so i think it's actually much for so what would like to say just so yeah the proposed a new

and for the position of

a special session makes a pleasure for me to be here

oh today will talk about a but it's at the more is what most applied to this to distributed resource

allocation problem in can be to systems

where the communication or more the second users

are supposed to be a a a a a a but randomly but i

a particular we will talk about social foraging

social sort

these systems are typically made up of a relation simple agents

in a a lot of locally to each other

and that with the empire

agents

follow a very simple rule

and even if there is not centralised four

need for um and then leads to

the merchants of one halogen original here that usually is unknown to the individual

that are examples of course clue don't call is

bird flocking willing

the application of which we want

to translate

five is part more

he's cognitive radio

we know how it this case

we have

to to kind of the users

primary users

that

um

are the owners

the red

and the second are you

these are kind of the users

that's a sense the channel in an opportunistic way

and trust me you local by channel

oh have

a second data the network used to get a dog

so we have start

without a central node

that that's controlled the access to the medium

that

our problem is how to coordinate yeah

from what actually many second the users

yeah know like this central i

a i just i mean my what condition

then

hence

in this context the by some

simple but robust

a a fraction mechanism

can be all real in

in particular we propose

at the strip of the rest are location based on board

they they that nearby by agent

and track beat each other

and for so um presents a location then prevents correlations among the location of different users

and a is crazy

so the search of the most of robert's slot to be used

can be modelled as the motion

or was formal press source

the rest of domain

yeah

i

i frequency plane or the frequency a

looking for for edge

for a represents a actually a function inversely proportional

the if you know level

sense by the

and that's work would tend to be in this time frequency region where the that's interference

what's that is fine to be one

i always regions

in the location of different users

and you might spread

in rest

rest of the location can be more the that as the this for like mean they of this sort of

