In this thesis, we study possible homotopy types of four families of simplicial complexes-the Morse complex, the generalized Morse complex, the matching complex, and the independence complex-using discrete Morse theory. Given a...
We introduce a new notion of equivalence of discrete Morse functions on graphs called persistence equivalence. Two functions are considered persistence equivalent if and only if they induce the same persistence diagram. We...
In his December 2014 interview with Michelle Dubert-Bellrichard, Stephen Lovegrove shares his story coming to Winthrop as an "out" student recently kicked out of a religious college. Lovegrove details his perception of the...
Mathematicians have long been interested in studying the properties of simplicial complexes. In 1998, Robin Forman developed gradient vector fields as a tool to study these complexes. Having gradient vector fields to study these...
The goal of this project is to construct a discrete Morse function which induces both a unique gradient vector field and homological sequence on a given tree. After reviewing the basics of discrete Morse theory, we will show...
In topology, simplicial complexes can be reduced to smaller complexes of the same simple homotopy type through a series of elementary collapses. It is a common goal to try to find the smallest complex that is of the same simple...
The field of topological data analysis seeks to use techniques in topology to study large data sets. The hope is that rather than single quantities that summarize the data, such as mean or standard deviation, information about...
Addressing the audience on media coverage of the political campaign, Chuck Todd said comedian Stephen Colbert is making a mockery of the system. The process is a mess, Todd said, but he wondered if Colbert is trying to influence...
Stephen J. Costello holds a BA, MA, and PhD in philosophy. He has addressed two parliaments—Stormont on human rights and the European Parliament in Brussels on mental health. He has twenty-five years’ experience giving seminars...
Dipender Gill and Stephen Burgess discuss the accompanying study by James Yarmolinsky and colleagues investigating the associations between genetically-proxied inhibition of antihypertensive drug targets and risk of common...
Searches for $CP$ violation in the two-body decays $D_{(s)}^{+}\rightarrow
h^{+}\pi^{0}$ and $D_{(s)}^{+} \rightarrow h^{+}\eta$ (where $h^{+}$ denotes a
$\pi^{+}$ or $K^{+}$ meson) are performed using $pp$ collision data...
Stephen J. Costello holds a BA, MA, and PhD in philosophy. He has addressed two parliaments—Stormont on human rights and the European Parliament in Brussels on mental health. He has twenty-five years’ experience giving seminars...
Onto My Love Saturday Midnight Michelle Today Firefly Black Midnight Bamboo Arms Caesaropapism A Day In My Life I Only For Stephen April 18, 1958 to July 15, 1977 with Emphasis on July 15 Ode to Little...
This study aimed to determine the effect of time of day on learning Mathematics by examining the optimal time of day to teach mathematics in a high school setting. Using a quantitative study, the data was gathered from high...
The first untagged decay-time-integrated amplitude analysis of $B^{0}_{s}
\rightarrow K^{0}_{\textrm{S}} K^{\pm}\pi^{\mp}$ decays is performed using a
sample corresponding to $3.0\,$fb$^{-1}$ of $pp$ collision data recorded...
A Dalitz plot analysis of B 0 → η c ( 1 S ) K + π - decays is performed using data samples of pp collisions collected with the LHCb detector at centre-of-mass energies of s = 7 , 8 and 13 Te V , corresponding to a...
DNA replication depends on primase, the specialised polymerase responsible for synthesis of the RNA primers that are elongated by the replicative DNA polymerases. In eukaryotic and archaeal replication, primase is a heterodimer...
Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are connected by organic linkers, are promising candidates for next-generation quantum technologies. MOMs readily form low-dimensional structures and so...
R-2-hydroxyglutarate accumulates to millimolar levels in cancer cells with gain-of-function isocitrate dehydrogenase 1/2 mutations. These levels of R-2-hydroxyglutarate affect 2-oxoglutarate-dependent dioxygenases. Both...
A comprehensive Raman resonance scattering study of ZnSxSe1-x (ZnSSe) solid solutions over the whole compositional range (0 ≤ x ≤ 1) has been made using 325 and 455 nm excitation wavelengths. The Raman scattering intensities of...
Antiphospholipid antibodies may occur spontaneously or associated with other diseases, including rheumatic autoimmunediseases and autoimmune thyroid diseases. One-third of patients with Systemic Lupus Erythematosus (SLE) possess...
Abstract: The cross-sections of ψ(2S) meson production in proton-proton collisions at s=13TeV are measured with a data sample collected by the LHCb detector corresponding to an integrated luminosity of 275pb-1. The production...