0:00:15i think it's safer to use these microphone
0:00:17so my my talk is entitled fusion of innovations it's
0:00:21uh the the the to is very brief and the talk is very brief size
0:00:24i i and i will let you go pretty one
0:00:27um yeah i M P sending this work which is actually
0:00:32uh a you the bench i number uh banning tried of uh john use D
0:00:36who was my for student and then a post can to make T and no
0:00:41uh starting a new job
0:00:43uh and the to go authors uh dot on a all blue and uh a us so that that are
0:00:49and them at
0:00:52so this some agency my gaze or of the the the biological agents are are humans so though a lot
0:00:59of the the behavior of bill i i'm trying to model in this talk
0:01:04uh could be applied a tree two forms of biological agents uh in fact the more of interaction is the
0:01:09fairly simple
0:01:11uh and what i'm discussing these uh uh you bought mechanism to oh feet to what we observe a when
0:01:18a in new innovations uh uh the many innovations and introduced in society and how this spread
0:01:25um even been officially innovations but not spread um simply yeah on contact
0:01:32uh so i a lot of the a them weak more this so that that based on the idea that
0:01:35i i uh i get in contact with some agent which she's has an infectious D
0:01:41and automatically the through that contact that i you contract a disease
0:01:45uh they wouldn't hold
0:01:47um and the balloon capture the dynamics there are observed in these more that
0:01:51so at typically actually innovation moves uh very slowly
0:01:56and that
0:01:56not reading these diffusion on a um and needs uh is slightly more complicated model but by was you we
0:02:02see my mother is very simple
0:02:04um so i the the idea ease uh the motivation is obviously of for engineers is mostly the standing how
0:02:11they would
0:02:12uh explore white all the data that we have now one social networks uh in a link that connections
0:02:18two and you know diffuse new product
0:02:21or actually to interpret what out uh would would be good
0:02:24uh ways of a a um and spreading ideas or new body
0:02:29okay so what was the what is the state of the art
0:02:33as you can imagine this problem has been studied in sociology and economics
0:02:38and the first person to produce the model that that seem to credibly present what was going on in
0:02:44in the observations
0:02:46uh was gonna vector
0:02:48you on a that in the nineteen seventy eight uh wrote in uh a
0:02:53they basically a the they're spay better on this problem
0:02:56and introduce ways
0:02:58it more which is called a actual model for collective behavior
0:03:02i actually
0:03:03if you high but that arised that uh innovation and uh is not adopted
0:03:07uh simply by absurd being your neighbours but by absurd being a sufficient number of your neighbours so if you
0:03:15that that actual or of um adoption that in uh uh uh in a local class that all of
0:03:21or um
0:03:22um you uh friends or neighbours
0:03:26uh then you have proper to adopt the innovation otherwise you will continue to two
0:03:32stay with the uh all the invention
0:03:34and easily the ants to adopt a new ideas he's in fact up in society
0:03:40so um
0:03:42the the group of nodes that introduces the innovation here to called the seed set
0:03:47in the T D L pay but it was a single a agent but uh it seems more realistic to
0:03:51assume that you have an initial set
0:03:54and they i D also is that each individual has but a different threshold do you want have to have
0:03:59the same for actual the cross the network
0:04:02so so the model of that actually simply if a fraction of agents
0:04:07um which is a few you large or adopted the innovation and you will adopt a
0:04:12so or um
0:04:13um do not but that also said that these probably ease of but that more that on or of to
0:04:18to to capture at their if X how decisions are made or or uh a more steps but had
0:04:25even for these these is actually the the the contagion own contact is not necessary the best model
0:04:31uh and uh you know what i get behaviour in not there uh uh if X make iteration could be
0:04:36model like the
0:04:38so i i these i mean up a better that was it a bit over a well we sign of
0:04:42the but then uh uh the in that is in these big top
0:04:46um and the ninety seeks uh about and the D a number of interesting experiment that expect that the i-th
0:04:53actually uh at to to validate these small the that was a purely to read you got more that
0:05:00so a the application was um the diffusion on all prescription there i
