there is any question or comments please feel free to to ask now you can do a number of things here for example you can just count how many people you see passing and um you you see over the different days and you can see as a function of the hour this doesn't uh teach you much about the physics. This is telling you about you know the the typical time where you go for lunch in the Netherlands or or other things like that. You can notice that for example on Fridays there are less people on campus. Not very interesting. Um one of the typical things that people have been studying for for a number of years is um the speed at which a crowd flows. And what is known is that if you increase the density, the average velocity decreases and typically decreases linearly. And this is a measurement that we did in this uh in this landing. But okay, not particularly interesting because indeed it's quite rare to have situation where you have more than one person, two person, you know, five person, you know, almost almost never. So okay, not not very interesting to study this type of things. Um so what can we do with this? So let's to see if we can make a model for how people are actually working. And uh and indeed this is a sort of uh PDF. You see the dashed line. I'm not sure how much visible it is, but the dashed line is typically the the average path that people will follow. And imagine that you are just looking at 250 trajectories out of our ensemble. We we say okay we do our experiment. We look at 150 person. Okay. Then we close it. then this is what you will see and so you will see that the probability distribution function of the longitudinal velocity now I'm conditioning people entering from the left okay there of course there are people coming left and right but imagine that I focus only on the one that I see coming from the left then you see that there is a PDF that it is peed roughly around 1 m/s which is roughly the average working speed and the transverse velocity has a similar variance and it is picked around zero so this is what you will If you uh have limited statistics, but if you keep recording, what you actually find is that you have a contribution of this PDF at negative values. So what does that mean? Well, these are the person like the red trajectory here of people that enters and then change their mind and go back. And these things here is statistically reproducible. I mean we have seen it everywhere in train station in this. So if I do an experiment for one month and then I do it another months I'll get the same PDF. Okay. So this is a I wanted to to talk about this because I think it's also a nice example of what I was just saying the interplay between psychology but also the role of statistics. If I had a limited statistic I could not study this phenomenology or if I was telling people just go straight they would do it. They would not go back. But I think you know in everyday reality this is a part of what is going on. And so of course then one natural question was uh how to model this and you know just to show the red curve here is a similar curve measured in a train station. Now in the train station also you see negative tail uh so a tail stand to negative value of a longitudinal velocity but also you see that here there is a a tail which much higher at larger velocity. These are people that are late for the train and that's the that's part of what happens in a train station. So the question how to model this? Well very simply we built a model which is basically a brownian active particle. So the velocity is the derivative of the position of acceleration is just given by confining potential. So basically parabolic potential and some noise because each trajectory has a noise. But the particular part is the kinetic term here that instead of being just a parabola is a double minimum potential. So let me show you a little bit more. So the potential for for the velocity velocity looks like this. So it means that the person entering from the left going to the right they have a velocity which is around this minimum oscillating a little bit but occasionally they can tunnel in the other minimum and that event will correspond basically to to uh you know changing their mind for whatever reason and going back. Okay. Now this is an extension of a model which was indeed put forward by Elinger Molner um in this social force description of crowds. So in that situation there uh the model will basically corresponds to a parabola centered around one. So this model doesn't um doesn't allow you to explain this inversion people going backwards. So I think this is a nice first example um to illustrate how indeed the real life data are richer than than and you know how statistics plays an important role in understanding what is really going on in a crowd. Now again from this uh which was our first experiment in a train station we'll be looking at the next uh next more complicated things which is now what happens if there are two persons that are coming in opposite direction uh and maybe they are close to each other. So how do they collide or don't collide and so these kind of things here um actually attract quite a bit attention. So you see that a loss count of you know many but basically the setting of the physical problem is really like this. So I would like to remind you again what we are doing here. So we are recording 247 for as much as we can as many days or years as we can and then we go on our data set and we look for situations that are the one we want to study. For example, if you want to study a single person, we look for situation where there is only one person and then we put that in the statistics. So here what we wanted to do was to look at the collision between two person. So we went on the database looking at situations where by chance there were two person coming like this and before of that and after that no other person were around so that they wouldn't disturb. Okay. So it's a sort of experiment that is done a posterior looking looking at you know the data set. So that's the setting and you know these are some other things that happen when when I when you study these kind of things but okay what I want to stress here is the fact that we tried to build on the model that I just discussed. So the langan equation that I just discussed for the active brown particle and the question is how can