Statistics and Probability Commons^™

Analyzing Label Structure And Regional Similarity In Watershed Data Via Spectral Clustering, Yifan Luo

25th Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2026)

This project focuses on identifying patterns of seasonal transitions and nutrient salt fluctuations within the watershed environment. To capture the complex relationships between multiple sampling sites and environmental variables, we represent the watershed dataset as a weighted graph, where nodes correspond to water samples and edge weights reflect similarity in environmental conditions or nutrient concentrations. Using the Gaussian kernel function, we encode the connectivity structure of this network and quantify how similar different nodes are. We then perform spectral embedding by projecting the high-dimensional graph into a lower-dimensional space using the eigenvectors of the Laplacian matrix. This approach preserves the …

The “How Many” Routine As A Catalyst For Computational Fluency And Student Participation, Lillian Iden, Ella Williams, Jen Munson, Sarah Larison, Leslie Yuqui

25th Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2026)

It is not uncommon to hear adults claim they are bad at math or always disliked the subject. This negativity often stems from early mathematical experiences which ranged from boring to highly discouraging and embarrassing. Thus a new emphasis in mathematics education recommendations is to change the narrative and help students develop joy, wonder, and curiosity about mathematics (MAISA & GELN, 2023). This is reflected in defining computational fluency (skill in carrying out arithmetic procedures like addition or multiplication) as comprised of flexibility, accuracy, efficiency, and appropriate strategy use (NRC, 2001). The “How Many” Routine, in which a carefully-designed image …

Investigations In Bertrand’S Paradox, Mary Moore, Hope Weeda, Annika Cunill Krones

25th Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2026)

Bertrand’s paradox is a classic problem that highlights how different notions of randomness can lead to different outcomes, even in a simple geometric setting. It concerns the lengths of chords chosen “at random” in a circle. In this talk, we begin by reviewing the three original methods Bertrand proposed for generating random chords, along with several related distributions that have been studied since. We then turn to a geometric application, examining triangles formed by two random chords that share a common endpoint. By joining the remaining endpoints, we obtain a random triangle and compute the probability that it is acute. …

A Computer Vision Approach To Analyzing Taxane Effects On Prostate Cancer Cells, Diana Elizabeth Dancea

Electronic Theses and Dissertations 2020 - Present

Actin is a family of proteins that help create the structure of the cytoskeleton, which gives shape to the cell. In many chemotherapy treatments, researchers target actin because it controls the cell division process. Therefore, if they are able to understand the actin fibers, that may help in formulating methods to stop or slow down cancer cells from reproducing. Another important protein is PAK6, which regulates actin. In our research, a collaborative effort with Prof. Michael Lu’s lab at Florida Atlantic University, we use machine learning techniques to analyze cells which had their PAK6 protein knocked out, and compare them …

Ownership Duration In The U.S. Business Jet Market, Yuchen Hu

SACAD: Scholarly Activities

This study analyzes ownership duration in the U.S. business jet market using FAA registry data as of February 16, 2026 (N=12,359). The analysis reveals a structured distribution with a mean of 5.86 years and a median of 5.00 years. Crucially, retention varies by acquisition status: new aircraft owners exhibit an average hold of 7.36 years, whereas pre-owned aircraft holders show a significantly higher turnover of 5.11 years, with most resales occurring within a 3–7-year window. These findings suggest that ownership behavior is driven by structured asset management and lifecycle planning, providing a predictive framework for identifying aircraft replacement and trade-in …

Drainage Proximity And Sinkhole Occurrence In Sivrihisar (Central Turkey): A Comparative Analysis Of Linear, Poisson, And Negative Binomial Regression Models, Bilge Bingül, Emrah Pekkan, Resul Çömert

International Journal of Speleology

This study investigates the relationship between sinkhole occurrence and distance to drainage in the Sivrihisar region (Central Turkey) and evaluates the suitability of different regression approaches for modeling clustered count data in karst terrains. A comprehensive inventory of 104 sinkholes developed within the Neogene lacustrine limestones of the Akpınar Formation was compiled using official records, remote sensing analyses, and detailed field surveys. Sinkhole occurrences were analyzed relative to a drainage network derived from a high-resolution Digital Surface Model and grouped by proximity to drainage lines. Linear Regression (LM), Poisson Regression (PR), and Negative Binomial Regression (NBR) models were comparatively applied …

Irreversible K-Threshold Dynamics On Corona And Base-B Corona Product Graphs, Eric J. Moon, Soumya Bhoumik, Paul Flesher

SACAD: Scholarly Activities

This poster studies the irreversible k-threshold process on corona-type graph products, where a vertex becomes colored once at least k of its neighbors are colored and then remains colored permanently. We focus on corona, double corona, and base-b corona product graphs built from cycles and complete graphs, with particular attention to how graph structure affects complete activation from a minimum seed set.

