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>> Very pleased today to have Danny Bassett joining us from the University of Pennsylvania Jan good returning to physics and state then ph the University of Cambridge did a post-doc down that received California Santa Barbara has one list of awards too long to mention all the expected and a young investigator work for the family agency as well as Sloan MacArthur Fellowship center and whatnot you can go look up the impressive list on some of that I've admired for a long time in her work bringing the mathematical in here and tools that work science together in.

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Thank you. For. Your actions so I'm supposed to hold this here for the audio recording that you won't hear so I'm going to very awkwardly stand here talking to the microphone for the next couple minutes so the topic of my talk will be networks thinking of themselves and what I'm going to try to do today is to give you a pretty broad picture of 3 different arms of research in my lab that are interested tainted in what I think is an interesting way and I'm going to going to try to.

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Convince you of that as well but before I do that I want to start with a really very broad question to get a situated in the high dimensional space of thinking about and ask the question What is knowledge and obviously from this set of pictures that I faced here you have an indication of maybe what I think knowledge is but when you see here the terminology might have something quite different in mind but I think something that might be common across all of our definitions of knowledge is actually very well articulated in this quote from John Dewey in his democracy and education where he says Knowledge is a perception of those connections of an object which determine its apply Kabila T. in a given situation thus we get a new event indirectly instead of immediately by invention ingenuity resourcefulness and ideally perfect knowledge would represent such a network of interconnections that any past experience would offer a point of advantage from which to get at the problem presented in a new experience there are many points about this passage that I like but the point I want you to focus on specifically is the fact that he immediately calls out that knowledge is composed of many connections and in fact and ideally perfect knowledge would represent such a network of and interconnections that you can actually make new decisions based on that knowledge so an open question that we ask in my lab is.

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How is it that we gain. This knowledge network and I think intuitively if you just sort of sitting over coffee or over a beer later in the evening you might think of 2 ways in which humans gain knowledge networks the 1st one is obviously just by curiosity you're curious about something you go seek information and then you find it you add that to your knowledge network and again do we agrees with that he says curiosity is not an accidental isolated possession it is a necessary consequence of the fact that an experience is a moving changing thing involving all kinds of connections with other things Curiosity is about the tendency to make these conditions perceptible.

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But curiosity in sort of self-motivated information seeking is not necessarily the only way in which we gain a network of knowledge another way that we gain a network of knowledge is actually by example and in order to illustrate that for you I'm going to give you an example.

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So this is a passage that's actually from Robert MacFarlane's book called Landmarks where he talks about one of his mentors that really was very meaningful in his life the mentors name is Roger deacon who was an English writer and documentary maker on waterways and he invites Roger to the University of Cambridge which is where he is currently studying to give a talk to all of the faculty at Cambridge and he's very much hoping that his mentor shows the sort of the stuff that he values and represent believes that this person represents but unfortunately what actually happens is this and so this is what Robert McFarlane says as he's listening to this talk from Roger Deacon his mentor I stared dedicatedly at my shoes embarrassed that my friend was failing to perform in front of my academic peers it was only later that I realized it wasn't a failure to perform but a refusal to con form Cambridge seminars I expect rigor and logic from their speakers a braced subtlety of exposition and explanation tested proofs of cause and consequence but water which was Roger subject doesn't do rigor in that sense and neither did Roger though his writing was often magnificently precise in his poetry for Roger water flowed fast and wildly through culture it was protean it was slip shape and so that was how he followed it in his lecture.

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Shipshape slipshod and shipshape at once moving from a word here to an idea they're pursuing waters influence too fast for his notes or his audience to keep up with joining his watery subjects by an invisible network of tunnels and drains and so what Raj Robert is actually indicating here.

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Or is that Roger's lecture showed by its actual architecture or the flow of thoughts in the lecture it showed the actual. Top a logical signatures of the content that he was actually trying to describe so waterways itself the way that he walked through those ideas is the same way in which water passes through the U.K. landscape and so this idea indicates to us that he is showing by example the content the architecture of the content that he has in mind so that obviously makes me think well let's think about lectures in general as a walk through a network and maybe the lecture architecture differs depending on what you're studying or what you're talking about so U.K. waterways may have this sort of much more fluid shape to them with many holes in sort of large torturous curvatures a lecture on linear algebra this is obviously a generalization but perhaps a little bit more structured than a lecture on U.K. waterways and finally lectures in history let's focus up here at the top left perhaps they have more linear structures to them because you follow history as you walk through time and try to explain and understand why something that happened previously guys what happens next in a more linear form.

