AATRN Networks Seminar, March 3 at 5pm CET by Daniel Hernández Serrano

[Jason Smith]

Dear AATRN Networks Seminar members,

Our next online seminar will be on Tuesday, 3rd March, at 5pm CET / 11am Eastern Time.

Speaker: Daniel Hernández Serrano

Title: From Persistence to Resilience: TDA for Measuring Robustness in Simplicial Complex Networks

Abstract: Persistent homology is a central tool in Topological Data Analysis, yet it does not quantify how fragile or structurally refined homological cycles are. In particular, classical Betti numbers ignore the dimensions of the simplices generating these cycles, as well as the higher-order adjacency relations among them. In this work, we investigate the robustness of simplicial networks by analyzing cycle thickness and cohesiveness under random failures and targeted attacks. Inspired by persistent homology, we introduce new filtrations based on simplicial elimination rules, leading to two new invariants: thick Betti numbers and cohesive Betti numbers. These invariants provide a refined characterization of homological features, quantifying link thickness and connection strength within cycles. Finally, we show that resilience to simplicial attacks can be systematically studied through biparameter persistence modules, where one parameter models the attack process and the other captures structural refinement via thickness or cohesiveness.

We will meet in the following coordinates:

https://stockholmuniversity.zoom.us/j/65622268279?pwd=YUsxeGNEeEFKRDFsaTRzRzh2VVMzQT09

Meeting ID: 656 2226 8279

Passcode: 557173

Our seminar usually occurs on the first Tuesday of every month, and you can follow our future planned list of speakers on our website sites.google.com/view/aatrn-networks-seminar.

You may also be interested in adding AATRN’s Google calendar (link), which contains other seminar information.

Best,

The AATRN Networks Seminar organisers

Daniela Egas Santander, Henri Riihimäki, Jason Smith

https://www.youtube.com/@aatrn1