0:00:15so i think it's actually much for so what would like to say just so yeah the proposed a new
0:00:19and for the position of
0:00:21a special session makes a pleasure for me to be here
0:00:24oh today will talk about a but it's at the more is what most applied to this to distributed resource
0:00:30allocation problem in can be to systems
0:00:32where the communication or more the second users
0:00:35are supposed to be a a a a a a but randomly but i
0:00:41a particular we will talk about social foraging
0:00:44social sort
0:00:46these systems are typically made up of a relation simple agents
0:00:49in a a lot of locally to each other
0:00:52and that with the empire
0:00:54agents
0:00:54follow a very simple rule
0:00:56and even if there is not centralised four
0:00:59need for um and then leads to
0:01:01the merchants of one halogen original here that usually is unknown to the individual
0:01:07that are examples of course clue don't call is
0:01:09bird flocking willing
0:01:13the application of which we want
0:01:15to translate
0:01:16five is part more
0:01:18he's cognitive radio
0:01:19we know how it this case
0:01:21we have
0:01:22to to kind of the users
0:01:23primary users
0:01:25that
0:01:26um
0:01:27are the owners
0:01:28the red
0:01:29and the second are you
0:01:31these are kind of the users
0:01:33that's a sense the channel in an opportunistic way
0:01:36and trust me you local by channel
0:01:38oh have
0:01:39a second data the network used to get a dog
0:01:41so we have start
0:01:43without a central node
0:01:44that that's controlled the access to the medium
0:01:47that
0:01:47our problem is how to coordinate yeah
0:01:50from what actually many second the users
0:01:52yeah know like this central i
0:01:54a i just i mean my what condition
0:01:56then
0:01:57hence
0:01:57in this context the by some
0:01:59simple but robust
0:02:01a a fraction mechanism
0:02:03can be all real in
0:02:06in particular we propose
0:02:08at the strip of the rest are location based on board
0:02:10they they that nearby by agent
0:02:12and track beat each other
0:02:14and for so um presents a location then prevents correlations among the location of different users
0:02:20and a is crazy
0:02:22so the search of the most of robert's slot to be used
0:02:25can be modelled as the motion
0:02:26or was formal press source
0:02:28the rest of domain
0:02:30yeah
0:02:30i
0:02:31i frequency plane or the frequency a
0:02:33looking for for edge
0:02:35for a represents a actually a function inversely proportional
0:02:38the if you know level
0:02:40sense by the
0:02:42and that's work would tend to be in this time frequency region where the that's interference
0:02:47what's that is fine to be one
0:02:49i always regions
0:02:51in the location of different users
0:02:52and you might spread
0:02:53in rest
0:02:56rest of the location can be more the that as the this for like mean they of this sort of
0:03:01for word
0:03:03in particular
0:03:05i
0:03:05the knows the wrestlers that
0:03:07so that was issue
0:03:08sure sure of chosen by note i for is red
0:03:11in the rest of me
0:03:14can be in this case the entries of is back can get time slot the frequency
0:03:17chump
0:03:19second i i
0:03:20is the interference profile sense
0:03:23on the rest
0:03:24but may i know i
0:03:25so in this case the E power force there so uh
0:03:29a a firm that want to me my
0:03:31J A and J R
0:03:33represents the a function are also to
0:03:35they allowed to implement
0:03:38a features of a fraction of also
0:03:40between the
0:03:41the the rest of
0:03:43yeah J
0:03:44are the entries of an identity matrix of the graph
0:03:47this described
0:03:48special the hall
0:03:50oh
0:03:50now
0:03:51in particular
0:03:52it is good are what one word zero
0:03:55if no G is
0:03:58you is a need of one of all not that so if it is inside scoring rate
0:04:02well wise
0:04:03so it's in this case what one
0:04:05yeah yeah the wife
0:04:08it's important remark
0:04:09that's even a this is warming up guns
0:04:12you know issue
0:04:13so the secondary users are
0:04:15i'm not moving at to just the rest
0:04:17are moving in this rest to me
0:04:19these with visions a J
0:04:21the best this a supposition
0:04:23of
