Mathematics Commons^™

Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek

Mathematical and Statistical Science Faculty Research and Publications

COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …

Cubic Rank Transmuted Modified Burr Iii Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Seyed Morteza Najibi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability …

The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.

Domino Steganography, Robert Bosch, Aaron Kreiner

Faculty & Staff Scholarship

No abstract provided.

Assessing Program Outcomes Of An M.Ed. Curriculum And Instruction Program: A Comparison Of Face-To-Face To Completely Online Deliverables, James A. Telese, Gregory Chamblee

Teaching and Learning Faculty Publications

Many mathematics education degree programs, especially at the graduate level, are now transitioning to an online format. There is a need to document how mathematics content and content pedagogy are assessed in an online environment. The objectives of this chapter are to document how a public higher education institution in Texas transitioned their master's degree program for mathematics teachers from a face-to-face program to an online program and how this transition impacted the assessment process related to the learning of content and pedagogical content knowledge.

"Lagrangian Disks" In M-Theory, Sebastián Franco, Sergei Gukov, Sangmin Lee, Rak-Kyeong Seong, James Sparks

Publications and Research

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G₂ holonomy spaces and to Spin(7) metrics on 8-manifolds with T² fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M₄] on …

Testing Gene-Environment Interactions For Rare And/Or Common Variants In Sequencing Association Studies., Zihan Zhao, Jianjun Zhang, Qiuying Sha, Han Hao

Michigan Tech Publications, Part 1

The risk of many complex diseases is determined by a complex interplay of genetic and environmental factors. Advanced next generation sequencing technology makes identification of gene-environment (GE) interactions for both common and rare variants possible. However, most existing methods focus on testing the main effects of common and/or rare genetic variants. There are limited methods developed to test the effects of GE interactions for rare variants only or rare and common variants simultaneously. In this study, we develop novel approaches to test the effects of GE interactions of rare and/or common risk, and/or protective variants in sequencing association studies. We …

Uniformly Resolvable Decompositions Of Kv In 1-Factors And 4-Stars, Melissa S. Keranen, Donald L. Kreher, Salvatore Milici, Antoinette Tripodi

Michigan Tech Publications, Part 1

If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. A uniformly resolvable {X, Y }-decomposition of the complete graph K_v is an edge decomposition of K_v into exactly r X-factors and s Y -factors. In this article we determine necessary and sufficient conditions for when the complete graph K_v has a uniformly resolvable decompositions into 1-factors and K_1,4-factors.

Perfect 2-Colorings Of The Grassmann Graph Of Planes, Stefaan Dewinter, Klaus Metsch

Michigan Tech Publications, Part 1

We construct an infinite family of intriguing sets, or equivalently perfect 2-colorings, that are not tight in the Grassmann graph of planes of PG(n, q), n ≥ 5 odd, and show that the members of the family are the smallest possible examples if n ≥ 9 or q ≥ 25.

Identities And Inequalities For The Cosine And Sine Functions, Iosif Pinelis

Michigan Tech Publications, Part 1

Identities and inequalities for the cosine and sine functions are obtained.

Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green

Walden Dissertations and Doctoral Studies

A school district located in the southeastern United States uses benchmark tests as formative assessment to provide teachers with data to differentiate their instruction to meet the individual needs of students in their classrooms. Despite this effort, student achievement in mathematics in this school district has not improved. The purpose of this study was to gain an understanding of how middle-grade mathematics teachers used the benchmark results as formative data to guide instruction and meet student needs. The conceptual framework that grounded this study was the model of formative assessment developed by Black and Wiliam. For this basic qualitative study, …

Mathematics Cognitive And Content Abilities Across The Vincentian Student Population, Brendalee Rorena Cato