I extend it now for a situation where you have two persons that arrive like this. First of all the previous corridor was a quite narrow corridor. So basically all the person passing in that corridor they will walk in the middle of a corridor. So if you think about that you can think about the trajectory of the single individual as you know trajectories where there is some noise there are some fluctuations and the average part is uh the classical path is the you know the desired path that people like to walk in the narrow corridor everybody basically wants to walk through the um through the center of the channel but in a larger corridor it doesn't matter right maybe I arrive with a pass I enter the station here and I can just go through along this line and some other person enter more there and they just want to go through the important things is don't you don't hit against a wall against other persons okay so then one natural question is what is what is the line what is the path through which people like to walk each one of them may have a different um coordinate for the path they want to follow and on top of that they may have some oscillations at the work. Okay. So, [clears throat] so as I said, we selected from the data a situation like this where there was one person coming this way, a person coming that way with some impact parameter and then we look if indeed we observe something like this. So the this person try to avoid the collision and then um decide this is safe enough and then keeps walking straight in this way and that a person doing the same. Okay. So is is this what is going on or not? And so the model as I just said need to be extended a little bit because now the um lateral offset so the ycoordinate that in the case of a small corridor was fixed basically at the center of the corridor. now is also a variable that I indicate with YP. So a person entering by itself will have some value of YP and then we'll do uh oscillations around this part YP. But now if there is somebody coming against me the value of YP itself needs to change because I kind of take uh you know another track to try to avoid the person. So you see that what we did here is just minimally extending the previous line equation and we add another equation here for the change of average path that each one of the person is trying to follow and this F vision here is sort of social force that um yeah is responsible to try to avoid the collision and of course we don't wait the last millimeter to to to to avoid another person if I see somebody that it is already coming I I just do it already no few meters before and so this is a little bit longer range force and you know if that doesn't work then eventually there is also short range uh maneuver okay so long story but what the main the results that we have here is that if I look at the impact parameter before let's say the collision I call a collision if there is no collision so it's like a planets you know they don't touch each other but you know because they have an entraction force they are colliding. So you see that here if I have a large uh distance like 1 meter um one meter is here or 2 mters then after the collision I stay around the same values. But if original impact parameter so this this distance here between the two part is smaller uh for example smaller than 05 something like that then you see that after the collision you you land around 075. So that that is telling you that below that distance people actually do something and to avoid the collision and you know somehow this is a distance that it is felt safe. Of course there is quite some scatter each one may do different different assessment. Very good. So let me skip uh let me skip this. And so now we can actually get to the more challenging question. So what happens if we are in the most generic situation? Do people have in mind some uh some some average path that they're following and maybe not because if I am for example in a big station everybody has a different destination I want to go to exit C or B and you know of course what they will do has to do with the fact that they need to uh route around some geometrical obstacles so avoid the collision with other persons uh but also they have a different uh different goals so this data here that I'm going to show like many others also coming from a collaboration that we had with the Dutch railways um that had instrumented with a large number of sensor a number of stations in the Netherlands and that uh gave us the possibility to analyze years of data on train platforms. So [clears throat] the situation is a bit like this. For example, imagine that there is a person exiting from a train. So this is seen from above is is a train platform and this person want to go to the exit for example or to this position here. So of course this would be um the straight path but actually um maybe for whatever reason there is some some average path that person want to follow and on top of that there are actually fluctuations. The fluctuation really come from the fact that nobody really works like a robot. Right? as you work, you oscillate a little bit, maybe you distract yourself, look at the telephone or whatever, and so the trajectory has a noise. Um, very good. So now what I'm going to do is to discuss a few of a few difficulties, right? And then I'm going to uh discuss a model that it is generalizing what I discussed before to a most generic situation. Okay? So bear with me. uh we discussed the case of a narrow corridor. A narrow corridor was very simple because I know that everybody wants to call walk through the center and there are fluctuations. But if you think about this, what I did before was actually simplification. I just looked at person entering from one side and going in the other direction. Some of them were going backward. Now what happens in reality is that you have person going this way and that way. Okay. So if you want to model that you can still keep here um a transversal potential. So this will be the transverse Y is the transversal direction and X is the longitudinal direction. So this would be the confining potential for a brown motion. But as you see here there is a probability distribution function for the velocity that can tell you that either you go roughly at minus 1 m/s or plus 1 m/s. Okay good. So this is already giving you an indication that there