0:04:24so they are related to this special edition
0:04:29attraction and repulsion can be chosen instead several
0:04:32weight however allow for a simple mathematical
0:04:35they should be
0:04:36uh we have chosen a um
0:04:38um
0:04:39what for i
0:04:39from
0:04:40function
0:04:41and that is financial bound
0:04:42vol
0:04:43so that's
0:04:44the a joint you here
0:04:45okay a with respect to these
0:04:47in the rest of this assume this kind of four
0:04:49it's important to note is that there is a unique
0:04:52i
0:04:52of the a fraction propulsion
0:04:54potential actual function
0:04:56these
0:04:56mean
0:04:57is really
0:04:58to the so called it really this done
0:05:00in the biological literature
0:05:02is the distance of which a fraction
0:05:04and also a
0:05:05and can be set
0:05:07choosing rubber is good vision
0:05:09C and C a
0:05:10yeah a action at of pops concert
0:05:12what
0:05:13in in our setting
0:05:14there are also is useful to a hold collision
0:05:17between in the location of different used
0:05:19so we choose the i believe in this
0:05:21we proportional the
0:05:23this that
0:05:24in the me
0:05:26that can be and
0:05:27of the
0:05:29but
0:05:29channel
0:05:30for for for example the duration
0:05:31of the time and times
0:05:33so a the right solution to the previous problem can get you the
0:05:37for a a simple steepest simple approach
0:05:40where each no is at the position of its own wrestlers
0:05:44and the rest
0:05:45really according to the agree
0:05:47gender the
0:05:49fourteen potential function
0:05:50i shows
0:05:51four
0:05:52it's important to remark
0:05:53that these
0:05:54rule
0:05:56to be he needs
0:05:57the computational
0:05:58just not wrong
0:05:59so a lot of gradient of this
0:06:02it's five
0:06:03a to the point X i
0:06:04it well
0:06:05which we are also
0:06:07or some force
0:06:08that the rest of six i are receiving
0:06:11a a from the results of the need
0:06:14J
0:06:15it's was important from that's at the E
0:06:18each of that
0:06:18row
0:06:19information to each with neighbour
0:06:22a a a a a a the information about the position he's
0:06:25he's going to i
0:06:28this is
0:06:29whole
0:06:30they
0:06:30read red provide represents it
0:06:32a position of the psd L
0:06:35a primary user
0:06:37and and that is changing
0:06:39time
0:06:39simulation
0:06:40the we though that are moving on the
0:06:43frequency a
0:06:44represents this
0:06:45a a a a a uh uh this
0:06:46the
0:06:47i i i i and the red it is pressed
0:06:49that are mean trying to find
0:06:51a position where there is more for so less interference
0:06:55a at the same time
0:06:56so is fine
0:06:57a to require on
0:06:59a is what we see that so it's
0:07:01they are trying to keep
0:07:02this warm of a spread a small as possible and the would lead someone allocation
0:07:10but
0:07:11i'm going to present one of the main result
0:07:13you one of the more
0:07:15you features of this or with that is
0:07:18intrinsic of of implementing of the centralized make
0:07:21for sparse
0:07:22chuck
0:07:24i said before that
0:07:26basically is movement movement happens
0:07:28in um
0:07:29the in the rest of me so it's kind of a big issues
0:07:32but the communication
0:07:34between
0:07:35no
0:07:36for some
0:07:37in this part
0:07:38so
0:07:39basically
0:07:40to nodes that that actually are the course for each other
0:07:43can exchange information and can hold
0:07:46to use the same channel
0:07:48that
0:07:49to to note that that actually a far away from each other
0:07:54is no
0:07:54is not
0:07:55actually
0:07:56they don't communicate with other
0:07:58so they don't perceive repulsion
0:08:00and they are allowed to use
0:08:01same channel use the same press
0:08:03a so
0:08:04but
0:08:06or in a a a a in this example we particular we're
0:08:09to a network composed of a hundred nodes
0:08:12and with you there in just a a weighted channel of a these node so
0:08:16share
0:08:17with different colours we identified a different channels they cannot board
0:08:22where yeah
0:08:23and that's it
0:08:24as we can see it never happens choosing probably you can these
0:08:28we
0:08:29yeah
0:08:30the rest
0:08:31that's two nodes
0:08:32are are in this say
