A Topological Lowpass Filter for Quasiperiodic Signals

This article presents a two-stage topological algorithm for recovering an estimate of a quasiperiodic function from a set of noisy measurements. The first stage of the algorithm is a topological phase estimator, which detects the quasiperiodic structure of the function without placing additional restrictions on the function. By respecting this phase estimate, the algorithm avoids creating distortion even when it uses a large number of samples for the estimate of the function

Analyzing wireless communication network vulnerability with homological invariants

This article explains how sheaves and homology theory can be applied to simplicial complex models of wireless communication networks to study their vulnerability to jamming. It develops two classes of invariants (one local and one global) for studying which nodes and links present more of a liability to the network's performance when under attack.Comment: Submitted to ICASSP 201