i think it's safer to use these microphone so my my talk is entitled fusion of innovations it's uh the the the to is very brief and the talk is very brief size i i and i will let you go pretty one um yeah i M P sending this work which is actually uh a you the bench i number uh banning tried of uh john use D who was my for student and then a post can to make T and no uh starting a new job uh and the to go authors uh dot on a all blue and uh a us so that that are and them at um so this some agency my gaze or of the the the biological agents are are humans so though a lot of the the behavior of bill i i'm trying to model in this talk uh could be applied a tree two forms of biological agents uh in fact the more of interaction is the fairly simple uh and what i'm discussing these uh uh you bought mechanism to oh feet to what we observe a when a in new innovations uh uh the many innovations and introduced in society and how this spread so um even been officially innovations but not spread um simply yeah on contact uh so i a lot of the a them weak more this so that that based on the idea that i i uh i get in contact with some agent which she's has an infectious D and automatically the through that contact that i you contract a disease uh they wouldn't hold um and the balloon capture the dynamics there are observed in these more that um so at typically actually innovation moves uh very slowly and that not reading these diffusion on a um and needs uh is slightly more complicated model but by was you we see my mother is very simple um so i the the idea ease uh the motivation is obviously of for engineers is mostly the standing how they would uh explore white all the data that we have now one social networks uh in a link that connections two and you know diffuse new product or actually to interpret what out uh would would be good uh ways of a a um and spreading ideas or new body okay so what was the what is the state of the art um as you can imagine this problem has been studied in sociology and economics and the first person to produce the model that that seem to credibly present what was going on in in the observations uh was gonna vector you on a that in the nineteen seventy eight uh wrote in uh a they basically a the they're spay better on this problem and introduce ways it more which is called a actual model for collective behavior i actually if you high but that arised that uh innovation and uh is not adopted uh simply by absurd being your neighbours but by absurd being a sufficient number of your neighbours so if you cross that that actual or of um adoption that in uh uh uh in a local class that all of or um um you uh friends or neighbours uh then you have proper to adopt the innovation otherwise you will continue to two stay with the uh all the invention and easily the ants to adopt a new ideas he's in fact up in society um so um the the group of nodes that introduces the innovation here to called the seed set in the T D L pay but it was a single a agent but uh it seems more realistic to assume that you have an initial set and they i D also is that each individual has but a different threshold do you want have to have the same for actual the cross the network um so so the model of that actually simply if a fraction of agents um which is a few you large or adopted the innovation and you will adopt a so or um um do not but that also said that these probably ease of but that more that on or of to to to capture at their if X how decisions are made or or uh a more steps but had even for these these is actually the the the contagion own contact is not necessary the best model uh and uh you know what i get behaviour in not there uh uh if X make iteration could be model like the so i i these i mean up a better that was it a bit over a well we sign of the but then uh uh the in that is in these big top um and the ninety seeks uh about and the D a number of interesting experiment that expect that the i-th actually uh at to to validate these small the that was a purely to read you got more that um so a the application was um the diffusion on all prescription there i uh the a sinus it to set the patient the diffuse of the the the the the data are option by a the doctors patient in a has system um and a but it actually a the sort of court operated these hypotheses uh are usually may my go not the gonna a there that that an actual behavior as explain what is going on um any is also explains he i of are they of a uh uh the other uh diffusion of innovations each D would flash on or new technologies um a because a similar trends were found in in in those a fee um like at on camp in into doesn't in two D and two doesn't of five um a uh to call their uh uh a a not this study uh um of these uh a problem and try to uh to look at instead of having it at that we six actual more will happen if you had that on to actual so you or sports possibly change of mood and therefore um some you what let less six test subset steve two or or your neighbours and some days you what are more step that so active to your neighbour um or or you were simply you know a little bit jet legs like M or your be an L O or or more uh a sharp and so you would make decisions depending on having more or less people around you that uh uh adopt the innovation um and can also started to do some serious and i E D got work on these problem a in this think figure a like to D than the we uh exam i mean whether