 change in collective groups I guess. Thank you. Can you all hear me well? I guess so. I can hear myself. I'll try to be on time. All right, so I'm gonna tell you this a little bit modified title. I thought about it more and I think it sounds better like this about the effect of the interaction network and the kind of information that you're exchanging on the collective behavior. This work I mainly did with Vali, a friend in Turkey and his student Ege. He's a great student. They're both at Ankara where I'm just coming from right now. And I'm based in Chicago usually but I'm also affiliated to a bunch of places. I'm kind of delocalized so I belong to everywhere and nowhere. So the motivation for this is what I'm going to tell you about now. I'm going to talk about a very specific model and some very fresh results but I also want to always make a connection to some kind of broader motivation of the questions that I want to... I think that we can address with this kind of models. And the broader question is how does self-organization in this case some kind of dynamical consensus depend on the interaction network? Who's talking to whom? And in this specific place the kind of information exchange which could be either position information or velocity heading information in the term of physicist but that really means if information or where we are or where we're going. So it's broader than that. And I feel that this could be have a very broad kind of perspective for different systems. Of course there are the physical systems but there's biological processes. I point out that this space in which we're moving we self-organize this could be an abstract space or be a configuration space behavioral space or something like that. So it could be broader than just physical collective motion but also collective behavior in general. Animal groups, social systems and swarm robotics. And this points to a thread that has been a little bit part of this conference regarding universality in this kinds of systems. As a physicist I feel that it's really interesting to look for new kinds of universalities in this systems. I don't want to sound arrogant. I think for we all agree that for many here the way the physicists look at these problems seems arrogant already but I also want to point out to my physicists colleagues and friends that I'm not telling them what they should be doing. We've seen very beautiful talks about how you can extend statistical mechanics and other fields into the area of for example active matter and you can look at all kinds of extensions of the universality that we're used to as physicists into those fields. But I do believe that if we're really talking about collective behavior we should try to find new ways of expressing universality and it is frustrating because we can barely use some of the tools that we're used to which are beautiful and instead we have to think and take some baby steps but of course I'm not telling my physicists colleagues what they should be doing. I just would encourage people I wish more people would try to look toward these kind of other universality concepts. However having said that what I'm going to look at are very specific cases a very specific model which I wish and I hope that in the future with a lot of more work we can show some kind of universal behavior. Before I do that though I'm going to tell you about three very briefly I really don't have much time. Other projects I've been working on which kind of go in the same direction. One is a fascination I have on the dynamics of modular hierarchical structures. You see modular hierarchical structures meaning modules that organize into modules that organize into modules all over nature. It seems to be a very universal principle and if we want to start understanding what that means we can look at modular hierarchical networks which is a work that I did with Benjamin Meyer, the student of Dirk Brockman and Dirk who are in Berlin in which we can try to see like if we go from a disconnected extremely modular network to a random network what kind of processes what kind of benefits it has or disadvantages it has for the kind of processes that you could expect to have there. What we found and I really don't have much time but is that there's some kind of optimal point of intermediate modularity modular hierarchical structure or hierarchical modularity in which you have some optimal diffusion and optimal search processes and that this relates to a small world phenomenon. On the other side again a different problem we were looking some years ago to what happens with opinion formation dynamics this was related to the first talk to some extent in which you can have a network where you have different opinions say green and red here the connections tell you to what extent people are sharing those opinions and what we showed in this work some years ago was that if you allow the rewiring to happen in a such a way that people tend to be with those that agree with them and you impose the kind of interactions that you expect to find online you have much more easier the fragmentation of the network into one network that things red one network that things green and that don't talk to each other. We also understood the mechanism for that this has had a second life because of course today you understand these things as as filter bubbles and we have the emergence of post news and the emergence of Donald Trump etc so with that you got we got a lot of interest in that a lot of interest in that and now working with some Chilean people which my original country to analyze data and try to see this kind of dynamics oh and this comes from a different from a different talk to just show that there was a lot of interest there was a lot of press because really there's some kind of intuition of universal behavior that people don't even know how to think about in this specific system but I think we can contribute something from the perspective of a physicist and the third thing I'm going to mention is a project I'm doing with people in China professor Han and Yat-ing Shan who was saying who did these experiments actually I need to start the second one and it's an application of the model that I'm going to tell you in a minute about which we use it to control groups of robots that are in this particular case it's a quite simple setup so it's they're extremely noisy but despite that and there's time lags at all kind of issues but despite that they managed to organize in some kind of collective dynamics all right the other thing I'll tell you before I really go into matter is the experimental insights of these thought of what is the difference between having different communication networks having different kinds of interactions information exchange and a lot of it comes from the original insights some are priori some are posteriori to be honest come from work of Ian Cousins lab and this is work we were actually worked on together or this paper that I think did a lot of things but one of the things that we did that was I find it quite interesting was that when you