okay all speak from here for them morning uh and as that's uh the but by the is global immersion behaviours using close of regions and the mike what they're could make it so uh i'm presenting the the work and the we are no the support from the national science foundation under the from a your for are i'm i'm gonna switch between the slides and uh i became an expert in extracting videos used from uh from you to be today so i'm gonna try to multi rate my by your inspired okay and that's we these movies uh if i can get them so i'll do a replay here and but you see is is agents they seem to be and a place called in agents and they randomly go around and the suddenly one of the agents kind of uh finds an interesting object and the before you know it other agents find the same interesting object and the although uh most of them seem to be randomly going around in fact you us a human looking at this video recognise that's something is happening and the some of the ends discovered that if they go to the bank and cash the the the the i'm or whatever or the you role they will become re so that's my first comp now what it look at uh i'd C another if you do because i want to contrast these biological and the and the and show you that there are different types of behaviours and which one i'm um i'm talking i'm uh referring to so if find correct here you want see much you'll see some flashing point i don't know from where you are you C one or two here and there and this time goes and if you are oh if you but you tension you'll see that uh so that only there's starts building up if you more flesh so these are fireflies and the they essentially arg again in synchrony and they start flash okay the is not that good but still you list straight stores the N that you have synchrony and mike this fire flies now before you didn't really see synchrony you just saw a random ants moving around and then if you of the start moving and the that's what i call a globally motion behaviour no this last movie i find it fascinating has we'll to do with the talk but since i told you i figured well not this one sorry uh i want to move it here or less there and um play it and what you see is again a cloud of agents what's called in dance they are actually called army hence and what you see is they go around and the wrong and each and these chasing the n-th in front of it and the you don't know it this is kind of mystery and what happens is that is and sour so fess it with the for all mean of the n-th in front and for some reason they got into this circle that they keep circling for ever that they eventually that okay so that's another type you could call of a synchrony okay so this is my background but ask me at the end if i have any by or inspired because this is a of as far as i could go um the high or the uh i'm not that your stage yeah okay so what we would like is actually abstract from these some uh uh something and the well i don't i'm not gonna claim a end that i can explain any of the behaviours i i still want to abstract some could three six of what we just saw and the this can be for colonies these of uh in sect for hz for cyber networks uh for cyber physical systems so the model is sufficiently abstract that if you two we could enough maybe we can that seated to different application but the point i want to make is that use or combine distributed interactions that somehow how lead to complex behaviours okay the ends the find the the the the the dine and suddenly while some of them kept going around a randomly some of about there's start moving the the and they it uh they so they perform a collective task and achieve a collective decision they could move call only or or some other but they perform this we'd all it clear hierarchical structure nor ready clearly the so each agent is very limited just like a uh we like so the there is no global centralized uh control they have very special spatial uh a narrow spatial sense in that good cognitive abilities and some force but still be all these apparent brandon behaviour of individuals you can find some word in eight to complex behaviour and that's what will try to model now i want to distinguish from the fireflies and the fireflies flies which are a uh an example of coupled biological by nee any well see like there's um very similar to what happens with the heart we've reasons and the paskin can model for the card R based make a by the way the the paper has a type points a is the R peacemaker maker so its pacemaker that's what we men and the fireflies flashing in synchrony pulse cup well other people's couple biological oscillators you latest that you'll and the and actually for the power greed also you find this coupled oscillators they are essentially more uh bayes on the query remote those models of dynamical systems that are couple what we like is to explain uh some of type of behavior not by using coupled oscillators late there's but by using stochastic networks are explain what that means what we mean by that and the come come up with long term limits or average as just like the previous speaker in a sense uh uh use some of that so we don't want to focus our attention when we talk about global behavior on the random behavior all of the the ends when you the ants moving the line we are not interested on the other and that were kind of moving around we want to abstract is a behaviour of the fact that some of the N squirting late it and care the the the time okay we'll see that the techniques are based on their about equally it's uh the