 Thinking of speaking to a physics audience, I gave a title, which is kind of physics-y. But then Dima convinced me to change the talk. So this will be a highly experimental talk, despite the fact that I'll only talk about theory mostly. And so my name is Alex Kulakov. You don't know me. I'm at Coltsman Harbour Lab, and I'm a computational neuroscientist slash theorist. So my talk will have two halves. And the largest half will be the, I'll be talking about low-dimensionality of perceptual factory space, whatever it means. And I'll just try to convince you, maybe bring you to the camp that the number of dimensions in alfaction is low. And then the second half, I'll try to basically marry the primacy model with the low-dimensionality and see if there are some testable predictions of that fusion of theories. And so the main hypothesis, there are basically two viewpoints, I think, that could be formulated, which are diametrically opposite. And one of them is that the number of alfactory dimensions is the same as the number of, roughly the same, of the same order of magnitude, hundreds, maybe thousands of dimensions. So for each receptor would correspond to a significant fraction of the dimension. And the second viewpoint is that the number of dimensions, whatever it means, I'll try to define it later, is much lower than the number of receptors. I have to start the timeline. So the reason why I will basically talk about try to convince you that hypothesis two is true is, I think, twofold. One of them is, one of the reasons is cynical and it's not really scientific. It's that if the hypothesis number one is true, then, oh, one of those bodies is white. How many theories does it take to figure out? So if the number of dimensions is high, so basically it will take us a lot of time to figure it out. Probably not in my lifetime. So my only hope to figure out how affection works is that the hypothesis number two is true. It's the same hypothesis or suggestion of Freeman Dyson to look for extraterrestrial life in the solar system because otherwise we have no chance to find it. So the second probably is more scientific, is that the experiments, there is apparently enormous redundancy in the olfactory system. The olfactory perception can sustain tremendous, these very robust collisions. So if we remove a large number of receptors, we more or less retain the same ability to smell and that kind of suggested that there are more than one receptor per dimension, per olfactory dimension, because if you knocked out one receptor and there would be important impairment in the process. So I'll try to basically convince you that hypothesis two has at least the legitimacy, some legitimacy. And I'll start from some old study and I apologize for you that we did some years ago and just as an introduction to this topic. So this is based on this data set which no one actually brought to our attention. And I'd like to thank you for that, which was published as a book by Andrew Dramniks. There were already two talks I think about it in this meeting. So it's basically a book by Andrew Dramniks which contains pages, each page is dedicated, it contains tables, each table is dedicated to individual odorants, most of the odorants are molecular, and this particular example is heptanol and there's a list of words on the page and there are 146 words and the numbers that you see is percent of people out of army of observers that recognize that this word applies to the smell. So it's averaging over a large number of people about 150 people per smell. And so therefore this basically represents a snapshot of affection in the communist society where everybody has the same sense of smell. So but probably like understanding affection in the communist society is a good start and then we'll try to figure out what the diversities are. And of course like as Noam described, I mean the first compelling thing that you can do with this is to put it in PCA space, in principal component space which we did and if you spin it, so what we notice is if you spin this cloud of points each dot here represents individual molecule and those are principal components space that are dimensions which Noam described. So you will see that they occupy, if you look from a certain direction, you will see that they cluster around some curved manifold that looks like letter C. So we thought that maybe this is, we need to instead of principal component analysis we need to embed the molecules in a more curved space because principal components analysis approximates the molecules with the flat spaces. So that we did, so we actually invented the new technique for doing it which is basically fitting the cloud of points with the polynomial second degree surfaces which you can see here. We call this surface potato chip just because of the resemblance and the way how you find the parameters of the surface is that you see those lines, those red lines connect the odorants with the nearest points on the surface and you minimize the total square length of those lines. And after you figure out, I mean this is the same surface shown in two, from two directions, after you optimize the parameters of the surface you will see in 146 dimensions here you only see three dimensions well we actually see two but it's in three dimensions but in the entire 146 dimensional semantic space the two-dimensional manifold, two-dimensional potato chip captures about 50% of data. So that was compelling to us and somewhat surprising. So what are the two dimensions that you can find on the surface and one of the dimensions, I mean you can basically judge what the dimensions are with some degree by looking at the words which have semantic descriptors that have high positive and negative loadings along certain dimensions. So for example the vertical dimension you can just look that it's, you can just see that this is associated with pleasantness with norms findings. Of course so the other dimension is more subtle so I have no semantic skill so I just ask people, I pulled a bunch of opinions of what it may mean and of course I mean this, the meaning of this second dimension is somewhat anecdotal so we actually have the complete definition of the dimension of the computer but if you want to label it with something it's kind of fun to do. Some people suggest that it's debility because there are some