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So this motivates the question is there an optimal way of walking through a network in lectures or in books or in the papers or grant proposals that each of you is writing yesterday today tomorrow. OK So that sounds a little bit abstract but I want to make it more concrete So let's focus on this is this specific question let's imagine that I'm standing in front of a class of undergraduates at Penn and I'm teaching a set of topics let's say there are 15 ideas that I want to translate and those 15 ideas are related to one another in a pretty heterogeneous way like this OK so here are my 15 ideas.

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And I'd like to translate that picture to undergraduates in my lecture I have to translate this object linearly because time is one dimensional and you need to also a big question is how do I take this potentially high dimensional object map into the one dimension of time so that the people on the other side can optimally reconstruct what that network actually was to make that a little bit more precise concrete again let's imagine that this is the brain of the speaker or writer so this is you you have your ideas that you want to translate you have to map them into the one dimension of time because you can only pass through one concept at a time whether you're speaking or writing right in any of our communication that we that we often use and you do you want to do that in such a way that the person the listener or the reader of your ideas can optimally reconstruct what that potentially high dimensional object was.

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So an interesting question is what is a good walk through this network one potential definition is that it minimizes the reconstruction error or maximizes the perception of the accurate perception of the initial network typology OK so let's build a behavioral experiment where we can test this kind of learning and this type of reconstruction and mapping in humans.

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So we're going to do here's our network here are the individual nodes on the edges inside of the network what I'm going to say is that each node in this network is a specific stimuli and that stimulus could be a word an image or a movement and then every edge inside of this graph indicates an allowable transition between nodes and allowable temporal transition I'm allowed to go from.

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Number 9 to Number 10 but I'm not allowed to go from number 9 to number 4 because there's no direct edge between them right then what I'm going to do is I'm going to construct a sequence of stimuli by taking a random walk on this graph only obeying the edges that actually exist not traversing any edges that don't exist so it's just a stream of stimuli like this and then in order for me to understand how humans are responding and get an indication of whether they're capturing and understanding the network architecture I have a particular task that they have to perform on either each stimuli or a certain set of stimuli so they're going to perform a task and then their time to react to that task will be a measure of how well that edge in the graph was learned.

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So here's a very simple example of how to put that into a laboratory experiment with humans imagine that I have and this is what we actually have here's a human hand on a laptop keyboard Here's a stream of stimuli and those stimuli are taken as a walk on a graph the actual graph that we're using is this same graph here and the stimuli here has 5 buttons are 5 boxes that indicate which one to press so this says press the 5th button next press the 1st and 3rd button press 3 and 4 press 5 press 2 right and this stream of commands is drawn from a random walk on the on the graph where every node in the graph is a movement.

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Right so what do people actually do here is their reaction time of human participants as they are asked to perform this probabilistic sequential motor learning task what you see is on average a fairly swift reaction time to nodes in the graph that are inside one of these clusters and a striking slowing of the reaction time on edges that cross the boundaries between 2 clusters.

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Yes. That's a good question probably. I want to say it's about 10 percent. So about 10 percent of one seconds I think I have a figure later that I'll show you that will give you an indication of that. But what I want you to notice is the slowing but I also want you to notice why it's surprising because it might initially seem as if that's maybe not surprising the reason that it is actually quite surprising is that this is a very particular kind of graph so if anybody is thinks a lot about graphs you might notice that this is a K. for regular graph so every node inside of this graph has exactly 4 connections so you can look at here it has 3 connections internal one X. turn on any of these have exactly 4 connections coming out of them which means if I'm taking a random walk on the graph that every edge is traversed an equivalent number of times in the limit as time goes to infinity and the transition probability on any one of those edges is 25 percent right I'm sitting at a node and I have a 25 percent chance going here 25 percent chance of growing here here or here so it's very surprising about this is that people are slowing here when they don't when they shouldn't necessarily if they were accurately predicting the probability with which they would see that edge occurring.

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So the striking slowing occurs at the cluster boundary is indicating to us that what they are perceiving is not necessarily the local contact of any but this growth structure of the fact that there are 3 different clusters in here and then they are interconnected by these cross cluster edges.

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Now over the since we actually showed this particular fact where you have very swift responses inside of one of these clusters and slower responses between the clusters We've also asked the question of well what if we had shown that seems sort of information but on a different graph architecture and is it possible that some graph architectures are more learnable than others and where by learnable I mean that they will induce a swifter reaction time or people will show a swifter reaction time to those graphs so we explicitly compared what happens when we study a modular graph versus when we show a random walk on a lot of graph like this and what we see on average is that the reaction time to the modular graph is significantly lower than the reaction time on the lattice graph even if the stimuli or the commands are exactly the same so what that suggests is that the graph typology perhaps is important in learning ability of an architecture now you're probably wondering what is it that individuals are humans are thinking that's certainly something that I've been wondering and why would it be that we would see this this soloing at the cluster boundaries even though the transition probabilities are exactly the same they're all this 25 percent chance of occurring.

