### Mathematics Colloquium

** Naoki Masuda
**

University of Buffalo

**Title:** Temporal networks: State-transition dynamics, embedding, and switching network modeling

**Date:** Friday October 13, 2023

**Place and Time:** Love 101, 3:05-3:55 pm

**Abstract.**
Two salient features of empirical temporal (i.e., time-varying) network data are the time-varying nature of network structure itself and heavy-tailed distributions of inter-contact times. Both of them can strongly impact dynamical processes occurring on networks. In the first part of the talk, I introduce modeling of heavy-tailed distributions of inter-contact times by state-dynamics modeling approaches in which each node is assumed to switch among a small number of discrete states in a Markovian manner. This approach is interpretable, facilitates mathematical analyses, and seeds various related mathematical modeling, algorithms, and data analysis (e.g., embedding of temporal network data). The second part of the talk is on modeling of temporal networks by static networks that switch from one to another at regular time intervals. This approach facilitates analytical understanding of various dynamics (e.g., epidemic processes, evolutionary dynamics) on temporal networks as well as an efficient algorithm for containing epidemic spreading as convex optimization. Finally, I will touch upon my interdisciplinary collaborations on genomic data (analyzed as static multilayer networks) very briefly.