Physical Sciences and Mathematics Commons^™

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Saturated Hierarchical Atomic Incremental Learning (Shail): A Behavioral Learning Perspective On Staged Mastery And Saturation, Ernest Fokoue

Articles

We introduce Saturated Hierarchical Atomic Incremental Learning (sHAIL), a learning paradigm in which complex tasks are approached through a sequence of simpler atomic subtasks, each mastered to saturation before progression. The central mechanism is a saturation criterion that detects when learning dynamics enter a plateau region, triggering consolidation and subsequent ascent to a higher level of task complexity. We develop a theoretical framework for sHAIL and show that it naturally gives rise to \emph{staircased convergence}: alternating phases of rapid improvement and genuine plateau. Within each level, classical convergence guarantees apply under standard smoothness conditions, while the hierarchical transitions are driven …

No Intelligence Without Statistics: The Invisible Backbone Of Artificial Intelligence, Ernest Fokoue

Articles

The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars—Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification—demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the …

Decorrelation, Diversity, And Emergent Intelligence: The Isomorphism Between Social Insect Colonies And Ensemble Machine Learning, Ernest Fokoue, Gregory Babbitt, Yuval Levental

Articles

Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation— through stochastic response to local cues and positive feedback—map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that …

A General Weighting Theory For Ensemble Learning: Beyond Variance Reduction Via Spectral And Geometric Structure, Ernest Fokoue

Articles

Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines, kernel ridge regression, Gaussian process regression, and other regularized reproducing kernel Hilbert space (RKHS) methods whose variance is already tightly controlled by regularization and spectral shrinkage. This paper develops a general weighting theory for ensemble learning that moves beyond classical variance-reduction arguments. We formalize ensembles as linear operators acting on a hypothesis space and endow the space of weighting sequences with geometric and spectral constraints. …

On The Scientific Stature Of Data Science: The Epistemological Unicorn, Ernest Fokoue

Articles

Data Science has ignited unprecedented academic, industrial, and pedagogical fervor, yet its status as a \textit{science} in the classical sense---comparable to physics or biology---remains profoundly unsettled. This article interrogates the epistemological foundations of Data Science by examining its hybrid theoretical lineage, from the Universal Approximation Theorem to the No-Free-Lunch Theorems, with special emphasis on the fundamental Bayesian optimality results for both regression and classification. We argue that Data Science is in a vigorous \textit{gestational period}, characterized not by an absence of principles but by a creative tension between empirical pragmatism and deep mathematical theory. The Cross-Validation score emerges as the …

Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski

Mathematical Modelling and Numerical Simulation with Applications

The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …

Learning Ordinal Geometry: Semantic–Aware Kernels For Ordered Categorical Data, Ernest Fokoue

Articles

Ordinal data arise ubiquitously in survey research, psychology, medicine, economics, and recommender systems, yet kernel methods for such data typically rely on either nominal encodings or arbitrary numeric codings. The former discards order information; the lat- ter imposes a fictitious metric structure. This paper develops a principled framework for kernel design on ordinal scales and introduces a new class of Semantic–Aware Ordinal Ker- nels (SAOK) that simultaneously capture ordinal order and semantic proximity between categories. We begin by formalizing order–preserving embeddings of finite chains and characterizing a broad family of chain distances that are conditionally negative definite. Through Schoen- berg …

On Fibonacci Ensembles: An Alternative Approach To Ensemble Learning Inspired By The Timeless Architecture Of The Golden Ratio, Ernest Fokoue

Articles

Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to the unfolding of leaves, this humble sequence reflects a universal grammar of balance. In this work, we introduce \emph{Fibonacci Ensembles}, a mathematically principled yet philosophically inspired framework for ensemble learning that complements and extends classical aggregation schemes such as bagging, boosting, and random forests \citep{Breiman1996Bagging, Breiman2001RandomForests, Friedman2001GBM, Zhou2012Ensemble, HastieTibshiraniFriedman2009ESL}. Two intertwined formulations unfold: (1) the use of normalized Fibonacci weights -- tempered through orthogonalization and Rao--Blackwell optimization -- …