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I think what is happening in this is our hypothesis is that they are building expectations about the network structure by remembering what just happened to create some sort of expectation of the transitions that they're likely to see. So let's make out a little bit more specific here is a person in the experiment this is at time T. plus one and then this is the stimuli that they saw at time T. right so in order for them to build an expectation of transitions they have to always remember 2 things One is what is happening right now or they have to realize what's happening right now and remember what happened just before.

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So we could say that their probability of recalling X. T. minus delta T.. Is perhaps nonzero instead of actually remembering what exactly happened so in other words if. If they don't have a perfect memory or have been distracted by something that they have been thinking about they might not remember exactly what happened just before but what happened to before or 3 before or 4 before or 5 before and how long potentially they were distracted or how poor the the focus is now so what we can do and I put the link down here this is a pre-print that IS ON ARCHIVE if you're curious to work through the actual theory behind it but I'm just going to give you the high level version of it now for purposes of time but what we do is that we call on the free energy principle to suggest that the brain minimizes the errors in the predictions but also the computational resources that are required to make their predictions and that balance gives us a very simple distribution with an inverse temperature parameter beta here and I'm going to show you exactly what that gives us in terms of their predictions of the graph architecture So here's the person again and what you see is the probability of remembering what happened just before now if you were in 1st temperature parameter beta goes to 0 then you have an equal probability of remembering anything that happened in the experiment up till this point OK So this is this means that what you're building in your expectation of the graph is a fully connected network you anticipate that any of these transitions are possible and equally possible OK Right that's what happens if you have no memory and that obviously minimizes mental resources right you don't have to remember anything for that prediction on the other hand if you have a perfect memory your beta goes to infinity and you have that gives you a delta function right here at 0 what you have is a perfectly accurate prediction of what will happen what just happened and then you build a perfectly accurate prediction of what the network architecture actually is and that's this here which is the exact graph that we had shown the human participants.

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But we actually don't see very many people who have either this effect or this effect what we actually see. Is something much more like this so when data is close to one you have a high probability of remembering what just happened but you you have a non-zero chance of remembering what has happened previously and that that probability of remembering something in the past sort of decreases with the age of the information right so something that happened at the very beginning of the experiment you're unlikely to say is predictive of what just happened.

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And what happens there and if you have this. Big to go around one is that this is the expectation that you have in your head so you have a high expectation of following along these edges that had occurred recently in time and you have a decreased expectation of these edges which occur more intermixed at longer time intervals in the experiment and this is this prediction is exactly consistent with the reaction time difference that we see in the humans the actual human participants so that suggests to us that they are pretensions building a prediction in their head of what the architecture actually is and that it depends on the top logical distances inside of the graph Now if that's true yes yeah exactly.

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That's a really good question I mean I don't know what space means in this case because it's just a single stimulus that's 5 buttons and you're pressing that what it says right and then and then as soon as you do that there's a number another stimulus and then another so this 2 dimensional representation what.

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It was nothing special about the stimuli though so I don't know or is your question really about space versus time or is it did you remember what just happened or can you perceive what's in front of you right now because those are slightly different. Yeah yeah yeah that's a good question and I don't know if there's an exact I'll have to think about whether there's a good experiment to probe those 2 I think because the stimulus is right in front of them it's unlikely that they're not perceiving it but I'm making that as an assumption and I think it's more likely that they're forgetting what just happened and but again that is an assumption so I think it would be interesting to think about tasks that would help us to distinguish that yeah.

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So the actual graph that we showed people so that where this the stimuli were drawn as a random walk on this graph but this picture I'm showing you is basically the predicted. Probability transition probability that we think the human has in their mind so that's not what we showed them there is actually a disconnect between what we showed them and what their behavior seems to indicate to us that they are perceiving No These ones are just predicted this is sort of the picture in their head if you.

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That's right yeah yeah but it does make it I think that's an important point and it and it suggests if this is a picture that they have in their head. Of their and their interests a page of what is coming next inside of the stream of stimuli then we can make a prediction in a new experimental context so specifically what we did is that we now showed a separate set of individuals a ring graph like this what we didn't show them the graph we showed them a stream of stimuli and commands from that ring graph and then we asked the question if every few stimuli we thought we threw in a violation of that graph are people surprised because if they are then that indicates to us that they have an implicit perception of what this is even if they can't.

