Physical Sciences and Mathematics Commons^™

Signal Transmission In Epithelial Layers, Filippo Posta

Dissertations

Cell signaling is at the basis of many biological processes such as development, tissue repair, and homeostasis. It can be carried out by different mechanisms. Here we are focusing on ligand mediated cell-to-cell signaling in which a molecule (ligand) is free to move into the extra-cellular medium. On the cell layer surface, it can bind to its molecule-specific receptors located on the cell plasma membrane. This mechanism is the subject of many experimental and theoretical studies on many model biological systems, such as the follicular epithelium of the Drosophila egg, which motivates this work.

Here, we present a general mathematical …

Rogers-Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills, Peter Zimmer

Department of Mathematical Sciences Faculty Publications

In this survey article, we present an expanded version of Lucy Slater's famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the publication of Slater's papers, and older identities (such as those in Ramanujan's lost notebook) which were not included in Slater's papers. We attempt to supply the earliest known reference for each identity. Also included are identities of false theta functions, along with their relationship to Rogers-Ramanujan type identities. We also describe several ways in which pairs/larger sets of identities may be related, as well as dependence relationships between identities.

Modeling The Hydrolyzing Action Of Secretory Phospholipase A2 With Ordinary Differential Equations And Monte Carlo Methods, Zijun Lan Dozier

Theses and Dissertations

Although cell membranes normally resist the hydrolysis of secretory phospholipase A2, a series of current investigations demonstrated that the changes in lipid order caused by increased calcium has a relationship with the susceptibility to phospholipase A2. To further explore this relationship, we setup ordinary differential equations models, statistic models and stochastic models to compare the response of human erythrocytes to the hydrolyzing action of secretory phospholipase A2 and the relationship between the susceptibility of hydrolysis and the physical properties of secretory phospholipase A2. Furthermore, we use models to determine the ability of calcium ionophore to increased membrane susceptibility.

A Statistical Look At Maps Of The Discrete Logarithm, Nathan Lindle

Mathematical Sciences Technical Reports (MSTR)

Cryptography is being used today more than it ever has in the past. Millions of transactions are being conducted every hour using encrypted channels, most of which use the Internet as their medium. It is taken for granted by the average user that these transaction are secure, but mathematicians and computer scientists alike are constantly testing the algorithms being used. Several of these cryptosystems use the transformation

g^x = y (mod n)

The appeal of this transformation is that it is quite simple to calculate gx mod n; exponentiation by squaring is fairly simple and quick even using …

Blair Family - Ciphering Book (Sc 1659), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 1659. Ciphering book created by Blair family member in Fleming County, Kentucky. Although undated, the book contains several mathematical problems with dates ranging from 1792 to 1796. Fleming County, which is noted in one of the problems, was established in 1798.

The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow

Articles and Preprints

We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

Effects Of Context Of Natural And Artifactual Objects On Categorization, Linsey Walker

Honors Theses

Categorization of animals and vehicles in different contexts was investigated in three experiments using event related potentials (ERPs). The presence of a background and congruency of the background in relation to the object were both manipulated in order to determine the effects of context on visual processing. In Experiment 1, adults were presented with images of animals and vehicles in two conditions: situated in a congruent context (e.g. an animal in a field) and in the absence of a context (an animal in a white homogeneous background). In experiment 2, adults were presented with images of animals and vehicles in …

Foundations And Interpretations Of Quantum Mechanics, Cory Johnson

Honors Theses

The first famous thought experiment of Einstein gives rise to his theories of relativity, the bedrock of modern astrophysics and cosmology. His second famous thought experiment begins the investigation into the foundations of quantum mechanics. It leads to a paradox, inspiring various 'no-go' theorems proven by Bell, Kochen, and Specker. Physicists and philosophers worldwide become increasingly dissatisfied with the probabilistic complementarity interpretation (Born-Bohr) and eventually offer their own accounts of the theory. By the end of the 20th century two alternative approaches stand out as the best candidates: Both the hidden variables interpretation (de Broglie-Bohm) and the many worlds interpretation …