The Blurred Boundaries Of Care: A Qualitative Analysis Of Nurse-Doula Role Conflict, Curisa Mae Tucker Phd, Rn, Maria Mcclam, Kelly Russin Dnp, Rnc-Ob, Chse, Nansi Boghossian, Rachel Gulczinski, Lauren Workman

Faculty Publications

Introduction:

Methods:

Association Between The Dietary Index For Gut Microbiota (Di-Gm) And Colorectal Cancer In The Plco Cohort, Bezawit E. Kase, Angela D. Liese Ph.D., Jiajia Zhang Ph.D., Elizabeth Angela Murphy, Susan E. Steck Phd, Mph, Rd

Faculty Publications

Objectives: The study aimed to examine the association between a dietary index for gut microbiota (DI-GM) and the risk of incident colorectal cancer (CRC). Clarifying the role of diet-induced alterations in the composition and function of gut microbiota on the development of CRC can contribute to prevention efforts. Methods: Participants from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening trial enrolled in the intervention arm and who completed baseline assessments were included in the analysis (n = 55,685). The DI-GM is a literature-derived index used to score diet quality in terms of maintaining healthy gut microbiota. A time-dependent Cox model …

Association Between The Dietary Index For Gut Microbiota (Di-Gm) And Colorectal Cancer In The Plco Cohort, Bezawit E. Kase, Angela D. Liese, Jiajia Zhang, Elizabeth Angela Murphy, Susan E. Steck

Faculty Publications

Objectives: The study aimed to examine the association between a dietary index for gut microbiota (DI-GM) and the risk of incident colorectal cancer (CRC). Clarifying the role of diet-induced alterations in the composition and function of gut microbiota on the development of CRC can contribute to prevention efforts. Methods: Participants from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening trial enrolled in the intervention arm and who completed baseline assessments were included in the analysis (n = 55,685). The DI-GM is a literature-derived index used to score diet quality in terms of maintaining healthy gut microbiota. A time-dependent Cox model …

Dietary Inflammatory Index And Objective Disease Activity In Ibd: No Association Found, Rúbia Moresi Vianna De Oliveira, Ana Carolina Junqueira Vasques, Stefhani Andrioli Romero, Nitin Shivappa Mbbs, Mph, Ph.D., Michael David Wirth, James Hébert Scd, Glaucia Fernanda Soares Ruppert Reis, Cristiane Kibune Nagasako

Faculty Publications

Background

Inflammatory Bowel Disease (IBD) involves genetic and environmental factors, but the relationship between disease activity, adiposity, and diet remains unclear.

Objective

To investigate the association between endoscopic/radiological activity of IBD, body adiposity, and the Dietary Inflammatory Index with or without adjustment for energy density (E-DII or DII).

Method

An observational, cross-sectional study was carried out. Endoscopic activity was defined by an endoscopic Mayo score >2, Crohn’s Disease Endoscopic Index of Severity (CDEIS) > 5, and/or the presence of a deep ulcer in any intestinal segment. Body adiposity was estimated using the body mass index, waist circumference, and waist-hip ratio (WHR). …

Circulating Levels Of Insulin-Like Growth Factor I (Igf-I) And Risk Of Multiple Myeloma: An Observational And Mendelian Randomisation Study, Yolanda Benavente, Sara Hermosa, Nikos Papadimitriou, Alyssa I. Clay-Gilmour Ph.D., Elizabeth E. Brown, Jonathan N. Hofmann, Nathaniel Rothman, Qin Lan, Sonja I. Berndt, Demetrius Albanes, Mark Purdue, Mitchell J. Machiela, Stephen J. Chanock, Parveen Bhatti, Wendy Cozen, Aaron Norman, Susan L. Slager, James R. Cerhan, Vincent Rajkumar, Et. Al.

Faculty Publications

No abstract provided.

