Combinatorial Invariants Of Rational Polytopes,
2021
University of Kentucky
Combinatorial Invariants Of Rational Polytopes, Andrés R. Vindas Meléndez
Theses and Dissertations--Mathematics
The first part of this dissertation deals with the equivariant Ehrhart theory of the permutahedron. As a starting point to determining the equivariant Ehrhart theory of the permutahedron, Ardila, Schindler, and I obtain a volume formula for the rational polytopes that are fixed by acting on the permutahedron by a permutation, which generalizes a result of Stanley’s for the volume for the standard permutahedron. Building from the aforementioned work, Ardila, Supina, and I determine the equivariant Ehrhart theory of the permutahedron, thereby resolving an open problem posed by Stapledon. We provide combinatorial descriptions of the Ehrhart quasipolynomial and Ehrhart series …
A Partition Of Unity Method For Divergence-Free Or Curl-Free Radial Basis Function Approximation,
2021
Boise State University
A Partition Of Unity Method For Divergence-Free Or Curl-Free Radial Basis Function Approximation, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright
Mathematics Faculty Publications and Presentations
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants to these vector fields and/or their potentials based only on discrete samples. Additionally, it is often necessary that the vector approximants preserve the div-free or curl-free properties of the field to maintain certain physical constraints. Div/curl-free radial basis functions (RBFs) are a particularly good choice for this application as they are meshfree and analytically satisfy the div-free or curl-free property. However, this method can be computationally expensive …
Coloring Permutation-Gain Graphs,
2021
Wright State University - Main Campus
Coloring Permutation-Gain Graphs, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich generalizes ordinary graph coloring. Kim and Ozeki observed thatcorrespondence colorings generalize various notions of signed-graph col-orings which again generalizes ordinary graph colorings. In this notewe state how correspondence colorings generalize Zaslavsky’s notionof gain-graph colorings and then formulate a new coloring theory ofpermutation-gain graphs that sits between gain-graph coloring and cor-respondence colorings. Like Zaslavsky’s gain-graph coloring, our newnotion of coloring permutation-gain graphs has well defined chromaticpolynomials and lifts to colorings of the regular covering graph of apermutation-gain graph
Math 111: Introduction To Statistics And Probability,
2021
CUNY York College
Math 111: Introduction To Statistics And Probability, Yu Wang
Open Educational Resources
Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.
Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks,
2021
University of South Florida
Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos
Mathematics and Statistics Faculty Publications
Imbalanced class distribution is an inherent problem in many real-world classification tasks where the minority class is the class of interest. Many conventional statistical and machine learning classification algorithms are subject to frequency bias, and learning discriminating boundaries between the minority and majority classes could be challenging. To address the class distribution imbalance in deep learning, we propose a class rebalancing strategy based on a class-balanced dynamically weighted loss function where weights are assigned based on the class frequency and predicted probability of ground-truth class. The ability of dynamic weighting scheme to self-adapt its weights depending on the prediction scores …
About Automorphisms Of Some Finite Groups,
2021
West Chester University
About Automorphisms Of Some Finite Groups, Sarah Emery
West Chester University Master’s Theses
This thesis gives an introduction to some topics from group theory, with a focus on automorphism groups of finite groups. Chapter one introduces the basic definitions and properties of groups and subgroups. In chapter two, the different classifications of functions between groups are defined and some properties thereof are given. Here we define automorphisms which are the focus of the paper. Chapters three and four deal with permutation groups and Sylow theorems respectively, and are discussions of some important groups, subgroups, and theorems pertaining thereto. The topics of these chapters help with our discussion of automorphism groups in the final …
Regularized Estimations In Some Statistical Problems,
2021
University of Central Florida
Regularized Estimations In Some Statistical Problems, Feng Yu
Electronic Theses and Dissertations, 2020-2023
In this dissertation, we consider estimations with regularization in three statistical problems relating to linear time system, stochastic block model and matrix variate regression. In the first part of the dissertation, we specifically investigate Mixture Multilayer Stochastic Block Model, where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. The Mixture Multilayer Stochastic Block Model was introduced by Bing-yi Jing [2020] and a clustering methodology, TWIST, is …
A Mathematical Model For Predicting Animal Population Persistence On Fragmented Landscapes,
2021
University of Central Florida
A Mathematical Model For Predicting Animal Population Persistence On Fragmented Landscapes, Allyson Jones
Electronic Theses and Dissertations, 2020-2023
The effects of roads, buildings, and cities on animal populations are widespread and, often times, disastrous. These structures fragment animals' homes, inhibiting their ability to obtain essential resources and to reproduce. The question arises then: Under what circumstances can an animal population persist in a fragmented landscape? To attempt to answer this question, we present a spatially explicit reaction-diffusion model with varying growth and diffusion rates that incorporates animal behavior at points where habitats are fragmented for four different habitats. The outcome of extinction or persistence of the animal population is determined by examining the effects of changing parameters on …
On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups,
2021
Bucknell University
On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank
Faculty Journal Articles
We determine the ranks of string C-group representations of the groups PSp(4,q)=Ω(5,q), and comment on those of higher-dimensional symplectic and orthogonal groups.
