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Articles 1 - 30 of 5892
Full-Text Articles in Physical Sciences and Mathematics
Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace
Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace
Electronic Theses, Projects, and Dissertations
Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …
Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad
Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad
Dissertations
The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …
The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi
The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi
LSU Doctoral Dissertations
Discriminant ideals are defined for an algebra R with central subalgebra C and trace tr : R → C. They are indexed by positive integers and more general than discriminants. Usually R is required to be a finite module over C. Unlike the abundace of work on discriminants, there is hardly any literature on discriminant ideals. The levels of discriminant ideals relate to the sums of squares of dimensions of irreducible modules over maximal ideals of C containing these discriminant ideals. We study the lowest level when R is a Cayley-Hamilton Hopf algebra, i.e. C is also a Hopf subalgebra, …
Finite Monodromy And Artin Representations, Emma Lien
Finite Monodromy And Artin Representations, Emma Lien
LSU Doctoral Dissertations
Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the …
Reducibility Of Schrödinger Operators On Multilayer Graphs, Jorge Villalobos Alvarado
Reducibility Of Schrödinger Operators On Multilayer Graphs, Jorge Villalobos Alvarado
LSU Doctoral Dissertations
A local defect in an atomic structure can engender embedded eigenvalues when the associated Schrödinger operator is either block reducible or Fermi reducible, and having multilayer structures appears to be typically necessary for obtaining such types of reducibility. Discrete and quantum graph models are commonly used in this context as they often capture the relevant features of the physical system in consideration.
This dissertation lays out the framework for studying different types of multilayer discrete and quantum graphs that enjoy block or Fermi reducibility. Schrödinger operators with both electric and magnetic potentials are considered. We go on to construct a …
Subroups Of Coxeter Groups And Stallings Foldings, Jake A. Murphy
Subroups Of Coxeter Groups And Stallings Foldings, Jake A. Murphy
LSU Doctoral Dissertations
For each finitely generated subgroup of a Coxeter group, we define a cell complex called a completion. We show that these completions characterizes the index and normality of the subgroup. We construct a completion corresponding to the intersection of two subgroups and use this construction to characterize malnormality of subgroups of right-angled Coxeter groups. Finally, we show that if a completion of a subgroup is finite, then the subgroup is quasiconvex. Using this, we show that certain reflection subgroups of a Coxeter are quasiconvex.
Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju
Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju
LSU Doctoral Dissertations
In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G′ = O1,n(R) be the Lorentz group, and let H′ = O1,n−1(R) ⊂ G′ be its subset. The de Sitter space dSn is a one-sheeted hyperboloid in R1,n isomorphic to G′/H′. A spherical distribution is an H′-invariant eigendistribution of the Laplace-Beltrami operator on dSn. The space of spherical distributions with eigenvalue λ, denoted by DλH'(dSn), has dimension 2. We construct a basis for the space of …
The Modular Generalized Springer Correspondence For The Symplectic Group, Joseph Dorta
The Modular Generalized Springer Correspondence For The Symplectic Group, Joseph Dorta
LSU Doctoral Dissertations
The Modular Generalized Springer Correspondence (MGSC), as developed by Achar, Juteau, Henderson, and Riche, stands as a significant extension of the early groundwork laid by Lusztig's Springer Correspondence in characteristic zero which provided crucial insights into the representation theory of finite groups of Lie type. Building upon Lusztig's work, a generalized version of the Springer Correspondence was later formulated to encompass broader contexts.
In the realm of modular representation theory, Juteau's efforts gave rise to the Modular Springer Correspondence, offering a framework to explore the interplay between algebraic geometry and representation theory in positive characteristic. Achar, Juteau, Henderson, and Riche …
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine
Honors Program Theses and Research Projects
Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …
Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, Heather Moore
Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, Heather Moore
University Honors Theses
This thesis presents a surprising result that the difference in a certain sums of constant rotations by the golden mean approaches exactly 1/5. Specifically, we focus on the Birkhoff sums of these rotations, with the number of terms equal to squared Fibonacci numbers. The proof relies on the properties of continued fraction approximants, Vajda's identity and the explicit formula for the Fibonacci numbers.
