Mathematics Commons^™

The Dialogue Dilemma: The Role Of Patient-Clinician Communication For Low-Income People Who Smoke And Manage Multiple Conditions, Monique T. Cano, Michael R. Lindstrom, Ricardo F. Muñoz

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: Adults from low-income backgrounds who smoke face significant health disparities related to tobacco use, often at disproportionately high rates. These individuals are more likely to endure multiple mental and physical (MP) health conditions, which can negatively influence their self-rated health (SRH). The quality and effectiveness of patient-clinician communication (PCC) can influence how patients perceive their own health. Understanding how PCC influences SRH among low-income adults who smoke and suffer from multiple MP conditions is essential for clinical care as multimorbidity is on the rise. This study examines how PCC may influence the health perceptions of low-income adults who smoke …

Quantization For A Condensation System, Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma

School of Mathematical & Statistical Sciences Faculty Publications

For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), represents the rate at which the nth quantization error of order r approaches zero as the number of elements n in an optimal set of n-means for μ tends to infinity. If Dr(μ) does not exist, we define D−−r(μ) and ¯¯¯Dr(μ) as the lower and the upper quantization dimensions of μ of order r, respectively. In this paper, we investigate the quantization dimension of the condensation measure μ associated with a condensation system ({Sj}Nj=1, (pj)Nj=0,ν). We provide two examples: one where ν is an …

Ai Meets Economics: Can Deep Learning Surpass Machine Learning And Traditional Statistical Models In Inflation Time Series Forecasting?, Ezekiel N.N. Nortey, Edmund F. Agyemang, Enoch Sakyi-Yeboah, Obu-Amoah Ampomah, Louis Agyekum

School of Mathematical & Statistical Sciences Faculty Publications

This study examined the forecasting ability of deep learning (DL) and machine learning (ML) models against benchmark traditional statistical models for the monthly inflation rates in the USA. The study compared various DL and ML models like transformers, linear regression, gradient boosting (GB), extreme gradient boosting (XGBoost), and adaptive boosting (AdaBoost) with traditional baseline time-series models like autoregressive integrated moving averages (ARIMA) and exponential smoothing (ETS) with Holt-Winters seasonal method utilizing data sourced from the Federal Reserve Bank of St. Louis. The study consistently showed that all DL and ML models outperformed the traditional approaches. In particular, the Transformer (RMSE …

Shaping Mathematics Identity: An Exploratory Study On Specifications Grading In Calculus I At A Hispanic-Serving Institution, Luis M. Fernandez, Kaitlyn Stephens Serbin, Cristina Villalobos, Shaghayegh Azadi Setayesh, Guillermo Garza

School of Mathematical & Statistical Sciences Faculty Publications

Calculus I courses play a pivotal role in shaping students' STEM pathways, making it essential to adopt pedagogies that foster both achievement and mathematics identity development, particularly among underserved groups such as Hispanic students. This study explores the impact of Specifications Grading, an alternative assessment method where students meet specific course learning objectives through multiple attempts, on students’ mathematics identity development. Through a comparative case study of two Calculus I students at a Hispanic-Serving Institution, one enrolled in a specification graded course and the other in a traditionally-graded course, we examine shifts in their self-perceptions of competence, interest, recognition in …

Trimming Five Generated Gorenstein Ideals, Luigi Ferraro, W. Frank Moore

School of Mathematical & Statistical Sciences Faculty Publications

Let (𝑅,𝔪,𝕜) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. It follows from a result of Buchsbaum and Eisenbud that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by 𝔪; we say that J is a trimming of I. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of 𝑅/𝐽 and computed a DG algebra …

Data-Driven Survival Modeling For Breast Cancer Prognostics: A Comparative Study With Machine Learning And Traditional Survival Modeling Methods, Theophilus Gyedu Baidoo, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Background This investigation delves into the potential application of data-driven survival modeling approaches for prognostic assessments of breast cancer survival. The primary objective is to evaluate and compare the ability of machine learning (ML) models and conventional survival analysis techniques, to identify consistent key predictors of breast cancer survival outcomes.

Methods This study employs data-driven survival modeling approaches to predict breast cancer survival, including survival-specific methods such as the Cox Proportional Hazards (CPH) model, Random Survival Forests (RSF), and Cox Proportional Deep Neural Networks (DeepSurv), as well as machine learning models like Random Forests (RF), XGBoost, Support Vector Machines (SVM) …

On The Determinant Of Up On Mk(P,Χ), Xingyu Huang, Timothy J. Huber, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

In this work, for p a prime, we compute the absolute value of the determinant of the UpUp-operator on the vector space Mk(p,χ)Mk(p,χ) of holomorphic modular forms of weight k and level Γ0(p)Γ0(p) with character χχ. As an implication, we confirm a number of conjectures of the second author.