Flexible Modeling Of Non-Gaussian Longitudinal Data: Some Approaches Using Copula, Subhajit Chattopadhyay

Doctoral Theses

Longitudinal data are common in medical and biological sciences, where measurements are gathered from subjects over time to explore relationships with explanatory variables (covariates) and to uncover the underlying mechanisms of dependence among these measurements. The responses observed at each instance can be either discrete or continuous. One of the primary challenges in longitudinal data analysis lies in the non-Gaussian nature of the response variables. As a result, there are relatively few multivariate models in the literature that effectively address the specific characteristics observed in such datasets. In this dissertation, we address four problems concerning longitudinal data analysis by developing …

Power Approximations With Non-Normal Data In Generalized Linear Mixed Models In R Using Steep Priors On Variance Components, Carlie Prinster, John Stevens

Mathematics and Statistics Student Research and Class Projects

ENAR Spring 2026 Conference presentation on Power Approximations with Non-Normal Data in Generalized Linear Mixed Models in R Using Steep Priors on Variance Components

Associational Inference With Many Potential Covariates: Bayesian Information Criterion Elastic Net, Farideh Bagherzadeh Khiabani, I-Chan Huang, Jose Miguel Martinez Martinez, Shizue Izumi, Sedigheh Mirzaei, Tiange Zheng, Irina Dinu, Yutaka Yasui

COBRA Preprint Series

Background: An emerging feature in modern biomedical research is collecting and analyzing numerous variables. In the presence of many potential covariates, inference becomes challenging requiring both distinguishing a set of covariates truly associated with an outcome and estimating their corresponding regression coefficients consistently. Traditional statistical inference typically focuses on estimating coefficients assuming a pre-specified set of covariates. Further, advanced machine/statistical learning methods performing both selection and estimation predominantly focus on outcome prediction rather than association inference.

Methods: Motivated by our epidemiological research on long-term childhood cancer survivors, where we aimed to investigate associations between a large pool of longitudinal symptom …

Database-Driven Revelations In Epilepsy: Patient Reporting Accuracy And The Circadian Timing Of Seizures, Ithay Biton

Theses and Dissertations

For over thirty years, patients have been visiting the Arkansas Epilepsy Program for diagnosis and treatment for seizures and seizure-like episodes. As part of their clinical evaluation, patients often undergo ambulatory EEG (electroencephalogram) monitoring. This routine process produces valuable data for treating the patient. In this study, over 2000 ambulatory EEG reports from 1998 to 2016 were reviewed. A large database of seizures was created from the reports, with information on 407 patients, 1611 EEG-confirmed seizures, and 1726 patient-reported seizures (IRB Protocol #17-093). The database was used to address two important issues in epilepsy. The first topic of the study …

Ulk4 And Cdkn2a Polymorphisms Influence The Risk Of Developing Monoclonal Gammopathy Of Undetermined Significance, José Manuuel Sánchez-Maldonado, Angelica Macauda, Antonio José Cabrera-Serrano, Hauke Thomsen, Murat Güler, Rob Ter Horst, Bethany Van Guelpen, Pavel Vodicka, Stefano Landi, Subhayan Chattopadhyay, Pelin Ünal, Lucía Ruiz-Durán, Delphine Casabonne, Hartmut Goldschmidt, Istemi Serin, María Carretero-Fernández, Elena Cabezudo, Fernando Reyes-Zurita, Alyssa I. Clay-Gilmour, Et. Al.

Faculty Publications

Monoclonal gammopathy of undetermined significance (MGUS) is a necessary precursor condition to multiple myeloma (MM). Given the role of autophagy in modulating MM risk, we investigated whether genetic variation in autophagy-related genes influences susceptibility to MGUS. We analyzed the association of 34,042 common autophagy-related single nucleotide polymorphisms (SNPs) with MGUS across six independent cohorts, five from Europe and one from North America, comprising 2317 MGUS cases and 282,358 controls. We also assessed their impact on immune parameters, including absolute counts of 91 blood-derived immune cell subsets and 103 circulating immunological proteins. Meta-analysis revealed a genome-wide significant association between the ULK4 …

Impact Of Medicaid Enrollment Timing On Tumor Stage At Diagnosis And Survival In Breast, Colorectal, And Lung Cancer, Gabriel A. Benavidez, Stella Coker Watson Self Ph.D., Ms, Anthony Alberg Ph.D., M.P.H., Janice Probst, Jan Marie Eberth

