Applications of Topological Data Analysis to Statistical Physics and Quantum Field Theories

This thesis motivates and examines the use of methods from topological data analysis in detecting and analysing topological features relevant to models from sta-tistical physics and particle physics.In statistical physics, we use persistent homology as an observable of three dif-ferent variants of the two-dimensional XY model in order to identify relevant topo-logical features and study their relation to the phase transitions undergone by each model. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and demonstrate its use in detecting topological defects called vortices. By considering the fluctuations in the output of logistic regression and k-nearest neighbours mod-els trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.In particle physics, we investigate the use of persistent homology as a means to detect and quantitatively describe center vortices in SU(2) lattice gauge theory in a gauge-invariant manner. The sensitivity of our method to vortices in the deconfined phase is confirmed by using twisted boundary conditions which inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a k-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical β and critical exponent of correlation length for the deconfinement phase transition. We also use persistent homology to study the stability of vortices under gradient flow and the classification of different vortex surface geometries

Probing center vortices and deconfinement in SU(2)\mathrm{SU}(2) lattice gauge theory with persistent homology

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in $\mathrm{SU}(2)$ lattice gauge theory in a gauge-invariant manner. We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase. This inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a simple $k$-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical $\beta$ and critical exponent of correlation length $\nu$ of the deconfinement phase transition.Comment: 18 pages, 19 figures, accepted versio

Persistent homology as a probe for center vortices and deconfinement in SU(2) lattice gauge theory

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology, produces a quantitative description of how the connectivity and structure of data changes when viewed over a sequence of scales. We propose that this presents a means to directly probe topological objects in gauge theories. We present recent work on using persistent homology to detect center vortices in SU(2) lattice gauge theory configurations in a gauge-invariant manner. We introduce the basics of persistence, describe our construction, and demonstrate that the result is sensitive to vortices. Moreover we discuss how, with simple machine learning, one can use the resulting persistence to quantitatively analyse the deconfinement transition via finite-size scaling, providing evidence on the role of vortices in relation to confinement in Yang-Mills theories.Comment: 9 pages, 4 figures. Proceeding for the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany. A condensed writeup of results from arXiv:2207.1339

Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in SU(2) lattice gauge theory in a gaugeinvariant manner. We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase. This inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a simple k-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical β and critical exponent of correlation length ν of the deconfinement phase transition

R-loop formation during S phase is restricted by PrimPol-mediated repriming

During DNA replication conflicts with ongoing transcription are frequent and require careful management to avoid genetic instability. R-loops, three stranded nucleic acid structures comprising a DNA:RNA hybrid and displaced single stranded DNA, are important drivers of damage arising from such conflicts. How R-loops stall replication and the mechanisms that restrain their formation during S phase are incompletely understood. Here we show in vivo how R-loop formation drives a short purine-rich repeat, (GAA)10, to become a replication impediment that engages the repriming activity of the primase-polymerase PrimPol. Further, the absence of PrimPol leads to significantly increased R-loop formation around this repeat during S phase. We extend this observation by showing that PrimPol suppresses R-loop formation in genes harbouring secondary structure-forming sequences, exemplified by G quadruplex and H-DNA motifs, across the genome in both avian and human cells. Thus, R- loops promote the creation of replication blocks at susceptible structure-forming sequences, while PrimPol-dependent repriming limits the extent of unscheduled R-loop formation at these sequences, mitigating their impact on replication

An Equity-focused Assessment of the City of Richmond’s RVAgreen 2050 Planning Process

Local climate action and sustainability initiatives are often critiqued for their inattention to issues of equity and justice. In response, an increasing number of cities are now attempting to respond to this critique by making equity a more explicit goal of their climate action plans: Richmond Virginia is among those cities. The City of Richmond\u27s Office of Sustainability committed to prioritizing equity in the RVAGreen 2050 plan by recognizing how Richmond’s history of racism and structural inequalities have exacerbated climate concerns for largely Black and Latinx communities and centering historically marginalized communities of color in the engagement process. Students in URSP 637 Sustainable Community Development were asked to provide an external evaluation of the RVAGreen 2050 planning process. This report summarizes the findings of this evaluation and highlights recommendations for how to improve equity-centered engagement processed moving forward

Disseminating research with web CV hyperlinks

This is an accepted manuscript of an article published by John Wiley & Sons Ltd in Journal of the Association for Information Science and Technology on 03/07/2014, available online: https://doi.org/10.1002/asi.23070 The accepted version of the publication may differ from the final published version.Some curricula vitae (web CVs) of academics on the web, including homepages and publication lists, link to open‐access (OA) articles, resources, abstracts in publishers' websites, or academic discussions, helping to disseminate research. To assess how common such practices are and whether they vary by discipline, gender, and country, the authors conducted a large‐scale e‐mail survey of astronomy and astrophysics, public health, environmental engineering, and philosophy across 15 European countries and analyzed hyperlinks from web CVs of academics. About 60% of the 2,154 survey responses reported having a web CV or something similar, and there were differences between disciplines, genders, and countries. A follow‐up outlink analysis of 2,700 web CVs found that a third had at least one outlink to an OA target, typically a public eprint archive or an individual self‐archived file. This proportion was considerably higher in astronomy (48%) and philosophy (37%) than in environmental engineering (29%) and public health (21%). There were also differences in linking to publishers' websites, resources, and discussions. Perhaps most important, however, the amount of linking to OA publications seems to be much lower than allowed by publishers and journals, suggesting that many opportunities for disseminating full‐text research online are being missed, especially in disciplines without established repositories. Moreover, few academics seem to be exploiting their CVs to link to discussions, resources, or article abstracts, which seems to be another missed opportunity for publicizing research

Global human footprint on the linkage between biodiversity and ecosystem functioning in reef fishes

Copyright: © 2011 Mora et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Difficulties in scaling up theoretical and experimental results have raised controversy over the consequences of biodiversity loss for the functioning of natural ecosystems. Using a global survey of reef fish assemblages, we show that in contrast to previous theoretical and experimental studies, ecosystem functioning (as measured by standing biomass) scales in a non-saturating manner with biodiversity (as measured by species and functional richness) in this ecosystem. Our field study also shows a significant and negative interaction between human population density and biodiversity on ecosystem functioning (i.e., for the same human density there were larger reductions in standing biomass at more diverse reefs). Human effects were found to be related to fishing, coastal development, and land use stressors, and currently affect over 75% of the world's coral reefs. Our results indicate that the consequences of biodiversity loss in coral reefs have been considerably underestimated based on existing knowledge and that reef fish assemblages, particularly the most diverse, are greatly vulnerable to the expansion and intensity of anthropogenic stressors in coastal areas