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Tell us with words that this is what they they are perceiving so we threw in 2 kinds of violations so a violation that's only one hop distance away to hop distances away one hop distance is a no violation too distant distances is definitely a violations there is no connection from the white node to the blue one or we could have a violation which is the white one to the red one and so that should be particularly surprising so our prediction was that they would definitely be surprised indicated by a slowing reaction time if we show them white to blue and that they would be even more surprised meaning even slower reaction time if we show them white to red so here on the Y. axis is their change in reaction time if we show them a short violation versus no violation I want you to notice that this is greater than 0 significantly so that indicates to us that yes they slowed down when they saw a via an edge that was a violation and then here is a long violation versus no violation again significantly greater than 0 and then this is a long versa.

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Short and so again you can see it this is greater than 0 meaning that they slow down even more when you violate their expectations by a longer hop on the graph that was not expected so this is indicates to us that this architecture of the stimuli even though they're just seeing a stream of stimuli they're able to perceive were they show by their reaction times that they have some understanding that this is a ring structure that gets violated All right so humans are surprised by stimuli far away on the ring rather than closer indicating their implicit perception of the network topology so that has led us to a couple questions that we're trying to tackle in the next couple months slash years as these things go number one is when we employ these put pop processes of graph learning not just in the motor context we also have some data in the visual context and we're moving into concepts and words now they're quite interesting question is as we as we learn the is graphs in the world around us do we end up ever forming gaps inside of knowledge spaces and if we do what do we do with those knowledge gaps we have a paper that just came out this year by an Sizemore in the group in case you're curious about what these knowledge gaps look like and and how frequently they occur and why we've also been asking the question What is the optimal you learn about graph I told you that a modular graph tends to lead to swifter reaction times than this lattice like graph but the question is as you know those are just 2 potential architectures the possibilities for the number of architectures of this size and of larger sizes is massive Is there a way for us to identify what the optimally learnable graph is and then potentially I mean this is down the road use that architecture to inform the way that we present concepts in a classroom setting for example.

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And then lastly do different humans prefer to learn information on different graph architectures do some individuals prefer a graph architect information presented on modular structures and some individuals prefer information presented in a different organization what would that what would that mean. So this potential dependence of graft learnability on the specific human that is learning makes me think of this passage from Alexander Pope where he says there are some peculiar in each leaf and grain some unmarked fiber or some varying bean show only man be taken in the gross granted but as many sorts of mind as moss which is a sort of motivation of the fact that we can't actually treat every mind as the same every mind is actually different and an important question for us to ask is how are those differences reflected in their behavior but also where where do they draw from in terms of the biology of the brain so much of our work over the last few years has been focused on that question what is it about a certain specific brain and how it learns that allows for a particular feature of behavior.

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And specifically in the context of learning graphs were very interested in the question of what features of the brain might support the learning of graphs themselves either in words and images or in movements and then my differences in those features explain differences in the ability to learn so very early on in the lab and actually even before the lab existed we ben we went back to the drawing board and asked the question of Is there some future of architecture inside of a human brain that should make it most adaptable and most ready to learn in a variety of different contexts and as we were thinking about it we thought well there's clearly a very common refrain in the literature and evolution in development in biology more generally and in earth science pacifically that modularity of an organ or a system is something that allows for adaptation of that system over both short and long time scales so that's true in terms of the structure and morphology for example of.

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The be so Darwin finches but it's all. Also a concept that we can actually quantify in the organization of the human brain and we can do that in a quantitative way using tools from network science to identify modular architecture so we started by asking 2 pretty simple questions our brain networks actually modular number one and then number 2 does modularity help us to understand large scale signatures of adaptation and learning at this very very large sort of system scale the way that we have answered or tried to begin answering that question is to start with imaging much of our work it has been focused on using F. M.R.I. data although we also use data and I mean she is well actually show a little bit of data later in the talk.

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But we let's imagine that we start with some newer imaging measurement and then we have the human brain we parcel it it usually in to between 201000 different anatomically defined units and then we measure using this imaging technique the regional activity time series from that area then what we do is that we ask whether 2 regions of the brain show a similar pattern of activity as a potential indication of interaction or shared response to an external stimuli or potentially communication.

