Tuesday, August 14, 2018 - 1:00pm - 2:00pm
Matthew Wright (St. Olaf College)
This talk will introduce the Rank Invariant Visualization and Exploration Tool (RIVET). The first available software for two-parameter persistent homology, RIVET allows for the computation and visualization of both the bigraded Betti numbers and the rank invariant of two-dimensional persistence modules. The talk will demonstrate RIVET and explain the computational pipeline implemented in the software.
Monday, August 13, 2018 - 4:00pm - 5:00pm
Gregory Henselman (University of Pennsylvania)
This talk will introduce the central ideas of discrete Morse theory in high-performance (persistent) homology computation. Historically rooted in deep and beautiful structures from smooth geometry, this theory may be viewed, from a computational standpoint, as a very direct means of organizing cellular data to improve efficiency. Time permitting, we will discuss how the method of homological Morse reduction may be extended to the calculation of barcodes.
Monday, August 13, 2018 - 9:00am - 10:00am
Matthew Wright (St. Olaf College)
This talk will summarize the basics of persistent homology, including Rips and Cech complexes, filtrations, homology, the structure theorem for persistence modules, and barcodes.
This introductory talk is designed to reinforce the mathematical foundations of persistent homology, preparing participants for the subsequent talks in this workshop.
Thursday, June 7, 2018 - 11:00am - 11:50am
Sebastian Schreiber (University of California, Davis)
Two long standing, fundamental questions in biology are Under what conditions do populations persist or go extinct? When do interacting species coexist? The answers to these questions are essential for guiding conservation efforts and identifying mechanisms that maintain biodiversity. Mathematical models play an important role in identifying these mechanisms and, when coupled with empirical work, can determine whether or not a given mechanism is operating in a specific population or community.
Wednesday, June 22, 2016 - 2:00pm - 2:50pm
Yuncheng You (University of South Florida)
Stochastic viral dynamics modeled by stochastic differential equations with Beddington-DeAngelis functional response and rates driven by white noise will be presented. The stochastic positive invariance and the existence of stationary distribution are proved. Through estimation of the pathwise and asymptotic moment upper bounds, the moment Lyapunov exponent is shown to be nonpositive when the noise intensities are relatively small, and the persistence and extinction will be discussed.
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