1,627 research outputs found
Symmetries of Riemann surfaces and magnetic monopoles
This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bringâs curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bringâs curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models
This paper considers the specification of covariance structures with tail
estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk
matrix in the case of larger number of time series observations than assets in
a portfolio using quantile predictive regression models without assuming the
presence of nonstationary regressors and; (ii) the construction of a novel
variable selection algorithm, so-called, Feature Ordering by Centrality
Exclusion (FOCE), which is based on an assumption-lean regression framework,
has no tuning parameters and is proved to be consistent under general sparsity
assumptions. We illustrate the usefulness of our proposed methodology with
numerical studies of real and simulated datasets when modelling systemic risk
in a network
The Expressive Power of Graph Neural Networks: A Survey
Graph neural networks (GNNs) are effective machine learning models for many
graph-related applications. Despite their empirical success, many research
efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive
power. Early works in this domain mainly focus on studying the graph
isomorphism recognition ability of GNNs, and recent works try to leverage the
properties such as subgraph counting and connectivity learning to characterize
the expressive power of GNNs, which are more practical and closer to
real-world. However, no survey papers and open-source repositories
comprehensively summarize and discuss models in this important direction. To
fill the gap, we conduct a first survey for models for enhancing expressive
power under different forms of definition. Concretely, the models are reviewed
based on three categories, i.e., Graph feature enhancement, Graph topology
enhancement, and GNNs architecture enhancement
Measuring the impact of COVID-19 on hospital care pathways
Care pathways in hospitals around the world reported significant disruption during the recent COVID-19 pandemic but measuring the actual impact is more problematic. Process mining can be useful for hospital management to measure the conformance of real-life care to what might be considered normal operations. In this study, we aim to demonstrate that process mining can be used to investigate process changes associated with complex disruptive events. We studied perturbations to accident and emergency (A &E) and maternity pathways in a UK public hospital during the COVID-19 pandemic. Co-incidentally the hospital had implemented a Command Centre approach for patient-flow management affording an opportunity to study both the planned improvement and the disruption due to the pandemic. Our study proposes and demonstrates a method for measuring and investigating the impact of such planned and unplanned disruptions affecting hospital care pathways. We found that during the pandemic, both A &E and maternity pathways had measurable reductions in the mean length of stay and a measurable drop in the percentage of pathways conforming to normative models. There were no distinctive patterns of monthly mean values of length of stay nor conformance throughout the phases of the installation of the hospitalâs new Command Centre approach. Due to a deficit in the available A &E data, the findings for A &E pathways could not be interpreted
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Taking shape: The data science of elastic shape analysis with practical applications
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.A mathematical curve can represent many different objects, both physical and abstract,
from the outline curve of an artefact in an image to the weight of growing animal to
the set of frequencies used in a sound. Regardless of these variations, the curves can
almost always vary non-linearly. One way to study shapes and their potential variations
is elastic shape analysis, a rich theory of which has developed over the past twenty years.
However, methods of elastic shape analysis are seldom utilized in practical applications
on real-world data, especially outside of the mathematical shape analysis community.
Our aim in this thesis is to explore some practical applications of elastic shape analysis.
To do this, we work with various types of shape data, the majority of which are based on
image datasets. As our focus is on two-dimensional curves, it is important to be able to
robustly extract contours from images, before we can apply elastic shape analysis tools.
In order to analyse the shapes in a dataset, we turn to methods of machine learning, to
investigate the applications of elastic shape analysis in classification.
In this thesis, we introduce an anthology of projects, in order to emphasise and under-
stand the potential of elastic shape analysis in practical applications. There are four main
projects in this thesis: (i) Classification of objects using outlines and the comparisons
between methods of elastic shape analysis, geometric morphometrics, and human experts,
with a focus on ancient Greek vases, (ii) Mussel species identification and a demonstra-
tion that shape may not be enough in some applications, (iii) A novel tool to monitor
the development of k Ìak Ìap Ìo chicks, and (iv) Classifying individual kiwi based on acoustic
data from their calls.
By combining tools from computer vision and machine learning with methods of elastic
shape analysis, we introduce a practical framework for the application of elastic shape
analysis, through a data science lens
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