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Not all of those things are necessarily true for every measurement of functional connectivity. What I'm showing you right here is just an example which is based on a wave that coherence and this is using a partial ation of the brain into 112 different brain regions what this indicates to you is the strength of the way the coherence between region I and region J. in a given participation of the brain and using the time series from a given type of measurement so this is the sort of approach that we use to ask the question of whether the brain shows modularity and not just my lab but many other labs across the country and in fact the world have shown over the last couple years that there is very strong modular organization inside of the networks constructed in this way so here what you see on the right hand side is the brain both a lateral surfaces of the human brain and the media all surfaces of the human brain and then on the left what you see is regions of the brain as circles and then as connections between regions of the brain indicate a particularly strong level of this measurement of functional connectivity this picture we have actually threshold of the Matrix Matrix Excel Fiz has non-zero values in every element of that force simplicity of visualization but in all of the analysis that I'm going to show you we use the fully connected weighted graph not a binary version of it so this is just for for use a visualization here.

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I want you to also notice that the color coding is consistent across these 2 So for example these blue regions here are all in a visual cortex and they're relatively specially localized but I also want you to notice that there are regions of the brain that tend to form these network modules that are not specially localized So notice this red one here is composed of regions in post here prattle cortex in Superior frontal cortex and also region.

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In the midline as well so very very spatially distributed so there's not necessarily a simple rule that if you're especially close to another brain region you will have strong functional connections with them. So yes the answer to our 1st question is yes absolutely the system shows modularity. But then the next question is does that modularity matter for adaptation and for learning in this particular system so because this signature is so strong and so consistently observed across laboratories across different humans and across even different clinical populations and ages we decided to focus on what is it about this architecture that might change as a function of time and behavior so what we did is that we actually use a for the people who are really interested in the computational aspect we use what's called a multi layer modularity maximisation approach which is a community detection method that's developed for networks and specifically for networks that evolve in time so what you do is that you take each of the adjacency matrices which gives you the pattern of functional conative ity in the brain at a given time window and you connect it up with all future adjacency matrix using this big multilayer network.

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Format and then you apply a really nice algorithm to identify where the modules are and how they change the function of time in this multilayer system what we find is that is is pictorially shown at the top here. Just to simplify again the visualization what you see is that the modular modules of the brain stay consistent throughout time roughly but what changes actually is the intersection or the interactions between different modules and I One feature of these experiments that I particularly want you to focus on is.

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Shown up here in the very top node in this graph so notice this one. Node right here it has strong connections to the peach module initially but then over time it grows stronger and stronger connections to the yellow module and eventually has only very weak or not or 0 connections to the PH module so this is an indication of a change in the allegiance of a region to functional modules in the brain what that means is that the activity profile of that region has changed significantly over the course of the experiment so maybe initially it showed similar patterns of responses to the other regions in this speech module but by the end of the experiment it shows similar responses to the task as what is shown by the other yellow regions OK This actually happens very frequently in all of the experiments that we have studied and it also seems to happen particularly frequently in regions of the brain in frontal cortex and in parietal cortex and what we have actually seen over the last couple years is that flexibility particularly in front on Pradel cortex is predictive of individual differences so across human difference is in visual motor learning in cognitive flexibility in working memory performance particularly a 2 back the cognitive flexibility was measured by a trails B. score for the for those for which that makes sense and then it's also predictive of learning rate.

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We've shown over the or just this past year that we can also predict future learning based on this notion of sort of flexible modules and I'm going to show you just one slide from that study to make these ideas a little bit more concrete So what we predicted by the earlier study is that if you have relatively flexible boundaries between modules then you're able to adapt and learn more swiftly would suggest that brains that have very very strong connections between modules are potentially more constrained dynamically whereas those that have relatively weak connections between modules are those that can display more flexible dynamics over the course of a learning experiment so to test that prediction what we said is let's take 5 minutes of spontaneous or if you're if you're an animal person spontaneous activity if you're a human person resting state scan Let's take 5 minutes of that intrinsic activity before a person has ever started learning and the task and let's ask whether from the modular structure of that spontaneous recording we can predict how much they will learn in the future and this is a discrete sequence production task so it's a motor learning task that they learned over 6 weeks of practice so here's data from 5 minutes before they started a 6 week regime of training.

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When we ask this question for people who have the more strongly connected modules we anticipate that they would show weaker learning and for individuals who have more of the structure would we would anticipate better learning So here's the learning rate over 6 weeks of practice this is the exponential drop off in movement times that's the time it takes them to perform these sequences these motor sequences and here is the contact of any between the visual and motor cortex and what you see is that stronger connectivity is related to weaker learning and lower connectivity is related to higher learning and again this is 5 minutes arrestee before they started practicing so that suggests to us that this notion of modularity is not only present in humans and not only does flexibility in that modular structure during learning help us to understand behavior but actually you can use that same theory to predict behavior in the future to some degree obviously there's still a lot of scatter here so there's more to do but we're excited about the potential here.

