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