Understanding Waveguides In Resonance, Pieter Johannes Daniel Vandenberge
Understanding Waveguides In Resonance, Pieter Johannes Daniel Vandenberge
Dissertations and Theses
Several important classes of modern optical waveguides, including anti-resonant reflecting and photonic bandgap fibers, make use of geometries that guide energy in low refractive index material, a property that makes them of significant interest in numerous applications, notably including high-power delivery and guidance. These waveguides frequently exhibit resonance phenomena, in which their ability to propagate an input signal is sharply curtailed at particular operating frequencies. In this work we detail new advances in understanding these resonance effects and their implications for numerical modeling of these structures.
Part 1 focuses on the fields of slab waveguides, relatively simple structures for which …
New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman
New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman
Dissertations, Theses, and Capstone Projects
Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …
A Causal Inference Approach For Spike Train Interactions, Zach Saccomano
A Causal Inference Approach For Spike Train Interactions, Zach Saccomano
Dissertations, Theses, and Capstone Projects
Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …
Construction Of Quot-Schemes, Majid Dehghani
Construction Of Quot-Schemes, Majid Dehghani
Electronic Theses and Dissertations
The Quot Scheme is a construction representing parameter spaces for quotient objects of sheaves or coherent modules over a scheme. It encapsulates families of quotients by fixing a certain quotient's structure. The Hilbert Scheme, a specific type of Quot Scheme, focuses on parameterizing subschemes of a fixed projective space by fixing their Hilbert polynomials. After recalling the basic concepts of the theory, we explain the Grothendieck’s Quot scheme construction and its Grassmannian embedding. Then we continue to an explicit construction of Quot scheme in the case of graded modules over graded rings.
On A Class Of James-Stein’S Estimators In High-Dimensional Data, Arash Aghaei Foroushani
On A Class Of James-Stein’S Estimators In High-Dimensional Data, Arash Aghaei Foroushani
Electronic Theses and Dissertations
In this thesis, we consider the estimation problem of the mean matrix of a multivariate normal distribution in high-dimensional data. Building upon the groundwork laid by Chételat and Wells (2012), we extend their method to the cases where the parameter is the mean matrix of a matrix normal distribution. In particular, we propose a novel class of James-Stein’s estimators for the mean matrix of a multivariate normal distribution with an unknown row covariance matrix and independent columns. Given a realistic assumption, we establish that our proposed estimator outperforms the classical maximum likelihood estimator (MLE) in the context of high-dimensional data. …
The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka
The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka
Theses, Dissertations and Culminating Projects
No abstract provided.
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
Theses and Dissertations (Comprehensive)
The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …
The Deep Bsde Method, Daniel Kovach
The Deep Bsde Method, Daniel Kovach
Masters Theses
"The curse of dimensionality is the non-linear growth in computing time as the dimension of a problem increases. Using the Deep Backwards Stochastic Differential Equation (Deep BSDE) method developed in [HJE18], I approximate the solution at an initial time to a one-dimensional diffusion equation. Although we only approximate a one-dimensional equation, this method extends well to higher dimensions because it overcomes the curse of dimensionality by evaluating the given partial differential equation along "random characteristics''. In addition to the implementation, I also present most of the mathematical theory needed to understand this method"-- Abstract, p. iii
Solutions To The Kaluza-Klein Field Equations, Abel Eshete
Solutions To The Kaluza-Klein Field Equations, Abel Eshete
All Graduate Theses, Dissertations, and Other Capstone Projects
This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …
Graph Coloring Reconfiguration, Reem Mahmoud
Graph Coloring Reconfiguration, Reem Mahmoud
Theses and Dissertations
Reconfiguration is the concept of moving between different solutions to a problem by transforming one solution into another using some prescribed transformation rule (move). Given two solutions s1 and s2 of a problem, reconfiguration asks whether there exists a sequence of moves which transforms s1 into s2. Reconfiguration is an area of research with many contributions towards various fields such as mathematics and computer science.
