Mathematics Commons^™

Subject-Centered Approach To Integrate Faith And Learning, Valorie L. Zonnefeld

Faculty Work Comprehensive List

No abstract provided.

Symbolic Powers Of Edge Ideals, Mike Janssen

Faculty Work Comprehensive List

No abstract provided.

Table Of Contents (2015), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Modeling The Geographic Spread Of Rabies In China, Jing Chen, Lan Zou, Shigui Ruan

Mathematics Faculty Articles

Abstract

In order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans, in which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed, infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The existence of the disease-free equilibrium is discussed, the basic reproduction number is calculated, and the effect of moving rates of dogs between …

Some Problems In Differential And Subdifferential Calculus Of Matrices., Priyanka Grover Dr.

Doctoral Theses

A central problem in many subjects like matrix analysis, perturbation theory, numerical analysis and physics is to study the effect of small changes in a matrix A on a function f(A). Among much studied functions on the space of matrices are trace, determinant, permanent, eigenvalues, norms. These are real or complex valued functions. In addition, there are some interesting functions that are matrix valued. For example, the (matrix) absolute value, tensor power, antisymmetric tensor power, symmetric tensor power.When a function is differentiable, one of the ways to study the above problem is by using the derivative of f at A, …

Proceedings Of The Twentieth Conference Of The Association Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

The proceedings of the twentieth conference of the Associate of Christians in the Mathematical Sciences held at Redeemer University College from May 27-30, 2015.

Force To Change Large Cardinal Strength, Erin Kathryn Carmody

Dissertations, Theses, and Capstone Projects

This dissertation includes many theorems which show how to change large cardinal properties with forcing. I consider in detail the degrees of inaccessible cardinals (an analogue of the classical degrees of Mahlo cardinals) and provide new large cardinal definitions for degrees of inaccessible cardinals extending the hyper-inaccessible hierarchy. I showed that for every cardinal $\kappa$, and ordinal $\alpha$, there is a notion of forcing $\mathbb{P}$ such that $\kappa$ is still $\beta$-inaccessible in the extension, for every $\beta < \alpha$, but not $\alpha$-inaccessible. I also consider Mahlo cardinals and degrees of Mahlo cardinals. I showed that for every cardinal $\kappa$, and ordinal $\alpha$, there is a notion of forcing $\mathbb{P}$ such that for every $\beta < \alpha$, the cardinal $\kappa$ is still $\beta$-Mahlo in the extension, but not $\alpha$-Mahlo. I also show that a cardinal $\kappa$ which is Mahlo in the ground model can have every possible inaccessible degree in the forcing extension, but no longer be Mahlo there. The thesis includes a collection of results which give forcing notions which change large cardinal strength from weakly compact to weakly measurable, including some earlier work by others that fit this theme. I consider in detail measurable cardinals and Mitchell rank. I show how to change a class of measurable cardinals by forcing to an extension where all measurable cardinals above some fixed ordinal $\alpha$ have Mitchell rank below $\alpha.$ Finally, I consider supercompact cardinals, and strongly compact cardinals. I show how to change the Mitchell rank for supercompactness for a class of cardinals.

The Holomorphic Couch Theorem, Maxime Fortier Bourque

Dissertations, Theses, and Capstone Projects

We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy class deformation retracts into a point, a circle, a torus, or the unit tangent bundle of the codomain, depending on the induced homomorphism on fundamental groups. Quadratic differentials play a central role in the proof.

Some Applications Of Noncommutative Groups And Semigroups To Information Security, Lisa Bromberg

Dissertations, Theses, and Capstone Projects

We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL₂(F_p), and compute bounds on the girth of the Cayley graph of the subgroup of SL₂(F_p) for specific generators A, B. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.

