Mathematics Commons^™

Discrete Math For Computer Science - Chapter 10: Definition Of Functions: Properties Of Functions, Houman Kamran Habibkhani

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Discrete Math For Computer Science - Chapter 6: Proofs By Contradiction: Proofs By Cases, Houman Kamran Habibkhani

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Discrete Math For Computer Science - Chapter 5: Direct Proofs: Proofs By Contrapositive, Houman Kamran Habibkhani

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Discrete Math For Computer Science - Chapter 7: Sets And Subsets: Set Of Sets, Houman Kamran Habibkhani

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Generation Of Patient Specific Cardiac Chamber Models Using Generative Neural Networks Under A Bayesian Framework For Electroanatomical Mapping, Sunil Mathew, Jasbir Sra, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability …

Exploring The Potential Of Strongly Coupled Lagrangian Data Assimilation In An Ocean–Atmosphere System, Luyu Sun, Amit Apte, Laura Slivinski, Elaine T. Spiller

Mathematical and Statistical Science Faculty Research and Publications

Precise measurements of ocean surface flow velocities are essential for refining forecasts in a coupled ocean–atmosphere system. While oceanic data are generally sparse, surface drifters present an opportunity by providing detailed and frequently observed sea surface currents, which are a critical component in the dynamics at air–sea interface. Such observations could potentially address the usual data gaps in a coupled ocean–atmosphere assimilation system. In this study, we investigate the implications of assimilating drifter data within a coupled system with intermediate complexity based on a quasigeostrophic model—Modular Arbitrary-Order Ocean–Atmosphere Model (MAOOAM)—using observing system simulation experiments (OSSEs). Two main strategies for assimilating …

On Explicit Solutions For Coupled Reaction-Diffusion And Burgers-Type Equations With Variable Coefficients Through A Riccati System, Jose M. Escorcia, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable coefficients such as the diffusive Lotka-Volterra model, the Gray-Scott model, the Burgers equations. The equations' integrability (via the explicit formulation of the solutions) is accomplished by using similarity transformations and requiring that the coefficients fulfill a Riccati system. We present traveling wave-type solutions as well as solutions with more complex dynamics and relevant features such as bending. A Mathematica file has been prepared as supplementary material, verifying the Riccati systems used in the construction of …

On Realizability Of Some Graphs, Runze Wang

Communications on Number Theory and Combinatorial Theory

A graph H is said to be realizable by a graph G if for any vertex v in G, the induced subgraph of G on the neighborhood of v is isomorphic to H. In this paper, we show that a complete multipartite graph is realizable if and only if each of its parts has the same size; characterize the graphs by which a complete multipartite graph with each part having the same size is realizable; show that all cluster graphs are realizable; prove that a wheel is realizable if and only if it has four vertices; prove that …

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Addressing Class Imbalance Problem In Health Data Classification: Practical Application From An Oversampling Viewpoint, Edmund F. Agyemang, Joseph A. Mensah, Eric Nyarko, Dennis Arku, Benedict Mbeah-Baiden, Enock Opoku, Ezekiel Nii Noye Nortey

School of Mathematical & Statistical Sciences Faculty Publications

While analyzing health data is important for improving health outcomes, class imbalance in datasets poses major challenges to machine learning classification models. This work, therefore, considers the class imbalance problem in stroke prediction using models such as K-nearest neighbors, support vector machine, logistic regression, random forest, and decision tree. This work balances the stroke dataset, thereby enhancing model performance, through various oversampling strategies: random oversampling (RO), ADASYN, SMOTE, and SMOTE–Tomek. Compared to the results of the imbalanced dataset, all applied oversampling techniques enhanced the correct classification of stroke events by the ML model. Among these, RO–SVM with RBF kernel was …

Hilbert’S 10th Problem Via Mordell Curves, Somnath Jha, Debanjana Kundu, Dipramit Majumdar

