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