that was convergence and or what was the issue of that there meaning meeting um know the the the the the the configurations for the optimal seed set the was it's but i to these you know if an across society and these was a problem a camp it looked into and he proved of for sure like the problem is np-hard at which is not very good um however uh that's subsequently to cover the problem again a in looked at uh the if fact of connect T V uh well leave the model underlying the connect D V Ds that on them graph in particular watts sees uh uh famous for the small world more they'll uh that is uh embrace by mania as a as a reasonable more for social of networks so what's this cast the value elements or of um a a a a a a diffuse on of information uh with respect to be to these small that's all the data elements of having a good model for for this source and that V D and how would that affect fact the diffusion of innovation uh in practice um so also what's not these that um all these graph connectivity be he always found that he had to had this in me to get significant mass oh any other up there if uh somehow they was like nation uh in the process then uh you would probably stop you would not have to type society all i like that um about okay but that prove that these uh that to the optimize optimization of the C D's np-hard hard they don't no either significant to results uh in fact to conduct that i the fixed point so or here this paper or does if you a a has i if you want sort a sort of um interesting results some that so then i talk more that he's a graph the agents out of the bad texas and the the edges capture or they're connect D V D and for me to the static the half door you could imagine that it would be interesting to extend these results to a stochastic have um a the neighbour her they neighbourhood be represented by these uh uh uh and i of G um um and just these are the neighbours that can in a gender i so each agent does i said has its an actual which i indicate as feel by which is a number between zero and one not i K zero i have a subset of in T V so the has that these innovation and these is the seed set and i D not these by this can be that fee zero which is obviously a subset of the to six so the global been of a doors oh oh have already been exposed uh to the innovation is a represented by this set uh and they good be also was simply the be the promoters you with a P all all mathematically the interaction model is simple um is a if uh a the a a the name in it's that if the intersection between the seats set and the initial group um is a um did F X uh the the node i is such that the fraction of nodes uh the this containing in the neighborhood be sufficiently high uh then that the i will adopt deterministic tell thickly um the innovation either otherwise Z will uh uh is training set so be do not by feel value uh uh the adopt there's at at at each iteration of these are going so we imagine that every time uh we we compute um what use the fraction all of the nodes in the neighbourhood the are part of these um i is a set of a top there and the new the group is called by if yeah and they all that all group um of adopt there's at the at iteration of these are go me simply the union a cross this set and so obviously agent i we adopt the innovation at step and a E for these you on all a adopt there's intersex sexed neighbour with a sufficient number of agent so the question is we a you know actual of i don't and if not what at the fixed point and which one of the peak peaks point will be selected to given an initial set so these is simply the mathematical so the of these i take a question you have to define an object which is called the coherence that and the coherence set i um is defined uh a um a relative uh uh um to these a particular for soul we group in a and uh and number of agents uh each agent as the fee i and we say that a a non empty subset of the where to C is a coherent set is the intersection between these site and the neighbour or bad every agent in this set is such that these inequalities matt uh in in these what you mean is that for each member of this that the the fractional neighbours the V sides in the set is the bob the agents specific so actual and so these coherence measure this coherent set essentially measure of how um how well connected are um the these these group of not so if the these is a coherent set uh you know this is what so the important point is that because of these the finish shown well how it is that the members of these uh coherent set can not adopting innovation a less for somebody's on somebody inside the set adopts the innovation so they need somebody inside to convince them they want to otherwise and this is an example so you have an i took these is the simple topology um and here i set up that that actual um in a particular way i say that for not wanting one and to that actual these point five minus a a small you C don't important porn the three four five and six if instead that point five plus some at C so here you good uh easily compute uh the coherence set uh the that in these network oh well easy he computes list take you a while because he's it can be a other a problem and there are menu coherent sets but is not a to identify them uh once you the i'd when made it possible that's of these side and for example is not need if you difficult to see they want to city for one here and set because uh