Mathematics Commons^™

Nonlinear Dynamics And Stochasticity Of Core Genetic Regulation, Hongguang Xi

Mathematics Theses - Archive

Bacillus subtilis is one of the very well-studied organisms in biology. Recent results show that an alternative competence regulation circuit for this bacterium, differing only in the order of the composite negative feedback loop onto the master competence regulator gene comK, despite presenting equivalent functionality, exhibits physiologically important differences.It is not clear why Nature only selects a specific gene regulation circuit other than a plethora of equivalent others. Here, we hope, from the point of view of reverse engineering, to discover the fundamental reasons for natural selection of a particular circuit structure over another. Based on the wild-type Bacillus subtilis …

On Primitivity And Dimension Of Finite Semifields And Their Planes, Linlin Chen

Mathematics Dissertations - Archive

The study of semifields was originated by L.E. Dickson in 1905 and was greatly developed in the 1960s by Albert, Knuth, Walker, Kleinfeld among others. Two problems of interest in this area are the primitivity of semifields and the dimension of semifields.For the first problem, we provide an equivalent condition for the right (or left) primitivity of finite semifields and with this result, we find that the classical Knuth binary semifields of order 2^{15}, 2^{17} and 2^{19} are all right and left primitive; the Albert semifields of order 2^i, where i=7, 9, 11, 13 are all primitive. Also we prove …

U.S. Oil Reserves And Peak Oil, Trang Luong

Undergraduate Journal of Mathematical Modeling: One + Two

We use calculus methods to estimate the quantity of U.S. oil reserves. We consider a model that consists of an exponential function with four unknown constants. We fit real oil production data to determine the unknown constants. With the constants determined we use the function to find the year in which the U.S. oil production reached its peak. We also estimate the amount of petroleum produced until the end of 2006, and the undiscovered oil reserves to be produced in the future.

The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon

Undergraduate Journal of Mathematical Modeling: One + Two

The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum search …

Speleothem Laminae Counting And Growth Rate, Corey Wilson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine if there is a correlation between annual laminae in speleothems and Uranium dating. To do this, we counted laminae using high-resolution images and calculated a line of the best fit for the resulting data. We found that our data could supplement Uranium dating, but unless more data is obtained, laminae counting gives relatively imprecise age and growth rate estimates.

A Characterization Of Topologically Completely Positive Entropy For Shifts Of Finite Type, Ronnie Pavlov

Mathematics Preprint Series

A topological dynamical system was defined by Blanchard ([1]) to have topologically completely positive entropy (or t.c.p.e.) if its only zero entropy factor is the dynamical system consisting of a single fixed point. For Z d shifts of finite type, we give a simple condition equivalent to having topologically completely positive entropy. As an application, we use our characterization to derive a similar equivalent condition to t.c.p.e. for the subclass of Z d group shifts, proved by Boyle and Schraudner in [3]. We also give an example of a Z 2 shift of finite type which has topologically completely positive …

Shifts Of Finite Type With Nearly Full Entropy, Ronnie Pavlov

Mathematics Preprint Series

For any fixed alphabet A, the maximum topological entropy of a Z d subshift with alphabet A is obviously log |A|. We study the class of nearest neighbor Z d shifts of finite type which have topological entropy very close to this maximum, and show that they have many useful properties. Specifically, we prove that for any d, there exists δd > 0 such that for any nearest neighbor Z d shift of finite type X with alphabet A for which (log |A|) − h(X) < δd, X has a unique measure of maximal entropy µ. We also show that any such X is a measure-theoretic universal model in the sense of [25], that h(X) is a computable number, that µ is measure-theoretically isomorphic to a Bernoulli measure, and that the support of µ has topologically completely positive entropy. Though there are other sufficient conditions in the literature (see [9], [15], [22]) which guarantee a unique measure of maximal entropy for Z d shifts of finite type, this is (to our knowledge) the first such condition which makes no reference to the specific adjacency rules of individual letters of the alphabet.

Classification Of Noncommutative Domain Algebras, Alvaro Arias, Frédéric Latrémolièr

Mathematics Preprint Series

Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of Cn defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete classification of these algebras based upon techniques inspired by multivariate complex analysis, and more specifically the classification of domains in hermitian spaces up to biholomorphic equivalence.

On Several Conjectures From Evolution Of Dispersal, Isabel Averill, Yuan Lou, Daniel Munther

Mathematics and Statistics Faculty Publications

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17–36 [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]]] concerning the dynamics of a diffusion–advection–competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal …

High-Order Central Finite-Volume Schemes For Atmospheric Modeling, Kiran Kumar Katta

Open Access Theses & Dissertations

Atmospheric numerical modeling has been going through drastic changes over the past decade, mainly to utilize the massive computing capability of the petascale systems. This obliges the modelers to develop grid systems and numerical algorithms that facilitate exceptional level of scalability on these systems. The numerical algorithms that can address these challenges should have the local properties such as the high on-processor operation count and minimum parallel communication i.e., high parallel efficiency. They should also satisfy the following properties such as inherent local and global conservation, high-order accuracy, geometric flexibility, non-oscillatory advection and positivity preservation properties. The goal of this …

Analysis Of Intermittence And Log-Periodicity Of Foreign Exchange Rates Near A Crash, Arturo Casillas

