arXiv subjects

Mary Barker

Publications and source records attributed to Mary Barker.

6 recordsLinked to original sources

arXiv2023

The structure of deviations from maximum parsimony for densely-sampled data and applications for clade support estimation

How do phylogenetic reconstruction algorithms go astray when they return incorrect trees? This simple question has not been answered in detail, even for maximum parsimony (MP), the simplest phylogenetic criterion. Understanding MP has recently gained relevance in the regime of extremely dense sampling, where each virus sample commonly differs by zero or one mutation from another previously sampled virus. Although recent research shows that evolutionary histories in this regime are close to being maximally parsimonious, the structure of their deviations from MP is not yet understood. In this paper, we develop algorithms to understand how the correct tree deviates from being MP in the densely sampled case. By applying these algorithms to simulations that realistically mimic the evolution of SARS-CoV-2, we find that simulated trees frequently only deviate from maximally parsimonious trees locally, through simple structures consisting of the same mutation appearing independently on sister branches. We leverage this insight to design approaches for sampling near-MP trees and using them to efficiently estimate clade supports.

q-bio.PE↗

arXiv2023

Representing and extending ensembles of parsimonious evolutionary histories with a directed acyclic graph

In many situations, it would be useful to know not just the best phylogenetic tree for a given data set, but the collection of high-quality trees. This goal is typically addressed using Bayesian techniques, however, current Bayesian methods do not scale to large data sets. Furthermore, for large data sets with relatively low signal one cannot even store every good tree individually, especially when the trees are required to be bifurcating. In this paper, we develop a novel object called the "history subpartition directed acyclic graph" (or "history sDAG" for short) that compactly represents an ensemble of trees with labels (e.g. ancestral sequences) mapped onto the internal nodes. The history sDAG can be built efficiently and can also be efficiently trimmed to only represent maximally parsimonious trees. We show that the history sDAG allows us to find many additional equally parsimonious trees, extending combinatorially beyond the ensemble used to construct it. We argue that this object could be useful as the "skeleton" of a more complete uncertainty quantification.

q-bio.PE↗

arXiv2023

Crepant resolutions, mutations, and the space of potentials

The McKay correspondence has had much success in studying resolutions of 3-fold quotient singularities through a wide range of tools coming from geometry, combinatorics, and representation theory. We develop a computational perspective in this setting primarily realised through a web application to explore mutations of quivers with potential and crepant triangulations. We use this to study flops between different crepant resolutions of Gorenstein toric quotient singularities and find many situations in which the mutations of a quiver with potential classifies them. The application also implements key constructions of the McKay correspondence, including the Craw--Reid procedure and the process of associating a quiver to a toric resolution.

math.AG↗

arXiv2022

A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian

We introduce a nonconforming hybrid finite element method for the two-dimensional vector Laplacian, based on a primal variational principle for which conforming methods are known to be inconsistent. Consistency is ensured using penalty terms similar to those used to stabilize hybridizable discontinuous Galerkin (HDG) methods, with a carefully chosen penalty parameter due to Brenner, Li, and Sung [Math. Comp., 76 (2007), pp. 573-595]. Our method accommodates elements of arbitrarily high order and, like HDG methods, it may be implemented efficiently using static condensation. The lowest-order case recovers the $P_1$-nonconforming method of Brenner, Cui, Li, and Sung [Numer. Math., 109 (2008), pp. 509-533], and we show that higher-order convergence is achieved under appropriate regularity assumptions. The analysis makes novel use of a family of weighted Sobolev spaces, due to Kondrat'ev, for domains admitting corner singularities.

math.NA↗

arXiv2021

Quivers and moduli of their thin sincere representations in Macaulay2

We introduce the Macaulay2 package ThinSincereQuivers for studying acyclic quivers, the moduli of their thin-sincere representations, and the reflexive flow polytopes associated to them. We provide some background on the topic and illustrate how the package recovers examples from the literature.

math.AG↗

arXiv2020

The benefits of peer transparency in safe workplace operation post pandemic lockdown

The benefits, both in terms of productivity and public health, are investigated for different levels of engagement with the test, trace and isolate procedures in the context of a pandemic in which there is little or no herd immunity. Simple mathematical modelling is used in the context of a single, relatively closed workplace such as a factory or back-office where, in normal operation, each worker has lengthy interactions with a fixed set of colleagues. A discrete-time SEIR model on a fixed interaction graph is simulated with parameters that are motivated by the recent COVID-19 pandemic in the UK during a post-peak phase, including a small risk of viral infection from outside the working environment. Two kinds of worker are assumed, transparents who regularly test, share their results with colleagues and isolate as soon as a contact tests positive for the disease, and opaques who do none of these. Moreover, the simulations are constructed as a ``playable model" in which the transparency level, disease parameters and mean interaction degree can be varied by the user. The model is analysed in the continuum limit. All simulations point to the double benefit of transparency in maximising productivity and minimising overall infection rates. Based on these findings, public policy implications are discussed on how to incentivise this mutually beneficial behaviour in different kinds of workplace, and simple recommendations are made.

q-bio.PE↗