may be um some more than just a space potential. So here if I look at this space potential this doesn't tell me the fact that actually there are person that go either this way or that way. I may have to extend the space that I use to model the crowd including also the velocities. Now this is the other example I was discussing before the wide corridor. So if there is a wide corridor, a person entering here maybe just go like that or a person entering here just go go go like that and they don't feel the need to to go in the middle of this corridor because you know it just just works. And so if you think about this you like to have a situation where this person here that enters at this position just feel this potential and the person entering here feel this potential and so on so forth. So how to model that? Another complicated situation is a crossing. I think that here you have it shibuya you have this this crossing. So if you if you have a situation like this where there are person that go this way and you know vertically that way you understand that of course you cannot model this in terms of just the space potential because otherwise some people arriving here maybe just equally probably go up instead of straight. So again you need to consider the velocity as well. And so this take us to the the most general model maybe there are other model that are possible but again this builds on the idea of you know minimally expanding on what we have been doing before. So again you have a lang equation. So you have a noise here and you have an acceleration which is a gradient of some potential. But now um this potential here is a bit funny. Because you see here that it depends on the position and velocity of a person and this is also depending on the value of uh some slow mode some small slow variables that encode for position and velocity. Okay. And uh this uh slow variable um you may know them for whatever reason maybe because you know so this low variable somehow encode for what people would like to do. So maybe I like to stay uh close to the center of the corridor then this would be uh picked with x I don't know ys zero. Okay. So I may know in some situation uh what people want to do and this was the case of example I just discussed or you may try to get this from the data. So this procedure here may be a way to get these slow variables directly from the data having some filtering time and so you filter out somehow the faster fluctuation try to recover the fact that for example this person were going that way or you know 90° So if you if you have this setting here, if you have this model here, um a question. >> Yes, please. >> Uh what do you exactly mean by slow variables? >> Yes, as I as I try to say um the X and U is what you actually do and um the low variables is something that try to encode your intention in that moment. Maybe I want to get to that door. Okay. And so in that situation, you know, my velocity, my slow velocity will be that, but the actual velocity can be a little bit different. And uh as you'll see later, if the difference between my actual velocity and the slow velocity is big enough, I may actually change my root. Please, >> sorry, now that you're interrupted, just clarify. Are these dimensionless equations? Because of course if you look at the top one >> uh does not have the same dimensions as x and >> if you look at the second one the you have derivatives with respect to x and u and so something is >> yes >> there's some sort of implicit assumption about time scales here that I don't understand. >> Yes. Well, yes indeed. I mean this is just uh you you have you we have a we run this on the real data right as say you need to rescale or dimensionalize some way. So we have all the details in this paper if you like to see more about the model. So here I'm just discussing you know the basic idea behind that. Okay. So um >> just >> no sorry yeah just just so to here it's it's large >> so so um so these are very interesting questions so let me let me clear once more the fact that um um in principle what I just wrote here would not be needed right so what I what I want to say is that um in order to account for the phenomenology that I just discussed for example these situations Here you need to expand uh your potential uh having some additional information inside. Okay. And of course the things that I discussed before are situations where basically this knowledge I was inputting myself because I understand is a very simple physical setting. So you know understand that people typically want to go through the center of a corridor. Okay. And now here is a question. Of course, this is maybe in each person's mind and so I may not know it in the most general situation. So how do I disentangle between the actual dynamics of a person and the typical pattern that develop in that situation? So this is a trick to try to get from the data. So these and these are the things that I measure to get the evolution the persistent evolution of a position and it's a sort of filter. is a sort of you know low pass low frequency filter and which works remarkably well. So if I remember correctly toao is not very big actually it's in the order of 1 second or two seconds which is the typical you know response time of persons [clears throat] but let me show you please. >> Okay just one um I assume you're solving all the four equations simultaneously right like you're integrating in time all the four equations. >> Um not really I'm going to show you. So the first thing that I do here is to read this from the data. So this is a datadriven approach. So basically what I what I'm saying is this is a model. Of course I don't know this but I have a lot of data. So can I get the potentials from the data? Once I have a potential from the data indeed we do what you are saying. We can rerun synthetic simulations and we can compute all the statistics on those simulation compare with what we measure on the original data. So it's a sort of iterative process in some way. You understand it correctly? >> No, no, no, no. It's not it's not iterative. Let me let me let me show you for example uh here if you see indeed um I'm just plotting here some measured path and some simulated path. These are very few because otherwise here you see nothing. Uh we have so many data. And what I what I'm saying is that out of this trajectory, you