Walden Dissertations and Doctoral Studies

Mathematics achievement is a key component of student overall academic achievement. However, many students from Saint Vincent and the Grenadines (Vincentian students) continue to perform poorly on the regional Caribbean Secondary Examination Certificate (CSEC) mathematics examination. This poor mathematics performance is a concern for education stakeholders. The purpose of this quantitative, nonexperimental study was to explore the extent to which the CSEC mathematics scores of high-scoring Vincentian students versus low-scoring Vincentian students in the cognitive domains of knowledge, comprehension, and reasoning differ across the content domains of algebra; geometry; measurement; statistics; and relations, functions, and graphs (RFG). The theoretical foundation …

Neural Networks For Threshold Dynamics Reconstruction, Elisa Negrini, Almanzo Jiahe Gao, Abigail Bowering, Wei Zhu, Luca Capogna

Mathematics Sciences: Faculty Publications

We introduce two convolutional neural network (CNN) architec- tures, inspired by the Merriman-Bence-Osher (MBO) algorithm and by cellular automatons, to model and learn threshold dynamics for front evolution from video data. The first model, termed the (single-dynamics) MBO network, learns a specific kernel and threshold for each input video without adapting to new dynamics, while the second, a meta-learning MBO network, generalizes across diverse threshold dynamics by adapting its parameters per input. Both models are evaluated on synthetic and real-world videos (ice melting and fire front propagation), with performance metrics indicating effective reconstruction and extrapolation of evolving boundaries, even under …

A Filtration On The Cohomology Rings Of Regular Nilpotent Hessenberg Varieties, Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, Martha Precup, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in GL(n, C) / B such that its associated graded ring has graded pieces (i.e., homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in GL(n- 1 , C) / B, showing the inductive nature of these rings. In previous work, the first two authors, together with Abe and Masuda, gave an explicit presentation of these cohomology rings in terms of generators and relations. We introduce …

Graphs Admitting Only Constant Splines, Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

We study generalized graph splines, introduced by Gilbert, Tymoczko, and Viel (2016). For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type of cutset (e.g., a bridge), then the space of splines naturally decomposes as a certain direct sum of submodules. As an application, we use these results to describe splines on a triangulation studied by Zhou and Lai, but over a different ring than they used.

About Time: Visualizing Time At Burning Man, Gordon D. Hoople, Austin Choi-Fitzpatrick, Nathaniel Parde, Diane Hoffoss, Max Mellette, Rachel Nishimura, Virginia Gutman

The Transdisciplinary STEAM+ Journal

About Time was a 30 foot long, 3000 pound wooden sundial that went up in flames at Burning Man 2019. The piece reflected on the role time plays in our lives. We organize our lives around time—are enslaved to time—and yet we know so little about it. Physicists and philosophers continue to grapple with deep puzzles of time—Is time a fundamental quantity, independent of human actions or observations or is it an emergent property of our perception? This installation projected time using two sundials: a horizontal dial which swept time out across the desert floor and an …

Convex Relaxations Of A Continuum Aggregation Model, And Their Efficient Numerical Solution, Mahdi Bandegi

Dissertations

In this dissertation, the global minimization of a large deviations rate function (the Helmholtz free energy functional) for the Boltzmann distribution is discussed. The Helmholtz functional arises in large systems of interacting particles — which are widely used as models in computational chemistry and molecular dynamics. Global minimizers of the rate function (Helmholtz functional) characterize the asymptotics of the partition function and thereby determine many important physical properties such as self-assembly, or phase transitions. Finding and verifying local minima to the Helmholtz free energy functional is relatively straightforward. However, finding and verifying global minima is much more difficult since the …

Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

Dissertations

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between …

Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk

Department of Mathematics: Faculty Publications

One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …

Eigenvalue Problems For An Elliptic Equation With Two Singular Coefficients, Asror M. Shokirov

Scientific Bulletin. Physical and Mathematical Research

For the elliptic type of differential equation with two singular coefficients, the quadratic values of the Dirixle and Dirixle-Neumann problems were found in the quarter in that work. The field and boundary conditions for solving these problems are described in the polar coordinate system. The result is a rectangle in the polar coordinate system. Then, we used the method of separating variables in the right rectangle, that is, divided the variables by the equation and divided the problem into two distinct values for ordinary differential equations. The first of the ordinary differential equations is the substitution of , where the …