Other Applied Mathematics Commons^™

Asymptotic Expansion Of A Maier-Saupe Type Potential Near The Nematic-Isotropic Transition Point In Liquid Crystals, Ryan P. Oneill, Giangvuthanh Nguyen, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

In this paper we study a Maier-Saupe type bulk potential (Maier & Saupe, 1959) in the Landau-de Gennes free energy in the Q-tensor theory modeling nematic liquid crystal configurations. This potential was originally introduced in Katriel et al. (1986), which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. More specifically, we present a rigorous derivation of the asymptotic expansion of this singular potential near the nematic-isotropic transition point up to the 4-th order.

(Si13-04) System Of Variational Inclusions Involving Cayley Operator And Yosida Approximation Operator With Xor Operations, Mohd Iqbal, Tirth Ram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider and study a new class of system of variational inclusions called a system of variational inclusions involving Cayley operator and Yosida approximation operator with XOR operation. We have shown that our problem is equivalent to a fixed point equation. Based on fixed point formulation, an iterative algorithm is designed to obtain existence and convergence result for our problem.

Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong

Education Division Scholarship

Children spend most of their time at home in their early years, yet efforts to promote human capital at home in many low- and middle-income settings remain limited. We conduct a randomized controlled trial to evaluate an intervention which encourages parents and caregivers to foster human capital accumulation among their children between ages 3 and 5, with a focus on math and phonics skills. Children gain 0.52 and 0.51 standard deviations relative to the control group on math and phonics tests, respectively (p<0.001). A year later effects persist, but math gains dissipate to 0.15 (p=0.06) and phonics to 0.13 (p=0.12). Effects appear to be mediated largely through instructional support by parents and not other parent investment mechanisms, such as more positive parent-child interactions or additional time spent on education at home beyond the intervention. Our results show that parents can be effective conduits of educational instruction even in low-resource settings.

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

The Feasibility Of Utilizing The Open Dynamic Interaction Network (Odin) App To Assess Rema Data Across 30 Days Among Those Recovering From Alcoholism, Dennis E. Mcchargue, Bilal Khan, Jesscia Phelps, Patrick Duryea, Kimberly A. Tyler, Arthur Andrews, Ellie Reznicek, Lucy Napper, Mohamed Saad, Hsuan-Wee Lee

Department of Psychology: Faculty Publications

About ~4 million people with an alcohol use disorder receive treatment annually, and frequent relapse has produced a rapid revolving door between recovery and use. This paper presents preliminary data from a prospective micro-longitudinal study (30 days) that examines co-evolution of relapse risk processes of people with alcohol use disorders who entered a short-term residential substance use treatment. The primary goal of the current data was to assess the feasibility of using the open dynamic interaction network (ODIN) responsive ecological momentary assessment (rEMA). rEMA collected daily estimates on affect, urges, sober-support engagement, and use. The ODIN app administered twelve questions …

First-Order Algorithms For Convex Smooth Optimization Problems With Homogeneous Linear Constraints, Yidan Guo

All Dissertations

The purpose of this dissertation is to explore the first-order methods that can be used to solve an approximate solution for convex smooth problems with homogeneous linear constraints. It consists of three interconnected research projects.

In the first project, we study the problem of computing the projection of a given vector onto the kernel of a symmetric positive semi-definite matrix. The complexity of an algorithm for computing a numerical solution is evaluated by the total number of matrix-vector multiplications required for computing an approximate solution. Such problems arise commonly in consensus optimization, in which the total number of matrix-vector multiplications …

Optimization Strategies For Political Redistricting, Blake Splitter

All Dissertations

Political redistricting has remained a hot-button issue in the United States for several decades. Every ten years, most states need to redraw their districts to account for changing populations. Sometimes, these district plans can be drawn with the malevolent intention of aiding one political party over another. This dissertation summarizes four distinct methods of drawing these districts using computer algorithms while keeping several objectives in mind. We test these approaches on the case study state of South Carolina, since it provides a sufficiently challenging problem for us to test various algorithms. We find that many of these approaches improve upon …

Efficient First-Order Methods For Some Smooth Nonlinear Optimization Problems, Yunheng Jiang

All Dissertations

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Delta-Shaped Approximation Based Homotopy Analysis Method For Nonlinear Poisson-Type Partial Differential Equations, Cyril Ocloo

Dissertations

This research aims to solve nonlinear Poisson-type partial differential equations (PDEs) by the approach of the homotopy analysis method (HAM) incorporated with approximate particular solutions (APS) using Delta-shaped basis (DSB) approximations.

With the inclusion of the h auxiliary parameters, we tackle nonlinear problems by studying the mathematical characteristics of the h curve. This is to ensure the numerical convergence of the HAM.

In the solution process, we use the homotopy analysis method to convert a nonlinear PDE into linear inhomogeneous PDEs, which are solved using the method of approximate particular solutions with DSB.