can actually compute the low variables and then you basically just build an histogram. So your potential is just an histogram. How often do you see a person with some position, some velocity and some slow position, slow velocity, okay? And you just put it there. Um in that way uh you you actually measure some potential. For example, some of this potential I've plotted here. Okay. Now I'll I'll discuss it a little bit more. Um once you have this potential once you have a U what you can do is actually to rerun this with this that you have learned numerically from the data and uh and you produce some new trajectories and now you can do independent statistical testing. For example, you say, okay, I want to see how frequently I have people known at the distance between the center. I compute a PDF and here again I comput the PDF and you check how how well this capture the statistics. Is it clear? >> Yeah. Thank you. >> Other questions. Okay, let me let me then um yeah, let me let me comment one second on this. So, so this situation here you see that you have different parabas here and the dashed line here was the potential of the very first things that I showed you. The narrow corridor and then this parabolic potential was explaining you all the data. But here what we are doing is basically looking for persons that had instantaneously some slow variables with this coordinate. Then the stantaneous potential that they feel is the green one. Now because of noise it can happen that they get kicked to the right to the right to the right sufficiently persistently that this low variable changes for example to this coordinate and now they will move with the red potential. Okay. So that's that's how it works. Instantaneously they feel a potential but they have some slow variables and as the slow variable changes in phase space, position and velocity uh the potential may change. And the interesting things is that if you do this for example in the wide corridors you see that you see that in the narrow corridor this potential here basically envelope to the dashed line. But in the wide corridor it is actually much more interesting because you see that basically you have a flat situation but for each one of these slow variable here you basically have a confining parabola. So if you are here you are happy you keep oscillating with the red potential. That's basically what what this uh this construction is telling you. And if you now go in a very complicated situation like here for example there are person exiting from the train from this side. Some of them go that side, some of them go that side. So I had no idea how to write analytically the potential that we will feel. Uh you can digest it in this data-driven approach and this allow you to reproduce the statistics that it is observed. So the very nice things is that actually this is datadriven but you know it gives you some potential that you can look into and so you can understand actually what is what is going on. Okay. Now, one of the interesting question is uh what do we do with all this or why a statistical description may be important? Well, of course, having a statistical description means assigning probability to trajectories. So, you may be able for example to say if a trajectory is common or is rare. Now, I'm not saying is something dangerous going on, but you know, just the fact that it is rare, you know, will tell you something. Um you can even do realtime forecast. So if you know that the trajectory develop in some way for example person that in the first three seconds behave and match this typically finish at exit B and the one that do these other things exit A then you can actually in real time assign a probability that this person here on the base of what you just saw will actually develop in this or that way. Um, of course all things that I said here as a proof of concept we have been averaging 24/7. But the potential that I just discussed of course depends on the hour of the day. So if I do the same analysis condition that it is noon or it is 2:00 or 5:00 I may get a different potential. For example, I may get mostly a flow in this direction or another moment I get mostly flow in the opposite direction. So all these things of course can be naturally embedded. It's just that it is more complicated than no to get out all the fine level of information that you have in such a huge data set. And then another important point is that it give you a framework to quantify the how effective can be things like nudging. you may want to intervene. Maybe you put some or you change a little bit the geometry to improve the flow for example and then you can quantify things and you know what we're talking about is indeed the know probability associated to trajectory. So you can think in terms of either of or integral and in this datadriven approach really talking about no learning the the shape of the potential the the shape of the action. Okay. Now what I discussed so far is basically generic framework that allow you to digest the data millions hundreds of millions of trajectories and then eventually to go there and to look at the minima to look at what are the the the most relevant part. If you think in terms of an analogy with quantum mechanics you have a classical path that minimize your action and on top of that you have fluctuation. So here is not too different right? You have person entering here go to A or go to B and the average of a path going to A and B would be the classical path and on top of that you have a fluctuation. Uh the difference with quantum mechanics is that in quantum mechanics you know what is the classical theory and then of course the question is what is the role of the fluctuations here if you like fluctuations are more universal than uh knowing what is the classical path because the average path that people follow in train station for example is influenced by many things is influenced by um you know what you may be influenced. For example, here is raining. There is not raining. So, I prefer to pass that way. Who here I need to climb. There are many many many factors that can influence uh what is the average choice. And so, one of the question is indeed how do we choose a path? And now um you know situation for example if if person were light we would have the answer right because we know that um light will minimize the the optical length. Um