0:00:15okay all speak from here for them morning
0:00:19and as that's uh the
0:00:20but by the is global immersion behaviours using close of regions
0:00:24and the mike what they're could make it so uh i'm presenting the the work
0:00:29and the we are no the support from the national science foundation under the from a your for are
0:00:35i'm i'm gonna switch between the slides and uh
0:00:38i became an expert in extracting videos used from uh from you to be today
0:00:43so i'm gonna try to multi rate my by your
0:00:46inspired okay
0:00:48and that's
0:00:49we these movies
0:00:51if i can get them
0:00:53so i'll do a replay here and but you see
0:00:56is is agents
0:00:58they seem to be and
0:01:00a place called in agents and they randomly go around
0:01:03and the suddenly one of the agents
0:01:06kind of uh finds an interesting object
0:01:09and the
0:01:10before you know it
0:01:12other agents
0:01:13find the same interesting object
0:01:15and the although
0:01:17uh most of them seem to be randomly going around
0:01:21in fact
0:01:22you us a human looking at this video
0:01:26that's something is happening
0:01:29and the
0:01:30some of the ends discovered
0:01:32that if they go to the bank and cash the the the the i'm or whatever or the you role
0:01:38they will become re
0:01:39so that's my first comp
0:01:43what it look at uh
0:01:45i'd C
0:01:48if you do
0:01:49because i want to contrast
0:01:51these biological and the and the and show you that there are different types of behaviours and which one i'm
0:01:58um i'm talking i'm uh referring to
0:02:01so if find correct here
0:02:04you want see much you'll see some flashing point i don't know from where you are you C one or
0:02:10two here and there
0:02:12and this time goes and if you are
0:02:16if you
0:02:16but you tension you'll see that uh
0:02:19so that only there's starts building up if you more flesh
0:02:22so these are fireflies
0:02:24and the they essentially arg again in synchrony
0:02:27and they start flash
0:02:30okay the is not that good
0:02:32but still you list straight stores the N
0:02:35you have synchrony and mike this fire flies
0:02:39before you didn't really see synchrony you just saw a random ants moving around
0:02:43and then if you of the
0:02:47and the that's what i call a globally motion behaviour
0:02:51no this last movie
0:02:54i find it fascinating has we'll to do with the talk but since i told you i figured well not
0:03:00this one sorry
0:03:02uh i want to move it
0:03:07or less there
0:03:09and um
0:03:10play it
0:03:12and what you see
0:03:13is again
0:03:14a cloud of agents
0:03:16what's called in dance
0:03:18they are actually called army hence
0:03:21and what you see is they go around
0:03:23and the wrong
0:03:24and each and these chasing
0:03:26the n-th in front of it
0:03:28and the you don't know it
0:03:30this is kind of mystery
0:03:32and what happens is that is and sour so fess it
0:03:35with the for all mean of the n-th in front
0:03:38and for some reason they got into this circle
0:03:41that they keep circling for ever
0:03:43that they eventually that
0:03:45okay so that's another type
0:03:47you could call of a synchrony
0:03:49so this is my background but ask me at the end
0:03:52if i have any by or inspired because this is a of as far as i could go
0:03:58um the high or the uh i'm not that your stage yeah
0:04:02okay so what we would like is actually
0:04:07from these
0:04:09some uh uh something
0:04:11and the
0:04:12well i don't
0:04:13i'm not gonna claim a end that i can explain any of the behaviours
0:04:18i i still want to abstract some could three six of what we just saw
0:04:24and the this can be for colonies these of uh in sect
0:04:28for hz
0:04:29for cyber networks
0:04:31uh for cyber physical systems
0:04:33so the model is sufficiently abstract
0:04:36that if you two we could enough maybe
0:04:38we can that seated to different application
0:04:41but the point i want to make is that use or combine distributed interactions
0:04:46that somehow how lead to complex behaviours okay the ends the find the
0:04:51the the the the dine
0:04:53and suddenly
0:04:55while some of them kept going around a randomly
0:04:58some of about there's start moving the the
0:05:01and they it uh they so they perform a collective task and achieve a collective decision
0:05:07they could move call only or or some other
0:05:11but they perform this we'd all it clear hierarchical structure nor ready clearly the
0:05:17so each
0:05:18agent is very limited
0:05:20just like a uh we like so the there is no global centralized
0:05:25uh control
0:05:26they have very special spatial uh a narrow spatial sense
0:05:30in that good cognitive abilities and some force
