oh to more late

that kind of behaviour in other works

we have used a diffusion adaptation to model for example

a flight formations symbols

to models warming of be is moving from one place to another

to uh to model bacteria more to two we had then the a people in this conference on a in

how but T search for four

or hell fish just want to go that is of four

to move to the than insertion of food so these are all examples of highly dynamic environments with the agents

some moving the topology of the network is changing of time

your neighbours are changing all the time

okay

so

nodes need to do adaptation in all the to learn

what's happening at on them and all that also to says what the neighbours think about the situation

okay

so before i start let me just evade be talk to day i'm going to show a video of it's

not my you to download it from the internet

and this a figure illustrates the behavior that i'm going to model today use see

and a a a group of fish lots of fish being

right

uh followed by a a group of shot

now

i'm going to model of is as two separate networks called in a thing we've each other be sharks form

a network of nodes to are in eighteen with each other

and the purpose is to encircle

a a group of fish and the fish is on the network of feature

that are call the meeting with each other and the purpose is to try to get away way and also

find before for done go dollars

before the locations of these are two separate networks

they have their on an object is but at the same time

they have

some form of a competitive interaction between each other okay so that we show you this C behaviour in in

nature of forced you see here it is

you see how we we shocks is a fish

and then they are back them one at a time that's have they

and they a function

okay so that it is they all have a code in a of this some not shocks the thing this

the all phones

no okay so

if five

you want to see if again

so that's what they do okay

that's how they

they play for four days circle circle the fish and then they are dark at one at a time okay

case of course this is this

a small example the

but i i'm sure that

there are more

complex examples in nature are okay so now let's come back to the math okay to new method

and to that modeling i'm going to do

to model that kind of behave and i'm going to use a call diffusion adaptation algorithms

so that we force motive the algorithms for you

by and that's what i need and that's for that consists of a collection of notes these nodes have a

adaptation and learning abilities select me motivated for us assume you have a collection of and know

that collected to each other through neighbourhoods circuits so you have a topology and this topology can change with time

because "'cause" and going to use it for the application

at hand

and that's assume

i'm not going to both

in the case the movie the deviations and the arguments of come just going to highlight the main ideas is

friend interested in the details the references

well help you with that of kid just because but i don't have time here to go through all the

deviations

but i going to highlight the main ideas

we set of nodes they have a model objective and that object of for example is that you all effect

of W O

this this down real all could the present the location of for all of them would like to know what

the food is

or it would represent the location of the are all of them would like to know with the shock is

an avoid it right

so a so you have a collection of a with the common object and each node each node

has an index K each node has access to some measurements

but related to that the objective for example each node

can sense it distance

do that objective and noisy distance and is noise

and can also sense in what that action that the object of its i know the distance and i of

the direction but all of this is up to now

okay okay because you are innovative noisy environment then each node in the network has access to that kind of

information

now how do they work together so that the local or the nation of from local cooperation they can improve

the estimate of word

V four days or of where the but a is all

improve the estimate of what have a parameter the network is trying to estimate a cam just using

the fish as an example in this context okay

and now you can formulate a global optimisation problem like this which says

a i have and nodes

all these nodes would like to find a weight vector

data you or the location of what that were for them looking for in order to minimize the sum of

the squares

okay this could be one cost function K

of course this is a global optimisation problem and we don't want to solve

it in a global man and we would like to solve it in a distributed manner okay because

every node K only has access to information coming from its in egypt neighbours okay so how do for that

problem in a distributed manner and we have started this problem in late data several publications only earlier

and we motivate the algorithms and we started its performance convergence performance times and performance is that is the performance

okay so he i'm just summarising the algorithm and all the set and done

this is one of the algorithms that you have one

that performs very very well okay and why i mean these algorithms we also insisted on coming up with a

good things that are simple to implement

because i believe that in applications like we one i'm showing you hear and i'd these agents i'm not very

sophisticated bill might be able to be implementing very complex

algorithm so we would like to see if you can him late

these kinds of complex behaviour through simple procedure is okay so this is one of the algorithms we have i

call it the at the diffusion fusion algorithm had that then combine "'cause" it consists of two steps