even if you are ants apparently there are some recent studies that show for example if you have some some different types of surfaces here and the ants walk at different speed. So it's a bit similar to a situation with light in in material with different index of refraction then you you can find you know all you know snail law and these kind of things and what about humans so what are humans doing so some years back in the context of this yearly festival that we have inovven which is called glow um we we did an experiment so basically people move around the city visiting different spots where there are different light exhibit and we made an installation here. So you see one of our sensor and this is a Philip stadium and people coming from this side uh basically the natural uh way to pass would go to pass from between this pillar and the stadium. That's the shortest path because of you know how the path was curved. But then occasionally when too high density was developing here you see that some of the person will pass from the other side. Now this is a very complicated experiment because there are very important psychological impact due to the fact that this is a bicycle lane. So uh you know before venturing in a bicycle lane in the Netherlands uh you know so so it's real life as I said uh you know it's not as simple as changing the index or refraction and so this is from our sensors and this is you know what what you see and um [clears throat] I spent a couple of nights there and we recorded for one week so the experiment the the the festival is one week long and Well, the conclusion is that unfortunately is not long enough and the density is not large enough to see all the things that we wanted to see. But we definitely could see that if a number of person in our field of view was increasing behind some threshold then some people would pass also from the other from the other side. So this is the the the number of person passing through the short route the red one. So if I keep going like this would mean 100% through short route and but you see that at some point some of them start to pass on the sect. Anyways um I remained with a number of questions and so there is a take two to this type of problem and this was uh more recent actually was published this year in PNAS. Um again now this is a train platform. So there is a train here that you don't see. Um but you can you can figure out where there are the doors of a train. Uh because you see that there are person exiting and some of this person go this way and some of the person go that way. Actually the part of the platform that I'm showing you here. So on this platform there is only one exit here on the on the left. So everybody needs to go that way and the shortest route somehow is to pass from here. But of course if here there are too many persons maybe somebody decide to go the other way. So this is a work in collaboration with Zishi and Alesandro. Um so let me let me spend a few more words. So in the Netherlands the train can stop where it likes. So there is it's not like in Japan but I know the door is always here. So we figure out where the door is from you know seeing the person getting out of the train. And so we distinguish three scenarios. A scenario where the door lands here. So here there is a kiosk selling coffee. The exit is on this side. So here there is a door here. We look at the person that exit from here. Then there is a scenario um this other scenario uh where the door is here and then there is this other scenario. Now you can imagine that if you are here there is not much difference in length you know passing from this side or that side. So probably you will get a tendency to have roughly 50/50 person going from here and to there. But here you would expect that 100% of a person go that way. And here you are a little bit more at the edge. And so what we started to look is what happens as the density in this region increases. And what you can see is quite interesting. So this is a bit dense plot but let me just explain it briefly. So you see this is the case this case here this is the intermediate case and this is the other case uh I see that there is a mismatch in the label just to confuse you but okay don't just don't just don't just don't just don't just don't just don't just don't just don't just don't just don't just listen to me so the interesting things here are the blue bars so if I look at the first bar which is almost invisible this is telling you that in this scenario basically the probability to have somebody passing from the long route is almost zero is I don't know maybe with very large densities here it becomes maybe 5%. You see this is the here is the density. So the different situation correspond to different densities. So that's what happened for this situation. If you are in the intermediate situation you see that at increasing the density there is a much more much stronger increase in the probability of people choosing for the other route. So that will be the solid blue bar. Okay. But now if you look at what is the probability of a person taking the long route conditioned on the fact that the person before also took the long route then you need to look at the second bar and you see this is much higher. So here we go from something like you know 5% to almost 40%. So this is a little bit a sort of avalanche particularly in a situation where I'm already at the edge. It looks like if a person before me choose the other path that's a strong trigger for the person also to go that way. Of course we check it that this person are not in the same social group. So definition of social group you look you follow this person throughout all the platform. If they stay close by to out to the exit, maybe they were friends or family or whatever and so of course no they will take the same route but no that it is not something that actually impacted on our results here and so again um why this happened I don't know so just a sort of a speculation so this is not something I can say for sure but again some conscious choice that we make and when we move around are connected with uh the effort we need to put right if there is a route that it is flat and another one which is very steep I will choose this one and now here I'm navigating a train platform and there are other person that are waiting or coming against and so on so