A Sparse Hierarchical <i>hp</i>-Finite Element Method on Disks and Annuli.
Papadopoulos, I Olver, S Journal of scientific computing volume 104 issue 2 51 (23 Jan 2025)
A sparse spectral method for fractional differential equations in one-spatial dimension
Papadopoulos, I Olver, S Advances in Computational Mathematics volume 50 issue 4 (01 Aug 2024)
On manifolds with almost non-negative Ricci curvature and integrally-positive $$k^{th}$$-scalar curvature
Cucinotta, A Mondino, A Mathematische Annalen volume 394 issue 2 (15 Feb 2026)
Fri, 13 Mar 2026
13:15
L6

Persistent Cycle Representatives and Generalized Persistence Landscapes in Codimension 1

Leon Renkin
(Max Planck Institute of Molecular Cell Biology and Genetics)
Abstract

A common challenge in persistent homology is choosing "good" representative cycles for homology classes in a way compatible with persistence. In this talk, we discuss a geometric framework for codimension-1 persistent homology that addresses this issue using Alexander duality.

For an embedded filtered simplicial complex, connected components of the complement induce cycle representatives for a homology basis. The evolution of these cycles along the filtration can be tracked via the merge tree of the complement and the elder rule. This leads to the notion of cycle progression barcodes, associating to each persistence interval a sequence of representative cycles evolving through the filtration.

Applying geometric functionals to these progressions produces generalized persistence landscapes, which extend classical persistence landscapes and allow geometric information about cycle representatives to be captured without fixing a single filtration value. This provides a way to distinguish data sets with similar persistent homology but different geometric structure.

Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data
Medaglia, A Pareschi, L Zanella, M Journal of Computational Physics volume 503 (15 Apr 2024)
CORRIGENDUM: An entanglement monotone from the contextual fraction (2025 New J. Phys. 27 054506)
Chan, T Constantin, A New Journal of Physics volume 28 issue 2 029501 (01 Feb 2026)
Testing the assumptions of linear prediction analysis in normal vowels
Little, M McSharry, P Moroz, I Roberts, S (03 Jan 2006)
The τ -function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant
Desiraju, H Journal of Mathematical Physics volume 60 issue 11 (01 Nov 2019)
Painlevé/CFT correspondence on a torus
Desiraju, H Journal of Mathematical Physics volume 63 issue 8 (01 Aug 2022)
Fredholm determinant representation of the homogeneous Painlevé II τ-function
Desiraju, H Nonlinearity volume 34 issue 9 6507-6538 (01 Sep 2021)
Subscribe to