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