Digital Commons Network^™

Qualitative Analysis For A Two-Component Peakon System With Cubic Nonlinearity, Shaojie Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

This paper is devoted to studying a two-component peakon system with cubic nonlinearity, which is a two-component extension of the cubic Camassa–Holm equation. We first discuss the local well-posedness for the Cauchy problem of the system. Then, in light of a fine structure of the system, we present the precise blow-up scenario for strong solutions to the system and derive a new blow-up result with respect to initial data. Finally, peakon solutions are discussed as well.

Bi-Dbar-Approach For A Coupled Shifted Nonlocal Dispersionless System, Junyi Zhu, Kaiwen Shao, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

We propose a Bi-Dbar approach and apply it to the extended coupled shifted nonlocal dispersionless system. We introduce the nonlocal reduction to solve the coupled shifted nonlocal dispersionless system. Since no enough constraint conditions can be found to curb the norming contants in the Dbar data, the “solutions” obtained by the Dbar dressing method, in general, do not admit the coupled shifted nonlocal dispersionless system. In the Bi-Dbar approach to the extended coupled shifted nonlocal dispersionless system, the norming constants are free. The constraint conditions on the norming constants are determined by the general nonlocal reduction, and the solutions of …

The History Of Mathematics: A Source-Based Approach, Volume Ii (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: The History of Mathematics: A Source-Based Approach, Volume II by June Barrow-Green, Jeremy Gray, and Robin Wilson. Providence, Rhode Island: MAA Press, an imprint of the American Mathematical Society, 2022. 687 pp. ISBN: 978-1-4704-4382-5

Mathematics In The Woods: Exploring Low-Income Parents’ Perceptions Of And Involvement In Their Children’S Mathematical Learning, Lulu Sun

Northwest Journal of Teacher Education

This article features data from a three-day mathematics camping trip that offered parents and their children time and space to enjoy non-digital activities and mathematics-building tasks. Drawing upon data from a larger qualitative study of children and their parents, this article specifically focuses on 10 parents’ perceptions of their children’s mathematics learning, problem-solving, and wellbeing. Findings suggest that, although parents are interested in their children’s mathematics learning, they are most concerned with their children’s development of problem-solving abilities and social skills. Moreover, students’ own learning experience is important for their mathematics learning.

Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler

Mathematics & Statistics ETDs

Debiased Sinkhorn divergence (DS divergence) is a distance function of

regularized optimal transport that measures the dissimilarity between two

probability measures of optimal transport. This thesis analyzes the advantages of

using DS divergence when compared to the more computationally expensive

Wasserstein distance as well as the classical Euclidean norm. Specifically, theory

and numerical experiments are used to show that Debiased Sinkhorn divergence

has geometrically desirable properties such as maintained convexity after data

normalization. Data normalization is often needed to calculate Sinkhorn

divergence as well as Wasserstein distance, as these formulas only accept

probability distributions as inputs and do not directly …

Statistical Methods For Differential Gene Expression Analysis Under The Case-Cohort Design, Lidong Wang

Mathematics & Statistics ETDs

Differential gene expression analysis has the potential to discover candidate biomarkers, therapeutic targets, and gene signatures. How to save money when using an unaffordable sample is a practical question. The case-cohort (CCH) study design can blend the economy of case-control studies with the advantages of cohort studies. But it has not been seen in the medical research literature where high-throughput genomic data were involved.

A score test does not need to fit the Cox PH model iteratively; hence, it can save computing time and avoid potential convergence issues. We developed a score test under the CCH design to identify DEGs …

Functional Consequences Of Extended High Frequency Hearing Impairment: Evidence From The Speech, Spatial, And Qualities Of Hearing Scale, Udit Saxena, Srikanta K. Mishra, Hansapani Rodrigo, Moumita Choudhury

School of Mathematical & Statistical Sciences Faculty Publications

Hearing loss in the extended high frequencies, despite a normal audiogram, could affect speech-in-noise recognition. However, it is not known if extended high frequency (EHF) hearing loss is associated with everyday listening and communication deficits. The present study aimed to determine the functional effects of impaired EHF hearing among adults using the Speech, Spatial, and Qualities of Hearing Scale (SSQ). A secondary objective was to evaluate the relationship between objective (speech-in-noise recognition) and subjective (SSQ) measures of hearing function. Listeners with EHF hearing loss provided lower SSQ ratings compared with their EHF-normal counterparts. The lower ratings could not be attributed …

Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

One-Point Gleason Parts And Point Derivations In Uniform Algebras, Swarup Ghosh, Alexander J. Izzo

Faculty Articles & Research

It is shown that a uniform algebra can have a nonzero bounded point derivation while having no nontrivial Gleason parts. Conversely, a uniform algebra can have a nontrivial Gleason part while having no nonzero, even possibly unbounded, point derivations.

Modularity And Boolean Network Decomposition, Matthew Wheeler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Canalization And Other Design Principles Of Gene Regulatory Networks, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Model-Free Identification Of Relevant Variables From Response Data, Alan Veliz-Cuba, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Approach To The Gaussian Rbf Kernels Via Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We use methods from the Fock space and Segal–Bargmann theories to prove several results on the Gaussian RBF kernel in complex analysis. The latter is one of the most used kernels in modern machine learning kernel methods and in support vector machine classification algorithms. Complex analysis techniques allow us to consider several notions linked to the radial basis function (RBF) kernels, such as the feature space and the feature map, using the so-called Segal–Bargmann transform. We also show how the RBF kernels can be related to some of the most used operators in quantum mechanics and time frequency analysis; specifically, …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

A Comparison Of Cryptographic Methods, Christopher Gilmore

Senior Honors Theses

While elliptic curve cryptography and quantum cryptography are significantly different branches of cryptography, they provide a suitable reference point for comparison of the value of developing methods used in the present and investing in methods to be used in the future. Elliptic curve cryptography is quite common today, as it is generally secure and efficient. However, as the field of cryptography advances, the value of quantum cryptography’s inherent security from its basic properties should be considered, as a fully realized quantum cryptosystem has the potential to be quite powerful. Ultimately, it is of critical importance to determine the value of …

Music Genre Classification By Convolutional Neural Networks, Usame Suud

Mathematics & Statistics ETDs

In today’s world, deep learning models are widely used in a variety of fields. Audio

applications include speech recognition, audio classification, and music information

retrieval. In this paper, we will focus on the classification of music genres using an

artificial neural network. The development of audio machine learning techniques has

created an independence from traditional, more time-consuming signal processing

techniques. Starting with raw audio data, we will gain an understanding of what

audio is and its digital representation. Then, the focus will be on obtaining frequency

information from audio signals through the use of spectrograms. Transforming the

spectrograms into the …

Minimizers Of Nonlocal Polyconvex Energies In Nonlocal Hyperelasticity, José C. Bellido, Javier Cueto, Carlos Mora-Corral

Department of Mathematics: Faculty Publications

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz’ fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola’s identity, the integration by parts of the determinant and the weak …

Alternative Siar Models For Infectious Diseases And Applications In The Study Of Non-Compliance, Marcelo Bongarti, Luke Diego Galvan, Lawford Hatcher, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we use modified versions of the SIAR model for epidemics to propose two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of an infectious disease. The SIAR model distinguishes between symptomatic infected (I) and asymptomatic infected (A) populations. One modification, which is simpler, assumes a known proportion of the population does not comply with government mandates such as quarantining and social-distancing. In a more sophisticated approach, the modified model treats non-compliant behavior as a social contagion. We theoretically explore different scenarios such as the occurrence …

One Iteration For The Second Boundary Condition For The Nonlinear One Dimensional Monge-Ampere Equation, Gerard Awanou

Mathematics Colloquium Series

The design of lenses and mirrors, in free form i.e. with no a priori symmetry assumption, has a long list of applications including materials processing, energy concentrators, medicine, antennas, computing lithography, laser weapons, optical data storage, imaging etc. The design process can be reduced to solving a generalized Monge-Ampere equation where the unknown is a function with a convexity property and subject to a constraint that a generalized gradient maps a given domain onto a prescribed one. The latter type of constraint is known as second boundary condition. The model one dimensional Monge-Ampere equation is nonlinear in the first order …

Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii

LSU Master's Theses

At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence ��ⁿ(0) (�� ∈ ℕ) for �� = ��¹ ∪ ��² ∪ ��³, where ��₁(��) = ����, ��₂(��) = ���� + ��, and ��₃(��) = ���� - ��, and �� = …

Studying Extended Sets From Young Tableaux, Eric Nofziger

Rose-Hulman Undergraduate Mathematics Journal

Young tableaux are combinatorial objects related to the partitions of an integer and have various applications in representation theory. They are particularly useful in the study of the fibers arising from the Springer resolution. In recent work of Graham-Precup-Russell, an association has been made between a given row-strict tableau and three disjoint subsets of {1,2,...,n}. These subsets are then used in the study of extended Springer fibers, so we call them extended sets. In this project, we use combinatorial techniques to classify which of these extended sets correlate to a valid row-strict or standard tableau and give bounds on the …

On The Smallest Non-Trivial Action Of Saut(Fn) For Small N, Reemon Spector

Rose-Hulman Undergraduate Mathematics Journal

In this paper we investigate actions of SAut(F_n), the unique index 2 subgroup of Aut(F_n), on small sets, improving upon results by Baumeister--Kielak--Pierro for several small values of n. Using a computational approach for n ⩾ 5, we show that every action of SAut(F_n) on a set containing fewer than 20 elements is trivial.

Generalized Inverses Of Elements Of Rings And Matrices Over Rings, K. Manjunatha Prasad

Interdisciplinary Collection

It is well known that a square matrix with all its columns linearly independent has a unique inverse G satisfying AG=GA=I. However, if A is not square or if columns of A are not linearly independent, then such an inverse does not exist. Moore and Penrose independently generalized the notion of inverses to singular matrices. This led to the theory of generalized inverses. In the course of time different generalized inverses like group inverse, Drazin inverse, Core inverse etc., were introduced. The present author introduced Core-EP inverse in 2013. The author has also worked on the theory of generalized inverse …

How To Get The Most Accurate Measurement-Based Estimates, Salvador Robles, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we want to estimate a quantity y that is difficult -- or even impossible -- to measure directly. In such cases, often, there are easier-to-measure quantities x₁, ..., x_n that are related to y by a known dependence y = f(x₁,...,x_n). So, to estimate y, we can measure these quantities x_i and use the measurement results to estimate y. The two natural questions are: (1) within limited resources, what is the best accuracy with which we can estimate y, and (2) to reach a given accuracy, what amount …

Anomaly Detection In Crowdsourcing: Why Midpoints In Interval-Valued Approach, Alejandra De La Pena, Damian L. Gallegos Espinoza, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations -- e.g., when preparing examples for a machine learning algorithm -- we need to label a large number of images or speech recordings. One way to do it is to pay people around the world to perform this labeling; this is known as crowdsourcing. In many cases, crowd-workers generate not only answers, but also their degrees of confidence that the answer is correct. Some crowd-workers cheat: they produce almost random answers without bothering to spend time analyzing the corresponding image. Algorithms have been developed to detect such cheaters. The problem is that many crowd-workers cannot describe …

Dielectric Barrier Discharge (Dbd) Thrusters -- Aerospace Engines Of The Future: Invariance-Based Analysis, Alexis Lupo, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most prospective aerospace engines is a Dielectric Barrier Discharge (DBD) thruster -- an effective electric engine without moving parts. Originally designed by NASA for flights over other planets, it has been shown to be very promising for Earth-based flights as well. The efficiency of this engine depends on the proper selection of the corresponding electric field. To make this selection, we need to know, in particular, how its thrust depends on the atmospheric pressure. At present, for this dependence, we only know an approximate semi-empirical formula. In this paper, we use natural invariance requirements to come up …

Hunting Habits Of Predatory Birds: Theoretical Explanation Of An Empirical Formula, Adilene Alaniz, Jiovani Hernandez, Andres D. Munoz, Vladik Kreinovich

Departmental Technical Reports (CS)

Predatory birds play an important role in an ecosystem. It is therefore important to study their hunting behavior, in particular, the distribution of their waiting time. A recent empirical study showed that the waiting time is distributed according to the power law. In this paper, we use natural invariance ideas to come up with a theoretical explanation for this empirical dependence.