Connectionists: Western-Fields Seminar Series | Jeannette Janssen

[Lyle Muller]

The tenth talk in the 2021 Western-Fields Seminar Series in Networks, Random Graphs, and Neuroscience<http://www.fields.utoronto.ca/activities/21-22/western-fields> is Thursday 9 December at noon ET.

Jeannette Janssen<https://mathstat.dal.ca/~brown/researchprofilepics/jj%20-%20research%202.pdf> will give a talk titled “Graphons as blueprints for spatial random graphs” (abstract below). Dr. Janssen is a Professor in the Department of Mathematics and Statistics at Dalhousie University. She has made fundamental contributions in graph theory, including the study of geometric graphs, spread of information on graphs, and infinite graphs.

This seminar series has featured monthly virtual talks from a diverse group of researchers across computational neuroscience, physics, and graph theory. A summary and list of featured talks can be found at the series website<http://www.fields.utoronto.ca/activities/21-22/western-fields>.

Registration link: https://www.fields.utoronto.ca/cgi-bin/register?form_selection=western-fields

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Given a compact measure space $S$, a graphon is a symmetric, measurable function  $w:S\times S\rightarrow [0,1]$. A graphon corresponds in a natural way to a distribution on graphs. A graph can be sampled from this distribution by taking vertices $x_1,x_2,\dots ,x_n$ chosen u.a.r. from $S$, and then connecting each pair $x_i,x_j$ with probability $w(x_i,x_j)$ (conditionally independently). Graphons provide a very general framework to define spatial random graphs: let $S$ be a metric space, and let $w$ have the property that $w(x,y)$ decreases as $y$ moves further away from $x$, thus making links more likely between vertices that are closer together.

I will start by discussing spatial graphons and the theory of graph limits, and then show (1) how the spatial layout of the graphon can be retrieved from the sampled graph (joint work with Aaron Smith) and (2) how graphons can provide a framework for signal processing on graphs sampled from the framework (joint work with Mahya Ghandehari and Nauzer Kalyaniwalla).

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Lyle Muller
http://mullerlab.ca<http://mullerlab.ca/>

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