0:05:06uh the a sinus it to set the patient the diffuse of the the the the the data are option
0:05:11by a the doctors patient
0:05:14in a has system
0:05:17and a but it actually a the sort of court operated these hypotheses uh are usually may my go not
0:05:24the gonna a there that that an actual behavior as explain what is going on
0:05:30um any is also explains
0:05:32he i of are they of a uh uh the other uh
0:05:37diffusion of innovations each D would flash on or new technologies
0:05:41um a because a similar trends were found in in in those a fee
0:05:47like at on camp in into doesn't in two D and two doesn't of five um a uh to call
0:05:52their uh uh a a not this study uh um of these uh a problem and try to uh to
0:05:59look at instead of having it at that we six actual more will happen if you had that on to
0:06:02actual so you
0:06:04or sports possibly change of mood and therefore
0:06:07um some you what let less six test subset steve
0:06:10two or or your neighbours and some days you what are more step that so active to your neighbour
0:06:16um or or you were simply you know a little bit jet legs like M or your be an L
0:06:21O or or more uh a sharp and so you would make decisions
0:06:25depending on having more or less people around you
0:06:29that uh uh adopt the innovation
0:06:31um and can also started to do some serious and i E D got work
0:06:35on these problem
0:06:37a in this think figure a like to D than the we uh exam i mean whether that was convergence
0:06:41and or
0:06:42what was the issue of that there meaning meeting um know
0:06:47the the the the the
0:06:48the configurations for the optimal seed set
0:06:51the was it's but i to these you know if an across society
0:06:54and these was a problem a camp it looked into and he proved of for sure like the problem is
0:06:59np-hard at which is not very good
0:07:02um however uh that's subsequently to cover the problem again
0:07:07a in looked at uh the if fact of connect T V
0:07:11uh well leave
0:07:13the model underlying the connect D V Ds that on them graph in particular watts sees uh uh famous for
0:07:19small world more they'll
0:07:21uh that
0:07:22is uh embrace by mania as a as a reasonable more for social of networks
0:07:26so what's this cast
0:07:28the value elements or of um
0:07:31a a a a a a diffuse on of information
0:07:34uh with respect to be to these small that's all the data elements of having a good model for
0:07:39for this source and that V D and how would that affect fact the diffusion of innovation
0:07:45uh in practice
0:07:48so also what's not these that um
0:07:51all these graph connectivity be he always found that
0:07:55he had to had this in me to get significant mass
0:07:58oh any other up there if uh somehow they was like nation
0:08:03uh in the process then uh you would probably stop you would not have to type society all
0:08:10i like that
0:08:11um about okay but that prove that these uh that to the optimize optimization of the C D's np-hard hard
0:08:17they don't no either significant to results
0:08:20uh in fact to conduct that i the fixed point so or here this paper or does if you
0:08:25a a has i if you want sort a sort of
0:08:28um interesting results some that
0:08:31so then i talk more that he's a graph the agents out of the bad texas
0:08:35and the the edges
0:08:37capture or they're connect D V D
0:08:39and for me to the static the half door you could imagine that it would be interesting to extend these
0:08:44results to a stochastic have
0:08:46um a the neighbour her they neighbourhood be represented by these uh uh
0:08:54uh and i of G
0:08:56um um and just these are the neighbours that can in a gender i
0:09:02so each agent does i said has its an actual which i indicate
0:09:06as feel by which is a number between zero and one
0:09:09not i K zero i have a subset of in T V so the has that
0:09:13these innovation and these is the seed set
0:09:16and i D not these by this can be that fee zero
0:09:19which is obviously a subset of the to six
0:09:22so the global been of a doors oh oh have already been exposed
0:09:26uh to the innovation is a represented by this set
0:09:30uh and they good be also was simply the be the promoters you with a P
0:09:35all all mathematically the interaction model is simple
0:09:40is a if uh a the a a the name in it's that if the intersection between the seats set
0:09:46and the initial group um is a um did F X
0:09:51uh the the node i
0:09:53is such that the fraction of nodes
0:09:55uh the this containing in the neighborhood be sufficiently high
0:09:59uh then that the i will adopt deterministic tell thickly um the innovation either otherwise Z will uh uh is