0:05:33but still be all these apparent brandon behaviour of individuals
0:05:36you can find some word in eight to complex behaviour and that's what will try to model
0:05:43i want to distinguish
0:05:45from the fireflies
0:05:47and the fireflies flies which are
0:05:49a uh an example of coupled
0:05:51biological by nee any well see like there's
0:05:56very similar to what happens with the heart
0:05:58we've reasons and the paskin can model for the card R
0:06:01based make a
0:06:02by the way the the paper
0:06:05has a type points a is the R
0:06:07peacemaker maker so its pacemaker that's what we men
0:06:10and the fireflies flashing in synchrony pulse cup well other people's couple biological oscillators you latest that you'll and the
0:06:16and actually for the power greed also
0:06:18you find this coupled oscillators they are essentially more uh bayes on the query remote those models of dynamical systems
0:06:25that are couple
0:06:26what we like
0:06:27is to explain
0:06:29uh some of type of behavior
0:06:32not by using
0:06:34coupled oscillators late there's but by using
0:06:37stochastic networks
0:06:39are explain what that means
0:06:40what we mean by that
0:06:42and the
0:06:43come come up with long term limits
0:06:46or average as just like the previous speaker in a sense uh uh use some of that
0:06:52so we don't want to focus our attention when we talk about global behavior on the random behavior all of
0:06:58the the ends when you the ants moving the line we are not interested on the other and that were
0:07:04kind of moving around we want to abstract is a behaviour of the fact that
0:07:09some of the N squirting late it and care the the the time
0:07:13okay we'll see that the techniques are based on their about equally it's
0:07:18the model is essentially a Q model generalized for stochastic networks
0:07:22and the the notion of state is gonna rise as empirical distributions so we are not on the focus
0:07:28on the state of each individual agents and but more on average behavior on empirical distributions
0:07:34and then after some real normalization in thing
0:07:37the system go to go go very large then uh we can that we can come up with appropriate eventually
0:07:44equations uh ordinarily fresh or difference equation
0:07:47and starting to clear of those it questions will lead to the
0:07:50to them
0:07:51to the global behavior and also in so a set certain case we can explain synchrony
0:07:57so that's that's uh uh that's uh we are going just the for you two
0:08:01to kind of have an intuition
0:08:03of a these uh
0:08:05these are regarding gleam it's send these types of we meets when the when the the system uh grows large
0:08:11uh i just want to distinguish here
0:08:14um that uh we have a some some highly nonlinear
0:08:18uh system
0:08:19and that the system can be locally it behaving here uh and so you you may have fast fluctuations and
0:08:26that's uh uh diffusion type run and approximations
0:08:30um you want to the long term the uh uh a behaviour that's the globally global equally so this would
0:08:37be this line or that line
0:08:39uh it's so that's by the mean field methods that we are gonna use here
0:08:43but the from uh uh in these types of so cost the stochastic that were type systems from time to
0:08:48you have actually
0:08:50a uh uh a dramatic changes and so it could be changing from this local behavior he have to that
0:08:55local behavior
0:08:57and that
0:08:57would be a rare event and the uh you'd use uh other techniques based on large deviations but we are
0:09:03gonna i uh call see that these mean field map in try to abstract as the system grows large and
0:09:08you were and you
0:09:10kind of factor out to the randomness of the in V jules
0:09:13and the and try to abstract
0:09:14the emergent the behavior
0:09:18our model for these uh uh agents is an event based okay we are not gonna model
0:09:24each individual V jewel
0:09:25by some dynamically question okay we are gonna say simply that they are you and
0:09:32and um
0:09:33and then we are going to impose a a a a model
0:09:36uh that generalise as uh the a model by and two is uh two thousand sick
0:09:42uh the model of and to as you can think of a as whatever i se but restricted to one
0:09:47of these uh
0:09:47circles here so what is inside out the agents and they have some some interactions
0:09:53and then uh uh uh we called is a the super nodes and then the super nodes have some sparse
0:09:58interactions their actions among the ills make themselves you could think of this as a
0:10:02as a um and
0:10:04that somehow uh are randomly going around and they find the some trails on which they leave their for
0:10:11um there are chemicals sent and then other aunts find that
