Moments approaches for asymptotic inverse problems of depolymerisation and fragmentation systems

TL;DR

This paper reviews moment-based approaches to solve inverse problems related to depolymerisation and fragmentation systems, focusing on estimating initial distributions and fragmentation characteristics from experimental data.

Contribution

It introduces moment methods for inverse problems in depolymerisation and fragmentation systems, connecting theoretical models with biological experiments.

Findings

Effective estimation of initial size-distributions from moments.

Inference of fragmentation characteristics from size distribution data.

Application to biological systems and experimental validation.

Abstract

Shrinkage of large particles, either through depolymerisation (i.e. progressive shortening) or through fragmentation (breakage into smaller pieces) may be modelled by discrete equations, of Becker-D\''oring type, or by continuous ones. In this note, we review two kinds of inverse problems: the first is the estimation of the initial size-distribution from moments measurements in a depolymerising system, in collaboration with Philippe Moireau and inspired by experiments carried out by Human Rezaei's team; the second is the inference of fragmentation characteristics from size distribution samples, in collaboration with Miguel Escobedo and Magali Tournus, based on biological questions and experiments of Wei-Feng Xue's team.