forth so putting yourself behind somebody can be a way to reduce uh but this is just speculation as I said these are the data so we are sure about the data to understand why we enter in the h psychology ology part. All right. So I hope this gave you a little bit of insight on something which is different before we characterize the part and the fluctuations and you know there is a large complexity. Maybe we have unconsciously we have in mind the functional that we try to minimize and part of this functional can be the time to destination but not only so it could be called it maybe discomfort functional and of course if it takes too long to get to destination that's a discomfort but also if it takes too much effort that's that's also part of a discomfort. All right, I see that I have still a few minutes. So I like to to to discuss some other point. Um and one of these is indeed the fact that often we talk about people walking but we also stop right we stop or we start working in a number of models actually there are um models as they are called the first order model where it says velocity equals something but actually uh we do have some inertia right there are situation where we need to accelerate or decelerate and so we made this installation here you see these are our boxes with our sensors this is Google street view So and this is the crossing between the university campus and the train station. So here you you form quite a number of um bunch of people and crowd particularly later in the afternoon people going back to the train station and this is what our boxes see. So the nice things we see also cars and there are also there is also bicycle lane here. So in principle this data could be used also to see the interaction between humans and bike and cars. So from this depth uh uh field sensors we can reconstruct the 3D um pix map and so you see oh we see things these are two persons here on a bike and they're passing a bottle of beer probably to each other. This is real life uh data. So all things and then when you put all this data together you can actually measure uh for example the the dependency of the velocity as a function of time. So when you see that people start to move unfortunately we didn't have the recording of the green or the red of a traffic light but you can stitch the data together looking at when they start to move and see how you go from a resting situation to a walking situation. And this is basically how the acceleration goes. And similarly for the situation where you stop. And so you have a red the traffic light or how people uh wait at the traffic light. And so what you can see here is that basically they start to occupy space and as the density increases they start to compress laterally but not longitudinally. And so they probably want to keep a distance from the person in front. So that now that you get a green light, you don't step on on another person. And uh and you can also notice that for example uh with a red light people are standing then they start to walk and as they start start to step into the street they accelerate probably because you know that you know the green doesn't last forever. So uh the moment that you are in the street you want to go. Now the last topic is about nudging. O promised that if there was a bit of time I would like to say a few words about an agent. So this is another experiment that we did a few years back. So we built basically all this setup here with the collaborators and you can see already here that there was a screen. In this screen we could project some sign like this. For example in this moment there is an arrow to the left or we could change the illumination of these lights here and there. And then the idea so so basically there was some some some light effect here and this light effect was attracting a group of persons and then the light effect was stopped and so this was a sort of trick to form a cluster small group here and then this group will start to work and uh you know these different type of sign were changing constantly over the evening and the different evenings and So the our question was you know which route would you choose? So the the setup was designed to be as symmetric as possible left and right. So this is something that was done in collaboration with several other partners of intelligent lighting institute Philips lighting and so on. So this is this is the setup and this is what we were recording from our sensor. You see some some people even stop there. I mean again this is all sort of things will happen in real life. And so the question was can we quantify some symmetry induced by the different stimuli and indeed there is some uh some small asymmetry that can be associated with the presence particularly with the presence of the of the arrows. And the interesting things is that if you ask we didn't do it but if you ask the person exiting from this you know how did you choose to pass from here probably they didn't even remember that there was an arrow and so the idea of a nudging is exactly like when you navigate and there is some arrow that indicate an exit and a museum and then if you if you take somebody at the exit and say how many how many indication did you saw you know you you don't even remember you do a processing consciously So for the future what we would like to have is even a situation like this. So this is some sort of proof of concept. It's a beam that it is projecting uh different things on the floor. So you may think of you know for example person stepping in on the train platform and then finding an indication given the real uh time information on the density may root a person in one direction another one. So this is something that we definitely would like to pursue in the future and something else that we are looking into is very dense crowds. So situations like this we did very recently just before coming here some experiment in Pmplona during the city festival and you see that we can reach quite some interesting density with the idea that maybe we can see some nonlinear realology situations like formation of lanes which would be similar to shear bands and ninearology okay so this concludes this very general overview I wanted to give of what we've been doing over the years. It's impossible to acknowledge all the person that contributed. So we have a huge number of students that over the years