0:10:15and the and and then these trails form but from time to time
0:10:19at uh and then moves from one trial to another trail in somehow
0:10:23this might reinforce one one specific trail and most of the n-th might going to their trade so that's what
0:10:29we want to explain
0:10:30so we'll have super nodes M of them
0:10:32we can also was room
0:10:34that the the age
0:10:35actually want to achieve different the pipes of of uh activities tasks
0:10:40so we call them
0:10:41"'kay" class uh K classes
0:10:43um and um
0:10:45and also uh we assume that uh uh uh agents have a set the find finite capacities so they cannot
0:10:52yeah had they don't have infinite capacity
0:10:54um and the the events real oh are so that's so we're giving model events are going to occur they
0:11:00interact and the in the uh and everything happens that the random times
0:11:06essentially we have a four types of process is uh going on here you know have a these events that
0:11:13uh might a wry are a rival a
0:11:16um at the no the
0:11:18uh at an agent uh uh inside one of these this super agents uh and we
0:11:23as some up plus some process with some rate
0:11:26lamb the
0:11:27then the um the the is usual in uh giving theory you also have some uh even things influence time
0:11:34so the event happens and then the uh maybe
0:11:38uh it will last for a while and then the it will wither away and that's uh exponential so with
0:11:43the certain then rate you
0:11:46and then that there is interaction among the among these agents here so if an agent the is moving along
0:11:53a certain trial maybe interacts
0:11:55uh is uh at random times we'd out their agents and then the other agent comes and the drawing the
0:12:01and sometimes an agent jumps from one trail to another trail and the and the will call these the by
0:12:07parameters gamma and so yeah my supp K will be in a and the gamma as super i J will
0:12:15uh in in their super melt
0:12:20what happens in these things is that
0:12:22if you really want to focus on the in V jewels
0:12:26then that you have a very large
0:12:29uh configuration space we call that the local configuration space and essentially each agent i told you could be could
0:12:36be doing good could be tasked with the K different class of task
0:12:40so uh each agent the would the have and one up to when K
0:12:44and the this eight top we'll defined the state of the local agent and this can be a very large
0:12:50or can be a very large and and the the state that of local interactions
0:12:54uh because of the finite the capacity uh has some restrictions but you have a very large
0:13:00um uh configuration local configuration space
0:13:03let's call simply by this kept the lex
0:13:06the vector
0:13:07of a all the interaction so you you
0:13:10you vector rise
0:13:11all the nodes
0:13:13at the at the all the sensors
0:13:16and um
0:13:19and the and then that uh if you want to study the dynamics of the system
0:13:23uh uh by by paying attention how the local states evolve over time you'd get an intractable problem
0:13:31instead of doing local you do global and the global is a weird the empirical distribution uh comes into play
0:13:38and basically what you look is the percentage of nodes
0:13:41in that a super node
0:13:43uh uh uh that have a certain configuration at time at time T so so you say if there was
0:13:50um the a one uh one agent
0:13:53what absence of the agent what this why would be telling you is the percentage of nodes
0:13:59that the uh uh are occupied by the agent and the percentage of nodes of in the that the that
0:14:05have no way and so this is generalising
0:14:09um and the
0:14:11this uh this vector here that represents
0:14:14uh all the possible values of the uh the of this empirical distribution
0:14:19uh this vector or or that represents might be legal distribution
0:14:23is going to represent the uh the global behaviours behavior on the bn bad in that
0:14:29um the interesting thing is that the you can prove uh it takes a while but it can prove that
0:14:34this why and is actually a jump markov process
0:14:36and then that
0:14:37you can use uh uh uh a result
0:14:40uh uh well it takes a again us prove basically use the fact it's a jump markov process
0:14:46then you right to the the the
0:14:49the transition rates
0:14:50for the jump markov process and then you use them
0:14:53use a some uh martine gay you'll uh but uh results and that essentially what it comes out
0:14:59is that when you at the the mention of the system the number of agents
0:15:04uh in each of the super nodes
0:15:07not the the super not structure
0:15:09the the number of support node
0:15:12is fixed but a so the number of trails is fixed but the number of agents in each trial