Solitons, Breathers And Rogue Waves Of The Yajima–Oikawa-Newell Long Wave–Short Wave System, Marcos Caso-Huerta, Bao-Feng Feng, Sara Lombardo, Ken-Ichi Maruno

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we consider the recently-introduced Yajima–Oikawa–Newell (YON) system describing the nonlinear resonant interaction between a long wave and a short wave. It extends and generalises the Yajima–Oikawa (YO) and the Newell (N) systems, which can be obtained from the YON system for special choices of the two non-rescalable, arbitrary parameters that it features. Remarkably, for any choice of these latter constants, the YON system is integrable, in the sense of possessing a Lax pair. New families of solutions, including the bright and dark multi-solitons, as well as the breathers and the higher-order rogue waves are systematically derived by …

Critical Appraisal Of Multidrug Therapy In The Ambulatory Management Of Patients With Covid-19 And Hypoxemia Part I. Evidence Supporting The Strength Of Association, Eleftherios Gkioulekas, Peter A. Mccullough, Colleen Aldous

School of Mathematical & Statistical Sciences Faculty Publications

This critical appraisal is focused on three published case series of 119 COVID-19 patients with hypoxemia who were successfully treated in the United States, Zimbabwe, and Nigeria with similar off-label ivermectin-based multidrug treatments that may include ivermectin, nebulized nanosilver, doxycycline, zinc, Vitamins C, and Vitamin D, resulting in rapid recovery of oxygen levels. We used a simplified self-controlled case series method to investigate the association between treatment and the existence of hospitalization rate reduction. External controls of hospitalized patients were compared against the subgroup of patients with baseline room air SpO2 ≤ 90% to investigate the association between treatment and …

Critical Appraisal Of Multidrug Therapy In The Ambulatory Management Of Patients With Covid-19 And Hypoxemia. Part Ii: Causal Inference Using The Bradford Hill Criteria, Eleftherios Gkioulekas, Peter A. Mccullough, Colleen Aldous

School of Mathematical & Statistical Sciences Faculty Publications

We continue the critical appraisal of three published case series of 119 COVID-19 patients with hypoxemia, treated in the United States, Zimbabwe, and Nigeria with similar ivermectin-based multidrug treatments, to assess the available evidence supporting a causal relationship between treatment and reduction in hospitalizations and mortality. A narrative review was conducted to assess the Bradford Hill criteria for a causal association. We used a previously proposed refinement of the Bradford Hill criteria that reorganized them into three categories of direct, mechanistic, and parallel evidence. The efficacy of the two most aggressive ivermectin-based multidrug protocols is supported by the Bradford Hill …

Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If, in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where 𝑚≥3, inscribed in a unit circle.

Dynamic Mean-Field Theory For Continuous Random Networks, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of generalized Gaussian random variables. The equation controls the time evolution of a macroscopic state interpreted as neural activity, which depends on position and time. Such a network corresponds to a statistical field theory (SFT) given by a momenta-generating functional. Discrete versions of the mentioned networks appeared in spin glasses and as models of artificial neural networks. Each of these discrete networks corresponds to a lattice SFT, where the …

Quantization Dimensions For Inhomogeneous Bi-Lipschitz Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

Let ν be a Borel probability measure on a d-dimensional Euclidean space R d , d ≥ 1 , with a compact support, and let ( p 0 , p 1 , p 2 , … , p N ) be a probability vector with p j > 0 for 0 ≤ j ≤ N . Let { S j : 1 ≤ j ≤ N } be a set of contractive mappings on R d . Then, a Borel probability measure μ on R d such that μ = ∑ N j = 1 p j μ ∘ S − …

Heart Disease Prediction Using Ensemble Tree Algorithms: A Supervised Learning Perspective, Enoch Sakyi-Yeboah, Edmund F. Agyemang, Vincent Agbenyeavu, Akua Osei- Nkwantabisa, Priscilla Kissi-Appiah, Lateef Moshood, Lawrence Agbota, Ezekiel N.N. Nortey

School of Mathematical & Statistical Sciences Faculty Publications

Heart disease stands as a leading cause of morbidity and mortality globally, presenting a significant public health challenge. Therefore, early prediction and detection are critical, leading to timely and appropriate interventions at early stages. Four ensemble tree-based algorithms were used in this study: adaptive boosting, extreme gradient boosting, random forest, and extremely randomized trees, investigating their ability to predict heart disease. Data related to heart disease clinical features was obtained from the open Kaggle Machine Learning Dataset repository. Adaptive Boosting stands out as the highest performer, achieving an average testing accuracy of 93.70%, precision of 93.71%, recall of 93.70%, and …