really helped enormously both a bachelor, master student, a PhD student. So these are the persons that um you know mostly contributed in recent years and um and also um colleagues from psychology and ethics. And um if you want to know more uh about indeed this this analogy between crowds and as I like to call it ratified gas for the case with very low density or you know fluid dynamics or even complex fluids. like to discuss or maybe collaborate, you are welcome to contact me and um you can find more information on our website and this is indeed the recent review that Michael was just uh mentioning. So thank you very much for your attention. Be happy to take any question. >> Thank you. So is there any question? Yes. Uh so thanks for uh this nice talk. Uh so I have a curiosity. Um so you were showing uh some optimality principle at some point where you were showing like the map principle and so on. So my question is so given that the uh Newton's equation motions are can be obtained as a consequence of an optimal principle. Do you think that the equations that you have shown could be obtained via some lran some action principle? >> Yes, I think so. uh indeed I mean the the the modeling this datadriven modeling that I was expressing in terms of a sort of languation could actually be rewritten in terms of the integral which is the or you know an action principle. Um what is uh very difficult is not to do it it mathematically but really to figure out no to figure out what are the factors that play a role there and um in all things that I've been doing was mostly about proof of concept let me say and the fact that indeed this equation can show this phenomenology and just to give you an example when you think about a single person working I could actually look into that and say okay what is this person maybe is a child or is an adult. So you can start to see that for example there are correlation between the height of a person and the average speed right. So when you have a crowd and you think that as a gas and it's a bit like not treating all the gas the same or starting to think in terms of okay this is a polyatomic gas which is composed in this percent by this type of particles. Imagine again a train station. There are commuters that know the the station very well. Maybe they go faster because you know they know the schedule. They are just late. Person that go on this station for the first time. Person that go there but they are not on a rush. You know families that you know maybe have a priority not to lose each other. If you think about that of course is reasonable to think that they have you know very different dynamics. I want to give you another example still. Um you know the social force right we have measured the social force correspondent to person trussing like this we get something right we we wrote down exactly the shape and the parameters in the paper but imagine that now uh I am in this corridor and I see somebody on the other side that it is you know coming against me with a knife like this. I guess that you know in that moment the social force becomes much more long range. So this is part of the fact that there are some something that I don't know how to define but I will call it normal situations right and then there could be also some exceptional situations. So we have done our best increasing the statistics really to try to capture also these u no more rare events but we didn't disentangle them right so we put everything for the moment in the same sample and building a statistical model for all this indeed with enough statistics we could also say okay what happens no to the commuters what happens to the person that you know for some reason I understand it's the first time they navigate this station so you that will be a sort of second order no improvement. I don't know if this answer your question. So, so that it is really so I wouldn't say that you know the the physics or you know mathematical model is the complex part and this is really something that it is data driven having enough data on which you can confront yourself and then decide what is part of what is what are the key part in that functional Thank you. [clears throat] Another question. >> Um I was wondering like your experiment or like your observation were like in Netherlands, right? So if you would measure it in like in the different countries, let's say India or Japan, I guess the outcome would be different because people would be differently socialized or would you use the model in a different city? Yeah, thanks. Thanks for the question. So the question is if I will see some uh some difference in different countries, maybe you know there are some some cultural differences or you know just um for sure the answer is yes. Okay, I can already imagine even if I didn't measure but I'm sure the person have measured it that uh the average working speed may relate for example to the height the average height of a population right so now if you are interested in the type of physics model you know the average speed is just a parameter right so you know if you want to to make something that it is more accurate in a country or another one you may have some some parameter which are specific that may have to be measured and fine-tuned. Um but I think that um the mathematical framework and model behind is quite general. [clears throat] >> Now of course you know as I as I said there are some some things that may not emerge in some context. For example, if you remember the corridor in the university was showing a PDF in the train station. You see that there are also people running. So if you if you take that model that has for example also the option to have people running then you can think this is fitting basically everything and you know different settings or different countries this balance may change right or many are running or not. So in that sense uh no studying these things allow you to understand what is the minimal but generally more flexible model that allow you then to tune the specific parameters very nice talk. Um I was curious about something you mentioned in one of the first slides about the interaction between uh this research and people working in ethics like I guess there must be a balance between of course this is surveillance of people but of course like any you know research involving humans there's a trade-off