things which are edible here but there are also some things which are not really nasty but other people say that it's related to kitchen so it's probably, there's burnt stuff. The craziest suggestion I got from John Lisbon that it's related to auditory pitch so only John Lisbon could actually have made this suggestion so because if you look at the words which are on the right and the words which are on the left you could associate them with things which are different in auditory pitch but probably the most compelling idea for what the second dimension means is trying to correlate it with properties of the molecules we also know the properties of the molecules which compute some computational chemistry packages we find that a lot of properties which are related to hydrophobicity or polarity of the molecules such as water of hydration or the divide type of moment they are correlated with not strongly but it's very narrow correlation with the second dimension so those are the two dimensions which we find in the data set and they capture about 50% when we include the curvature of the surface but then we thought that why limit ourselves with two dimensions so Dimo suggested that we go to higher regress by regress to higher dimensions we have to do it carefully because we want to be because the number of parameters will increase so we actually have to do cross validation and make sure control the parameters make sure that we don't overfit so this is actually included variance after cross validation it never can go to 100% it goes to about 80% so what you can see here is that the two dimensional data set the potato chip which I described before captures a little bit over 50% of variance after cross validation but the three dimensional potato chip which we call potato captures somewhat more and then when we go to hyperspud of about seven dimensions we get to basically it asymptates at about 80% of variance but we can also do some other tricks such as we can estimate the residual amount of noise even after using 150 observers there's still some degree of noise present in the data set that's our estimate so we cannot explain only 12% of the data set after cross validation also interestingly the data set contains mixtures so we can test, we can figure out the hyperspud for the curved manifold for one molecular order and then test mixtures try to see how far mixtures are from that hyperspud that we did and that's the curve for the 15 mixtures which are present there in the same data set and what is interesting is that at low levels of variance there is one mixtures actually require one extra dimension to be explained which you could call a mixture dimension it's interesting that you can actually with some precision you can identify whether the percept belongs to the mixture or not from the data set so you can actually use this extra dimension to classify odorants into mixtures or monomolecular odorants and then when you go to high levels of variance or of precision the difference between space of mixtures and the space of monomolecular odorants disappears so for example the 7 dimensional data set already includes both mixtures and monomolecular smells so that for us was a motivation basically to try to find some other example of low dimensional representation I guess the key thing here in this data set is that it's curved so the idea is that I guess what is suggested by this data is that the richness of alfactory perception emerges from the fact that the sensory manifold is curved so as you proceed, although the number of parameters that determine the position of an odorant in this sensory manifold is small, it may be close to 10 when as you move along the manifold the percepts will vary dramatically because of its curved nature, so maybe the richness of alfactory percept is perceived as a sensory result of this curvature or it's very interesting, they actually cluster so there is a pole of pleasantness and the pole of unpleasantness and this is the pole of pleasantness, unfortunately it's at the bottom I just put it to and to ask me this so you see that the smells actually cluster along the pleasantness pole and there is some clustering along the pole of unpleasantness but in the middle there is another interesting thing is that this potato chip it expands in the middle which means that if the smells is neither pleasant nor unpleasant, probably people spend more time describing it so so this probably the clustering it's not clear whether it's real or it's just produced by sample of the smells that they used which emerges from flavor yeah there is nothing of course we did it or you would need about 50 I mean this curve will be flat you will not see any which will go like this yeah of course we randomize that yep do I have explanation I mean I guess it's a mixture I would call it mixture dimension again we have it in the computer I'll try to show you there isn't much I can extract from the semantic descriptors I was prepared for this question but I have to I have to go through all the talk and now you all saw it so oh that's the slide the mixture dimension so basically there are words which are suggested for increased complexity and the interesting thing is again you can actually discriminate look at the smell look at the descriptors of the smell and you can tell with 70% chance for the balanced data set so it's 20% above chance you can tell whether this person belongs to the mixture which I find funny because probably not many people can tell whether they smell molecular smell or mixture but those are the sets of words I mean we call it the mixture dimension just for the lack of better description so I have to go back we have a 2 yeah we are running it we are running it right now it takes us some time it's just so many smells also I mean it's a bit different format from the Dramnik data set you have only 19 I think descriptors and you know fewer people so some care has to be taken about statistics yeah there's many of them yeah we run a very exhaustive basically semantic analysis with doing Google searches I mean I don't know if you saw it there is appendix to our paper where we run Google searches with the words so we find actually using one of the basic approximations in semantics we find that there are about 60 dimensions in just the words so I think the appropriate choice for the number of