model is essentially a Q model generalized for stochastic networks and the the notion of state is gonna rise as empirical distributions so we are not on the focus on the state of each individual agents and but more on average behavior on empirical distributions and then after some real normalization in thing the system go to go go very large then uh we can that we can come up with appropriate eventually equations uh ordinarily fresh or difference equation and starting to clear of those it questions will lead to the to them to the global behavior and also in so a set certain case we can explain synchrony so that's that's uh uh that's uh we are going just the for you two to kind of have an intuition of a these uh these are regarding gleam it's send these types of we meets when the when the the system uh grows large uh i just want to distinguish here um that uh we have a some some highly nonlinear uh system and that the system can be locally it behaving here uh and so you you may have fast fluctuations and that's uh uh diffusion type run and approximations um you want to the long term the uh uh a behaviour that's the globally global equally so this would be this line or that line uh it's so that's by the mean field methods that we are gonna use here but the from uh uh in these types of so cost the stochastic that were type systems from time to time you have actually a uh uh a dramatic changes and so it could be changing from this local behavior he have to that local behavior and that would be a rare event and the uh you'd use uh other techniques based on large deviations but we are gonna i uh call see that these mean field map in try to abstract as the system grows large and you were and you kind of factor out to the randomness of the in V jules and the and try to abstract the emergent the behavior so our model for these uh uh agents is an event based okay we are not gonna model each individual V jewel by some dynamically question okay we are gonna say simply that they are you and and um and then we are going to impose a a a a model uh that generalise as uh the a model by and two is uh two thousand sick uh the model of and to as you can think of a as whatever i se but restricted to one of these uh circles here so what is inside out the agents and they have some some interactions and then uh uh uh we called is a the super nodes and then the super nodes have some sparse interactions their actions among the ills make themselves you could think of this as a as a um and that somehow uh are randomly going around and they find the some trails on which they leave their for um there are chemicals sent and then other aunts find that and the and and then these trails form but from time to time at uh and then moves from one trial to another trail in somehow this might reinforce one one specific trail and most of the n-th might going to their trade so that's what we want to explain so we'll have super nodes M of them we can also was room that the the age actually want to achieve different the pipes of of uh activities tasks so we call them "'kay" class uh K classes um and um and also uh we assume that uh uh uh agents have a set the find finite capacities so they cannot the yeah had they don't have infinite capacity um and the the events real oh are so that's so we're giving model events are going to occur they interact and the in the uh and everything happens that the random times so essentially we have a four types of process is uh going on here you know have a these events that uh might a wry are a rival a um at the no the uh at an agent uh uh inside one of these this super agents uh and we as some up plus some process with some rate lamb the then the um the the is usual in uh giving theory you also have some uh even things influence time so the event happens and then the uh maybe uh it will last for a while and then the it will wither away and that's uh exponential so with the certain then rate you and then that there is interaction among the among these agents here so if an agent the is moving along a certain trial maybe interacts uh is uh at random times we'd out their agents and then the other agent comes and the drawing the trial and sometimes an agent jumps from one trail to another trail and the and the will call these the by parameters gamma and so yeah my supp K will be in a and the gamma as super i J will be uh in in their super melt so what happens in these things is that if you really want to focus on the in V jewels then that you have a very large uh configuration space we call that the local configuration space and essentially each agent i told you could be could be doing good could be tasked with the K different class of task so uh each agent the would the have and one up to when K and the this eight top we'll defined the state of the local agent and this can be a very large or can be a very large and and the the state that of local interactions uh because of the finite the capacity uh has some restrictions but you have a very large um uh configuration local configuration space let's call simply by this kept the lex the vector of a all the interaction so you you you vector rise all the nodes at the at the all the sensors and um and the and then that uh if you want to study the dynamics of the system uh uh by by paying attention how the local states evolve over time you'd get an intractable problem so instead of doing local you do global and the global is a weird the empirical distribution uh comes into play and basically what you look is the percentage of