0:10:05training set
0:10:07so be do not by feel value uh uh the adopt there's at at at each iteration of these are
0:10:13going so we imagine that every time
0:10:15uh we we compute
0:10:17um what use the fraction all of the nodes in the neighbourhood the are part of these um i is
0:10:24a set of a top there
0:10:26and the new the group is called by if yeah
0:10:30and they all that all group um of adopt there's at the at iteration of these are go me simply
0:10:36the union
0:10:37a cross this set
0:10:39and so obviously agent i
0:10:42we adopt the innovation at step and a E for these you on all a adopt there's
0:10:47intersex sexed neighbour with a sufficient number of agent
0:10:51so the question is we a you know actual of i don't
0:10:54and if not what at the fixed point
0:10:56and which one of the peak peaks point will be selected to given an initial set
0:11:01so these is simply the mathematical
0:11:03so the of these i take a question you have to define an object which is called the coherence that
0:11:09and the coherence set
0:11:11i um is defined uh a um
0:11:15a relative uh uh um
0:11:18to these a particular for soul we group in a and
0:11:22uh and number of agents
0:11:23uh each agent as the fee i
0:11:26and we say that a a non empty subset of the where to C is a coherent set
0:11:31is the intersection between these site
0:11:33and the neighbour or bad every agent in this set is such that these inequalities matt
0:11:40uh in in these what you mean is that
0:11:43for each member of this that the the fractional neighbours the V sides in the set
0:11:48is the bob
0:11:49the agents specific
0:11:51so actual
0:11:52and so
0:11:53these coherence measure this coherent set essentially measure of how um how well connected are
0:11:59um the these these group of not so if the these is a coherent set uh
0:12:04you know
0:12:05this is what
0:12:08the important point is that because of these the finish shown
0:12:11well how it is that the members of these uh coherent set can not adopting innovation a less
0:12:17for somebody's on somebody inside the set adopts the innovation so they need
0:12:21somebody inside
0:12:23to convince them they want to otherwise
0:12:26and this is an example
0:12:28so you have an i took these is the simple topology
0:12:31um and here i set up that that actual
0:12:34um in a particular way i say that
0:12:36for not wanting one and to that actual these point five minus a a small you C don't
0:12:42important porn the three four five and six
0:12:44if instead that point five plus
0:12:46some at C
0:12:48so here you good
0:12:50uh easily compute uh the coherence set
0:12:53uh the that in these network
0:12:55oh well easy he computes list take you a while because he's it can be a other a problem and
0:13:00there are menu coherent sets but is not a to identify them uh once you the i'd when made it
0:13:06that's of these side
0:13:08and for example is not need if you difficult to see they want to city
0:13:11for one here and set because
0:13:13uh you see that they all have chronic T V D uh the smaller than two
0:13:20a a and is for has an L connect T V D uh a city so the you can actually
0:13:26uh break you P the coherence so
0:13:29or this is just to point out that that are menu coherent sets there not how to identify but that
0:13:33are many of them in the E D the be yet target problem in these it ice on aids
0:13:37we the fact um there was pointed out to to finding the best C is an np-hard problem so you
0:13:43have he relates with these aspect
0:13:46oh why better why the important to define coherence that because then you can define us a mean a clear
0:13:53way what of the fixed points
0:13:55for the diffusion of innovation according to that to actual model that
0:13:58and so given a graph
0:14:00thank even then these uh a actual it's
0:14:04is they up not set is if you have not up this that at feast a of then you can
0:14:09uh be sure
0:14:11uh that these are top their set is a fixed point
0:14:14if the complement of these are their set
0:14:16uh is actually coherence set
0:14:18so that would be a fixed point
0:14:22and the pro of is very simple or uh or you just a apply the definition of coherence set
0:14:27to the uh uh to the complement all these set of a there's send you figured out that it it
0:14:33by you late
0:14:34it is below bill actual right
0:14:36uh and body uh element in fees below of actual
0:14:40and that is uh what motivates definition of coherence
0:14:44so do is the main out of this talk
0:14:47um and uh thank you for being so patient to a it to these