School of Mathematical & Statistical Sciences Faculty Publications

We show that for 5 / 6 -th of all primes p, Hilbert’s 10th problem is unsolvable for the ring of integers of Q ( ζ 3 , 3 √ p ) . We also show that there is an infinite set S of square-free integers such that Hilbert’s 10th problem is unsolvable over the ring of integers of Q ( ζ 3 , √ D , 3 √ p ) for every D ∈ S and for every prime p ≡ 2 , 5 ( mod 9 ) . We use the CM elliptic curves y 2 = x …

Analytical Method For Solving Systems Of Fractional Initial Value Problems Using The Modified Atangana-Baleanu Derivative, Lana Mohammad Aref

Thesis/ Dissertation Defenses

This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving …

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Sobolev Regularity For The Bergman Projection On Relatively Compact Domains In Hermitian Manifolds, Philip Harrington

Mathematical Sciences Faculty Publications and Presentations

Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L< ^>2$$\end{document} Sobolev regularity of the Bergman projection acting on L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L< ^>2$$\end{document} sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel

CODEE Journal

We consider an extension to the classical SIR compartmental model from mathematical epidemiology as applied to the spread of COVID-19 on a college campus. While the classical SIR model does not allow for recovered individuals to lose immunity, we alter the equations to allow for such (due to the rise of new variants), leading to a SIRS-type model. We study the system of ODEs analytically and through numerical simulation. Finally we discuss a quantitative approach for how college administrators can decide when to implement stricter non-pharmaceutical interventions (social distancing, mask mandates, quarantine, etc.) to eradicate the infection from the campus …

Semilinear Klein-Gordon Equation In Space-Time Of Black Hole Which Is Gaining Mass In The Universe With Accelerating Expansion, Karen Yagdjian, Anahit Galstyan

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we consider the propagation of waves in the space-time of a single black hole with a static Schwarzschild radius in the expanding universe, namely, the solutions of the linear and semilinear Klein-Gordon equations.

Modelling The Behavior Of Human Crowds As Coupled Active-Passive Dynamics Of Interacting Particle Systems, Thoa Thieu, Roderick Melnik

School of Mathematical & Statistical Sciences Faculty Publications

The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model reliably such human crowd systems with complex social interactions, stochastic tools play an important role for the setting of mathematical formulations of the problems. In this work, using the description based on an exclusion principle, we study a statistical-mechanics-based lattice gas model for active-passive population dynamics with an application to human crowd behaviors. We provide representative numerical examples for the evacuation dynamics of human crowds, where the …

Volatility Modelling In Garch Frameworks: A Comparative Analysis Of Non-Gaussian Error Distributions With Skewed Parameters., Olatunbosun Adewale Akanbi, Timothy Olabisi Olatayo, Abass Ishola Taiwo

Al-Bahir

Forecasting volatility in financial time series remains challenging due to their asymmetric nature and excess kurtosis. This study evaluates and compares the performance of four variant of GARCH models incorporating skewed non-Gaussian error innovation distribution. The performances of these GARCH family of models under the skewed error innovation distributions were evaluated for three different unique data sets to have a more robust assessment of the performance of these skewed error innovation distributions. This study leverage on daily closing prices of Bitcoin, Naira to Dollar Exchange rates and daily Nigeria All Share Index between January 1, 2015 and January 26, 2024. …

Non-Orientable Surfaces Bounded By Knots, Megan K. Fairchild

LSU Doctoral Dissertations

The non-orientable 4-genus of a knot $K$ in $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ in $B^{4}$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots, torus knots, and Whitehead doubles. We also will view obstructions to a knot bounding a M\"{o}bius band given by the double branched cover of $S^{3}$ branched over $K$. Additionally, we discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used …

On Examples And Classification Of Frobenius Objects In Rel, Ivan Contreras, Adele Long, Sophia Marx, Rajan Amit Mehta

Mathematics Sciences: Faculty Books

This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022.

The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, …

Voronoi Conjecture For Five-Dimensional Parallelohedra, Alexey Garber, Alexander Magazinov

School of Mathematical & Statistical Sciences Faculty Publications

We prove the Voronoi conjecture for five-dimensional parallelohedra. Namely, we show that if a convex five-dimensional polytope P tiles ℝ5 with translations, then P is an affine image of the Dirichlet-Voronoi polytope for a five-dimensional lattice.
Our proof is based on an exhaustive combinatorial analysis of possible dual 3-cells and incident dual 4-cells encoding local structures around two-dimensional faces of five-dimensional parallelohedron P and their edges aiming to prove existence of a free direction for P paired with new properties established for parallelohedra (in any dimension) that have a free direction that guarantee the Voronoi conjecture for P.