Faculty Publications

Background: Medicaid-insured patients experience higher rates of late-stage cancer diagnosis and worse survival than non-Medicaid patients. The impact of Medicaid enrollment timing on cancer outcomes is less clear. This study examines the association between Medicaid enrollment and timing with tumor stage and cancer-specific survival for breast, colorectal, and lung cancers. Methods: We analyzed SEER-Medicaid linked data for 276,755 breast, 104,784 colorectal, and 101,058 lung cancer patients < 65 years of age. Patients were categorized as non-Medicaid enrollees, pre-diagnosis enrollees (≥12 months before), or post-diagnosis enrollees (≤12 months after). Multivariable logistic regression estimated odds ratios of late-stage diagnosis, and cause-specific Cox proportional hazards models were used to assess cancer-specific survival, adjusting for demographic and socioeconomic factors. Results: Compared to non-Medicaid enrollees, post-diagnosis enrollees had the highest odds of late-stage diagnosis (breast cancer: OR: 3.41; colorectal cancer: OR: 3.78; lung cancer: OR: 1.87). Pre-diagnosis enrollees also had increased odds, but the …

Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh

SMU Data Science Review

Violence and overdose events in Las Vegas occur at rates above the national average, with fewer than half of violent injuries reported to law enforcement [2,7]. The Cardiff Model offers a proven framework for standardized data collection and sharing between hospitals and public safety partners, yet many implementations still rely on manual entry. We propose an ambient triage pipeline integrated with Oracle-Cerner electronic health record systems to listen to nurse–patient dialogue, convert speech to text, extract Cardiff fields, and write standards-based FHIR Bundles for analytics. Using SMART on FHIR standards and Cerner Millennium APIs, the study evaluates whether ambient capture …

Availability Model To Evaluate Ai Data Centers’ Role In Grid Stability, Troy Mcsimov, Trevor S. Kunz, Jeffrey Billo

SMU Data Science Review

The United States has made it clear; it is imperative that the US wins the global AI race. This paper focuses on one of the most challenging puzzle pieces surfaced at the POWER Data Center conference (San Antonio, Sept. 30.); for Electric Reliability Council of Texas (ERCOT) the limiting factor is not generation alone but the need to balance generation and load to preserve grid reliability.

The regulatory landscape fundamentally changed with the passage of Texas Senate Bill 6 in June 2025, which mandates new large loads must "contribute to the recovery of the interconnecting electric utility’s costs" (Texas Legislature, …

Rural–Urban Differences In Cognitive Outcomes Among Older Adults: The Roles Of Falls And Depressive Symptoms, Ayse Malatyali, Tom Cidav, Lisa A.K. Wiese, Jian Zou, Monique J. Brown Ph.D., Mph, Junfeng Ma, Breno S. Diniz, Ladda Thiamwong

Faculty Publications

Background: Older adults with Alzheimer’s Disease and Related Dementias (ADRD) experience a higher risk of falls. However, research lacks evidence on the effect of fall exposure on cognitive impairment and dementia. We investigated the association of falls and depressive symptoms with cognitive impairment and dementia in a nationally representative sample. Methods: We analyzed data from 6221 participants (age ≥ 65) in the Health and Retirement Study (HRS) from the 2018–2020 waves, using Multinomial logistic regression models. Measures included the HRS health status questionnaire, HRS cognition scale, and the Center for Epidemiological Studies Depression scale. Results: Prevalence of fall exposure across …

Rural–Urban Differences In Cognitive Outcomes Among Older Adults: The Roles Of Falls And Depressive Symptoms, Ayse Malatyali, Tom Cidav, Lisa A.K. Wiese, Jian Zou, Monique J. Brown Ph.D., Mph, Junfeng Ma, Breno S. Diniz, Ladda Thiamwong

Faculty Publications

Background: Older adults with Alzheimer’s Disease and Related Dementias (ADRD) experience a higher risk of falls. However, research lacks evidence on the effect of fall exposure on cognitive impairment and dementia. We investigated the association of falls and depressive symptoms with cognitive impairment and dementia in a nationally representative sample. Methods: We analyzed data from 6221 participants (age ≥ 65) in the Health and Retirement Study (HRS) from the 2018–2020 waves, using Multinomial logistic regression models. Measures included the HRS health status questionnaire, HRS cognition scale, and the Center for Epidemiological Studies Depression scale. Results: Prevalence of fall exposure across …

Averaging Principle For A General Class Of Periodic Functions In Discrete Spaces, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

In this work, we develop a periodic averaging principle for arbitrary discrete time domains, leveraging a novel definition of periodicity. This definition does not rely on the classical requirement for the time domain itself to be periodic. We implement this averaging principle across diverse discrete time domains and explore a range of periodic functions within this extended context. The paper contains several examples with numerical simulations, providing visual demonstrations of our results. This highlights the versatility of our averaging principle and its potential to understand dynamics of nonautonomous recurrences with complex temporal patterns.

