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