0:08:34a a rest
0:08:35but a if they are far such as far away
0:08:38and they don't have that i
0:08:43that's now everything on the time
0:08:46this is just a a
0:08:48and easy down
0:08:49where we can peaks
0:08:50the position of the primary
0:08:52i
0:08:53and the money that
0:08:54he
0:08:54where we can is are position
0:08:56to use
0:08:57is
0:08:58see
0:08:59in the middle right dots
0:09:01and uh uh we can see out is warm in to people's in for each other
0:09:06feel the gas
0:09:07let
0:09:07uh a the primary users
0:09:09and that that same time
0:09:11you might spread and would lead you
0:09:13these
0:09:15each other
0:09:16however is is
0:09:17is is how well knowledge
0:09:19primary users are you
0:09:21four and a
0:09:22at least i the least
0:09:24so what we propose
0:09:26it's
0:09:26a model of the primary users so
0:09:28if
0:09:28time
0:09:30probably in some knowledge about
0:09:32the it is some is unknown
0:09:34right
0:09:36so in particular we propose
0:09:38um that the primary users T V
0:09:40when
0:09:41channel
0:09:42can be more as oliver james and i'm
0:09:45i the right by the transition rate
0:09:48from i a lot
0:09:49um
0:09:50from i one you
0:09:52now suppose the that's this
0:09:54patients are no
0:09:55really efficient
0:09:57and it is also known the average power yeah i
0:10:00all one over a some channel
0:10:02it is possible to about
0:10:03close of four
0:10:04the
0:10:05temporal wrote it of the expect
0:10:08you
0:10:08condition it to the observation time what C
0:10:11so i i i you particular are you the channel and T what is your sense of i
0:10:16this is the expression
0:10:17of them from either
0:10:20otherwise
0:10:21we have that
0:10:22what is a portal
0:10:23use a port and because they you they allow house
0:10:26the construction the construction of a my
0:10:29all
0:10:30expected interference
0:10:32where this warm actually pen
0:10:34no okay
0:10:35for time frequency slots where there
0:10:38that's that's interference
0:10:40let that
0:10:41one
0:10:42such is fine
0:10:43the basic required
0:10:44about
0:10:45a receive S
0:10:47and
0:10:48is an example actually
0:10:50and
0:10:51in in the the expected interfere
0:10:54time
0:10:54it's use
0:10:55right
0:10:56right
0:10:57using a grey scale
0:10:58so it you can of the time
0:11:00here is
0:11:01i think people to zero
0:11:03we have to these joint
0:11:05um
0:11:06yeah yeah easy
0:11:08is it that
0:11:09a right by the right
0:11:11three his joint
0:11:12uh uh actually um
0:11:14i
0:11:15or for by the dark
0:11:17area so there areas
0:11:18where it is more
0:11:20right
0:11:20more
0:11:21and
0:11:22as as we can see this work
0:11:24from the initial position
0:11:26the fine read location
0:11:27and so the rest of this fine i a location
0:11:30close that was in in time
0:11:32where the prediction of the variance
0:11:34so is better
0:11:35on one i usually at of spectrum
0:11:37what is be satisfy
0:11:40force
0:11:40it it required
0:11:41about
0:11:43to each
0:11:43yeah
0:11:46in particular at this whole we fall i i four was
0:11:49all the fact that really stick channel
0:11:52i
0:11:53have
0:11:53on this
0:11:54or procedure
0:11:55so that that
0:11:56that feeding in position or some my
0:11:59i is question so it can this work out that you've the solution
0:12:02even in the presence of such random in practice
0:12:05some of the no
0:12:07we consider a particular to so to make
0:12:09no
0:12:10a round of a remote
0:12:12so we model the graph
0:12:14right in in rash
0:12:15i'm the users as a random graph
0:12:18so
0:12:18considering that large
0:12:20my
0:12:20right
0:12:21row yeah this sequence
0:12:23of a laplacian matrix
0:12:24where we uh can be decomposed the sum of the next i R
0:12:29the right
0:12:30row
0:12:30and
0:12:31is a sequence
0:12:32zero we i
0:12:35moreover
0:12:36we consider that
0:12:37each you are not communication channel uses a you
0:12:40either
0:12:41a into them is a zero means
0:12:42and
0:12:43uniform stupid
0:12:44ever
0:12:45you particular or however condition and and he is one errors
0:12:49i
0:12:50and the how how it happens
0:12:52what's so for consensus on
0:12:53it it can be once the convert
0:12:55are
0:12:56so what would you throw but