Implementing Bluetooth Support In Wifi-Based Mobile Ad-Hoc Networks, Christopher Dragga

Mathematics, Statistics, and Computer Science Honors Projects

Mobile ad-hoc networks (MANETs) provide a useful means of connecting computers in unusual situations, such as search and rescue. However, they ignore those small, highly mobile devices that only support Bluetooth, a low-range, low-bandwidth Wifi alternative that consumes significantly less power. Allowing these devices to connect to Wifi MANETs could permit a variety of applications, from text messaging to VOIP to parallel processing. Bluetooth features several unusual characteristics that could make this difficult, though. In this project, I implemented this kind of integration and analyzed its success through physical testing and models both analytical and simulated.

On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt

Electronic Theses and Dissertations

Let G be a graph. For k ≥ d ≥ 1, a k/d -coloring of G is a coloring c of vertices of G with colors 0, 1, 2, . . ., k - 1, such that d ≤ | c(x) - c(y) | ≤ k - d, whenever xy is an edge of G. We say that the circular chromatic number of G, denoted χ_c(G), is equal to the smallest k/d where a k/d -coloring exists. In [6], Pan and …

An Optimal-Order Error Estimate For A Family Of Ellam-Mfem Approximations To Porous Medium Flow, Hong Wang

Faculty Publications

Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent nonlinear partial differential equations, which present serious mathematical and numerical difficulties. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The ELLAM-MFEM time-stepping procedure, in which an Eulerian–Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for …

Adjoints Of Composition Operators With Rational Symbol, Christopher Hammond, Jennifer Moorhouse, Marian Robbins

Mathematics Faculty Publications

Building on techniques developed by C. C. Cowen and E. A. Gallardo-Gutiérrez [J. Funct. Anal. 238 (2006), no. 2, 447–462;MR2253727 (2007e:47033)], we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H ² . We consider some specific examples, comparing our formula with several results that were previously known.

A Note On Mustata's Computation Of Multiplier Ideals Of Hyperplane Arrangements, Zach Teitler

Zach Teitler

In 2006, M. Mustata used jet schemes to compute the multiplier ideals of reduced hyperplane arrangements. We give a simpler proof using a log resolution and generalize to non-reduced arrangements. By applying the idea of wonderful models introduced by De Concini–Procesi in 1995, we also simplify the result. Indeed, Mustat¸˘a’s result expresses the multiplier ideal as an intersection, and our result uses (generally) fewer terms in the intersection.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

The Signed-Graphic Representations Of Wheels And Whirls, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.

Connectivity In Frame Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).

Comparison Of Machine Learning Algorithms For Modeling Species Distributions: Application To Stream Invertebrates From Western Usa Reference Sites, Margi Dubal

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Machine learning algorithms are increasingly being used by ecologists to model and predict the distributions of individual species and entire assemblages of sites. Accurate prediction of distribution of species is an important factor in any modeling. We compared prediction accuracy of four machine learning algorithms-random forests, classification trees, support vector machines, and gradient boosting machines to a traditional method, linear discriminant models (LDM), on a large set of stream invertebrate data collected at 728 reference sites in the western United States. Classifications were constructed for individual species and for assemblages of sites clustered a priori by similarity on biological characteristics. …

Hands-On Activities And Activities Involving Technology To Help Students Construct Concepts And Gain A Deeper Understanding And Appreciation For Mathematical Concepts Based On The Utah Core Curriculum For Algebra Ii, Brookeann Watterson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Research shows there are several methods that expand students' understanding, appreciation for, and interest in mathematics by following teaching strategies. These strategies include incorporating hands-on activities, technology, discovery learning, cooperative learning, and having activities be applicable to real world contexts. This project focuses specifically on activities based on objectives from the Utah State Core for Algebra II that incorporate such strategies in five units: (I) absolute value, (2) exponential growth /decay and logarithms, (3) trigonometric functions, (4) probability, permutations and combinations, and (5) statistics.

Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …

Cultural Advantage For Cities: An Alternative For Developing Countries, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

An Alternate Approach To Alternating Sums: A Method To Die For, Arthur T. Benjamin, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Mixtures Of Truncated Normal Data Assimilation Models For Parameter Estimation And Prediction In Hydrological Systems, Darl D. Flake Ii

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Physical models in the hydrological sciences are often calibrated using methods that do not formally quantify uncertainty in the model parameters. Additionally, many competing hydrological models exist and are used to model the same processes. Considering existing mechanistic models of rainfall-run off in a statistical context can assist hydrologists in understanding the true physical process taking place. This paper introduces a data assimilation mixture model of runoff that yields statistical estimates of hydrological mode l parameters and predictions. This statistical model incorporates two commonly used hydrological models, each with strengths and weaknesses. The mixture framework allows comparisons between models as …

A Note On Ill-Posedness Of The Cauchy Problem For Heisenberg Wave Maps, Luca Capogna, Jalal Shatah

Mathematics Sciences: Faculty Publications

We introduce a notion of wave maps with a target in the sub- Riemannian Heisenberg group and study their relation with Riemannian wave maps with range in Lagrangian submanifolds. As an application we establish existence and eventually ill-posedness of the corresponding Cauchy problem.

Representations Of The Temperley-Lieb Algebra, Anne Moore

Mathematics, Statistics, and Computer Science Honors Projects

This paper gives an introduction to Temperley-Lieb algebra that is easily accessible to undergraduates, presenting TL diagrams, the method for multiplying the diagrams, and the properties of the multiplication that it is necessary to preserve in a representation. The paper also gives a method for finding representations of the TL monoids (sets of diagrams classified by number of vertices) using Young tableaux, and shows that these representations are all of the irreducible representations. While ideas of Hecke algebra imply the fact that this method produces representations, this paper provides a direct proof, strictly within the field of representation theory. It …

The Devil’S Calculus: Mathematical Models Of Civil War, Ajay Shenoy

Honors Scholar Theses

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test …

The Propagation Of Non-Lefschetz Type, The Gottlieb Group And Related Questions, John Oprea

Mathematics and Statistics Faculty Publications

This is a brief note which indicates how the property of being non-Lefschetz may be propagated by equivariant symplectic maps. We also discuss some questions related to the Gottlieb group and nilpotency of symplectic manifolds.

Differential Equations: A Universal Language, Bethany Caron

Senior Honors Projects

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” – David Hilbert Differential equations are equations of one or more variables that involve both functions and their derivatives. These equations have many applications to the everyday “non-math” world, including modeling in engineering, physics, biology, chemistry, and economics. Differential equations are used when a situation arises where one needs to study a continuously changing quantity (expressed as a function) and its rate of change (expressed through its derivatives). The solutions to differential equations are functions that make the original equation hold true, and they can …

A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken

Senior Honors Projects

Graph theory is a branch of mathematics which studies graphs a collection of a set of edges and vertices used to sometimes model structures. My interest in graph theory began last semester in a math/computer science course entitled “Discrete Structures." One aspect which makes graph theory an appealing area to research is the amount of understanding that comes from a relatively short amount of time spent learning the subject material. The visual appeal of being able to draw a graph along practical applications that surface daily make graph theory a prime candidate for further research. Through research of the history …

Mathematical Analysis Of Allelopathy And Resource Competition Models, Ian Pablo Martines

Mathematics Dissertations

Mathematical population models of nutrient recycling and allelopathy are presented. The chemostat limited-resource model forms the basis for each of the models, amended with the dynamics of nutrient recycling and allelopathy. Nutrient recycling considers the explicit mortality of the population as providing additional recycled nutrient available to the remaining organisms. Also considered is allelopathy in which one population produces a poison to increase the mortality of another population. In this study we explore allelopathy in which the poison producer increases toxicity as the nutrients are limited. In addition to the chemostat model, we also consider the associated gradostat, two chemostat …

An Improved Multi-Set Algorithm For The Dense Subset Sum Problem, Andrew Shallue

Scholarship

No abstract provided.