set of words is about 60 in alfactory background so if you run if you find the web pages with Google with alfactory background you find that number of dimensions will be close to 50 so but also each of those dimensions is a mixed dimension so probably it will include more words from the Dramnik's but even with your data set because it has so many smells it's very compelling so the next thing I would like to talk about is alfactory genome so if there is this low dimensionality maybe it has imprint in alfactory genes so this is just the general introduction of how many genes we have and the empty spaces are super genes and the full are genes these are the data that we have we downloaded it from the database so what you can do is you can compute for example a distance matrix for different alfactory genes which is the number of substitutions that you have to that different sequences contain and amino acids so this is an example of such table for humans and then you can try to do PCA analysis on this data and it comes up with very interesting pictures that you can see here so those are genes also during that published paper where he described alfactory genome which has a very similar picture with this three-legged structure I mean this actually includes in our analysis both genes and pseudogenes the pseudogenes were fixed by an algorithm which Doron once had developed so you can see there are a lot of empty dots which are pseudogenes which also include so it has this beautiful three-legged structure which was compelling and interesting for us so we thought about it and then one of the things which was real bummer is the including dimensionality just to show you the negative result so that we don't cheat you know that we don't cheat so if you look at the included variance in this PCA analysis of the genes as a number of dimensions you see that there is like an 80% variance which is at 300 dimensions so if you look at this in the sequences of alfactory receptors it's enormous it's hundreds so that was real bummer for us and then yeah we looked at the entire sequence we looked at binding sites it turns out that there is an enormous redundancy in the sequence so you can actually get the same picture if you cut out the random subsequence so there is apparently a co-evaluation in different positions in the receptor but if you just look at the binding sites you will see a very similar structure except it will be less well defined it will be a bit puffier so that was interesting that was disappointing because there are legs coming out in more than three dimensions so they stick out in a lot of dimensions which I cannot show you but this picture just quantifies that so but then I actually I'm not going to show you this but I managed to generate exactly the same picture from random data after staring at this for a few years I managed to in MATLAB write a program of five lines that generates exactly the same picture so I actually realized what is wrong with it and what is wrong with it is that the the distance matrix which is measured in the number of substitutions doesn't really replicate the functional distances between genes so if you just take a cloud of points and you compute distances between points and then you compute an exponential function of that distance you will find a very similar structure to this so that meant to me that actually the large distances are probably not correctly reproduced by just the number or not correctly captured by the number of substitutions so probably if you see two OR genes which are different by two or one substitution they are very close to each other in this genetic space but if they are more than one substitution they probably have a pretty wrong idea about how far they are and fortunately well we use different matrices we use the multiple sequence alignment just like aligning all genes to this common frame but this particular result is obtained by just pairwise alignment which is probably most precise phylogenetic 3 doesn't have dimension it will have families for example this is family 7 which is almost entirely bad in humans those families are derived from phylogenetic analysis so they actually are they cluster out in this PCA space I'm just trying to there is a these are pseudogenes which are fixed by Doran's algorithm they have very small, they have point mutations such as frame shifts or like some nonsense no, no, those are not included what they were I mean I looked at the alignments they look very nice actually no, I mean the alignment that I looked at multiple sequence alignment is very nice it's actually on our website I mean you can check it out so there is no pieces there there is no like half gene so the hypothesis was that the long distances are messed up but probably short distances are short that the fact that the genes have small number of substitutions between each other it's not so irrelevant so fortunately for us there was actually an algorithm which was developed in 2000 which deals with exactly this problem which is called isomap isomap what it does it ignores the long distances so this is an example of isomap algorithm run on a surrogate data set which is called swiss roll where you have a set of data and they say that obviously these distances are not because the relevant dimension it's a two-dimensional set of points so these distances are wrong but the distances between nearest points are probably correct so what isomap does it attempts to compute it ignores the long distance information and only takes the short distances and then recomputes long distances through via the short distances using what they call geodesics which are the shortest distances on the swiss roll right so this algorithm is capable of unrolling the swiss roll to say so basically it's capable of recovering the long distance information from just nearest neighbor or short distance information so we use this alignment or distance matrix for this actually includes both humans and mice and after running isomap on it we find that with here I think humans are blue and mice are red we find that if you run the isomap analysis the actual number of dimensions is not so large it's probably close to 10 to capture 90% of variance also there are some limitations to isomap algorithm which don't allow it to approach 100% because simply because it only uses it can only unfold