Geometric Separation And Packing Problems, Ivo Vigan

Dissertations, Theses, and Capstone Projects

The first part of this thesis investigates combinatorial and algorithmic aspects of geometric separation problems in the plane. In such a setting one is given a set of points and a set of separators such as lines, line segments or disks. The goal is to select a small subset of those separators such that every path between any two points is intersected by at least one separator. We first look at several problems which arise when one is given a set of points and a set of unit disks embedded in the plane and the goal is to separate the …

New Results On Randomized Matrix Computations, Jesse Lowell Wolf

Dissertations, Theses, and Capstone Projects

The aim of this thesis is to present new results in randomized matrix computations. Specifically, and ultimately, we show how to modify, or preprocess an ill conditioned matrix having small numerical nullity (co-rank) into a nonsingular well conditioned matrix. This has intrinsic theoretical interest and we show a sample application to accurate solutions of nonsingular and ill conditioned linear systems. We discuss both multiplicative and additive preprocessing; in fact the multiplicative case assists in the derivation of the additive case. In the additive case, we approximate a nonsingular ill conditioned matrix by a singular well conditioned matrix which is then …

Antigen Discovery For The Identification Of Vaccine Candidates And Biomarkers Using A T Cell Driven Approach In Combination With Positional Scanning Peptide Libraries, Valeria A. Judkowski, Radleigh Santos, Gonzalo R. Acevedo, Marc Giulianotti, Jon R. Appel, Silvia A. Longhi, Karina A. Gomez, Clemencia Pinilla

Mathematics Faculty Articles

The prevention and treatment of infectious diseases is highly dependent on the availability of reliable diagnostic tests and protective or therapeutic vaccines. There also exists an urgent need to develop reliable biomarkers to monitor treatment success and to predict disease progression from asymptomatic to symptomatic disease in several disease scenarios. The elucidation of the disease-relevant antigens that elicit the protective immune responses is critical and required for the development of biomarkers, diagnostics, and vaccines. However; one of the main obstacles to the study of antigen specificity in human T cells is their low frequency in PBMC samples. To overcome this …

Some Studies On Selected Stream Ciphers Analysis Fault Attack & Related Results., Subhadeep Banik Dr.

Doctoral Theses

Stream Ciphers are important Symmetric Cryptological primitives, built for the purpose of providing secure message encryption. As no formal security proofs exist, our confidence in these algorithms is largely based on the fact that intense cryptanalysis has been carried out over several years without revealing any weakness. This thesis makes some independent contributions to the cryptanalysis of a selection of stream ciphers.In this thesis, we take a closer look at two stream ciphers viz. RC4+ designed by Maitra et al. at Indocrypt 2008 and GGHN designed by Gong et al. at CISC 2005. Both these ciphers were designed as viable …

Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali

Pomona Faculty Publications and Research

At the beginning of last summer I wrote about a neat trick to make your summer a productive one. And I heard from some of you who took me up on this suggestion; it seems that this actually works for many people! So, this year, for those who are willing to experiment with new ideas, I have another summer recommendation: Let us clean!

A Mathematical Foundation Of The Quantum-Classical Correspondence, Nina Culver

Honors Program Theses and Projects

In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities …

Commutative N-Ary Arithmetic, Aram Bingham

LSU New Orleans Theses and Dissertations

Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes …

Nonparametric Bayesian Quantile Regression Via Dirichlet Process Mixture Models, Chao Chang

Arts & Sciences Graduate Student Theses and Dissertations

We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing …

Regularity Of The Bergman Projection On Variants Of The Hartogs Triangle, Liwei Chen

Arts & Sciences Graduate Student Theses and Dissertations

The Bergman projection is the orthogonal projection from the space of square integrable functions onto the space of square integrable holomorphic functions on a domain. Initially, the projection is defined on the L2 space, but its behavior on other function spaces, e.g. Lp, Sobolev and Holder spaces, is of considerable interest.In this dissertation, we focus on the Hartogs triangle which is a classical source of counterexamples in several complex variables, and generalize it to higher dimensions. We investigate the Lp mapping properties of the weighted Bergman projections on these Hartogs domains. As applications, we obtain the Lp regularity of the …

Incompatibility Of Diophantine Equations Arising From The Strong Factorial Conjecture, Brady Jacob Rocks

Arts & Sciences Graduate Student Theses and Dissertations

The Strong Factorial conjecture was recently formulated by Arno van den Essen and Eric Edo. The problem is motivated by several outstanding problems including the Jacobian, Image, and Vanishing conjectures. In this defense, we discuss how the conjecture can be reformulated in terms of systems of integer polynomials and we present several special cases in which the conjecture holds.

