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IMA Data Science Seminar - Mauro Maggioni
Speaker: Mauro Maggioni
Title: Two estimation problems for dynamical systems: linear systems on graphs, and interacting particle systems
Abstract: The first one is the following: suppose we have a linear dynamical systems on a graph, represented by a matrix A. For example, A may be a random walk on the graph. Suppose we observe some entries of A, some entries of A^2, …, some entries of A^T, for some time T, and wish to estimate A. We are interested in the regime when the number of entries observed at each time is small relative to the total number of entries of A. When T=1 and A is low-rank, this is a matrix completion problem. When T>1, the problem is interesting also in the case when A is not low rank, as one may hope that sampling at multiple times can compensate for the small number of entries observed at each time. This is joint work with C. Kuemmerle and S. Tang.
The second problem is when the dynamical system is nonlinear, and models a set of interacting agents. These systems are ubiquitous in science, from modeling of particles in Physics to prey-predator and colony models in Biology, to opinion dynamics in social sciences. Oftentimes the laws of interactions between the agents are quite simple, for example they depend only on pairwise interactions, and only on pairwise distance in each interaction. This is joint work with F. Lu, J. Feng, P. Martin, J.Miller, S. Tang and M. Zhong.

Jan 17, 2023 01:25 PM in Central Time (US and Canada)

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