Mathematics Commons^™

Spike Timing-Dependent Plasticity And Random Inputs Shape Interspike Interval Regularity Of Model Stn Neurons, Thoa Thieu, Roderick Melnik

School of Mathematical & Statistical Sciences Faculty Publications

Background/Objectives: Neuronal oscillations play a key role in the symptoms of Parkinson’s disease (PD). This study investigates the effects of random synaptic inputs, their correlations, and the interaction with synaptic dynamics and spike timing-dependent plasticity (STDP) on the membrane potential and firing patterns of subthalamic nucleus (STN) neurons, both in healthy and PD-affected states. Methods: We used a modified Hodgkin–Huxley model with a Langevin stochastic framework to study how synaptic conductance, random input fluctuations, and STDP affect STN neuron firing and membrane potential, including sensitivity to refractory period and synaptic depression variability. Results: Our results show that random inputs significantly …

Dissections Of Lacunary Eta Quotients And Identically Vanishing Coefficients, Timothy Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

For any function A(q)=∑∞n=0anqn defineA(0):={n∈N:an=0}.Now suppose C(q) and D(q) are two functions whose m-dissections are given byC(q)=c0G0(qm)+c1qG1(qm)+…+cm−1qm−1Gm−1(qm),D(q)=d0G0(qm)+d1qG1(qm)+…+dm−1qm−1Gm−1(qm).If it is the case that ci=0⟺di=0, i=0,1,…,m−1, then we say that C(q) and D(q) have similar m-dissections, and then it is also clear that C(0)=D(0), in which case we say that C(q) and D(q) have identically vanishing coefficients. In the present paper some new 4-dissections of particular eta quotients are developed. These are used in conjunction with known 2- and 3-dissections to prove many results on the identical vanishing of coefficients of various eta quotients, results which were found experimentally …

Class Groups And Selmer Groups In Special Families, Debanjana Kundu, Abhishek _

School of Mathematical & Statistical Sciences Faculty Publications

We explore the relationship between (3-isogeny induced) Selmer group of an elliptic curve and the (3 part of) the ideal class group, over certain non-abelian number fields.

A Proposal To Explore Geometry With Geogebra: Graphical Exploration And Formal Demonstration Of The Collinearity Of The Barycenters Of A Polygon, Saulo Mosquera Lopez, Marlio Paredes, Walter Castro

School of Mathematical & Statistical Sciences Faculty Publications

This paper illustrates an example of a mathematical activity that teachers and students can replicate to create an experience that resembles professional mathematical activity. We extend the property “Consider a triangle ABC, any straight line and let A’, B’, C’ be the reflections of the points A, B, C on the straight line then the barycenters of the triangles ABC, A’BC, AB’C and ABC’ are collinear and the line of collinearity is perpendicular to the straight line” for any quadrilateral. It is proved that there are four additional triangles, for a total of eight, whose barycenters are collinear and that …

High Moment And Pathwise Error Estimates For Fully Discrete Mixed Finite Element Approximations Of The Stochastic Stokes Equations With Multiplicative Noise, Liet Vo

School of Mathematical & Statistical Sciences Faculty Publications

This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler–Maruyama scheme for time discretization and its fully discrete mixed finite element discretization. Optimal rates of convergence are established for all pth moment errors for p ≥ 2 using a novel doubling of moments technique. The almost optimal rates of convergence are then obtained using Kolmogorov’s theorem based on the high moment error estimates. Unlike for the velocity error estimate, the high moment and pathwise error estimates for the pressure approximation are proved in a time-averaged norm. In addition, the …

Circle Actions On Oriented 4-Manifolds, Donghoon Jang, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In this present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah–Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah–Hirzebruch formula, then there exists a corresponding 4-dimensional oriented S1-manifold.

Predictors Of Nursing Students' Stress, Anxiety, And Depression During The Covid-19 Pandemic In A Hispanic-Serving University In South Texas: A Cross-Sectional Study, Maria I. Diaz, Eleftherios Gkioulekas, Nancy Nadeau

School of Mathematical & Statistical Sciences Faculty Publications

Background: In nursing education, there have been several studies on the impact of the COVID-19 pandemic on the ability of nursing students to cope while in nursing school.