0:14:51uh as for a given to not graph these is what you can say about this speaks points
0:14:55if there is no uh feast a
0:14:58is a which is included in in
0:15:01such that the seed
0:15:03includes a dot
0:15:06and the complement of P studies coherent
0:15:09then the innovation will D fuse while out
0:15:11the network
0:15:13he instead
0:15:15there exist a unique feast that the contains the C the C D the initial the up there's
0:15:21the complement is coherent
0:15:22then obviously that is the fixed point
0:15:25and that can also be extended uh in uh the case where this seat
0:15:30is actually contained
0:15:32in it but you'll are uh a a set feast are
0:15:36such that
0:15:38um so what you know there was there is not a unique
0:15:41feast on there are many piece data
0:15:43and they are all uh uh a index by these substitute stick subscript I S
0:15:47assuming that that are K of them
0:15:50and the C D in one of these
0:15:52uh then um what happens is that the adoption of be innovation will be meted to the intersection of all
0:16:01these sets P start of it
0:16:05and these is an example so you and all this search able the here set is uh uh read that
0:16:10um and uh extensive is not too hard once you place the C to few your out if there is
0:16:16a coherent set the will be a fixed point
0:16:19so for the example that i uh provided before
0:16:22um i you have it is these uh these uh the actual does we said
0:16:26um which is point five minus that in for not one and two and point five plus types you on
0:16:32for the remaining no
0:16:34and if the seed node in this case not one
0:16:37and final adopter set a remains one and to so if uh the evolutionary is not one
0:16:43you're are out of luck you evolution with no i
0:16:46um so you will only convenes beans your next door keyboard and that would be
0:16:52um so these these
0:16:54uh this is also uniquely defined so you also know in this case uh that you want to have at
0:17:00uh uh the possibly
0:17:03or all in discussed bidding up in a uh even more recent paper and by a at all a or
0:17:10simple all
0:17:11how we want to pronounce it uh is my in pronunciation
0:17:15it and two doesn't and and he published uh an article uh in the science magazine
0:17:20a and and i think with beautiful experiment that a is was a like experiment and i think uh again
0:17:26it has a network of patients
0:17:28uh and how they
0:17:30no prescription of new
0:17:32i practise is well if using across the to work
0:17:36the be you'll the experiment this the he somehow on be this fifteen and it
0:17:40agents to communicate with a fixed topology that he had P D their mean and he use to topologies
0:17:47one is a perfect a regular lattice this topology and the other one is that on number graph so yes
0:17:51actually D Y are
0:17:53uh the the the topology a that uh more war
0:17:58and to all experiments he not east
0:18:01that's somehow how the lack teeth
0:18:03topology was more class that was
0:18:06seemingly be more effective to spread innovation
0:18:09then the is more words type of network was
0:18:13which is somewhat counterintuitive as there is out to because we have told that small what net had in fact
0:18:19diffusion fusion of ideas in
0:18:21uh and uh the six degree of separation
0:18:24among a a a members of society or diffusion all of information seems to
0:18:29to be a a by they data on them midi whiting
0:18:34uh i i is suggest that that these are actually not uh um
0:18:39completely counting to E D
0:18:41uh but a standing in some cases gonna actually we can a week and the option because a may eight
0:18:47these school queen and set and uh was that an next then
0:18:51these each but apps an extreme
0:18:53case of that
0:18:54so i depends on the size of the class that that's basically the bottom line and how that size of
0:18:59the class the
0:19:00you lace the threshold
0:19:01which are obviously starting that chant tall up what did not
0:19:05really control
0:19:06because he was a using a real agents so the had they on
0:19:09actual so the only thing that he decoding control was
0:19:13the flash
0:19:14so he couldn't necessarily relate what keyed at billy how the threshold and the class size
0:19:20interacted that each other
0:19:22so the fact of class is actually
0:19:25uh we think not uh not to the other
0:19:28uh and so the the the they've
0:19:31finding the fact if if you'll a a complicated problem
0:19:35but essentially a good guideline would be
0:19:38to search for positions that was not a lead to have a large coherent sets as complement
0:19:47and that concludes my talk thank