0:15:17grows very large if you do that
0:15:19then you can show
0:15:20um uh using the ornaments i mentioned before
0:15:23that in fact a
0:15:25that the empirical distribution
0:15:27um goes to
0:15:29this uh uh ordinary differential equation
0:15:32and the the right hand side
0:15:34basically has has a all these terms here
0:15:37but basically they can grouped into to two terms i mentioned to you this comes from
0:15:41uh markov of process is a transition mark a transition rates
0:15:45the first one is when some how a an extra agent
0:15:50active and the blue ones uh comes from the fact that extra agent
0:15:56uh you reduce the number of edges by one and so that's basically this the balancing act
0:16:01uh that uh is the vector field of the the sorting in different equation
0:16:06um there are uh is several um
0:16:09so could make
0:16:10the one i want to make is this one here
0:16:13that the fixed points of this still be I E the points where the right hand side is gonna be
0:16:17zero respond to the globally clear beer
0:16:20and the then one can show that in fact
0:16:24the um and the very reasonable conditions there is an a uh uh um there is a uh uh it's
0:16:29least one equally have
0:16:30they are multiple there that there could be multiple E clear be a which would lead to what we call
0:16:35matt the stability so row and so very dramatic changes in in the global behavior like i was saying all
0:16:42the ends being on one trial suddenly switching to another trail
0:16:45and the the interesting point is that by using
0:16:48some uh uh uh river reverse ability of stochastic networks results results set go back to the
0:16:54to the a you can show that the the the solution
0:16:58uh is actually L most affected form is not exactly affected form because of the
0:17:04the partition function the normalization function but it's almost like a pair a like
0:17:09uh um
0:17:10and the and the these roles that the P here in the solution
0:17:14these roles
0:17:15uh we'll a be expressed in terms of the lamb the and gamma step the i should before
0:17:22um so i'm gonna
0:17:26kind of a a i'm gonna that simply finally say that there is synchronous globally equally a
0:17:31and the sink as globally clear essentially
0:17:34is when all these
0:17:36roles here
0:17:37are equal
0:17:38okay and other there's certain conditions you can actually show
0:17:41that uh there is a solution
0:17:44uh which which are leads to these roles being all equal
0:17:47and the those conditions are essentially
0:17:50that the gamma as need to satisfy the gamma it
0:17:54and them use need to satisfy some algebra
0:17:56some algebra condition
0:17:59and the and basically uh they they uh uh uh the what happens at each
0:18:04super or know that is kind of a balancing act a if one is running too fast the other has
0:18:09to run to slow so but on average you get some think that is not the function
0:18:13all of the the individual agents but is a function of a the class is
0:18:18so um that's all i wanted to say about and sent bees
0:18:23uh the the a clearly uh we are not explaining and but we are explaining how
0:18:29the will can emerge from random interactions
0:18:32that we should not focus on the in D V jewels but should focus on some average behaviour in the
0:18:38background the and keep going round
0:18:40that's the diffusion approximation but we don't care about that we care about trained about the the
0:18:46the drift plates say
0:18:48and the different the a a global behavior as we have noticed to at those equations we have not yet
0:18:54you know able to do that but we have to stare those equations
0:18:57look for choice of parameters that can exploit a a a explain actually
0:19:01different that if the a and so just five met the stability uh uh uh show that in fact you
0:19:06get met to be able to
0:19:08and i'm gonna stop
0:19:27no no the that are not groups of nodes
0:19:30the classes are tasks that the agent could be performing
0:19:37uh each they can be in the the K tuple in each of the K tuple L
0:19:41yeah each age
0:19:51what we have in terms of our model so we have these local node
0:19:57and we have these that we have these large nodes
0:20:01you could sing
0:20:02if this was like the power greed you could
0:20:04think able the load in a C
0:20:06and then the C is are connected them mind themselves so you have the super nodes
0:20:10so what seems side is the local
0:20:13is like the N
0:20:14and what i'm saying is that
0:20:16these red things are
0:20:17groups of and in this space
0:20:19you trail
0:20:21and the and each and could actually
0:20:23for and so i think that's not very realistic but could actually being trying to perform
0:20:28two different task
0:20:36what exact