Purpose statement: The goal of this study is to assess undergraduate nursing students' support mechanisms as predictors of stress, anxiety, and depression during the COVID-19 pandemic within a Hispanic-serving institution in South Texas.

Methods: Across-sectional design was used in this study. An online survey using self-reported questionnaires was used to gather data from an undergraduate nursing student cohort during the Fall 2021 semester. Linear regression was used to identify the predictors of …

“What Makes It Eigen-Esque-Ish?”: A Form-Function Analysis Of The Development Of Eigentheory Concepts In A Quantum Mechanics Course, Megan Wawro, Kaitlyn Stephens Serbin

School of Mathematical & Statistical Sciences Faculty Publications

Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how “eigen” develops over time in one quantum mechanics course by analyzing form-function relations (Saxe, 1999) for eigentheory concepts over 22 class sessions. We share results concerning our microgenetic and ontogenetic analyses of the creation of form-function relations and their shifts over time by characterizing the continuity and discontinuity of the various functions and forms associated with concepts …

Conditional Quantization For Some Discrete Distributions, Edgar A. Gonzalez, Mrinal Kanti Roychowdhury, David A. Salinas, Vishal Veeramachaneni

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 finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support {12𝑛:𝑛∈ℕ}. We have …

Derived $P$-Adic Heights And The Leading Coefficient Of The Bertolini–Darmon–Prasanna $P$-Adic $L$-Function, Francesc Castella, Chi-Yun Hsu, Debanjana Kundu, Yu-Sheng Lee, Zheng Liu

School of Mathematical & Statistical Sciences Faculty Publications

Let E/Q be an elliptic curve and let p be an odd prime of good reduction for E. Let K be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which p splits. The goal of this paper is two-fold: (1) we formulate a p-adic BSD conjecture for the p-adic L-function LBDP p introduced by Bertolini–Darmon–Prasanna [Duke Math. J. 162 (2013), pp. 1033–1148]; and (2) for an algebraic analogue F BDP p of LBDP p , we show that the “leading coefficient” part of our conjecture holds, and that the “order of vanishing” part follows from the expected …

How Much Should Consumers With Mild To Moderate Hearing Loss Spend On Hearing Devices?, Vinaya Manchaiah, Steve Taddei, Abram Bailey, De Wet Swanepoel, Hansapani Rodrigo, Andrew Sabin

School of Mathematical & Statistical Sciences Faculty Publications

Background: This study examined the relationship between hearing device price and sound quality. Method: A novel consumer-centric metric of sound quality (“SoundScore”) was used to assess hearing devices’ audio performance. Each hearing device is tested with two fittings. The “Initial Fit” is designed to approximate the most likely fitting for an individual with a mild-to-moderate sloping sensorineural hearing loss. The “Tuned Fit” includes adjusting parameters optimized to hit prescriptive fitting targets (NAL NL2) on an acoustic manikin. Each fitting is evaluated across five dimensions. Both fittings are combined using a weighted average to create a single number from 0 to …

The Improved New Intersection Theorem Revisited, Lars Winther, Luigi Ferraro

School of Mathematical & Statistical Sciences Faculty Publications

We prove a generalized version of Evans and Griffith’s improved new intersection theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dimR−dimR/I. This improves the bound htI obtained by Avramov, Iyengar, and Neeman in 2018.

Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The generalized absolute value equation (GAVE) has wide applications in scientific computing. Establishing a high performance computing method to solve the GAVE is a hot research topic in recent years. In this paper, with the aid of the maximum function, the GAVE is decomposed of two equations, and then we present the relaxation maximum-based (RM) iteration method. To see the feasibility of the method, we discuss the necessary and sufficient conditions for the GAVE to have a unique solution. Next, the convergence analysis of the RM iteration is discussed under some convergence conditions. Moreover, some numerical examples of low and …

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 …