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Now I want to ask the question of whether or not that flexibility can be pushed around if it's useful for learning and if it's correlated with working memory performance and cognitive flexibility is it something we could move is it something that we could potentially enhance could we intervene in individuals who have just had a stroke and enhance flexibility at this scale to encourage rehabilitation more swiftly for example.

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Obviously there's a lot those are very very hard questions to ask whether they're open questions that we are excited to ask the 2 studies that we have performed to ask the question of could you move this around a little bit are shown here on the left hand side we show whole brain facts plex ability of individuals who are either taking a placebo or taking dextromethorphan which is a bit of a muddy drug but it is known to at least show some amount of advocacy in being an M D A receptor antagonist suggesting that it alters the senatorial inhibitory balance in the brain and what you can see is that on D.X. am the flexibility of the whole brain system is increased in these healthy subjects 41 healthy subjects and this is data from this Braun paper in 2016 is in collaboration with Andreas Meier Lindenberg and hike a toast to the essential Institute of Mental Health in Mannheim Germany.

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The other piece of data that we have is from the battle 2016 paper and that is all shown on the right hand side where we actually see that daily variations in brain flexibility are correlated with positive effect so the more positive effect on a given day within a single subject the higher the brain flexibility that's also modulating by fatigue and by a Rouse will.

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So that suggest to us this is a more correlate of a fact but it suggests to us that possibly there could be interventions that alter these points that would then alter the causally alter the brain flexibility that's not something we've proven with this data but it is a correlate of effect that motivates.

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A intervention study to potentially push the flexibility around our rate but before we get too excited about pushing flexibility higher and higher and higher I wanted to show you this fact which suggests to me that actually the relationship between higher order cognitive function specifically in the in the sense of cognitive flexibility working memory and learning rate on several different tasks is an inverted U. shaped curve.

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This is hypothesised this is clearly just drawn by me. So the day of the data sets that we have so far and that we've published indicate that flexibility is certainly increasing in development between the ages of $8.22 it's also increasing with positive mood and we can definitely push it up by rate and in indefinitely in a healthy individuals and in the in the kids as well what we see is that higher flexibility is correlated with better cognitive performance particularly on these sort of higher order tasks but I also wanted to mention that over here we've been studying individuals who have schizophrenia and also Also relatives of people with schizophrenia and what we see is that individuals with schizophrenia have higher flexibility than healthy controls we also know that people with schizophrenia have decreased executive function cognitive control working memory performance and many other things but specifically those so that suggest to us potentially that we're dealing with something like this which is inverted U. shaped curve and what we're hoping to do in the next couple months last years is to fill out this whole curve so we can really understand what is it about flexibility and up to what point is it useful and then how is it altered and how does it.

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How is it comprised in people with schizophrenia that differs and it may actually be harmful for cognitive function so that's sort of open questions there. All right so I wanted to leave you with one last piece one last idea. I want you to notice really quickly that both brains and these easily learnable networks that I talk to you about have modular structure and that's pretty curious to me I'm I'm curious about whether the architecture of an optimally learnable network is a top a logical reflection of the optimally developed neural network and is it important or is that just sort of happenstance could it tell us something about computation in the brain I don't know but I think these are questions that potentially are worth asking and that reminds me of this piece from Aristotle which motivated the title of the talk today where he says mind thinks itself because it shares the nature of the object of thought for becomes an object of thought in coming into contact with and thinking about its objects so that mind and object of thought are the same thing now.

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Obviously what Aristotle had in mind when he thinks about what mind does when it interacts with objects or stimuli in front of it is potentially quite different than what we as neuroscientists think about what mind does when it has objects or stimuli in front of it but if we were to ask the question what does becoming really mean to a neuroscientist So what does the mind do when it has an object of thought in front of it I think we have to go a little bit further than these.

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Studies that I've shown you before and really have a better understanding of what happens when the mind contemplates something but even to answer that question we have to go back even farther and ask the much more basic question of how brains responds dynamically to any external stimuli and how might this reconfiguration of the functional networks that I've just been talking about be driven Is there a perturb of a signal that's responsible and how is it propagated and that set of questions has motivated for us a whole arm of research where we're focusing on trying to understand when a region is stimulated or when it becomes particularly active How does that activity flow through the rest of the network and as the network architecture constrain the flow of that activity.