look at the actual data of two fish and one given species and you try to see how one fish is reacting to the other you could have two hypotheses right you can even just think that they're trying to stay close to each other in some kind of distance way or that they're trying to align a la victory model right and what you see in this plot I don't have much time to explain it either but you can kind of intuit here that in the the left right distance with respect to the turning force is turning social force I would call it the tendency to turn is what is critical so if you're too far to the right you're turning right which is the red color heat map and if you're too far to the left you're turning left but the other axis this y-axis is telling you the relative angle so in fact if you're too far to the right and you're and the neighbor is I mean if the neighbor is too far to the right and it's turning right or is turning left in fact you kind of react similarly and this what it's showing you is that for this particular case at least the signal for the position based interaction the exchange of information the position is much more strong than the signal for the alignment based interaction the exchange of information in the velocity another inspiration this happened after we finished our project with with Ian but it's related to things we've been talking for some time they did this beautiful experiment in which they could extract with a lot of work the interaction actual interaction network between a group of fish and they showed that the interaction network could have effects in the collective dynamics and that it was non-trivial and that's all I need to say about this as a experimental insights for this problem all right so sharing velocities of positions to velocities of positions to achieve collective motion I'm going to look at these two aspects how does it collective motion depend on what information you share velocity of positions and the network so let's first start by velocities or positions I'm almost embarrassed to show this transparency because we've been talking about the victory model for the whole conference but I just want to highlight that's a simulation I did ages ago there was this is a figure from the original paper if 95 in which you see that an order parameter that will be equal to one if they're aligned and zero if they're disordered goes down to zero as a noise increases and this looks very much or it looked originally as a second-order phase transition it turned out to be a week very small first-order transition and there's a whole lot of people here who worked a lot and it's really interesting how they managed to figure this this whole puzzle out but what I will tell you a little bit more about well it's the first thing I want to mention is that this is an explicit alignment model exclusively so you really don't exchange any information or where you are you do select the ones that are close to you but that I would argue is more the protocol of the interaction network in this particular case you really only connecting to the velocity of your neighbors so I'll introduce you here active elastic model with that we did some years ago and the rest of the talk has to do with how this behaves different than the evictric traditional victory model so I'll spend a couple of minutes just explaining you what this is I would say it's a very intuitive robot model sorry it was inspired a little bit of robot motion so these are like little robots you can think of little wheels and what you do is that you just put these agents that tend to move forward connect them with the certain springs the springs of a natural lens so they can have a linear attraction repulsion dynamics and you compute the elastic forces over this subject for example and then once you have these elastic forces by measuring center to center the distances you grab those forces and project them on the direction of motion and you add that to the self-propulsion force or velocity in this case because it's over damped in that sense at least in first equations or you project them perpendicular to the direction much and sorry you project them perpendicular to the direction motion and that gives you the angular rotational speed so mechanically this is just the same as pulling these robots from the nose you you add this component to the velocity to the speed you turn with this rate but it is not exactly a mechanical analogy because then we measures the distance center to center to analyze the elastic forces we do that explicitly to be at the opposite limit of the victory model so that there's no influence between the orientation and the elastic forces that these things are feeling I may mention that there was a parallel model that was developed originally also by in a shovel paper also by Thomas Vick checks group and then it was used by Christina Marquetti and some interesting active jamming analysis that was very similar to this one is also based in position but in that case agents are allowed to move sideways because they're thinking more microscopic cells or something that can be pushed diagonally and then the direction of motion relaxes into that direction alright so what does this model do this results from a little time ago already you we wire as I just told you I'm not showing you the springs but we wire these systems to their nearest neighbors in this case here we throw them randomly in a certain shape that we chose to be a square with two holes and then after we throw them randomly in that region we wire them locally in an interaction region that is you know very small I can't really keep my pulse steady enough to show you about what it is but it's something like this and you just connect them through the springs you choose the natural lens such that the initial random position is exactly their natural length so they end up being completely relaxed initially they're just pointing in different directions and the question is can this manage to go in one direction or rotate so we find we found numerically that you could get into this rotational or translational states it doesn't really depend on the crystalline structure this is color by angle this isn't the transition is very similar to the victory one but here is a stronger first order transition so you really have a by stable region here that's not the focus of what I'm talking about now so I'm not giving much information but it is it was surprisingly to some extent a symmetry breaking transition because it's not clear where these things while they're sharing information on their positions could agree on some specific direction of motion without having a leader pulling them or something like that but it ended up happening so after we published this in 2013 I mean when we publish this in 2013 we wanted to understand the mechanism and I'll also spend a minute because I do think that there's some universality in this mechanism or at least I hope and I think that if I want to make a grand claim it could be a mechanism for self-organization that people hadn't really considered before so the