okay okay each node note K the first think it does it starts with an estimate of for that

that's see think of it as the location of the predator or four

a first think it does it uses a a measurements it has for example it's S estimate of the this

that's and the direction

it uses that

information to try to improve one its current estimate

that we give it an improved in to need to estimate and then it costs also with its neighbours it

combines

for the convex combination here the estimates from its neighbours

two and up with it improved estimates so this is a two-step procedure

the D there's of the must not math methods don't matter what matters is the process the process is

you know

for example

this is a very different from consensus type solutions in consensus step solutions if a it's just if you are

a way if a are familiar with that

you try to

a you require a agents to reach consensus about some something to agree

i something a kiss all over that each each node is essentially a averaging the information from its neighbours

in these kind of applications that they showed you the example that i showed you you can not to require

you you should not expect be nodes to reach consensus

because the fish that's closest to the shot should behave in a different manner than the fish that's as to

the for don't far away from the shore

you have to allow for individual that's estimate of the situation as well

so that's why

these diffusion algorithms algorithms always consist of two steps one of them is con thought and with the neighbours let

me see what the neighbours think about with four days

but before i take that for granted that also want to says it from my perspective

okay

uh uh where the shark is a with before is

relative to me so you always have personal assessment

okay a local processing local adaptation and learning in addition to

collaboration with your neighbours okay so this is always there okay you always have these two steps

and this is called adapt then combine adaptation comes before combination you also have combined then at that

and you have several different variations of these algorithms this one works very well okay

and these coefficients they always add up to one

over the neighbours on these graph they are just a last what i just

yeah explain okay

now in nature there are many many examples of source stick kate organise behaviour that are right

okay from local interactions between you node you in one is the the fish

behave like it's forming this very but for geometric figure

right

but is not sense brain telling them sitting here on this side and telling and you position yourself at this

particular location right

this is happening this is the result of highly localised processing okay

the diffusion adaptation algorithm i showed you is one example of high localised processing because every node is only coordinating

with that in you jet neighbours

you also have this kind of behaviour of the fish

but i D S to of the boats fine in V formation i again that is more central

bad board telling them sitting on the side and telling them this is what you okay to cells okay so

these are examples of highly complex

so self organized behavior that the result from local processing at the local level look

so the algorithm i just described to you the diffusion algorithm that i described use one example of

localise processing that leads to this kind of behaviour in and i'm going to illustrate it do you to

but showing you how

this algorithm can in more the behaviour of sharks all for putting on face

in the case when you have two networks competing against each other right and trying to get the out that

and the other trying to get away from

from the forced okay

is so now

uh uh uh

so

oh this is known that for example here this kind of behaviour is known and uh in a at if

you have let's say the shock yet trying but are a group of fish that have force in moving together

in harmony the ford and then start the me a shot peers

now the fish is known to behave in this manner they have this found and effect behaviour at they turn

around

they do not on

okay and can almost a long this and shots so they turn around and come back from behind

okay so they are known to behave in that manner so about going to model

that behaviour so that you

okay and then he are also i shall video the we do that i show here you see it in

a different man that here you have the collection

a sharp sold bill things and you have some fish she and you see the end up in so

if a fish and then they start at back them one at a time but to side

and in the video "'cause" this are just illustrations from the which are this is from the I B B

ball you to the and other kind sent this and the this we goes from scientific american and this it

is it's from some other

or or go shown down

and down here a can now again like i said before don't to much about the math okay because we

don't have time to go through the D as but let me explain in high level

a big use the algorithm i should do before that's all you need to to in more like that kind

of behaviour

okay

i to think about that like this okay you have a group of fish they don't know where the four

days so that's one object objective they have an mind i need to find with the four days

they can use the diffusion adaptation algorithm to estimate where the location of before this is to local cooperation number

one

no but to they also need to stay away at i'm where

the shot are

right so they have a that estimation problem that they need to solve a need to know where the shocks

are

so you have to

diffusion adaptation process is that they need to do and right in a distributed manner

the sharks they need to know where the group of fish is so they need to track for example with

the centre of gravity of a group of fish is

uh uh that estimation problem i they can also use a themselves the diffusion adaptation algorithm of the form i