Wavelet Factorization And Related Polynomials, David Meyer

Arts & Sciences Graduate Student Theses and Dissertations

Our goal is exploring and better understanding factorizations of polyphase matrices for finite impulse response (FIR) filters. In particular, we focus on nearest neighbor factorizations discussed by Wickerhauser and Zhu that allow for efficient implementation of the discrete wavelet transform (DWT) for the algorithms of Daubechies and Sweldens and Mallat. Nearest neighbor lifting is a specific form of the general lifting scheme that improves the lifting algorithm by optimizing the number of efficient memory accesses. Nearest neighbor lifting factorizations are typically generated by implementing the Euclidean algorithm for Laurent polynomials, which introduces multiple choices of factorizations of a polyphase matrix …

Application Of Machine Learning To Mapping And Simulating Gene Regulatory Networks, Hien-Haw Liow

Arts & Sciences Graduate Student Theses and Dissertations

This dissertation explores, proposes, and examines methods of applying modernmachine learning and Bayesian statistics in the quantitative and qualitative modeling of gene regulatory networks using high-throughput gene expression data. A semi-parametric Bayesian model based on random forest is developed to infer quantitative aspects of gene regulation relations; a parametric model is developed to predict geneexpression levels solely from genotype information. Simulation of network behavior is shown to complement regression analysis greatly in capturing the dynamics of gene regulatory networks. Finally, as an application and extension of novel approaches in gene expression analysis, new methods of discovering topological structure of gene …

Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

MODVIS Workshop

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies that …

Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais

Student Research Symposium

Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.

To receive an invitation to download the app through Google Play, contact me at [email protected]

The Smallest Intersecting Ball Problem, Daniel J. Giles, Mau Nam Nguyen

Student Research Symposium

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.

Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori B. Ziegelmeir, Tom Halverson

Faculty Publications

No abstract provided.

How Does Tutoring To Develop Conceptual Understanding Impact Student Understanding?, Kelsey Cummings

Honors Program Theses and Projects

No abstract provided.

Exploring The Calkin-Wilf Tree: Subtrees And The Births Of Numbers, Kayla Javier

Honors Program Theses and Projects

No abstract provided.

An Analysis Of Numerical Methods On Traffic Flow Models, Terry Mullen

Honors Program Theses and Projects

In this thesis, we implement Euler's method and the Runge-Kutta method to solve initial value problems. A goal of the project is to compare the two methods on preliminary problems illustrating limitations and advantages. We also apply the Runge-Kutta method to a mathematical model of traffic flow. This thesis sheds light on how the fourth-order Runge-Kutta method is implemented to solve the Optimal Velocity Model (Kurata & Nagatani, 2003). We identify initial conditions and base cases to run simulations of the model. We consider one-car and two-car systems to validate the application of the fourth-order Runge-Kutta method and the Optimal …

Life On The Floodplain: An Analysis Of Falmouth, Massachusetts And Osaka, Japan, Shellie Johnson

Honors Program Theses and Projects

After Hurricane Katrina in 2005, the awareness of flooding threats to coastal areas increased. For Massachusetts in particular, Cape Cod is still at high risk of flooding with any storm that comes and goes. However, all of these recent devastating floods and natural disasters have caused insurance prices to skyrocket. With my research, I specifically looked at Falmouth, Massachusetts and the possibilities to lessen the risks and which of these options would be the most financially sound for a homeowner. The possibilities include elevating a house in a high flood risk zone, selling a current house to move in to …

Exploring Residents’ Attitudes Toward Solar Photovoltaic System Adoption In China, Yaqin Sun

Honors Program Theses and Projects

As the largest energy consuming country, China is facing environmental deterioration, which results from the overuse of non-renewable conventional energy such as coal. Solar photovoltaic (PV) energy, an unlimited and clean energy with minimal impacts on the environment, is considered to be a good alternative to alleviate this severe issue. A survey was designed and conducted among residents in some major cities. Based on the first hand data, basic statistical methods were utilized to examine Chinese residents’ knowledge of, concerns, and attitudes towards PV adoption. The research aims to identify the drivers and dynamics that most encourage customers to install …