Georgia Institute of Technology College of Sciences

We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. In the scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test. This is joint work with Justin Khim (UPenn).

Introduction of the new Faculty, Postdocs, Academic Professionals and Staff.

In this talk, i shall provide some optimal PIR bounds, which confirmed a conjecture on optimal RIP bound. Furtheremore, i shall also investigate some results on signals recovery with redundant dictionaries, which are also related to statistics and sparse representation.

The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will give a description of the Gromov-boundary of the ray graph in terms of long rays in the plane minus a Cantor set. This involves joint work with Alden Walker.