the flat space it cannot unfold something which has curvature to it it's one of the possible directions of extending how much time do I have to run so that's basically another evidence I think or motivation for us to look at our factory space as a low dimensional of course the really interesting question is if this is true if genetic space or the space of receptor sequences is low dimensional how do you align it with the perceptual space that would be very interesting in that direction if there is some kind of matrix which relates receptors to molecules to ligands which is more extensive than already exists in the literature would be useful in that so I would like to move along to the primacy coding for the second half of my talk and the question will be what would be the evolutionary model of the receptors which would be generated by the primacy model which Dima described yesterday and I'll remind you what the primacy model is so this is my experimental slide of the talk which is stolen from Tomboza's paper so those are the patterns of activation of glomeruli just by different smells and this is the fierce view on the same picture the circular spherical glomeruli the activation of different other identities will be produced by different combination patterns and as you increase the concentration of another and you recruit more glomeruli so the question of course is how is it possible that we link those two different concentrations into a single other quality and according to the primacy idea which Dima introduced yesterday we only look at the glomeruli which have strongest activation levels and those remain approximately invariant over a range of concentrations so that's the idea for at least within some range of concentrations how perceptual invariance for odorants can be generated so different odorants of course will be represented by different primacy glomeruli and the important parameter of this hypothesis is the number of primacy glomeruli which is in this case 2 we estimate from Dima's data that for mice it's somewhere between 15 and 20 but it's still less than the number of receptors so the primacy model suggests that small number of receptors activated first or activated at the highest level represent odorant identity in the concentration invariant manner so now we would like to ask a question what are the signatures of primacy coding mechanism in the responses of olfactory receptors and potentially in the sequences of olfactory receptors I mean it has to have some imprint in those things so and I hope I convinced you that the olfactory space is low dimensional so we have those primary or let's call them basic smells which I call here odor X and odor Y for two dimension I mean you can think about it for example as dimensions on the potato chip azimuth and elevation so they are not related to individual smells or molecules they probably but they'll treat them as individual molecules so they're probably a mixture so the receptor like olfactory receptor could be defined by binding constant by binding affinity to those two smells so it's a each receptor is a point in this two dimensional space defined by binding affinity to odor X and odor Y so this would be the second receptor at the ensemble of olfactory receptors is a cloud of points in this space so when odor X is present and as the concentration of odor X increases it will at some point it will divide the plane this two dimensional plane into the zone of active receptors and inactive receptors the ones which I bought C50 or the low C50 and as the concentration of odor is increased more and more receptors get recruited and at some point those two receptors will be recruited the earliest or they will be activated the highest level so those two receptors will be representing the stuplet of receptors will be represented within the primacy mechanism the identity of odor X and similarly as I increase the concentration of odor Y it will sweep the plane and it will activate those two receptors at the highest level at which point it will be represented the representation of odor Y will be formed as the pair of those two receptors so if you form a mixture of odor X and Y a different pair the plane will propagate as you increase the concentration of the mixture the plane will propagate will sweep through the surface from infinity and it will activate the other set of two receptors and that's the representation of the mixture of odor X and Y from the primacy model similarly there are other mixtures possible there is this mixture and there is this very subtle mixture coming at a very narrow angle here which believe me this point actually this segment is very important to me as a mathematician because it argues that this set of you see this is the complete repertoire of identities for this set of receptors so this set of receptors can represent one of those odor identities is represented by this thing sticking out of the surface which means that it's not just convex hull of the set of points there's more complexity to this so the odor identities are not just given by convex hull of the set of receptors they're also given by some hair that grows inside the surface so we call this hull instead of convex hull we call it a primacy hull because the definition of this it's a mathematical object which is defined as you basically sweep planes through the you sweep boundaries through the plane at different angles and then you activate p points at some point you sweep through p points and that's when you define that's when you put a segment there well that's exactly mathematical it's a new mathematical object that's what I'm trying to say it's not a convex hull which I find very interesting that like biology can actually generate new mathematical object but you could imagine that for example the set of odor identities would be given by a convex hull but this little thing sticking out argues that it's not it's more complex I think there are actually more identities that can be given than by a convex hull but that also means that there is reduced evolutionary pressure on the receptors within the hull because they represent nothing so they should be eliminated which is in principle a testable prediction so this simple model suggests that the receptors occupy a narrow manifold in the parameter space in the binding affinity space and we could try to