Three Imprimitive Character Sums,
2021
CUNY New York City College of Technology
Three Imprimitive Character Sums, Brad Isaacson
Publications and Research
We express three imprimitive character sums in terms of generalized Bernoulli numbers. These sums are generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko and Ramanujan in the context of modular forms and theta function identities. As a corollary, we obtain a formula for cotangent power sums considered by Apostol.
A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals,
2021
Richmond Public Schools
A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals, Nathan D. Potter, Hannah Adera Rooney, Melody Locher, Debra Kinsey
Journal of Mathematics and Science: Collaborative Explorations
How does the mathematics specialist provide a profound and lasting impact on instruction? We believe that a productive partnership between the principal and specialist, which we will call the principal-specialist relationship, is at the crux of the matter. When the principal-specialist relationship is built upon a foundation of a shared vision, clear roles, communication, and trust, both the teachers and students in the school benefit. We will explore the impact of the principal-specialist relationship on teacher success during the era of distance learning as necessitated by the COVID-19 pandemic. In order to explore how these ideas come alive in the …
A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$,
2021
Colby College
A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$, Huan Q. Bui
Honors Theses
In this thesis, we consider a class of function on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean norm, positive homogeneous functions appear naturally in the study of convolution powers of complex-valued functions on $\mathbb{Z}^d$. As the spherical measure is a Radon measure on the unit sphere which is invariant under the symmetry group of the Euclidean norm, to each positive homogeneous function $P$, we construct a Radon measure $\sigma_P$ on $S=\{\eta \in \mathbb{R}^d:P(\eta)=1\}$ which is invariant under the symmetry group of $P$. With this measure, we prove …
Optimal Claim Settlement Strategies Under Constraint Of Cap On Claim Loss,
2021
Shanghai Second Polytechnic University
Optimal Claim Settlement Strategies Under Constraint Of Cap On Claim Loss, Hong Mao, Krzysztof Ostaszewski
Faculty Publications – Mathematics
In this paper, we examine the question of how to devise an optimal insurance claim settlement scheme under the constraint of a cap on the amount of the claim payment. We establish objective functions to maximize the net benefit due to exaggerated claims while at the same time maximizing the total expected wealth of the insured. Then, we establish a dual objective function to minimize the total expected loss, including the perspective of the insurer. Finally, we illustrate applications of our work and provide numerical analysis of it along with an example.
Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups,
2021
Colby College
Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups, Qidong He
Honors Theses
Given a compact exceptional group $G$ and $m,s\in\mathbb{N}$, let $N(G,m)$ be the number of conjugacy classes of elements of order $m$ in $G$, and $N(G,m,s)$ the number of such classes whose elements have $s$ distinct eigenvalues. In string theory, the problem of enumerating certain classes of vacua in the string landscape can be rephrased in terms of the study of these quantities. We develop unified combinatorial algorithms based on Burnside's Lemma that can be used to compute both quantities for each of the five compact exceptional groups. Thus, we provide a combinatorial, alternative method to that of Djoković and extend …
Some Properties Of Extending Hypermodules, C11-Hypermodules And T-Extending Hyperrings,
2021
Faculty of Science
Some Properties Of Extending Hypermodules, C11-Hypermodules And T-Extending Hyperrings, Chokchai Wongyai
Chulalongkorn University Theses and Dissertations (Chula ETD)
In this research, extending hypermodules, C11-hypermodules and t-extending hyperrings are defined and studied. We characterize extending hypermodules, C11-hypermodules and t-extending hyperrings in many ways under some conditions of hypermodules and hyperrings. Moreover, some properties concerning subhypermodules of extending hypermodules and C11-hypermodules are investigated. Especially, we study C11-hypermodules in the case that they can be decomposed as a direct sum of two subhypermodules.