[00:44:34]
So in other words what we're trying to do is to understand what is it about the structure of large scale connections in the in the form of white matter tracks in the human brain mean for how activity can be confined in response to stimuli can flow through the system and change the functional network organization so if these regions become active where I'm showing these arrows How does that change the amplitude of not just those regions but everything else that they are interconnected with and can we understand something about the constraints that this architecture imposes on these dynamics OK so we've been formalizing those questions in the context of network control theory and this is a very in order to think about in our control you have to stipulate not only what the network is which in this case is the structural wires the white matter tracks connecting different parts of the brain but you also have to specify what a model of dynamics because that's what's going to tell you how the activity flows through the system right now when you're talking about dynamics in a brain there are many wonderful models of dynamics I'm going to start with a very simple list model that you could possibly think of I think if you have a simpler model please let me know but I think that this is probably the simplest one that we could imagine and that is where we have the state of the brain at time T. plus one being equal to your structural connectivity is a weighted adjacency matrix that's directly drawn from the pattern of white matter in the human brain times the state of the brain at time T. and then plus some control so here is your control energy injected at time T. and that's being injected into regions so our this is a one year discrete time and time invariant model it's also noise free so it's going to put that out there too so this is very a relatively simple model what we would like to do is to understand in this very simple model can we say something meaningful about the constraints that this piece imposes on the kinds of dynamics that we will observe.

[00:46:42]
We can do that in 2 ways we can study the actual controllability grammarian of the system and we can extract several different statistics that allow us to quantify whether the impulse response of the system and that's measured by this notion of average control ability or we can quantify notions of how you can push the system into very distant states on the energy landscape versus nearby on the energy landscape I'm just going to go through this quickly because of time you can also ask the question of if you know where the brain is right now and you want to push it to a very specific next state can you write down this cost function to say let's identify where we should be injecting energy to push the brain from this state to that state what does that mean and can we see evidence for that kind of model in.

[00:47:33]
Human brain dynamics as well plus of the tools that we are using but the data that we've initially acquired is to use the model to try to understand cognition and development and then to extend that into exile Genest stimulation in cognition and development we have shown over the last couple years that different brain regions have more or less power to alter whole brain dynamics and in fact the regions that are very well it will to push the system to distance states are those that are important for executive function and cognitive control.

[00:48:05]
We've also shown that the capacity for brain regions to change dynamics grow as children develop this is a study where we have 882 children from the ages of 8 to 22 and we show increases in these 2 types of controllability we also show the individual differences so where they are from this average line is correlated with their performance on cognitive tasks that demand executive function and cognitive control suggesting that these network models simply based on the underlying white matter architecture can tell you about how possible or how.

[00:48:41]
The prevalence the ease with which control can be exerted intrinsically in this system. So together these results suggest that this fairly simple theory is a useful marker of how the brain and the X. control to change network function and the very last piece of data I wanted to show you is pushing this in to exhaustion a stimulation can we use this simple model based on the structural connectivity to understand what happens when we stimulate a brain region how far does that structure go in telling you what will happen after you stimulate region of the brain so for this we're using a larger corner congressi a data from patients that have medically refractory epilepsy and we have patients who have volunteered to be part of a stimulation regimen where different regions of the brain are different electrodes are stimulated and we want to understand whether that pushes the brain into a state that is better for memory encoding specifically or not and what we actually see is that when we stimulate a region that has high modal controllability which is this statistic from the underlying structural network we see a change in the memory encoding state probability of this system and this is a positive relationship suggesting that when you stimulate regions that have this underlying structural architecture it pushes the brain potentially into states that are better for memory and coding so that has motivated a couple many open questions and that's just on archive so you can.

[00:50:10]
Review right now. But the open questions are how much energy is required for a state transition from one brain state to another does that change over development of said help us to understand the humans capacity for a task switching number to what Over what time scales or frequency bands is the theory most valid and that's where you started so in the lab and then number 3 by building this sort of 1st principles theory can we use network control to better optimize therapeutic inventions such as stimulation potentially also tasks based interventions like cognitive behavioral therapy or potentially medication for neurological disease or psychiatric disorders and those are all very open questions and I think an interesting directions for a future work.

[00:50:53]
So those are 3 different stories that I told you that I'm hoping actually over the next couple years to bring together so can we understand optimal learnability of graphs and understand what is it about the brain dynamics that allows for that optimal graph learning to happen what are the structural underpinnings that support those dynamics and that could potentially impinge on the learnability of graphs themselves so this is where the lab is going over the next few years and here's another pictorial sort of summary of what we did so we started.