you see that they all have chronic T V D uh the smaller than two um a a and is for has an L connect T V D uh a city so the you can actually uh break you P the coherence so or this is just to point out that that are menu coherent sets there not how to identify but that are many of them in the E D the be yet target problem in these it ice on aids we the fact um there was pointed out to to finding the best C is an np-hard problem so you have he relates with these aspect oh why better why the important to define coherence that because then you can define us a mean a clear way what of the fixed points for the diffusion of innovation according to that to actual model that and so given a graph thank even then these uh a actual it's um is they up not set is if you have not up this that at feast a of then you can uh be sure uh that these are top their set is a fixed point if the complement of these are their set uh is actually coherence set so that would be a fixed point okay and the pro of is very simple or uh or you just a apply the definition of coherence set to the uh uh to the complement all these set of a there's send you figured out that it it by you late it is below bill actual right uh and body uh element in fees below of actual and that is uh what motivates definition of coherence so do is the main out of this talk um and uh thank you for being so patient to a it to these uh as for a given to not graph these is what you can say about this speaks points if there is no uh feast a is a which is included in in such that the seed uh includes a dot and the complement of P studies coherent then the innovation will D fuse while out the network he instead there exist a unique feast that the contains the C the C D the initial the up there's and the complement is coherent then obviously that is the fixed point and that can also be extended uh in uh the case where this seat is actually contained in it but you'll are uh a a set feast are such that um um so what you know there was there is not a unique feast on there are many piece data and they are all uh uh a index by these substitute stick subscript I S assuming that that are K of them and the C D in one of these uh then um what happens is that the adoption of be innovation will be meted to the intersection of all these um uh these sets P start of it and these is an example so you and all this search able the here set is uh uh read that um and uh extensive is not too hard once you place the C to few your out if there is a coherent set the will be a fixed point so for the example that i uh provided before um i you have it is these uh these uh the actual does we said um which is point five minus that in for not one and two and point five plus types you on for the remaining no and if the seed node in this case not one and final adopter set a remains one and to so if uh the evolutionary is not one you're are out of luck you evolution with no i um so you will only convenes beans your next door keyboard and that would be um so these these uh this is also uniquely defined so you also know in this case uh that you want to have at all uh uh the possibly or all in discussed bidding up in a uh even more recent paper and by a at all a or simple all how we want to pronounce it uh is my in pronunciation it and two doesn't and and he published uh an article uh in the science magazine a and and i think with beautiful experiment that a is was a like experiment and i think uh again it has a network of patients uh and how they no prescription of new i practise is well if using across the to work the be you'll the experiment this the he somehow on be this fifteen and it agents to communicate with a fixed topology that he had P D their mean and he use to topologies one is a perfect a regular lattice this topology and the other one is that on number graph so yes actually D Y are uh the the the topology a that uh more war um and to all experiments he not east that's somehow how the lack teeth topology was more class that was seemingly be more effective to spread innovation then the is more words type of network was which is somewhat counterintuitive as there is out to because we have told that small what net had in fact diffusion fusion of ideas in uh and uh the six degree of separation among a a a members of society or diffusion all of information seems to to be a a by they data on them midi whiting um uh i i is suggest that that these are actually not uh um completely counting to E D uh but a standing in some cases gonna actually we can a week and the option because a may eight these school queen and set and uh was that an next then these each but apps an extreme case of that so i depends on the size of the class that that's basically the bottom line and how that size of the class the you lace the threshold which are obviously starting that chant tall up what did not really control because he was a using a real agents so the had they on actual so the only thing that he decoding control was the flash so he couldn't necessarily relate what keyed at billy how the threshold and the class size interacted that each other so the fact of class is actually uh we think not uh not to the other uh and so the the the they've finding the fact if if you'll a a complicated problem but essentially a good guideline would be to search for positions that was not a lead to have a large coherent sets as complement and that concludes my talk thank um