S-Magic Labelings Of Some Complete Tripartite Graphs,
2021
Faculty of Science
S-Magic Labelings Of Some Complete Tripartite Graphs, Sararat Numai
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Use Of Lymesim 2.0 To Assess The Potential For Single And Integrated Management Methods To Control Blacklegged Ticks (Ixodes Scapularis; Acari: Ixodidae) And Transmission Of Lyme Disease Spirochetes,
2021
Hollins University
Use Of Lymesim 2.0 To Assess The Potential For Single And Integrated Management Methods To Control Blacklegged Ticks (Ixodes Scapularis; Acari: Ixodidae) And Transmission Of Lyme Disease Spirochetes, Shravani Chitineni, Elizabeth R. Gleim, Holly D. Gaff
Undergraduate Honors Theses
Annual Lyme disease cases continue to rise in the U.S. making it the most reported vector-borne illness in the country. The pathogen (Borrelia burgdorferi) and primary vector (Ixodes scapularis; blacklegged tick) dynamics of Lyme disease are complicated by the multitude of vertebrate hosts and varying environmental factors, making models an ideal tool for exploring disease dynamics in a time- and cost-effective way. In the current study, LYMESIM 2.0, a mechanistic model, was used to explore the effectiveness of three commonly used tick control methods: habitat-targeted acaricide (spraying), rodent-targeted acaricide (bait boxes), and white-tailed deer targeted acaricide (4-poster …
Steepest Descent, Elastic Energy, And Stability In Infinite Dimensional Hilbert Manifolds,
2021
Northern Illinois University
Steepest Descent, Elastic Energy, And Stability In Infinite Dimensional Hilbert Manifolds, Scott W. Rexford
Graduate Research Theses & Dissertations
Consider constant-speed planar curves $\gamma =(x,y):[0,1]\to\mathbb{R}^2$ subject to $\gamma (0)=(0,0)$ and a prescribed value of $x(1)$, but with $y(1)$ unconstrained. We analyze the existence and the stability of critical curves of the elastic energy. Elastic curves are here thought of as points in an infinite-dimensional Sobolev manifold where the intrinsic gradient of the elastic energy vanishes. The admissible curves subject to constraints are members of a Riemannian submanifold using the ambient metric. A curve is stable with respect to the negative gradient flow if it is global or local minimum, and unstable otherwise. We analyze the stability of the classical …
Isolation Intervals Of The Real Roots Of The Parametric Cubic Equation,
2021
Technological University Dublin
Isolation Intervals Of The Real Roots Of The Parametric Cubic Equation, Emil Prodanov
Articles
The isolation intervals of the real roots of the real symbolic monic cubic polynomial $p(x) = x^3 + a x^2 + b x + c$ are found in terms of simple functions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$, $\pm \sqrt{-b}$, when $b$ is negative), and the roots of some auxiliary quadratic equations whose coefficients are also simple functions of the coefficients of the cubic. All possible cases are presented with clear and very detailed diagrams. It is very easy to identify which of these diagrams is the relevant one for any given cubic equation and …
Portfolio Selection Problem Based On Exponential Loss Function Under Independent Binomial Model In Set50,
2021
Faculty of Science
Portfolio Selection Problem Based On Exponential Loss Function Under Independent Binomial Model In Set50, Krerkkiat Charoenying
Chulalongkorn University Theses and Dissertations (Chula ETD)
In this thesis, we investigate the portfolio allocation problem in the Stock Exchange of Thailand by considering the stocks of the 48 biggest companies in terms of market capitalization, with the requirement that an investor wants to invest under these 48 assets only and their risk is measured by the exponential loss function. The stocks under consideration must be independent and the prices of the stocks at the maturity time are assumed to follow the well-known binomial model. The Pearson correlation test is used for selecting stocks with independence property. In this study, we are interested in an investor investing …