Group Approach To Geometric Quantization Of Two Physical Groups, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Physical systems as a rule are associated with a symmetry group. One way of quantizing the system is to use this symmetry group to construct a geometric form of quantization procedure. This group quantization procedure is discussed and illustrated here on two different systems. Group cohomology and extensions of groups play a key role. Many important groups in physics can be extended by the local U(1) group. The process is introduced here and applied to two nontrivial systems.

Hypergraph Association With Lie Algebra Of Upper Triangular Matrices And Its Application To Wireless Networks, Supriya S

Theses and Dissertations

A hypergraph is a generalized graph characterized by edges spanning more than one vertices describing multiple relationships among them. It provides a mathematical framework for comprehending and learning about a wide range of real-world challenges. On the other side, the theory of non-associative algebras, such as Jordan, Octonions, Malcev, and Lie, has found significant impetus in recent years. These structures proved intriguing from an algebraic standpoint; they generated novel concepts and approaches that aided in solving specific classic algebraic problems, also progressing towards application.

A preeminent observation that galvanizes this thesis is that hypergraph association is still unexplored in Lie …

Stochastic Games Of Parental Vaccination Decision Making And Bounded Rationality, Andras Balogh, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of …

Asymptotic Matrix Behaviors And Iterative Algorithms, Tin-Yau Tam

Mathematics Colloquium Series

This presentation examines the asymptotic behavior of matrix iterations, focusing on the QR and LR algorithms and their significance in eigenvalue computation. It highlights foundational developments by Rutishauser, Francis, and Kublanovskaya and modern refinements by Huang and Tam, particularly on matrix decompositions and spectral properties. Extensions of Yamamoto’s theorem, including recent works by Nayak and Shekhawat, and Huang and Tam, are discussed, connecting iterative processes to spectral radius formulas and Jordan decompositions. This is a joint work with Huajun Huang of Auburn University.

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

Optimized Hiv/Aids Resource Allocation In Ohio: A Linear Programming Approach, Godfred Ahenkroa Kesse

Data Science and Data Mining

This study employs a linear and integer programming approach to optimize HIV resource allocation in Ohio, aiming to minimize new infections and enhance the impact of limited resources. With the advances in HIV prevention and treatment, Ohio faces challenges in addressing disparities in access to healthcare, particularly among high-risk populations. The proposed model integrates data on infection rates, transmission patterns, demographic factors, and cost-effectiveness to provide a decision-support framework for policymakers. Using epidemiological data and equity constraints, the model prioritizes high-risk regions and populations while ensuring fair resource distribution. Results indicate that increased funding allocations significantly enhance the potential to …

Ultrathin-Layer Strain-Based Electronic Devices: From-First-Principles Derivation Of The Corresponding Equation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

Most information about the world comes from sensors -- and from the results of processing sensor data. In many practical situations -- e.g., in biomedical applications -- it is desirable to make sure that the sensors are as "invisible" as possible, in particular, that they are as small as possible. One way to achieve such small size is to use ultrathin-layer materials such as graphene. It is known that for such materials, strain causes electromagnetic effects -- which can be used to detect small strains. Interestingly, it turned out that the same equation describes the relation between strain and electric …

A Natural Extension Of F-Transform To Triangular And Triangulated Domains Necessitates The Use Of Triangular Membership Functions, Hana Zámečiková, Irina Perfilieva, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations when we process 1-D data, the method of F-transform turned out to be very useful. In this method, we can use either triangular membership functions or more complex ones. Because this method has been so successful in 1-D applications, a natural idea is to extend it to functions defined on 2-D and higher-dimensional domains -- e.g., to images. This method allows natural generalization to rectangular domains, where it indeed turned out to be very effective. A recent paper showed that it can extended to more general domains -- e.g., to triangular domains and to more general …