0:12:58we consider it a proposition
0:12:59which allows
0:13:00they but decision error with some use
0:13:03a statistical properties that we
0:13:05for to program
0:13:08so
0:13:09substituting in the expression on uh of the but i'm version
0:13:13forming out
0:13:14we we can write a partial in this way where now
0:13:18visions
0:13:19that
0:13:20right
0:13:21things
0:13:22the and pay
0:13:23because they are read station
0:13:24random bar
0:13:26and the ne K and that's O K A are now that to contribution
0:13:30a quantization noise
0:13:31and of
0:13:32uh
0:13:33and one of the
0:13:36so a now on the for
0:13:38of the function G of try out function G
0:13:42yeah a or of
0:13:44they then now
0:13:45of the overall system be expressed in compact for you know we and way
0:13:49for this he
0:13:50can be re than
0:13:51and the written as the sum
0:13:53oh but that there is a function of are that depends on the me graph
0:13:56on the spectrum
0:13:58and are are a function yeah
0:14:00that the base actually on the
0:14:03a random vectors
0:14:04and on the contribution of quantisation noise
0:14:08um
0:14:09what so what they do of the day what you want to say is that is where we got it
0:14:13can be seen people uh
0:14:15are a bit more also think approximation procedure
0:14:17and find its so if their basic function are
0:14:20with but you is met at each time he's
0:14:23and this brought by
0:14:25random
0:14:26yeah
0:14:26so what proved
0:14:28is that giving this competence
0:14:30which
0:14:31that
0:14:31these are quite common
0:14:33think
0:14:34additionally
0:14:35a a a sequence that satisfies
0:14:37addition
0:14:38for
0:14:39in english
0:14:40sides
0:14:41that
0:14:42we can assure also
0:14:43number
0:14:44oh
0:14:45that's what we got
0:14:46a a so it's probably one
0:14:48basic well
0:14:49all
0:14:50they
0:14:51a of this work out we with a very to this
0:14:54so we set E
0:14:56and a social solution set composed of
0:14:58zero
0:14:59of these that their function
0:15:01ah
0:15:03at the rest of course on me
0:15:07now a a relation to show
0:15:11mary
0:15:12but it you power
0:15:13a results
0:15:14so we can see there's more me
0:15:16frequency domain
0:15:17present
0:15:18five
0:15:19so of course in a really communication scenarios i
0:15:22maybe there
0:15:24because of
0:15:24but
0:15:25not
0:15:26so we consider a these where they runs but it's are problem
0:15:29without requiring sort transmission
0:15:31and source you find the right the face
0:15:33all uh each no
0:15:36in the figure we show that be if you're of the normalized
0:15:38simple
0:15:39but
0:15:40with respect to the iteration in
0:15:42four
0:15:42if if to what to establish a
0:15:46a mission
0:15:47read read is the i case
0:15:48green zero point than i zero point seven zero
0:15:51fine
0:15:52as we can see big vector
0:15:53but that that the call
0:15:55yeah
0:15:55as will always reached
0:15:57we a shown that the and don't expect
0:15:59row
0:16:00oh that are what we can see is that to reduce it will be a stuff should actually
0:16:05the network requires a longer
0:16:07to reach the final
0:16:10so
0:16:11we propose this this through with the resource allocation strategy
0:16:15me
0:16:16the
0:16:17for two if
0:16:19this form and
0:16:20a we you an S you know what fraction of also forces
0:16:24a
0:16:25to the Q five
0:16:26a was lost
0:16:27use
0:16:28what would be put i'm second the users
0:16:31you particular each node is supposed to be able to and only to nearby ones
0:16:35and this problems
0:16:35intrinsic capability
0:16:37to provides also used
0:16:39channel
0:16:40to a real
0:16:41for
0:16:42and
0:16:43at the end we have seen that the method is also about a packet drops
0:16:47with that that is only to slow down to convert
0:16:52can
0:16:53i
0:17:04or
0:17:08uh_huh
0:17:09well well what we have a a a a a a kind of a simulation all
0:17:13a we what we what we what we do
0:17:15select
0:17:17and
0:17:18press
0:17:18large now
0:17:19okay
0:17:20comp
0:17:21to
0:17:22and no so that the for a mean it will not and
0:17:25with
0:17:26channel
0:17:27of course
0:17:27we need
0:17:28so
0:17:28number of channel
0:17:29oh each
0:17:31that's
0:17:31and there are no
0:17:33sparse
0:17:39oh