A proper value of the h is …

The Role Of Sensing Modalities In Shaping Collective Motion And Group Behavior, Poorendra P. Ramlall

Doctoral Dissertations and Master's Theses

Collective behavior refers to the coordinated movements that emerge from simple interactions between individuals within a group. Traditionally, researchers have modeled these interactions assuming individuals can sense their surroundings in all directions, like having eyes all around their heads. While this is a useful simplification, it does not capture the diverse ways animals actually sense the world. In this thesis, we take inspiration from the natural world, particularly from animals like bats and dolphins that use a combination of hearing and sight to navigate their environments. We explore how combining these sensory cues in a three-dimensional space affects the way …

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

LSU Doctoral Dissertations

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Enhancing Decision In Information System Through Weighted Preliminary Pretopology Analysis, Mustafa Elsayed, Rifet Agassi

Journal of Engineering Research

It is clear from adequate study of the past decades that there has been rapid growth in the information system, which relies mainly on programming systems. This has led to the necessity of dealing with high efficiency with the information system necessary for decision support. Information systems are a mixture of software and hardware to store and process all the data required and are presented in a useful form to extract information by applying topological concepts. In this paper a pretopological space from an information system is to be constructed. The computation of decision accuracy stands as a pivotal stage …

Impact Of Covid-19 On Disaggregate Consumption And Online Retail Sales: Evidence From The Usa, Gulzar Ahmed, Olcay Akman

Spora: A Journal of Biomathematics

This study applies the difference-in-difference technique to analyze the consumption pattern during COVID-19 against pre-COVID-19 years. We analyze the online retail sales before and after COVID-19 using time series and linear regression models. Time series intervention analysis results suggest that COVID-19 has caused a statistically significant change in the mean level of online retail sales share in e-commerce. Using a difference-in-difference approach, we find a 4% decrease in aggregate consumption from March to December 2020 compared to the benchmark period although statistically insignificant. Further, using a fixed effects model with time dummies, we find a nearly 8% significant decrease in …

Capturing Latent Abilities And Latent Capacities Of Professional Golfers Using Nonlinear Mixed Effects Growth Modeling, Mac Wetherbee

Electronic Theses and Dissertations

This study demonstrates an effective and innovative approach to measuring the latent athletic abilities and capacities of professional golfers. I used nonlinear mixed effects growth modeling (e.g., Dynamic Measurement Modeling) to measure professional golfers’ ability levels and capacities for improvement. I accomplished this using a two-stage modeling approach. First, a crossed linear mixed effects model estimated each player’s ability level in each year. In the second stage, I used the results from the first stage to estimate several candidate nonlinear growth trajectories for players’ abilities over time. The quadratic growth trajectory was the best-fitting of these trajectories and was used …

Local Geometry Of Elementary Visual Computations, Peter Neri

MODVIS Workshop

Visual operators (e.g. edge detectors) are classically modelled using small circuits involving canonical computations, such as template-matching and gain control. Circuit models explain many aspects of the empirical descriptors that are used to characterize local visual operators, from sensitivity to classification images. Notwithstanding their utility, these models fail to provide a unified framework encompassing the variety of effects observed experimentally, such as the impact of contrast, SNR, and attention on the above descriptors. My goal is to start with a simple, plausible geometrical representation of the perceptual operation carried out by the observer, and to show that this representation is …

Analysis And Computation Of Constrained Sparse Coding On Emerging Non-Von Neumann Devices, Kyle Henke

Mathematics & Statistics ETDs

This dissertation seeks to understand how different formulations of the neurally inspired Locally Competitive Algorithm (LCA) represent and solve optimization problems. By studying these networks mathematically through the lens of dynamical and gradient systems, the goal is to discern how neural computations converge and link this knowledge to theoretical neuroscience and artificial intelligence (AI). Both classical computers and advanced emerging hardware are employed in this study. The contributions of this work include:

1. Theoretical Work: A comprehensive convergence analysis for networks using both generic Rectified Linear Unit (ReLU) and Rectified Sigmoid activation functions. Exploration of techniques to address the binary …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

Electronic Theses and Dissertations

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa

All Dissertations

Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Scholars Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Invariance Of Chsh Parameters When Projecting Weakly Signaling Distribution Into A No Signaling Subspace, Aaditya Paudel

LSU New Orleans Theses and Dissertations

The seminal 1935 paper by Einstein, Podolsky, and Rosen (EPR) sparked a fundamental debate in quantum mechanics about the completeness of physical reality through the EPR paradox. They questioned local realism by suggesting that particles could exhibit instantaneous correlations across any distance, challenging classical physics. Bell's theorem (1964) argued that no local hidden variable theory could replicate quantum predictions, introducing Bell's inequalities and their experimental tests. These tests, particularly through violations of Bell's inequalities, confirmed quantum predictions of non-local correlations that local realism could not account for. Quantum theory, while supporting such correlations, adheres to the no-signaling principle to prevent …