Extended High-Frequency Hearing And Suprathreshold Neural Synchrony In The Auditory Brainstem, Jithin Raj Balan, Sri Mishra, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Elevated hearing thresholds in the extended high frequencies (EHFs) (>8 kHz) are often associated with poorer speech-in-noise recognition despite a clinically normal audiogram. However, whether EHF hearing loss is associated with disruptions in neural processing within the auditory brainstem remains uncertain. The objective of the present study was to investigate whether elevated EHF thresholds influence neural processing at lower frequencies in individuals with normal audiograms. Auditory brainstem responses (ABRs) were recorded at a suprathreshold level (80 dB normal hearing level) from 45 participants with clinically normal hearing. The recording protocol was optimized to obtain robust wave I of the …

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 …

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 …

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 …

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.

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 …

Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

The local angle property of the (order-1) Delaunay triangulations of a generic set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations …

Ramanujan–Fine Integrals For Level 10, Shaun Cooper, Timothy Huber, Jeffery Opoku

School of Mathematical & Statistical Sciences Faculty Publications

We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequence, we establish and classify an infinite number of integral evaluations such as

∫e−2π/10√0q∏j=1∞(1−qj)3(1−q10j)8(1−q5j)7dq=14(10−45–√−−−−−−−−√−1). We describe how the results were found and give reasons for why it is reasonable to conjecture that the list is complete for level 10.

Image Of Mathematics: A Case Study Of Two Women's Early Mathematics Experiences, Lili Zhou, Elizabeth Suazo-Flores, Bima Sapkota, Rose Mbewe, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

People often view mathematics as abstract, cold, and irrelevant to real life, and their school experiences likely influence such views. In this case study, we investigated the mathematics experiences of two women who participated in an afterschool girls-only STEM club 30 years ago when they were in fifth and sixth grades. We explored how the participants' early in- and out-of-school experiences informed their images of mathematics. We collected data through a survey, focus group interviews, and individual interviews. We employed oral history methods in interviews to grant participants a significant degree of freedom to retrospectively recount and reconstruct their experiences. …

The Taylor Resolution Over A Skew Polynomial Ring, Luigi Ferraro, Desiree Martin, W. Frank Moore

School of Mathematical & Statistical Sciences Faculty Publications

Let k be a field and let I be a monomial ideal in the polynomial ring Q = k[x1, . . . , xn]. In her thesis, Taylor introduced a complex which provides a finite free resolution for Q/I as a Q-module. Later, Gemeda constructed a differential graded structure on the Taylor resolution. More recently, Avramov showed that this differential graded algebra admits divided powers. We generalize each of these results to monomial ideals in a skew polynomial ring R. Under the hypothesis that the skew commuting parameters defining R are roots of unity, we prove as an application that …

Polar Decompositions And Spectral Properties Of Linear Operator Pencils, Slaviša Djordjević, Jaewoong Kim, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair T=(T1,T2) . Using this decomposition, we define the generalized spherical Aluthge transforms for the linear pencil of an ordered pair T=(T1,T2) and give spectral properties between the linear pencil and the generalized spherical Aluthge transform of it. In detail, we study whether the spectral properties of the linear pencil of an ordered pair T=(T1,T2) are invariant under the generalized spherical Aluthge transform.

Editorial Insights: Reflections On The Volume And Charge To The Field, Heather Howell, Meghan Shaughnessy, Barbara Stengal, Carrie Wilkerson Lee, Liza Bondurant, Bima Sapkota, Gregory Benoit, Yvonne Lai

School of Mathematical & Statistical Sciences Faculty Publications

In this, the final chapter of Section 3, the authors document an interview that took place in June of 2024, as the editorial team wrapped up reviews of the chapters submitted to this volume. The interview was led by two of the advisory board members, Meghan Shaughnessy and Barbara Stengal, and included the editorial group, Heather Howell, Carrie Wilkerson Lee, Liza Bondurant, and Bima Sapkota, and other members of the advisory board, Greg Benoit and Yvonne Lai. The motivation to create this interview-based chapter was to capture some of the authors' own learning and reflection as they brought the volume …

Generalizations Of Some Q-Product Identities Of Ramanujan And Others, Timothy J. Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

By considering certain limiting cases of a WP-Bailey chain discovered by Andrews, and also limiting cases of certain classical summation formulae for basic hypergeometric series, we derive new expressions for certain Lambert series in terms of basic hypergeometric series. In some cases, the resulting series involve an arbitrary Bailey pair. This allows for the derivation of new basic hypergeometric expansions for some q-products and series that Ramanujan expressed in terms of Lambert series. Some of Ramanujan’s identities are extended to more general relations containing one or more free parameters.