arXiv subjects

Reemon Spector

Publications and source records attributed to Reemon Spector.

3 recordsLinked to original sources

arXiv2024

Persistent homology classifies parameter dependence of patterns in Turing systems

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter dependence of pattern topology in reaction diffusion systems, by examining the homology of sublevel sets of solutions to Turing reaction diffusion systems for a range of parameters. We demonstrate that a topological clustering algorithm can reveal how pattern topology depends on parameters, using the chlorite--iodide--malonic acid system, and the prototypical Schnakenberg system for illustration. In addition, we discuss the prospective application of such clustering, for instance in refining priors for detailed parameter estimation for self-organising systems.

q-bio.QM↗

arXiv2023

A Symmetry-based Framework for Model Selection of Coral Reef Population Growth Models

The problem of selecting a model given a set of candidates remains a challenging one that pervades many scientific fields. We employ techniques from the theory of Lie groups to analyse the symmetries in differential equation models of population growth, with the aim of informing the model selection problem. To illustrate the use of Lie symmetries in model selection, we apply them to simulated data and to coral reef data from the Great Barrier Reef, demonstrating that the trivial symmetries can distinguish between candidate models. A method for finding locally optimal parameters for multi-parameter symmetries is presented, and the paper concludes with related results, some open problems, and avenues of further research.

q-bio.QM↗

arXiv2021

On the Smallest Non-trivial Action of SAut(Fn) for Small n

In this paper we investigate actions of $\operatorname{SAut}(F_n)$, the unique index $2$ subgroup of $\operatorname{Aut}(F_n)$, on small sets, improving upon results by Baumeister--Kielak--Pierro for several small values of $n$. Using a computational approach for $n \geqslant 5$, we show that every action of $\operatorname{SAut}(F_n)$ on a set containing fewer than $18$ elements is trivial.

math.GR↗