mechanism they said like an all active matter system or active system you're injecting energy at the at the the smallest scale so those are if you think of this thing as a bunch of agents connected by springs it's a little bit like an elastic membrane right so that means that you're injecting energy at the smaller scales that is as the as the higher energy modes right because these things for the smaller scales it mean higher oscillations is typically higher energy modes and if you plot the energy that each one of these modes have like from bottom to top here over time in a simulation like this one similar not exactly this one you see that the higher energy modes is that starts to decay right and it has a lot of persistencies and weed behavior I think this could be done better with a different approach but this is what we got and I think it proves the point what you do see that there's a lot of persistence of some of these lower energy modes that can be a breathing mode or something like that that remains here and eventually it reaches all out of this scale of this thing because it's a zero mode which is a translational mode so if you think of it in this terms what needs to happen is that on one side you need to have a certain decay of higher energy mode but you also have to have that the local coupling of the way you're injecting energy at the smaller scale has to not go against this this the decay of higher energy mode so you you don't want to be repopulating these higher energy modes all the time because you're pointing in all kinds of directions that stretch the system in modes that are high and that cannot ever dissipate right so I think that this while it's a simple idea it gives me a lot of intuition and I really like thinking you know intuitively as a physicist and it goes to a very strong you know standard dynamics in physical system which is just general oscillations and I like this the analogy with a Gitter string just to have this in mind right so when you plug a Gitter locally you're exciting all kind of modes these propagates they do all kinds of messy stuff but eventually you hear the fundamental note eventually the string is oscillating collectively right we never think in physics at least when we're taught this as this is a self-organizing mechanism but deep inside it is I would argue right you're going from some kind of local disorder excitations into some time collective dynamics right so now if you add self-propulsion locally then you it just happens to be that you have to couple the way that that's a proportion this is connected to the elastic forces and you will get some kind of criterion for self-organization so let me give you the last part of the components and then I get to the results which are actually just like one slide so it's really it's a kicker of this analysis what we did now is that since we have this membrane we can decide to actually put these springs in different ways and we tried two different ways to do it instead of connecting nearest neighbors as we were doing before and in this case we took a square lattice but it doesn't matter we actually added some random connections that we're connecting long distance okay with the same active elastic model the same rules that I told you about but you can do random in different ways in a network so we chose to do random in two different ways one is the Erdos-Renny random graph which just takes a constant probability of any kind of two connections and the other one is a scale free graph in which you have some nodes that have a lot of connections and many nodes that have only few connections okay and then we could vary this factor P going from nearest neighbors to either the Erdos-Renny graph or to the scale free network graph but when you look at the number of the distribution of number of agents that have a certain number of connections per agent the Erdos-Renny ones give you a Poisson distribution this is the ideal this the points are what we actually simulating and this is finite system that we have and the random graph sorry the scale free gives you a power law distribution so results when you start adding random connections long distance connections and you're in the victory model I go back to the victory model protocol you see what you would expect so you start from nearest neighbor connections you have the transition a la victory model is a fairly small system so it's not too sharp but then as you go to the fully random network you're adding long distance connections when you add long distance connections you expect to have some kind of small world effect the victory model is nothing more than really some kind of delocalized I mean decentralized consensus problem so you will get this limit when you get to a fully random network and it doesn't matter if you do that with an address writing number random network or with a scale free angle network so this is the main result what I'm showing you now here is that when you do this with our model in which you don't exchange velocity so therefore you're not associated directly to a consensus problem but more to a complicated thing that I would that I made an allergy to elasticity with you get a very striking effect that when you go to a Nerdos-Renny random network you actually go towards also a slightly better performance meaning you have better resilience to noise your critical noise moves to the right however when you go to a free random network your system becomes very very unstable right so you actually your critical noise goes drastically down and I hope like in one minute I can tell you what the mechanism is these results we really just got them last week so I don't have a full demonstration but I think that the intuition that I created till now should allow you to understand why this is not so surprising because if I now just grab the same data that was simulated and put it in a graph right and these graphs are they're called force director graphs so somehow they push the nodes with less connections towards the edges you see that the one that gives you intermediate resistant to noise is a proximity graph it organized like this in this case right then the Nerdos-Renny graph gives you something very untangled so you can imagine that the collective modes will be somehow different but they will have some similarity to the just sheet however the scale free graph has a bunch of nodes that only have two connections we're limited to two connections because the one connection nodes didn't make much sense in our model and these actually have a lot of low energy high frequency excitations right so you're at a low energy easily can excite modes all around this this thing which will not self-organize because they're not coherent they don't have large scales they're actually acting only very locally so in some ways that's enough to understand the model I think and I hope that in the near future we'll be able to actually do again the graphs of how the modes decay and understand this problem fully and with that I finish and I will be happy to take some questions. Thank you very much Christian.