Open Access Theses & Dissertations

Many believe that financial indices near a crash exhibit a type of critical point characterized by log-periodic signatures. Models have been developed based on these ideas in an attempt to mathematically characterize financial data about to crash. Few of these models consider the property of intermittency. Intermittency is a concept borrowed from fluid dynamics that essentially implies that a system alternates between a stable, or predictable, state and unstable state. One model that attempts to characterize crashes incorporates intermittency in the form of log-stationary intervals. It models the asset price as a step function that follows an underlying power law. …

A Connection Between The Stochastic Heat Equation And Fractional Brownian Motion, And A Simple Proof Of A Result Of Talagrand, Zhixin Wu, Carl Mueller

Mathematics Faculty Publications

We give a new representation of fractional Brownian motion with Hurst parameter H<=1/2 using stochastic partial differential equations. This representation allows us to use the Markov property and time reversal, tools which are not usually available for fractional Brownian motion. We then give simple proofs that fractional Brownian motion does not hit points in the critical dimension, and that it does not have double points in the critical dimension. These facts were already known, but our proofs are quite simple and use some ideas of Levy.

Demazure Crystals, Kirillov-Reshetikhin Crystals, And The Energy Function, Anne Schilling, Peter Tingley

Mathematics and Statistics: Faculty Publications and Other Works

It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. In particular, certain Demazure crystals are isomorphic as classical crystals to tensor products of Kirillov-Reshetikhin crystals via a canonically chosen isomorphism. Here we show that this isomorphism intertwines the natural affine grading on Demazure crystals with a combinatorially defined energy function. As a consequence, we obtain a formula of the Demazure character in terms of the energy function, which has applications to Macdonald polynomials and q-deformed Whittaker functions.

Lefschetz Properties And Enumerations, David Cook Ii

Theses and Dissertations--Mathematics

An artinian standard graded algebra has the weak Lefschetz property if the multiplication by a general linear form induces maps of maximal rank between consecutive degree components. It has the strong Lefschetz property if the multiplication by powers of a general linear form also induce maps of maximal rank between the appropriate degree components. These properties are mainly studied for the constraints they place, when present, on the Hilbert series of the algebra. While the majority of research on the Lefschetz properties has focused on characteristic zero, we primarily consider the presence of the properties in positive characteristic. We study …

Small Sample Inference For Exponential Survival Times With Heavy Right-Censoring, Noroharivelo Volaniaina Randrianampy

Doctoral Dissertations

"We develop a saddlepoint-based method and several generalized Bartholomew methods for generating confidence intervals about the rate parameter of an exponential distribution in the presence of heavy random right-censoring. Butler's conditional moment generating function formula is used to derive the relevant moment generating function for the rate parameter score function which provides access to a saddlepoint-based bootstrap method. Moment generating functions also play a key role in the generalized Bartholomew methods we develop. Since heavy censoring is assumed, the possible non-existence of the rate parameter maximum likelihood estimate (MLE) is nonignorable. The overwhelming majority of existing methods condition upon the …

Volume 04, Matt Szemborski, Phillip Van Ness, Sarah Croughwell, Sarah Mayfield, Alyssa Strackbein, Marley Kimmel, Stephanie Skipp, Jamie Yurasits, Katherine Taggart, Alex Leonhart, Kristen Rawls, Andrew Armes, Amanda Haymens, Allison Paqlowski, Erica May, Stephanie Lane, Luke Acree, Cassandra L. Wilson, Stephanie Pishock, Erica Hopson, K. Juston Osborne, Katheryn Grayson, Kyle Fowlkes, Jessica Cox, Kaity Byrum, John-Harwood Scott, Ashley Johnson, Samantha Hockman, Emily Staskiel, Nancy Macdonald, R. Kruger Bressin, Benjamin P. Bilodeau, Andrea Irby, Kristin Macquarrie, Sarah Bietsch, Elizabeth Bednar

Incite: The Journal of Undergraduate Scholarship

Please note that part of pages 92-95 are redacted, in the digital copy, due to a misprint of the original printed article.

Introduction from Dean Dr. Charles Ross

The Internal Other: Transculturation and Postcolonial Magical Realism in Rushdie’s Midnight’s Children by Matt Szemborski

Photography by Phillip Van Ness

Photography “Waterfall” by Sarah Croughwell

Romancing the Bite: Statistical Analysis of Young Adult Vampire Novels by Sarah Mayfield

Photography by Alyssa Strackbein

Photography by Marley Kimmel

Wine and Society in the Viceroyalty of Peru by Stephanie Skipp

Analysis of Claud Monet’s Impression, Sunrise by Jamie Yurasits

Exploring Meaning: The Lindisfarne Gospels by …

Excluded Minors For Apex Classes Of Graphs, Christine A. Derbins

Honors Capstones

No abstract provided.

On Maximal Relatively Divisible Submodules, Brendan Goldsmith, Paolo Zanardo

Articles

In recent work Goebel and Goldsmith investigated the spectrum of maximal pure subgroups of certain Abelian groups. Here the situation relating to maximal pure submodules of a torsion-free module over an integral domain R is investigated. Connections to the level of coherency are established along with a detailed investigation of the situation where all maximal pure submodules are isomorphic to a product of copies of the ring R.

Oyun: A New, Free Program For Iterated Prisoner’S Dilemma Tournaments In The Classroom, Charles H. Pence, Lara Buchak

Faculty Publications

Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (oy-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner's dilemma tournaments, competitions between prisoner's dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, …

Stabilization And Classification Of Poincare Duality Embeddings, John Whitson Peter

Wayne State University Dissertations

We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.

This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In

particular, a Poincare embedding gives rise to a fiberwise duality

map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for

smooth embeddings.