Projections of health outcomes in the USA in 2050
 Rysava, K Thompson, R Lancet volume 404 issue 10469 2246-2247 (07 Dec 2024)
Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling
 Erban, R Winkelmann, S Bulletin of Mathematical Biology volume 87 issue 1 (27 Nov 2024)

Song of the Week: Robert Wyatt - Sea Song

Sea Song is the first track on the album Rock Bottom which Robert Wyatt released after becoming paraplegic following an accidental fall from a window. He has said that the accident saved him because he had become an alcoholic and was heading for disaster.

Chalkdust

Copies of the latest Chalkdust magazine are now available in the Common Room. This new edition features an interview with our own Robin Wilson.

Back issues and information about how to write for Chalkdust can be found here.

October's new starters

Konstantin Riedl, PDRA in Deep Learning, Machine Learning and Data Science

Nick Kuhn, PDRA in Algebraic Geometry, Geometry

Andrea Medaglia, PDRA in Nonlinear Aggregation-Diffusion PDE, Oxford Centre for Non-Linear PDE

Andrew Graham, PDRA in Number Theory, Number Theory

Nathaniel Pritchard, PDRA in Numerical Analysis, Numerical Analysis

Stephanie Abo, PDRA in Data-Driven Modelling of Collective Cell Behaviour, Mathematical Biology

The σk-Loewner-Nirenberg problem on Riemannian manifolds for k < n2
 Duncan, J Nguyen, L Analysis & PDE
Fri, 01 Nov 2024
15:00
L5

Generalized Multiple Subsampling for Persistent Homology

Yueqi Cao
(Imperial College London)
Abstract

Persistent homology is infeasible to compute when a dataset is very large. Inspired by the bootstrapping method, Chazal et al. (2014) proposed a multiple subsampling approach to approximate the persistence landscape of a massive dataset. In this talk, I will present an extension of the multiple subsampling method to a broader class of vectorizations of persistence diagrams and to persistence diagrams directly. First, I will review the statistical foundation of the multiple subsampling approach as applied to persistence landscapes in Chazal et al. (2014). Next, I will talk about how this analysis extends to a class of vectorized persistence diagrams called Hölder continuous vectorizations. Finally, I will address the challenges in applying this method to raw persistence diagrams for two measures of centrality: the mean persistence measure and the Fréchet mean of persistence diagrams. I will demonstrate these methods through simulation results and applications in estimating data shapes. 

Subscribe to