I’m happy to announce that the results of a fun project with Alice Patania, Giovanni Petri and Francesco Vaccarino are now available in a short paper in Physical Review E. Special thanks to the YRNCS who funded this collaboration through their Bridge Grant initiative.
Our paper, titled “Construction of and efficient sampling from the simplicial configuration model”, builds on recent work by Owen T. Courtney and Ginestra Bianconi. More specifically, we propose an efficient and provably correct MCMC algorithm for the maximally random ensemble of simplicial complexes with given degree and dimension sequences. This algorithm comes in handy when we use simplicial complexes as an abstraction for the structure of complex systems (as has been done more and more often recently). By randomizing a simplicial complex that encodes the structure of some system X, we get to tell what connection patterns in X are explained by simple local properties (degrees and dimensions), and what patterns are surprising. In our paper, we this method to show that the homology groups of a few real-world systems are decidedly not random, and we suggest some mechanisms that could explain these differences. But one could use the method to investigate different property; this will be dictated by application!
The next step will be to develop correlated variant of the ensemble (think of the degree-correlated CM) and to delve into combinatorial results (e.g., rigorously prove the traversability of the associated simplicial complex space).
In January 2016, Laurent Hébert-Dufrense, Antoine Allard, Pierre-André Noël, Eric Libby and I got together for a SFI working group, to investigate competitor dynamics on networks. Our starting point was the connection between voter models and the Moran process, and, more generally, questions about the political arena and biology. Our answers are now available in a Scientific Reports paper titled “Strategic tradeoffs in competitor dynamics on adaptive networks”.
In the paper, we introduce a voter model on the adaptive SBM (the structure of the network changes depending on who’s claiming what resources). It turns out that the model can be mapped to a well-known evolutionary game theory problem. The upshot? This gives us a game-theoretical perspective on network structure. In turn, this allows us to conclude that, for example, sustaining echo chambers is not a robust and viable strategy. So intead of fostering closed communities, strive for open discourse across boundaries.
So, two short news.
First, “Finite size analysis of the detectability limit of the stochastic block model” is now published in Phys. Rev. E; I’ll upload an updated version to the arXiv soon (after NetSci 2017). It is a long paper, so it was a long process. I’m glad to see it through! Our coolest result are, I believe, 1. the symmetry group of the SBM and 2. our approximation solution of the hypersurface equations. The first tells us what transformations of the parameters maintain the difficulty of the detectability/recovery problem, while the second determines the surface of constant detectability in the parameter space.
Second news: I’ll be giving an extra talk at NetSci, during the satellite sessions tomorrow (I’ve already announced this earlier on Twitter). I’ll present the Simplicial Configuration Model and some recent related work done with Alice Patania, Giovanni Petri and Francesco Vaccarino.
My submitted talk “Statistical mechanics of mesoscopic structure extraction” has been accepted at NetSci 2017. I will present an unifying view—already explored by many, but not quite complete—of community detection and mesoscopic structure in general, using the language of statistical mechanics. This is joint work with members of my research group, who will also present quite a few talk of their own, see this list of abstracts.
I’m now managing my website’s content with Jekyll. The rewrite took some time, but it is definitely worth it. Jekyll is much more powerful, flexible and efficient than my previous static website generator. Not that it was exactly hard to beat—up until now, I handled my website with a buggy, incomplete, and partial Jekyll clone of mine. Back then, my goal was to learn python with a practical project, and it definitely helped. But why reinvent the wheel when you know how to drive? Out with
static-science, ìn with
jekyll. Oh, and I also took this opportunity to reskin the site.
In the paper, titled “Growing networks of overlapping communities with internal structure”, we come up with a natural and dynamical explanation of the Dunbar number, i.e., an upper bound on the number of connection that individuals can sustain in a social network. We show how this number is related to the heterogeneity of the degree distribution of nodes within communities and investigates the consequences of this explanation for networks which have a growing and overlapping community structures.
