 Thank you, okay, okay, yes, yes, it works, okay, it works. And hi everybody, thank you to the organizers for letting me be here today in representation of Fernando Peruvani in our team in EES. And for letting me talk to you about our work with small groups of gregarious animals paying particular attention to the flocking patterns we observe. This work has been done in collaboration with Richard Bone and our several collaborators at the University of Toulouse. Our motivation is a set of experiments performed with small groups of sheep that were freed in a squared arena like the one you see here and observed for long times. And we managed to make two main observations, the first one being the existence of collective displacements triggered by any individual of the group, like the one you're going to see here, exactly this one, and there's going to be one exactly now, exactly this one. And the second observation is on the detail on how individuals perform these collective displacements. And to look into the detail, we use the tracking of these experiments and we notice that individuals tend to form lines during this collective displacement. This is a movie using actual data from a group of four sheep. And as you can see, they tend to follow each other. This is our two main observations. And using this information from the tracking, we are able to distinguish faces or regions of high degree of alignment, typically associated to these collective displacements from regions of a low degree of alignment. We can do slightly more since we have the information of the position and orientation of individuals at all times. We can calculate the probability of finding a neighbor at a given angle with respect to the orientation of the individuals. And we notice that during the motion phase, the probability of finding a neighbor is higher in front or in the back, I mean it's biased. And in the motion phase, it's less evident. It's rather homogeneous, the distribution, the probability of finding neighbors. By taking a closer look at the individual information, individual speeds of the sheep, and by plotting this information, we can localize quite easily these collective displacements. But in order to study this in more detail, we need a threshold velocity that lets us say when an individual is moving or not, okay? And to get this information, we go and plot the distribution of velocities of the individuals, which results to be a bimodal distribution like the one you see here. And using fitting curves for both modes, we can obtain the velocity threshold that allows us to translate the information from the raw data, from the tracking into a dichotomic signal for each individual that is telling us when it is moving or not. We realize that the collective displacements are still recognizable in this process signal. And now using this individual dichotomic signal, we can define two times, two characteristic individual times without a BWT, the first one being the time of motion of the individual and second one being the time of no motion. And we can perform some statistics on these times, okay? And we notice that the motion time distribution is exponentially decaying, typically associated to a Poisson process. And the no motion time distribution is rather different because it's more gamma shaped. I mean, it's consistent with a gamma distribution. This is telling us that the nature of both times is completely different and that if we want to model this individual behavior in terms of states, for example, we need to associate only one state to the motion phase and at least two states to the no motion phase. And following this suggestion from the data, oh, sorry, what happened there? Following this suggestion from data, we want to use a three state model where two of the states are going to be associated to no motion of individuals, as one and as two in this case and one to the motion phase. But if we do this, we have to answer to you two more questions. The first one and very important one, how can we distinguish these no motion states from the experimental data? I mean, it's not clear at this moment. And the second one is, what is the functional form of the rates because there are six possible transition rates involved? I mean, how do they look like or on what do they depend? Are the six rates involved in the experimental data? I mean, I should answer this. And for answer the first question, we go back at the videos we got and we notice that individuals before and after a run could be distinguished by the position of the head because typically an individual before a run spend most of the time with the head down grazing, eating grass and individuals after a run were standing with the head up for several seconds. So in this sense, we can associate, naively in some level, these behavioral states with our three individual states and we are going to say that as one is going to be associated to this grazing phase and is going to be running and as two is going to be standing with the head up state and we can add this information to the tracking from the experiments and we can calculate how often all these, I mean, six transition rates happen from in the experimental data. And we notice that although the six transition rates are present, there are only three that are most important ones depicted in blue here. So we can, oh my God, we can say that we are going to use an effective three state model that is cyclic and stochastic in nature, okay? And now I want to answer the question regarding the collective behavior. I mean, the interactions between particles and how do these rates affect the collective level? And for that, we have to take into account two main effects and to explain these two effects, let me give you an example. Imagine you have a group of ship, standing ship, okay? And one begins to move. This is going to be the incidental leader that is going to begin the collective motion. Some of them will follow, okay? And a guy, I mean, a ship inside of the group is going to face one, I mean, has to take a decision either following the running individuals or staying with the group, okay? So these two effects have to be involved in the transition rates because that's what we observe in the experiment. And this particular point, I have no idea why it's not working. Okay, so this point has been addressed in the past already with trainship and in quite some detail by Sylvain and collaborators in Toulouse where it results that the transition rates depend on how