[00:51:28]
With John Dewey motivating the question of knowledge as networks we talked a lot about Knowledge Network learning and then we crossed over the. Cross cluster edge of Alexander Pope into brain network dynamics where we went across Aristotle into brain network control so these are 3 very different arms as I said we're hoping to introduce you take them even more in the next couple years but be very happy to take questions on any of those and of course to acknowledge the people who are in my lab right now but a lot of the work was done by people who have just recently left so I wanted to make sure that I put their faces and names up here as well and obviously the funding agencies that have supported the work and with that thanks and I would love to take questions.

[00:52:17]
Thank you we were. Yeah that's a really great question so the question was is the flexibility just driven by weak noisy connections or weak in some important way right and. What I think is happening is that the flexibility measure that we have is driven is a quantification of how many times brain regions move between modules over the course of the experiment now if you have a brain region that's moving between 2 modules it's a motor a visual cortex and it's just sort of bouncing back and forth in in its pattern of functional connectivity that could mean that it's actually sharing information between the 2 and that might be important functionally However if you have a brain region that is has high levels of flexibility but because it showing some connectivity we kind of to be to 10 other different modules I would say that's more noisy so I think in fact I showed you that inverted U. shaped curve between cognitive function and flexibility that I am hypothesizing is there I actually think that these high levels of flexibility that we see in this case a friend acts are not the same kind of flexibility that we see in healthy controls I think that they are more of this sort of random associations of regions to other modules that are driven by transit fluctuations that are not useful for transporting information also Murs disease I can't necessarily comment on because I don't have any data on that but it would be interesting to to check.

[00:54:08]
Yeah. We haven't yet but again I think that would be really interesting. Right so there's very sort of simplistic notion might be that they have more rigid architectures and that would be interesting to see if that's true yeah we have yeah. Yeah. So those are great questions I think one way that you can tackle them is by there's a lot of data that's available for child directed speech but also speech of the parent with a child and so you can certainly take it into the linguistic domain and say what is the color currents of words that the parent uses does that have a certain architecture that is eventually reflected in the child's speech as well I think that would be interesting in terms of how it grows as a function of time the one way that we're trying to tackle that now is actually not in young children but in sort of college age where asking the question of how these concept graphs change over the course of a semester and then we're also looking at textbooks that are accompanying that class and when are concepts introduced and what is the co-occurring of concepts in the textbook so very early on in the textbook which concepts are introduced 1st and in what code currents Cochran's being at the sentence level and then how does that change as a function of time in the textbook and can we see that progression also in the way that students map the relationships between concepts on paper so we have them we give them these massive pieces of paper that are sort of 8 times the size of a normal page and then we give them the 50 concepts that are most germane to that class and we ask them to map out where those concepts would go.

[00:56:41]
Concepts to be close together if they are related in far apart if they're not related and then they draw the connections that they understand between those concepts on that piece of paper as well we do that multiple times throughout the course of the semester so we can see a change and we can ask how that change tracks with or doesn't track with the changes in the.

[00:57:00]
Co-occurring of those same concepts in the textbook So that's one way that we can tackle that but I think there. There's a lot of open space there in the back and then over here. I think actually both are true so the question is why is flexibility important in a task specific versus task general way so if you have a visual task is flexibility in the visual cortex important more so than other areas I think probably there are certainly it's known that there are regions of the brain mostly in front of product X. that are important for a task switching just in general and so I think that flexibility there is going to be important in a task general way I think that's the hypothesis.

[00:58:12]
But I also think that there will be an amount of flexibility inside of a given model that's important for the task that may also be relevant so I think if I was to guess my answer would be both are important but I don't have enough data from enough different tasks to really answer that empirically yet Yeah great yeah yeah.

[00:59:01]
I don't know. I don't know I mean I think that there is definitely the preferences for how we see information I think it's actually gets a question to the the question about how we see information and what our preference is in terms of its architecture I think certainly probably has to do with architecture of the world around us and if the architecture of the world around us has certain structure then we would prefer to see information in that way but our preference is that just because we've seen that from development or has changes in the brain over evolutionary time scales also made us prefer that because the world hasn't changed that much.

[00:59:43]
I don't know and I don't even know how to start as answering that question appeared I don't know it's sort of a philosophical there are genetic modular markers for modular working on that paper and there are yes which are. In the back. There is a really nice heritability study from Sophie for Andrea at Mount Sinai that is on heritability of the network control part so that structural bed at the end is definitely has a strong genetic underpinning.

[01:00:39]
We haven't done I don't know of any papers that have assessed that for the for the functional flexibility that I showed so I don't know the answer to that question. Thank you.