nodes in that a super node uh uh uh that have a certain configuration at time at time T so so you say if there was only um the a one uh one agent what absence of the agent what this why would be telling you is the percentage of nodes that the uh uh are occupied by the agent and the percentage of nodes of in the that the that have no way and so this is generalising there um and the now this uh this vector here that represents uh all the possible values of the uh the of this empirical distribution uh this vector or or that represents might be legal distribution is going to represent the uh the global behaviours behavior on the bn bad in that um the interesting thing is that the you can prove uh it takes a while but it can prove that this why and is actually a jump markov process and then that you can use uh uh uh a result uh uh well it takes a again us prove basically use the fact it's a jump markov process then you right to the the the the transition rates for the jump markov process and then you use them use a some uh martine gay you'll uh but uh results and that essentially what it comes out is that when you at the the mention of the system the number of agents uh in each of the super nodes not the the super not structure the the number of support node is fixed but a so the number of trails is fixed but the number of agents in each trial grows very large if you do that then you can show um uh using the ornaments i mentioned before that in fact a that the empirical distribution um goes to this uh uh ordinary differential equation and the the right hand side basically has has a all these terms here but basically they can grouped into to two terms i mentioned to you this comes from uh markov of process is a transition mark a transition rates the first one is when some how a an extra agent get active and the blue ones uh comes from the fact that extra agent uh you reduce the number of edges by one and so that's basically this the balancing act uh that uh is the vector field of the the sorting in different equation so um there are uh is several um so could make the one i want to make is this one here that the fixed points of this still be I E the points where the right hand side is gonna be zero respond to the globally clear beer and the then one can show that in fact the um and the very reasonable conditions there is an a uh uh um there is a uh uh it's least one equally have they are multiple there that there could be multiple E clear be a which would lead to what we call matt the stability so row and so very dramatic changes in in the global behavior like i was saying all the ends being on one trial suddenly switching to another trail and the the interesting point is that by using some uh uh uh river reverse ability of stochastic networks results results set go back to the to the a you can show that the the the solution uh is actually L most affected form is not exactly affected form because of the the partition function the normalization function but it's almost like a pair a like uh um and the and the these roles that the P here in the solution these roles uh we'll a be expressed in terms of the lamb the and gamma step the i should before um so i'm gonna um kind of a a i'm gonna that simply finally say that there is synchronous globally equally a and the sink as globally clear essentially is when all these roles here are equal okay and other there's certain conditions you can actually show that uh there is a solution uh which which are leads to these roles being all equal and the those conditions are essentially that the gamma as need to satisfy the gamma it and them use need to satisfy some algebra some algebra condition okay and the and basically uh they they uh uh uh the what happens at each super or know that is kind of a balancing act a if one is running too fast the other has to run to slow so but on average you get some think that is not the function all of the the individual agents but is a function of a the class is so um that's all i wanted to say about and sent bees uh the the a clearly uh we are not explaining and but we are explaining how the will can emerge from random interactions that we should not focus on the in D V jewels but should focus on some average behaviour in the background the and keep going round that's the diffusion approximation but we don't care about that we care about trained about the the the drift plates say and the different the a a global behavior as we have noticed to at those equations we have not yet you know able to do that but we have to stare those equations look for choice of parameters that can exploit a a a explain actually different that if the a and so just five met the stability uh uh uh show that in fact you get met to be able to and i'm gonna stop you no no the that are not groups of nodes the classes are tasks that the agent could be performing okay uh each they can be in the the K tuple in each of the K tuple L yeah each age yeah no what we have in terms of our model so we have these local node and we have these that we have these large nodes okay you could sing if this was like the power greed you could think able the load in a C and then the C is are connected them mind themselves so you have the super nodes okay so what seems side is the local is like the N and what i'm saying is that these red things are groups of and in this space you trail okay and the and each and could actually for and so i think that's not very realistic but could actually being trying to perform two different task okay what exact