many individuals are on each state. In my previous example, it depends on how many individuals are running and how many individuals are staying with the group, okay? There are some parameters involved, beta, mu, gamma and omega. But still, I mean, the two effects I explained to you are present because there is the trigger in effect of this collective cascade. It's here present, the inhibition or I mean the inhibition that the individual stays with the group is here in this term and we add a spontaneous term so any of the individuals of the group is able to perform the first transition towards the motion state, for example. The good thing of this is that we can fit all the parameters from the transition rates using experimental information, okay? From the experiments. And until this point, I explained to you how does this individual three state model arises from experimental observation. I mean, it's really data driven model. And now I want to address the second observation in the movies which concerns the alignment and the flocking patterns during the collective displacements, okay? And for that, I have to use an equation of motion that contains the whole richness of the three state model which is going to be contained in this variable. Each individual is going to have this variable that is going to contain the whole dynamics in the three states. And this variable is going to affect the velocity because the velocity is going to be non-zero only when they are in the motion state. And for the alignment mechanism, we wanted to see what kind of mechanism we had here and we wanted to compare two main mechanism, the first one being what has been called position alignment and the second one being the most common velocity alignment. In the first one, the individuals are going to be pulled towards the position of the neighbors and the second one is rather taking the average velocity. This is, I mean, the regular velocity alignment. On top of that, we are going to add a vision cone. We are going to restrict the vision of individuals into a cone of angle phi, mostly motivated by the observation that we see lines in the collective displacements. The good thing of doing this is that, still we have new parameters that we can fix with the experimental data. And if you notice, I explained at the beginning a three state model with a very rich model and with several parameters that we fixed with experiments. On top of that, now I'm putting a special dependent model for the individuals with some parameters that again can be fixed with experiments. And we see that the phenomenology of both alignment mechanism is completely different because in this case for a position alignment and although having a really low density of particles, we can see that the lines, I mean, these lines are quite stable and they form, so the individuals tend to follow each other. And on the other hand, with the velocity alignment, these lines are, I mean, they are not that stable. For example, here, you're going to see two that tend, I mean, try to be together and it breaks. I mean, I'm going to play again the movie here. For example, these two guys, I mean, they try to stay together but it broke and here again. I mean, so lines are not going to be stable in this case, mostly because of the cone of vision, okay? And we didn't just stay, we didn't want to stay at the qualitative level. We wanted to try to test this more quantitatively. And for that, we used two parameters, the first one being the regular polarization, while in fact a temporal average of the polarization. And we saw that this was not enough because although polarization distinguishes groups of, I mean, polarized groups from non-polarized groups, evidently, it doesn't distinguish between two particular configurations because this configuration here is polarized, okay? It's going to, polarization is going to give a high value but this one also, but we want to distinguish this particular lines configuration of the rest of polarized configurations. So we had to come out with another parameter that distinguishes again between polarized and non-polarized groups, but again, within the polarized group distinguishes the lines. So it's going to have a large value for lines and a small one for other polarized configuration. And what we saw that is that comparing our simulations with experimental measurements, we see that the first parameter, the polarization, regular polarization is not conclusive because although the position alignment result is close to experiments, the velocity at alignment is not that far away. But on the other hand, when we penalize or we, I mean, highlight this line within the polarized configurations, then we can see that the result is more conclusive. We can see that the effect of velocity alignment is less important in this case. This is telling that although, I mean, I believe that in reality, in these real systems, position alignment and velocity alignment are always present. But this is telling that in this case, particularly case of small group of ship, the position alignment is place an important role during this collective displacement, okay? And not the regular velocity alignment. Oh my God, this brings me to the conclusions, okay? Because in this talk, I try to show videos and our work concerning small group of ship where, first of all, we see intermittent collective dynamics that I try to lead you and argue that this is consistent with a three-state individual model. And we address also the dynamics and the flocking patterns observed during this collective displacement. And we, in this preliminary results, obviously, we see that position alignment seems to play an important role in this collective displacement. Evidently, this gets more interesting when we have, for example, I mean, we increase group size. It could be more interesting to study. And if we add a radius of interaction, because here, I didn't say, but for us, all the individuals see each other all the time because they were small groups. They were groups of two, three, four, and eight individuals. So without making much error, we can simplify it to say, okay, everybody's seeing with each other. But what happens if we increase the number of individuals and at the same time we put a radius of interaction, it could get more interesting. But the goal of this work was rather explaining and starting the nature of alignment in this system of ship, this small group of ship. And with that, I would like to thank you for your attention.