Controllability Of The Semilinear Benjamin–Bona–Mahony Dynamic Equation On Homogeneous Time Scales, Martin Bohner, Cosme Duque, Hugo Leiva

Mathematics and Statistics Faculty Research & Creative Works

This work investigates the approximate controllability and free-time approximate controllability of a generalized semi linear Benjamin–Bona–Mahony type dynamic equation defined on homogeneous time scales, subject to homogeneous Dirichlet boundary conditions. To accomplish this, the problem is framed within an abstract setting, employing the -semigroup theory on time scales. Moreover, we apply a technique introduced by Bashirov et al. [1, 2], which enables us to avoid relying on fixed point theorems.

An Seir Model On Time Scales With Discrete Applications To Tuberculosis, E. Akın, G. Yeni, D. Konur, S. R. Işık, M. R. Işık

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose a novel dynamical model on time scales consisting of new parameters to investigate the transmission dynamics of tuberculosis (TB), one of the deadliest infectious diseases worldwide, characterized by a long latency stage. The dynamical TB model, governed by the Susceptible–Exposed–Infected–Recovered (SEIR) framework within a unified form, yields a continuous model with a non-saturated incidence rate on the real numbers and discrete models with saturated incidence rates when different time domains are chosen. We analyze the stability of the equilibrium points of both the continuous TB model on the set of real numbers and the discrete …

Using Ensemble Disagreement To Stabilize Conformal Prediction Under Distribution Shift, Patrick D. Murphy

Master's Theses

Semantic segmentation of eelgrass from drone imagery is crucial for coastal habitat monitoring, restoration, and management, as these habitats continue to see rapid changes due to climate change and human influence. However, the reliability of generalizing a deployed classification model relies on both high-accuracy segmentation as well as robust uncertainty quantification that holds up when conditions change over years or locations. Conformal prediction (CP) is a method that converts a classifier's output into prediction sets with a guaranteed average coverage level for in-distribution data. However, the “vanilla” conformal score can often under-cover in hard or out-of-distribution (OOD) regions under drift. …

Molecular Lung Imaging Following Exposure To Radiation Predicts Long-Term Survival In Rats, Anne V. Clough, Kathrina Mpala, Taheri Pardis, Laura Norwood Toro, Andreas M. Beyer, Tracy Gasperetti, Ming Zhao, Sarah Kerns, Heather A. Himburg, Said H. Audi

Mathematical and Statistical Science Faculty Research and Publications

Delayed effects of acute radiation exposure (DEARE), including radiation pneumonitis (lung-DEARE), develop weeks to months after radiation exposure. Pathway-targeted biomarkers that capture early oxidative stress and cell death could improve risk stratification and provide objective measures of mitigator efficacy. The objective was to test whether molecular lung imaging predicts long-term survival and mitigator response after irradiation. Rats received 13.5 Gy leg-out partial-body irradiation with a subset treated with the radiation-injury mitigator lisinopril. Rats underwent lung imaging at weeks 2 and 4 post-irradiation with ^99mTc-duramycin (cell death) and ^99mTc-HMPAO (oxidative stress). Plasma mitochondrial damage-associated molecular patterns (mtDAMPs) were also …

Pointwise Self-Homeomorphic Generalized Inverse Limits, Ali H. Ali, Faruq A. Mena, Robert Paul Roe

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we find uncountable families of generalized inverse sequences on intervals, where the bonding functions consist of a finite number of line segments, such that the inverse limit spaces of these sequences are pointwise self-homeomorphic continua. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite D3 and a dendrite containing Dω. The dendrite D3 was obtained previously, by others, as a generalized inverse limit but the bonding function in that example contained infinitely many line segments. We show that the techniques we use on intervals can be extended to inverse limits where …