Mathematics Commons^™

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 …

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.

On The Probabilistic Cauchy Theory Of The Cubic Nonlinear Schrödinger Equation On Rd, D≥3, Árpád Bényi, Tadahiro Oh, Oana Pocovnicu

Mathematics Faculty Publications

We consider the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS) : i∂_tu + Δu = ±|u|²u on R ^d, d ≥ 3, with random initial data and prove almost sure well-posedness results below the scaling-critical regularity ^scrit = d-2/2. More precisely, given a function on R ^d, we introduce a randomization adapted to the Wiener decomposition, and, intrinsically, to the so-called modulation spaces. Our goal in this paper is three-fold. (i) We prove almost sure local well-posedness of the cubic NLS below the scaling-critical regularity …

Combinatorial Techniques In The Galois Theory Of P-Extensions, Michael Rogelstad

Electronic Thesis and Dissertation Repository

A major open problem in current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various fields. Obtaining detailed knowledge of the structure of quotients and subgroup filtrations of Galois groups of p-extensions is an important step toward a solution. We illustrate several techniques for counting Galois p-extensions of various fields, including pythagorean fields and local fields. An expression for the number of extensions of a formally real pythagorean field having Galois group the dihedral group of order 8 is developed. We derive a formula for computing the F_p-dimension of an n-th …

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!

Collective Action: Why The Future Is Brighter For Undergraduate Teaching In The Mathematical Sciences, Karen Saxe

Karen Saxe

This posting appeared as a blog posting in the AMS Blog (http://blogs.ams.org/matheducation/2015/05/20/collective-action-why-the-future-is-brighter-for-undergraduate-teaching-in-the-mathematical-sciences/) and in the AWM (Association for Women in Mathematics) Newsletter, July/August 2015. The URL for the AWM Newsletter is https://sites.google.com/site/awmmath/awm/newsletter. A link to the blog posting is connected to this listing. In addition, a pdf copy of the blog posting is attached to this reference.

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

Arts & Sciences Electronic Theses and Dissertations

We propose new nonparametric Bayesian approaches to quantile regression using

Dirichlet process mixture (DPM) models. All the existing quantile regression methods

based on DPMs require the kernel density to satisfy the quantile constraint, hence the

kernel densities are themselves usually in the form of mixtures. One innovation of our

approaches is that we impose no constraint on the kernel, thus a wide range of densities

can be chosen as the kernels of the DPM model. The quantile constraint is satisfied by a

post-processing of the DPM by a suitable location shift. As a result, our proposed models

use simpler kernels …

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

Arts & Sciences Electronic 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.

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

University of 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 …

Wavelet Factorization And Related Polynomials, David Meyer

Arts & Sciences Electronic 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 Electronic 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 …

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

Arts & Sciences Electronic 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 …

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 HaleyoBourke@yahoo.com

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.

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 …

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

Faculty Publications

No abstract provided.