test that interestingly we have primacy numbers more than two I described you with the primacy model with just two receptors identifying another you can have more than you have each receptor will be represented by a face on this hull which is for p equal 3 it's a triangle for p equal 4 it's a tetrahedron in general it's a simplex right so this is an example of primacy hull in three dimensions with primacy number three which is given by a triangle so this is a more complex example unfortunately I have to project it to 3D it's also a hull it's a five dimensional hull in six dimensions I have to show it it's a mess yes they should not be there they should become pseudogenes that's the idea no I didn't say that I'm not sure if you increase the concentration you have a glomerule which has lower affinity to the smell the question if they are activated at the higher level I don't think I've said that I think Dima has some data I'm not sure if he showed it yesterday which shows that of this glomerule of mitral cells you see an increase and I think later you see a decrease I think there is some imaging data on that there is actually a slight decrease but I think it's due to feedback it's due to basically presynaptic feedback that they receive yes so they shift earlier they shift earlier in the sniff cycle and they slightly increase the firing firing rate but the most interesting thing is that they shift earlier so there are actually two, I guess you're asking the right question because there are two ways to formulate the primacy model one is in time domain that the earliest ones activated are the primary ones another one is the strongest activated are the primary ones and I'm just simplifying things but there are those two formulations are related because if mitral cell receives a stronger drive from the receptor it will be both early activated and more strongly activated so this is an example very confusing example of a seven-dimensional well, each odorant per sep will be a seven simplex containing seven points seven points connected so you can actually test whether the primacy hall exists in this cloud of in this hall if you notice that the primacy hall is actually a surface so the remember the simplices, they tessellate the surface they are close to the surface so they share a lot of nearest neighbors a lot of simplices are basically touching each other so if you just randomize if you pull the simplices randomly from the same set of points you can generate an artificial cloud of points like randomly sampling of the data and you will find that the number of nearest neighbors will be smaller in this artificially re-sampled and that's how you can detect the the fact that this mass contains the surface okay, so for example in this huh well, thank you, I appreciate it I hope you are not being sarcastic I guess you can see this is one of the ways and I apologize if it's a bit confusing one of the ways to see it so this is basically the number of simplices that share certain overlap right, and this is these are seven simplices so each order of identities is seven receptors right, and those are the nearest neighbors they share a phase which is a six point phase right, and you see that in random data set the number of those this is a blue is a re-sampled data set, but just randomly pulling simplices the number of nearest neighbors is reduced compared to the primacy which suggests that this mass contains a primacy how, right, so I can this is testable prediction the prediction that the existence of primacy how becomes testable, so for example, how can you test it you can look at if you have a response matrix when you have responses of glomeruli for different, for different odorants and this is just an example that I show the numbers here are example number of spikes emitted by a given glomerulus or given receptor to an odorant and I've marked with red I marked the primary receptors for each odorant, so for this odorant you see the nine, seven and eight, they have strongest responses so it's the equal three model each odorant identity is given by a triangle so there are a bunch of odorants they have, I mean I'm hoping this is interesting, this is understandable if not please ask no I can use the functional data which yes yeah yeah I mean I tend to reduce complexity before I increase it but it doesn't make me happy I mean I guess I'm becoming biologist so then what you can define you can define this what to call a simplex matrix which tells you which receptors it basically is which matrix which tells you puts ones at the places for primary receptors for a given smell so this is one smell, those three receptors are primary right and in this matrix, so given the response matrix of receptors or glomerular you can find the primary receptors obviously that's what I'm saying but then you can also find the nearest neighbors like for example these two lines they're always the nearest neighbors because they share two receptors in primus and not model three right so this is just the geometric interpretation of what you see here so two, receptor number two, three and five, two, three and five is involved in this smell and this smell is represented by three, five and seven so you see that they're nearest neighbors so if only I had the response to test this I could actually run the analysis of nearest neighbors yeah I mean my test this is a great idea I mean I guess what you mean is if you yeah I mean I have data which is not probably going to convince you fully I mean I guess what you want to you would like to see as an I would like to see is some kind of functional test where you modify the percept by stimulating glomerular yeah but the test which I'm proposing is just statistical so we actually have Halemann-Coulson data which was published some years ago it's exactly what I need right so it has the receptor responses with their firing rates to the northern and I can generate the symplectic matrix and then I can run a nearest neighbor analysis and that's what my student did so for primacy number five I mean this is fly data right you indeed see in the re-sampled data you see reduced number of nearest neighbors and the p-value is significant and there is for people 7, 6 have one more significance so there is suggestion at least correlational I guess it's not really causal that there is some signature there is some