Mathematics Commons^™

Diagrams Of ⋆-Trisections, José Román Aranda, Jesse Moeller

Department of Mathematics: Faculty Publications

In this note we provide a generalization for the definition of a trisection of a 4-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform 1-surgery on closed trisections. The insight gained from this description leads us to the classification of an infinite family of genus three trisections. We include an appendix where we extend two classic results for relative trisections for the case when the trisection surface is closed.

Modeling Braids With Space-Varying And Time-Varying Stranded Cellular Automata, Brian Chan

Mathematical Sciences Technical Reports (MSTR)

Braids in a traditional sense and braids in a mathematical sense are wildly different outlooks on the same concept. Using cellular automata to represent and analyze braids is a way to bridge the gap between them. Joshua and Lana Holden and Hao Yang have previously worked on developing and expanding upon a Stranded Cellular Automata (SCA) model capable of representing many different braids and weaves. Continuing their work, we were able to devise a more user-friendly method for interacting with the model such that even those without a mathematical background can construct and analyze braids of their own. This paper …

Why Cutting Trajectories Into Small Pieces Helps To Learn Dynamical Systems Better: A Seemingly Counterintuitive Empirical Result Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, the more information we use in machine learning, the more accurate predictions we get. However, recently, it was observed that for prediction of the behavior of dynamical systems, the opposite effect happens: when we replace the original trajectories with shorter pieces -- thus ignoring the information about the system's long-term behavior -- the accuracy of machine learning predictions actually increases. In this paper, we provide an explanation for this seemingly counterintuitive result.

Why 3d Fragmentation Usually Leads To Cuboids: A Simple Geometric Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been empirically observed that the average shape of natural fragmentation results -- such as natural rock fragments -- is a distorted cube (known as cuboid). Recently, a complex explanation was provides for this empirical fact. In this paper, we propose a simple geometry-based physical explanation for the ubiquity of cuboid fragments.

Two Runners In The Time Of Social Distancing, Speedboats In The Gulf Of Finland: How To Best Pass?, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

If two runners follow the same running path, what is the best trajectory for the faster runner to pass the slower one, taking into account that they should always maintain a prescribed social distance? If a speedboat wants to pass a slower ship following a special canal in the Gulf of Finland, what is the best trajectory? In this paper, we provide answers to both questions.

Inverse Problems For Polynomial And Rational Matrices, Richard Allen Hollister

Dissertations

Inverse problems have long been studied in mathematics not only because there are many applications in science and engineering, but also because they yield new insight into the beauty of mathematics. Central to the subject of linear algebra is the eigenvalue problem: given a matrix, and its eigenvalues (numerical invariants). Eigenvalue problems play a key role in almost every field of scientific endeavor from calculating the vibrational modes of a molecule to modeling the spread of an infectious disease, and so have been studied extensively since the time of Euler in the 18th century.

If a typical matrix eigenvalue problem …

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

altREU Projects

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …

Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller

Theses and Dissertations

The Euler top is a completely integrable system with physical system implications and the Manakov top is its four-dimensional extension. We are concerned about their complete integrability and the preservation of this property under a specific discretization known as the Hirota-Kimura Discretization. Surprisingly, it is not guaranteed that under any discretization the conserved quantities are preserved and therefore they must be discovered. In this work we construct the Poisson bracket and Lax pair for each system and provide the Lie algebra background needed to do such such constructions.

Methods In Modeling Wildlife Disease From Model Selection To Parameterization With Multi-Scale Data, Ian Mcgahan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The effects of emerging wildlife diseases are global and profound, resulting in loss of human life, economic and agricultural impacts, declines in wildlife populations, and ecological disturbance. The spread of wildlife diseases can be viewed as the result of two simultaneous processes: spatial spread of wildlife populations and disease spread through a population. For many diseases these processes happen at different timescales, which is reflected in available data. These data come in two flavors: high-frequency, high-resolution telemetry data (e.g. GPS collar) and low-frequency, low-resolution presence-absence disease data. The multi-scale nature of these data makes analysis of such systems challenging. Mathematical …

Combination Of The Single-Valued Neutrosophic Fuzzy Set And The Soft Set With Applications In Decision-Making, Florentin Smarandache, Ahmed Mostafa Khalil, Dunqian Chao, A. A. Azzam, W. Alharby

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making …

Creative Assignments In Upper Level Undergraduate Courses Inspired By Mentoring Undergraduate Research Projects, Malgorzata A. Marciniak

Journal of Humanistic Mathematics

This article describes methods and approaches for incorporating creative projects in undergraduate mathematics courses for students of engineering and computer science in an urban community college. The topics and the grading rubrics of the projects go way beyond standard homework questions and contain elements of finding own project, incorporating historical background, inventing own questions and exercises, or demonstrating experiments to illustrate some aspects of the project. After analyzing challenges and outcomes of these projects, I identified several skills which help students be successful, including the skills of creativity. These skills are writing, oral presentation, math skills, and collaboration skills. I …

Lattice Of Maximal-Primary Ideals In Quadratic Orders, Ryan Bridges

Mathematics & Statistics ETDs

An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.

Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan

Department of Mathematics: Faculty Publications

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen

Mathematics & Statistics ETDs

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods …

Quantitatively Motivated Model Development Framework: Downstream Analysis Effects Of Normalization Strategies, Jessica M. Rudd

Doctor of Data Science and Analytics Dissertations

Through a review of epistemological frameworks in social sciences, history of frameworks in statistics, as well as the current state of research, we establish that there appears to be no consistent, quantitatively motivated model development framework in data science, and the downstream analysis effects of various modeling choices are not uniformly documented. Examples are provided which illustrate that analytic choices, even if justifiable and statistically valid, have a downstream analysis effect on model results. This study proposes a unified model development framework that allows researchers to make statistically motivated modeling choices within the development pipeline. Additionally, a simulation study is …

Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey

Mathematics & Statistics ETDs

Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive …

Assessing The Validity Of Sentiment Analysis Measures Through Polychoric Correlation, Kelli N. Kasper

Mathematics & Statistics ETDs

Sentiment analysis methods extract the attitude of a text via systematic algorithms. To evaluate the validity of common sentiment analysis methods, we use polychoric correlation to compare computer-mediated methods and human-rated analogues. Our main topics of interest are the internal consistency of the raters' scores, the level of consensus among raters, and how well raters' scores correlate with those given by sentiment analysis methods for randomly collected Twitter data.

Our analysis found that there is good validity for methods that measure negative and positive sentiments in short texts, both in terms of inter-rater consistency and when comparing raters to computer-mediated …

An Improved Method For Spectroscopic Quality Classification, Elizabeth G. Mayer

Mathematics & Statistics ETDs

Spectral quality classification is a vital step in data cleaning before the

analysis of magnetic resonance spectroscopy (MRS) data can be done. This

analysis compares five methods of quality classification; three of these are

legacy methods, Maudsley et al. (2006), Zhang et al. (2018), and

Bustillo et al. (2020), and two newly created methods that used a random forests

classifier (RFC) to inform their classifications. We found that the random forest

classifier was the most accurate at predicting spectra quality (balanced

accuracy for RF of 88% vs legacy of 70%, 72%, or 72%). A

Random-Forests-Informed Filtering method (RFIFM) for quality …

A Study Of The Efficacy Of Machine Learning For Diagnosing Obstructive Coronary Artery Disease In Non-Diabetic Patients, Demond Larae Handley

Theses and Dissertations

According to the Centers for Disease Control and Prevention, about 18.2 million adults age 20 and older have Coronary Artery Disease in the United States. Early diagnosis is therefore of crucial importance to help prevent debilitating consequences, and principally death for many patients. In this study we use data containing gene expression values from peripheral blood samples in 198 non-diabetic patients, with the goal of developing an age and sex gene expression model for diagnosis of Coronary Artery Disease. We employ machine learning methods to obtain a classification based on genetic information, age and sex. Our implementation uses feed forward …

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

An A Posteriori Error Analysis Of Stationary Incompressible Magnetohydrodynamics, Ari E. Rappaport

Mathematics & Statistics ETDs

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …

On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith

Articles

We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) …

On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, Osman Tunç, Erdal Korkmaz, Özkan Atan

Applications and Applied Mathematics: An International Journal (AAM)

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE).We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.

Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we prove a Meir-Keeler type common fixed point theorem for two mappings for which the range set of the first one is a family of soft sets, called soft set-valued map and the second is a point-to-point mapping. In addition, it is also shown that under some suitable conditions, a soft set-valued map admits a selection having a unique fixed point. In support of the obtained result, nontrivial examples are provided. The novelty of the presented idea herein is that it extends the Meir-Keeler fixed point theorem and the theory of selections for multivalued mappings from the …

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is …

Structure For Regular Inclusions. Ii Cartan Envelopes, Pseudo-Expectations And Twists, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce the notion of a Cartan envelope for a regular inclusion (C,Ɗ). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,Ɗ) regularly embeds. We prove a Cartan envelope exists if and only if (C,Ɗ) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property.

For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,Ɗ) in terms of a twist …

Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan

Department of Mathematics: Faculty Publications

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.