for word

in particular

i

the knows the wrestlers that

so that was issue

sure sure of chosen by note i for is red

in the rest of me

can be in this case the entries of is back can get time slot the frequency

chump

second i i

is the interference profile sense

on the rest

but may i know i

so in this case the E power force there so uh

a a firm that want to me my

J A and J R

represents the a function are also to

they allowed to implement

a features of a fraction of also

between the

the the rest of

yeah J

are the entries of an identity matrix of the graph

this described

special the hall

oh

now

in particular

it is good are what one word zero

if no G is

you is a need of one of all not that so if it is inside scoring rate

well wise

so it's in this case what one

yeah yeah the wife

it's important remark

that's even a this is warming up guns

you know issue

so the secondary users are

i'm not moving at to just the rest

are moving in this rest to me

these with visions a J

the best this a supposition

of

so they are related to this special edition

attraction and repulsion can be chosen instead several

weight however allow for a simple mathematical

they should be

uh we have chosen a um

um

what for i

from

function

and that is financial bound

vol

so that's

the a joint you here

okay a with respect to these

in the rest of this assume this kind of four

it's important to note is that there is a unique

i

of the a fraction propulsion

potential actual function

these

mean

is really

to the so called it really this done

in the biological literature

is the distance of which a fraction

and also a

and can be set

choosing rubber is good vision

C and C a

yeah a action at of pops concert

what

in in our setting

there are also is useful to a hold collision

between in the location of different used

so we choose the i believe in this

we proportional the

this that

in the me

that can be and

of the

but

channel

for for for example the duration

of the time and times

so a the right solution to the previous problem can get you the

for a a simple steepest simple approach

where each no is at the position of its own wrestlers

and the rest

really according to the agree

gender the

fourteen potential function

i shows

four

it's important to remark

that these

rule

to be he needs

the computational

just not wrong

so a lot of gradient of this

it's five

a to the point X i

it well

which we are also

or some force

that the rest of six i are receiving

a a from the results of the need

J

it's was important from that's at the E

each of that

row

information to each with neighbour

a a a a a a the information about the position he's

he's going to i

this is

whole

they

read red provide represents it

a position of the psd L

a primary user

and and that is changing

time

simulation

the we though that are moving on the

frequency a

represents this

a a a a a uh uh this

the

i i i i and the red it is pressed

that are mean trying to find

a position where there is more for so less interference

a at the same time

so is fine

a to require on

a is what we see that so it's

they are trying to keep

this warm of a spread a small as possible and the would lead someone allocation

but

i'm going to present one of the main result

you one of the more

you features of this or with that is

intrinsic of of implementing of the centralized make

for sparse

chuck

i said before that

basically is movement movement happens

in um

the in the rest of me so it's kind of a big issues

but the communication

between

no

for some

in this part

so

basically

to nodes that that actually are the course for each other

can exchange information and can hold

to use the same channel

that

to to note that that actually a far away from each other

is no

is not

actually

they don't communicate with other

so they don't perceive repulsion

and they are allowed to use

same channel use the same press

a so

but

or in a a a a in this example we particular we're

to a network composed of a hundred nodes

and with you there in just a a weighted channel of a these node so

share

with different colours we identified a different channels they cannot board

where yeah

and that's it

as we can see it never happens choosing probably you can these

we

yeah

the rest

that's two nodes

are are in this say

a a rest

but a if they are far such as far away

and they don't have that i

that's now everything on the time

this is just a a

and easy down

where we can peaks

the position of the primary

i

and the money that

he

where we can is are position

to use

is

see

in the middle right dots

and uh uh we can see out is warm in to people's in for each other

feel the gas

let

uh a the primary users

and that that same time

you might spread and would lead you

these

each other

however is is

is is how well knowledge

primary users are you

four and a

at least i the least

so what we propose

it's

a model of the primary users so

if

time

probably in some knowledge about

the it is some is unknown

right

so in particular we propose

um that the primary users T V

when

channel

can be more as oliver james and i'm

i the right by the transition rate

from i a lot

um

from i one you

now suppose the that's this

patients are no

really efficient

and it is also known the average power yeah i

all one over a some channel

it is possible to about

close of four

the

temporal wrote it of the expect

you

condition it to the observation time what C

so i i i you particular are you the channel and T what is your sense of i

this is the expression

of them from either

otherwise

we have that

what is a portal

use a port and because they you they allow house

the construction the construction of a my

all

expected interference

where this warm actually pen

no okay

for time frequency slots where there

that's that's interference

let that

one

such is fine

the basic required

about

a receive S

and

is an example actually

and

in in the the expected interfere

time

it's use

right

right

using a grey scale

so it you can of the time

here is

i think people to zero

we have to these joint

um

yeah yeah easy

is it that

a right by the right

three his joint

uh uh actually um

i

or for by the dark

area so there areas

where it is more

right

more

and

as as we can see this work

from the initial position

the fine read location

and so the rest of this fine i a location

close that was in in time

where the prediction of the variance

so is better

on one i usually at of spectrum

what is be satisfy

force

it it required

about

to each

yeah

in particular at this whole we fall i i four was

all the fact that really stick channel

i

have

on this

or procedure

so that that

that feeding in position or some my

i is question so it can this work out that you've the solution

even in the presence of such random in practice

some of the no

we consider a particular to so to make

no

a round of a remote

so we model the graph

right in in rash

i'm the users as a random graph

so

considering that large

my

right

row yeah this sequence

of a laplacian matrix

where we uh can be decomposed the sum of the next i R

the right

row

and

is a sequence

zero we i

moreover

we consider that

each you are not communication channel uses a you

either

a into them is a zero means

and

uniform stupid

ever

you particular or however condition and and he is one errors

i

and the how how it happens

what's so for consensus on

it it can be once the convert

are

so what would you throw but

we consider it a proposition

which allows

they but decision error with some use

a statistical properties that we

for to program

so

substituting in the expression on uh of the but i'm version

forming out

we we can write a partial in this way where now

visions

that

right

things

the and pay

because they are read station

random bar

and the ne K and that's O K A are now that to contribution

a quantization noise

and of

uh

and one of the

so a now on the for

of the function G of try out function G

yeah a or of

they then now

of the overall system be expressed in compact for you know we and way

for this he

can be re than

and the written as the sum

oh but that there is a function of are that depends on the me graph

on the spectrum

and are are a function yeah

that the base actually on the

a random vectors

and on the contribution of quantisation noise

um

what so what they do of the day what you want to say is that is where we got it

can be seen people uh

are a bit more also think approximation procedure

and find its so if their basic function are

with but you is met at each time he's

and this brought by

random

yeah

so what proved

is that giving this competence

which

that

these are quite common

think

additionally

a a a sequence that satisfies

addition

for

in english

sides

that

we can assure also

number

oh

that's what we got

a a so it's probably one

basic well

all

they

a of this work out we with a very to this

so we set E

and a social solution set composed of

zero

of these that their function

ah

at the rest of course on me

now a a relation to show

mary

but it you power

a results

so we can see there's more me

frequency domain

present

five

so of course in a really communication scenarios i

maybe there

because of

but

not

so we consider a these where they runs but it's are problem

without requiring sort transmission

and source you find the right the face

all uh each no

in the figure we show that be if you're of the normalized

simple

but

with respect to the iteration in

four

if if to what to establish a

a mission

read read is the i case

green zero point than i zero point seven zero

fine

as we can see big vector

but that that the call

yeah

as will always reached

we a shown that the and don't expect

row

oh that are what we can see is that to reduce it will be a stuff should actually

the network requires a longer

to reach the final

so

we propose this this through with the resource allocation strategy

me

the

for two if

this form and

a we you an S you know what fraction of also forces

a

to the Q five

a was lost

use

what would be put i'm second the users

you particular each node is supposed to be able to and only to nearby ones

and this problems

intrinsic capability

to provides also used

channel

to a real

for

and

at the end we have seen that the method is also about a packet drops

with that that is only to slow down to convert

can

i

or

uh_huh

well well what we have a a a a a a kind of a simulation all

a we what we what we what we do

select

and

press

large now

okay

comp

to

and no so that the for a mean it will not and

with

channel

of course

we need

so

number of channel

oh each

that's

and there are no

sparse

oh