showed you to estimate with the centre of gravity of the

group of fish is and track at that i'd because they need to follow that

and this so open so you can see that at the core of solving this problem you have to fall

for the or four

estimation problems all of them distributed estimation problems each one of them can be solved exactly in the same and

that okay so you see the uniformity here so one of these things is to try to show that with

this thing classifier algorithms with this same type of processing you can in one eight different kinds of behaviour

know because if you think about it this is something very very interesting

you see you you with think that to to model the uh the a flight formation in boards of the

the way but to a move you would need different kinds of algorithms and models those for each scenario and

interesting thing is with this same general kind of a with them they want a should do before you kind

of produce these different kinds of behaviour

okay

so here what you have just a a a a high level description you can divide the region at i

around the shark to for regions

region and one up here use the up here each in one

if if if is is region one T to means he's far away from the shot okay you defined this

C is in terms of a at I if it's away from the shock if you stay if you just

want to use

tracking where the for this and continues moving was before

no okay that's what it means

if if if fish finds itself so if if fish find itself

more

if a fish finds itself in region two

which means he's calls to or okay

then what you would do a double take it own i perpendicular to the direction of motion of the shot

so that's why he also needs to track where the shark is okay

so i'm telling you how they we use the information they get from the estimation process okay they

i get this information to do something with it they have to a decision with it's so well this fish

is tracking from local cooperation with the other fish with the shark is

if they that out they are to close to the shock that one move along a direction they would take

get to a like a should before the found in effect

they won't take a turn perpendicular to that that action this is what this not they me okay

if they are for example to to close to be we and one hundred eighty degree turn and move away

a okay

so essentially what this at is thing and what these conditions are telling you is how the fish use the

information they get from the solution of the distributed estimation problem okay they use it to evaluate how close they

are to a shock and then what decision they should make should they move

one you moving to the for should they

for all the found an effect well should they divorce and move back that that's actually what it means okay

and what that means is they are going to set their velocity vector that how long this uh and direction

of P

so the result of the estimation process affect how they said the velocity vector or okay

now

after the fish set but it like used for in the found an effect beta group with fish usually group

work "'cause" a how do they re group okay again

what they do is eight that for example and this step but it they become separate networks and that's what's

nice about that now you have set but at network

so one can say the out

okay i so one of them for example of this network can find which

one is which i if that is a net will close to it and which fish she's cost to it

and move in that direction so that they group

okay

so these sub networks can also track each other through local cooperation

and then take an action in the uh i i i uh uh

i um

a the act to that and move or or other subnet will give this one a we these sub networks

to group okay

so sing

yeah this fall all week is not working well here it's

chomping thing over several slides that

ones

the is

and a let me show the yeah as this we you before i come to you this is the case

of K using the kind of a bit they should you hit it is you have a group of fish

trying to find a for would okay it will be and then a shot at

so you can think that the fish they don't know what the for is they are called than eighteen to

find with the four days and moving in that direction but there was a of for the shot is

and the track it and then use see the found an effect and they group one on in you

continue their right you see so a this is all to produce with a kind of a with them i

showed you

however in this example i only have one network the fish networks so it's only the fish that's doing diffusion

adaptation

the problem i discussing today i'm showing to the case where you have to a networks a group of shocks

and facial case i'm going to show you that very so on

so what do they shot to do what do this shot do with the result of the estimation process with

a is out of tracking well the centre of gravity of a group of fish a

well where the closest fish is to sam what do they do with the result of that distributed estimation problem

the shocks they have a

several decisions to make

okay i'm not going to go again for all the mathematics but they have several say it's one of them

is chase if the fish just to a way they decide

that's just move towards the centre of gravity of that group

so they are tracking the centre of gravity that they set of the lost a vector do that that actually

are okay

once they get calls to it within a certain date as they decide to is or call it so they

move not a the attention or K they move along that that it's of that is to what the fish

were building but okay

so once they get close with it's or and they just they say a let me now is so call

it okay let's nice is it and and one at that time they take to are

you like that wide leans in and so the fish case so essentially they have a state machine that they

fall

and based on based on the estimation of sell the use the they transition from one state to another depending

