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