Hal so there are correlations in response data so the response data is not around the matrix there are correlations and the correlations are consistent with primacy model existing in loading number of dimension yes it increases it increases the significance increases both in surrogate data set and in real data set I guess the first what we find is the first p at which you have significance is the p which you are looking for this bump so this is basically the number of nearest neighbors it's the number of cells you have the nearest number of highest level with yourself and the number of your nearest neighbors is smaller than the number of cells that's why re-sampling doesn't change this number because re-sampling doesn't change the number of per sets if I vary the number of receptors I vary p as you increase there are some theoretical results which are very interesting to us that's what we breathe math so we can actually compute the number of per sets that you have as a function of p and the number of receptors there is a very interesting formula which is the number of per sets is p factorial times the number of receptors which gives you hundreds of millions like for realistic estimate for what human so it's p factorial times n I mean you could think that it's a binomial... anyway I can think that it's a binomial coefficient that's more interesting because the geometry of this random primacy hall is very interesting so these are the conclusions so we predict that there are higher order correlations which you can actually test so I'd like to... I have how much time? minus three? oh okay so I'd like to basically talk now about the models the network models at all you have a statistical result I mean even this data is a subset I should say that so this is one of the confounding issues there are only 24 receptors here because they can only I think it's a topic receptor that they put in in a in the cell where the receptor was knocked in the endogenous receptor was knocked in so then they can only put in 24 receptors yeah even this one is maybe like a half of the receptors bit more than a half so it becomes a statistical it basically reduces our statistical power that's what it does so then I would like to talk about network models so how can you process primacy and this is like the simplest possible network just coincidence detector that you can suggest that in pyriform cortex when mushroom body there would be cells that are listening to individual simplices to triangles that I presented to you before so when this triple of cells is activated they become primary and they will drive this pyriform cortical or mushroom body in itself and it will for example inhibit all others so there will be winner takes it all or you could have like multiple cells representing multiple phases of primacy simplex also so but the idea is that the connectivity in between the primary sensory area such as alfactory bulk monotonal loop will contain that information about primacy how right so we can also formulate therefore we can formulate if we know that there are correlations in the layout of only some subsets of receptor activations are relevant to the animal there are some correlations in the connectivity and the correlations have to be very high order right because they will involve the correlations will involve combinations which are p which are p receptors so it's not so straightforward to actually see them in the connection matrix so if we had a connection matrix I hope it's clear if we had a connection matrix we could run the same test that I showed you before if we had a just assuming that elements of connection matrix they are vertices I should say that this is each individual receptor is a vertex in the simplex and each cell becomes a simplex and the connections are connections they indicate which vertex belongs to which simplex if only I had data and fortunately to us recently the data was published by the group in Janelia Farm which shows larval connectivity from from antenna lobe to mushroom body so Albert Cardona actually was kind enough to give us this data before it was published so we had some time for data crunch and we run the same analysis on this data this shows actually a connection matrix number of synapses from 25 projection neurons but in this analysis we only used 22 I mean I'm sorry this is just this is more complete connection matrix on this one I threw away multiple glomerular projection neurons I'm not sure why I did it but just to be more conservative and then you get some basically statistical significance for the hypothesis with in this case the premise number was 5 I mean the p-value is not so dramatic as in response data but at least it suggests for us to look further also this is the most conservative result meaning that we normalize this matrix very extensively you can see that like for example these canyon cells were recently born so they have very few synapses there are a lot of confounding issues that you have to deal with such as issues of normalization and sifting through the data I don't question the data though because I mean that's the only thing I have if I start questioning the yeah but it was a single cell it was a single canyon cell from one animal so it's basically the shredder and for the number of claws I think they use like maybe 50 to 30% of claws from each canyon cell so there are two shredders that the data go through it's not really connection matrix in one animal it's one canyon cell in one animal right and there no it completely destroys no it destroys the correlation there's nothing it's to extrapolate really so I mean this is one animal so that's the significance although the animal is arguably the Razofila larva so there's not much but yes so there is nothing if you take a connection matrix and you take only one canyon cell from it and then you because canyon cells you cannot align you cannot align projection neurons between animals canyon cells are different between different animals right so it's like you take a connection matrix and you pull random lines from it and then you build a new connection model and it becomes like this type of correlation that destroys I guess I'd like to finish at this point and ask for questions and thank you for attention and for generous support of ICTP and obviously organizers for giving us this opportunity to meet