on how close they are to the centre of mass okay so this is just a producing

in figures and equations what i just explained in plain in plain walls okay so i'm not going to both

a all of these the there's of course that is

and that is small in that will not that behaviour so if if the shock as far away he just

keeps moving towers the centre of gravity

okay once to gets that he starts so

that group

can and not only that if if fish moves for that i they would like to keep the fish within

a circle of the fish of one of them moves away from the so they will track that vision bring

came back okay

so all of that

so all of that requires that you use the distributed estimation problem okay i'm i don't have much time to

both a the uh sort of these small in but you are that to get an idea i would like

to show you

no i would like to show you V uh defined assimilation simulation than at break for

here you see this example now you have to network

right

you see how the shots since so fish

okay

let me let you watch it and then and makes some comments

you see and then they at that one at that time

okay now think about this to you see this is an example of a highly dynamic network okay and that

network that's moving all the time

your neighbour are changing all the time feelings of bit topologies changing all the time

number one number two each one of these networks you have to networks each one of them has an objective

the fish wants to find a way before it's

but it the estimation process

what do for exactly for that's would would be moving as well

the shocks would like to know what the centre of gravity of the fish and want to track that and

in tap that

and also the fish would like to avoid the sharks okay

so you have several object is okay in a high dynamic environment and a highly caught productive

and competitive environment like and you end up with a high and and a network that's able to adapt and

learn

a in real time okay so this is

an example of adaptation at the higher level and learning at a high level and then usual and you can

see just simply using that diffusion algorithm that i expect you before you are able to reproduce the be here

that i showed do before uh in the video and a lot a like to the other the real example

of how shocked friends

i go off to fisher okay

and you i hope i conveyed the main idea okay of of this kind of behaviour i again this is

all signal processing what you're saying here

all generated using

a diffusion adaptation algorithm i showed you before and using the result of the distributed estimation process to make decisions

should they move closer or should i so oh that's essential the kind of the decisions you make a okay

so and we this of some reference if you are interested in more to learn more about this some going

to stop S so that we stay on time okay so if you have any quick questions

before i move on to the second part yes please

i

yes

they don't have a job from the for the uh

so okay in any of the like take advantage of the behavior have your of other one of knowing that

be have your of other one to to maximise its proof

a i okay in this in this particular the model that i have here the information that's shared between the

network is the positions of the centre of gravity of the large network and the position of the there's in

this small a network so they know essentially a deep but they don't know this strategy that the other group

is falling they just know where the locations are and they spun

according to be process you that explain you before T that you move away well you D for or you

take an i two degrees is uh okay so that's the this strategy to they use in this particular example

okay

now if they knew exactly what strategy each other group or i would assume that you got but have to

do better yeah that's a good question but that we haven't done that

okay yes

i

a yes okay right that's a very good question of course C M just showing a very uh uh the

networks behaving but then you need to study the steady-state behavior of these kinds of networks the converge and we

have done that and other walks okay we have shown we have a derived expressions for the mean squared error

in steady-state state okay

how how close they get to the location of if we have done that in previous works yeah

of course for small step-size a the step size have to be small amount

for them to converge

oh can maybe one more question just so that we stay on time yes

here you assume that the sharks for example have the same state machine in each of them right let's say

for example there are different groups of sharks right which like to like if an state machines very but but

i is a tight so

is

right which might apps

behaving hating using a different types of machines as i a good question we haven't done that but you know

this are all generalisations that are possible to pursue so okay yeah and and and see what kind of behave

that emerges from that kind of of assumption what you thing about the real life i mean i R D's

i mean it's state machines are

well already very uh i mean somehow

or the or already in the sharks or or yeah that i think we have to ask an animal behaviour

expert okay yeah all we all yeah or they are knowing okay we'll it would it some of the lead

to channel and they explain about

be thinking process that these animals both through these state machines and are trying to see if you can to

produce that kind of behaviour

using the signal processing algorithms and models that we have a okay but this are all good questions okay but

to and so then you have to get deeper into a right to how and most be uh you know

i want to be fit to the other because i don't want okay maybe we should move one i would

be glad to talk to you i your questions after this session okay sorry for that just because they have

to move on to the second