arXiv subjects

Shawn Walker

Publications and source records attributed to Shawn Walker.

5 recordsLinked to original sources

arXiv2024

A Taxonomy of Challenges to Curating Fair Datasets

Despite extensive efforts to create fairer machine learning (ML) datasets, there remains a limited understanding of the practical aspects of dataset curation. Drawing from interviews with 30 ML dataset curators, we present a comprehensive taxonomy of the challenges and trade-offs encountered throughout the dataset curation lifecycle. Our findings underscore overarching issues within the broader fairness landscape that impact data curation. We conclude with recommendations aimed at fostering systemic changes to better facilitate fair dataset curation practices.

cs.LG↗

arXiv2020

Ion-dependent DNA Configuration in Bacteriophage Capsids

Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy which combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is currently possible using the existing simulations, typically done at a molecular level. In particular, we are able to estimate bending and repulsion between DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and molecular dynamics simulations for small capsids.

cond-mat.soft↗

arXiv2019

Coefficient growth in square chains

Suppose $((\cdots((x^{2}-c_{1})^{2}-c_{2})^{2}\cdots)^{2}-c_{k-1})^{2}-c_{k}$ splits into linear factors over $\mathbb{Z}$ and $c_{k}\neq0$. We show that for each $j$ and each prime $p$, if $p\leq2^{j-1}$ then $p$ divides $c_{j}$. Consequently, $$\ln c_{j}>\frac{1}{4}\cdot2^{j}\,\,\mathrm{for}\,j\geq5$$ If we also have $p\equiv3\,(\mathrm{mod\,4)}$ then $p^{2^{j-\left\lceil \lg p\right\rceil }}$ divides $c_{j}$. Consequently, if $k\geq3$, there exists some absolute constant $\lambda>0$ so that, $$\ln c_{j}>\lambda k2^{j}\mathrm{\,\,for\,all\,}j$$ These estimates argue against the possibility of explicitly constructing polynomials of the given form for large $k$, as the coefficients quickly become too large to manipulate.

math.NT↗

arXiv2019

Fine Structure of Viral dsDNA Encapsidation

In vivo configurations of dsDNA of bacteriophage viruses in a capsid are known to form hexagonal chromonic liquid crystal phases. This article studies the liquid crystal ordering of viral dsDNA in an icosahedral capsid, combining the chromonic model with that of liquid crystals with variable degree of orientation. The scalar order parameter of the latter allows us to distinguish regions of the capsid with well-ordered DNA from the disordered central core. We employ a state-of-the-art numerical algorithm based on the finite element method to find equilibrium states of the encapsidated DNA and calculate the corresponding pressure. With a data-oriented parameter selection strategy, the method yields phase spaces of the pressure and the radius of the disordered core, in terms of relevant dimensionless parameters, rendering the proposed algorithm into a preliminary bacteriophage designing tool. The presence of the order parameter also has the unique role of allowing for non-smooth capsid domains as well as accounting for knot locations of the DNA.

cond-mat.soft↗

arXiv2017

Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes

We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, $C^3$, surface without boundary on general shape regular meshes. As an application, we consider a problem where the domain is split into two regions: one which has relatively high curvature and one that has low curvature. Using a graded mesh we prove error estimates that do not depend on the curvature on the high curvature region. Numerical experiments are provided.

math.NA↗