The k-coloring reconfiguration problem asks whether there exists a sequence of moves which transforms one k-coloring of a graph G into another. A move in this case is a type …
Echolocation On Manifolds, Kerong Wang
Echolocation On Manifolds, Kerong Wang
Honors Theses
We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.
In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …
Edge Colored And Edge Ordered Graphs, Per Gustin Wagenius
Edge Colored And Edge Ordered Graphs, Per Gustin Wagenius
Graduate College Dissertations and Theses
In this work, the current state of the field of edge-colored graphs is surveyed. Anew concept of unshrinkable edge colorings is introduced which is useful for rainbow subgraph problems and interesting in its own right. This concept is analyzed in some depth. Building upon the linear edge ordering described in a recent work from Gerbner, Methuku, Nagy, Pálvölgyi, Tardos, and Vizer, edge-ordering graphs with the cyclic group is introduced and some results are given on this and a related counting problem.
Computing The Canonical Ring Of Certain Stacks, Jesse Franklin
Computing The Canonical Ring Of Certain Stacks, Jesse Franklin
Graduate College Dissertations and Theses
We compute the canonical ring of some stacks. We first give a detailed account of what this problem means including several proofs of a famous historical example. The main body of work of this thesis expands on our article \cite{Franklin-geometry-Drinfeld-modular-forms} in describing the geometry of Drinfeld modular forms as sections of a specified line bundle on a certain stacky modular curve. As a consequence of that geometry, we provide a program: one can compute the (log) canonical ring of a stacky curve to determine generators and relations for an algebra of Drinfeld modular forms, answering a problem posed by Gekeler …
Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise
Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise
Masters Theses
The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …
A Map-Algebra-Inspired Approach For Interacting With Wireless Sensor Networks, Cyber-Physical Systems Or Internet Of Things, David Almeida
A Map-Algebra-Inspired Approach For Interacting With Wireless Sensor Networks, Cyber-Physical Systems Or Internet Of Things, David Almeida
Electronic Theses and Dissertations
The typical approach for consuming data from wireless sensor networks (WSN) and Internet of Things (IoT) has been to send data back to central servers for processing and analysis. This thesis develops an alternative strategy for processing and acting on data directly in the environment referred to as Active embedded Map Algebra (AeMA). Active refers to the near real time production of data, and embedded refers to the architecture of distributed embedded sensor nodes. Network macroprogramming, a style of programming adopted for wireless sensor networks and IoT, addresses the challenges of coordinating the behavior of multiple connected devices through a …
The Construction Of Khovanov Homology, Shiaohan Liu
The Construction Of Khovanov Homology, Shiaohan Liu
Master's Theses
Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent …
A Bridge Between Graph Neural Networks And Transformers: Positional Encodings As Node Embeddings, Bright Kwaku Manu
A Bridge Between Graph Neural Networks And Transformers: Positional Encodings As Node Embeddings, Bright Kwaku Manu
Electronic Theses and Dissertations
Graph Neural Networks and Transformers are very powerful frameworks for learning machine learning tasks. While they were evolved separately in diverse fields, current research has revealed some similarities and links between them. This work focuses on bridging the gap between GNNs and Transformers by offering a uniform framework that highlights their similarities and distinctions. We perform positional encodings and identify key properties that make the positional encodings node embeddings. We found that the properties of expressiveness, efficiency and interpretability were achieved in the process. We saw that it is possible to use positional encodings as node embeddings, which can be …
Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye
Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye
Electronic Theses and Dissertations
Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …
Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum
Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum
Master's Theses
We used Dr. M. L. Lapidus's Fractal Zeta Functions to analyze the complex fractal dimensions of 100 different modifications of the Sierpinski Carpet fractal construction. We will showcase the theorems that made calculations easier, as well as Desmos tools that helped in classifying the different fractals and computing their complex dimensions. We will also showcase all 100 of the Sierpinski Carpet modifications and their complex dimensions.