between the benefits and so what's what's the debate I'm curious about what's the ethical debate around this kind of research. Yes. So thanks. It's about the connection with ethics. So as I said, I've been discussing this with colleagues for a number of years, but I by no means an aspect. So I mean I may just give some some very simplistic. So there are of course ethic questions for what concerns doing experiment with humans which normally don't have major implication because the method we use are you know don't uh don't you're not able to recognize persons right they are anonymous so we don't treat personal data but of course that it is one of the aspect but the other aspect could be for example imagine you want to improve a situation on a on a train station for example, you have more passengers and so uh you're going to get more persons on the on the train platform. So you want to do something. There are two options. Either rebuild the station which is you know expensive or maybe you want to do something maybe to spread people through the through the platform uh you know intervening. Um and now you ask yourself for example um did I um improve the efficiency right and then the efficiency is what is the efficiency for you that once you get on the station or it is the efficiency maybe from the point of view of the the train company that wants to make a maximum use of the facility. So why I'm saying this? Because just let me give you a very simple example. Imagine that you have a stadium or something like that which has a number of entrance. Now you have a lot of people that are arriving. No, maybe they arrive from this street here and there is this door which is the closest and then there are a number of other doors. Okay. So in the stationary state if you have a lot of people entering the optimum in terms of you know filling in the stadium is that you just split equally uh you know the number of maybe you experience that in in the airport right when they say oh you go there and you say you see that it is much longer but of course if you have two entry point and a lot of people arriving you know the optimum is 50% here and 50% there this is the optimum from the point of view of infrastructure the optimum from your point of view was maybe better no to to go a little bit slower but still stay on this side. So I think that there are also ethical uh uh consideration in respect of uh you know how we choose uh what to do and that could be from the point of view of you know the single individual or individual individual in the crowd the cloud as such or you know maybe also person responsible running infrastructures but as I said yes >> that's definitely not um but it's multifaceted and it's not just about um um you implication of doing experiments. >> Yep. >> Very nice. I I was just going back to to the model you've shown and I was trying to test it in my mind. >> Yeah. And I I guess my question is uh up to which model the dynamics that you serve can be captured by the potential and which dynamics instead would require you to change the model or together because I was thinking for example if you consider a crowd with an external stimulus that varies very quickly. So you lose your separation of scales. At that point my goal keeps changing and so probably the variable separation won't anymore or a completely different case. I was thinking like I don't know in the traffic equations you can develop shops where would the hyperbolicity required for that come from would you entail it in the potential or would be out of that I don't get >> thanks for your question so a lot of interesting questions and so one of the question is um why the potential indeed you can think that you are forced that don't come from a potential right what we have been doing potential work quite okay. I mean it it wouldn't be much work to replace the framework working directly with forces instead of potential. But um the fact that there is some external forcing we do have external forcing when you look at what happens on a on a train platform. The schedule of the train is the forcing. So you you see that people will start to flow on the train platform just a few minutes before the arrival of the train. Okay. And then you know they entering the train the disappear. So there is clearly an external source that it is uh operating on your um now if it depends on the time scale at which it happens. If it is uh slow um and depends what you want to look at as I said all the analysis that we have been doing it could be condition on the amount of time before the departure of the train. So that will show you or you know just average everything which is what we have been mostly doing because of course otherwise was mostly about showing that um this can be done then of course it can be applied to many different situation. So your vis answered the second question then there was a third one right? Yeah, but they were all the same. And then I think that the the true question was like what can you in globate just change in your potential and which effects are instead associated to the model? >> Okay. Okay. So now now I remember the third point that that you asked was about shocks and the model that I shown you here is a model for is a single particle. So if you think in terms of you know part integral or so this would be you know one particle theory which may evolve it does evolve in a field which has some density. Okay. So for example as I said before if you do all these analysis at noon and maybe at noon there are few persons and five and the five is rush hour you see that a single person at noon or at five behave differently you get very different potential. Okay, because he's a person but it is moving in a landscape which is very different. Uh so you get this implicitly and maybe you get that when you rerun or use this potential you see that the average working speed is slower at five rather than a noon. Okay, in principle what you could do is also to do van body theory. So then you need to learn the potential with multiple particles. So, so this is this is hard but with with you know graph neural network and machine learning uh you you can you can do something in this direction. So if there is no further question okay so let's thank again [snorts] and if you want to speak with him yeah he will be act. It doesn't make any difference. [clears throat]