Summer has officially ended: on-campus activity levels are back to normal and classes are picking up. This means that, as usual, I can wrap-up summer conferences and announce my talks after the fact… I really ought to start announcing those prior to the conferences…
First thing first, my collaborators and I presented many new results at Netsci 2016 (Seoul, South Korea), I personally gave two talks about my upcoming paper on the finite size analysis of the detectability limit of the stochastic block model. The first presentation was part of the Statistical Inference for Networks Models satellite (SINM), and the second presentation took place during the lightning talk plenary session—quite the experience! My long-time collaborator Laurent Hébert-Dufresne also gave a lightning talk, where he introduced our new voter model on the adaptive stochastic block model. The associated paper is currently in submission, and available on the arXiv. Two new members of Dynamica—the Université Laval research group on Complex networks—also presented at NetSci: Charles Murphy gave a talk on growing random geometric networks, and Guillaume St-Onges presented a poster on coupled growth and spreading dynamics. Finally, Alice Patania presented our work on growing simplicial complexes, developed during my stay at the ISI Foundation. Slides, papers, and more can all be found on my publications page.
I also gave a tutorial on spectral graph clustering at the “CRM 2016 Summer School on Spectral Theory and Applications”, in Québec, Canada. This summer school is targeted towards graduate student beginning their PhD in mathematics, physics and applied mathematics. I produced a lot of material for the tutorial; You can head over to this page to download the slides, lectures notes and python notebooks used during the tutorial.
This year started pret-ty intensely, with a working group at the Santa Fe Institute and a month-long residency at the ISI Foundation. The dust is still settling, but a couple of interesting projects should come out of it, to be presented at NetSci 2016 and / or other conferences this upcoming summer.
I’m also happy to announce that a paper with a long history has finally been published in Physical Review E (and that it’s the Editor’s suggestion of the week)! The theory was mostly developed during Laurent Hébert-Dufresne’s time as a PhD student at Université Laval (circa 2014), but has since evolved into a sounder, more comprehensive framework. In the paper, we show how preferential attachment and delayed temporal scaling in the growth of a resource lead to a scale independent distribution of resources. It turns out that the delayed temporal scaling is strict enough to predict both the past and the present of a scale-free system, from a single snapshot of its present state. It will be interesting to see how this relatively simple mechanism can be coupled with other preferential attachment based model.
Between conferences, a month long summer school, a doctoral exam and multiple papers, suffice to say that 2015 has been a crazy year. As a result, I ended up updating this website much less than expected. The Christmas break should allow me to remedy the situation. In the meantime, three papers on which I collaborated appeared in PLoS ONE and Physical Review E. Head over to my publication page for more details. Until then, happy new year!
Summer 2015 will be action packed.
L. Hébert-Dufresne and I will be A. Allard’s new base camp in Barcelona, during the week of May 24th. Our joint work has always been fruitful and fun, and this visit should lead to interesting new projects.
The following week, I will be attending the 2015 edition of NetSci, in Zaragoza, Spain, alongside with many current and past colleagues. This year, we are presenting two poster contributions.
The first contribution summarizes the results of a collaboration with E. Laurence, Sergey Melnik that started back in November 2014 when he visited our research group in Québec. In a nutshell, we adapted a set of iterative equations that exactly solves bond percolation on arbitrary networks to the more general cascade dynamics of James Gleeson and colleagues. Bond percolation, node percolation and the Watts threshold model are all special cases of this approach (!).
The second contribution introduces a large class realistic of benchmark graphs for community detection. These graphs are based on the Structural Preferential Attachment principle, and exhibit extremely varied structural features depending on the choice of parameters. Stay tuned, because the source code and associated publication will be available soon.
Exciting times ahead!
Surya Ganguli gave an excellent talk on deep learning ideas derived from statistical physics. As a “community detection” guy, I found the Networks Science Workshop especially interesting. Half of the invited speakers presented recent results in that area of network science. There was, two particularly noteworthy talks.
The accepted papers can be found on the workshop page.
I’m very happy to announce that my M.Sc. thesis has been been accepted by the review committee, and is now officially available online While the thesis is mostly written in French, you will find two English chapters, namely a chapter on cascading detection (see this arXiv paper), and a chapter that contains preliminary results taken from a paper that I’m currently writing with L. Hébert-Dufresne (now a James S. McDonnell Postdoctoral Fellow at the Santa Fe Institute). In that chapter, we propose that the internal structure of communities arises from the juxtaposition of two simple stochastic processes. [September 22nd, 2016 update: A much improved version of the paper now appears in Phys. Rev. E.]