A generalized reduction lemma is used to relate threshold dynamics on layered corona graphs to smaller residual graphs, yielding explicit formulas for the irreversible k-threshold conversion number on both corona and double corona families. The …

Complex Systems Mapping Of Fiscal Growth Dynamics At Strategic Maritime Chokepoints Using Time-Series Slopes, Rahul Balamurugan, Preethi Nanjundan, Avichal Sharma

Northeast Journal of Complex Systems (NEJCS)

This study examines how maritime and trading states allocate public resources between defence, health, and economic growth around three strategic chokepoints the Strait of Malacca, the Strait of Hormuz, and the Suez Canal. The analysis extends the classic “guns versus butter” framing by treating defence and health spending as co-evolving components of an interconnected fiscal-growth system. Using World Development Indicators data (1999-2024), trend slopes are estimated for military spending (% of GDP), healthcare spending (% of GDP), and GDP growth (annual %). Two derived indicators are computed, a defence-to-health slope ratio (military slope/health slope) and a fiscal-balance proxy (health slope …

Psychosocial Mediators Of A Physical Activity And Dietary Intervention In Pregnant Women With Overweight Or Obesity, Meghan Baruth, Sarah Wilcox, Jihong Liu, Rebecca Schlaff

Faculty Publications

Background

Mediation analyses provide insight into both ‘pieces’ of the mediation chain; they allow us to look into the ‘black box’ that is behavior change. They allow researchers to better understand the ‘how’ of an intervention’s effects and/or the ‘why’ behind why an intervention worked or did not work. The lack of publications in pregnant populations highlights the need for additional studies to be conducted and published. The purpose of this study is to examine the psychosocial mediators of physical activity and dietary outcomes in a sample of pregnant women with overweight or obesity participating in the Health in Pregnancy …

Preliminary Sonification Of Enso Using Traditional Javanese Gamelan Scales, Sandy Hs Herho, Rusmawan Suwarman, Nurjanna J. Trilaksono, Iwan P. Anwar, Faiz R. Fajary

Northeast Journal of Complex Systems (NEJCS)

Sonification—the mapping of data to non-speech audio—offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870–2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two- dimensional acoustic phase space. Recurrence-based diagnostics, convex hull ge- ometry, and coupling analysis reveal that the sonification …

Sex-Specific Differences In Lung Mitochondrial Function And Injury In Rats Exposed To Hyperoxia, Taheri Pardis, Abraham G. Taye, Devanshi D. Dave, Elizabeth R. Jacobs, Guru Prasad Sharma, Anne V. Clough, Ranjan K. Dash, Said H. Audi

Mathematical and Statistical Science Faculty Research and Publications

Hyperoxia is both an essential therapy and a contributor to lung injury in acute respiratory distress syndrome. We hypothesized that adult female rats are relatively protected from hyperoxia-induced acute lung injury (HALI) compared with males and that this protection is associated with sex-dependent differences in lung mitochondrial bioenergetics and H₂O₂ production. Adult rats were exposed to room air (normoxia) or hyperoxia (>95% O₂) for up to 60 h. Lung injury was assessed by pleural effusion, lung wet weight, pulmonary vascular filtration coefficient (K_f), histologic injury scores, and cleaved caspase-3 (CC3) staining. …

Empirical Benchmarks For Interpreting Effect Sizes In Violent Crime Interventions, Kohta James Matsukawa Hansen

Theses and Dissertations

Criminal justice researchers apply Cohen’s (1988) benchmarks to classify effect sizes as small, medium, or large, despite these standards never being meant for broad, decontextualized use (Cohen, 1988; Gies et al., 2024; Goulet-Pelletier & Cousineau, 2018; Lakens, 2013; Milner et al., 2023). Repeatedly doing so may weaken statistical validity, distort findings, and impede effective policymaking. This study introduces the first effect size benchmarks specifically designed for violent crime interventions.

Using a quasi-meta-analysis framework, 1,605 effect sizes from 104 violent crime intervention studies from the CrimeSolutions clearinghouse were converted to Cohen’s d. Three new discrete benchmarking methods were created using a …

The Kaczmarz Algorithm In Hilbert C∗-Modules, Daniel Alpay, Chad Berner, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert C^∗-modules and establish analogues of its effectiveness in both finite-dimensional and stationary cases. Consequently, we demonstrate that continuous families of elements in a Hilbert space can be uniformly recovered using the Kaczmarz algorithm. Additionally, we develop a normalized Cauchy transform for continuous families of measures and use it to provide sufficient conditions under which standard frames in Hilbert C(X)-modules can be generated by the Kaczmarz algorithm and …

Sequences That Do Frame Reconstruction, Chad Berner

Mathematics and Statistics Faculty Research & Creative Works

Frames allow all elements of a Hilbert space to be reconstructed by inner product data in a stable manner. Recently, there is interest in relaxing the definition of frames to understand the implications for stable signal recovery. In this paper, we relax the definition of a frame by allowing the operator in the frame decomposition formula to not be invertible. We provide a complete classification of sequences that allow this decomposition via a type of frame operator. In addition, we provide several examples of sequences that allow this reconstruction property that are not frames and illustrate in which ways they …

Maddenlite, Sergio Pena

Presentations - 2026

Problem •“What If” scenarios impossible to test accurately •Commercial games rely on arcade physics •Spreadsheets lack visual engagement

Motivation •Passion for football analytics •Desire to simulate cross-era matchups •Apply math models to real-world sports data

Solution •Python based simulation engine using historical play-by-play data •Simulates outcomes based on probability

Deep Learning Frameworks For Biological Data Integration And Generation, Alexa Beachum

Statistical Science Theses and Dissertations

Data integration represents a key area of research for analyzing the rapidly growing volume of high-dimensional biological data across sources, stages, and modalities. To model and understand these complex, often non-linear relationships, deep learning has become an increasingly powerful tool. Here, we present two novel deep learning frameworks that address distinct but complementary integration challenges. The first framework aligns single-cell omics data across temporal stages, and the second bridges imaging and omics modalities to generate patient-level molecular profiles.

In Chapter 1, we briefly summarize existing approaches---both statistical and deep learning-based---for single-cell omics data integration and discuss their limitations for handling …

Next-Generation Democratic Cyber Statecraft - Balancing The Signal: Shutdown Shocks And Democratic Digital Governance, Scott M. Di Panni

School of Public Policy Capstones

This paper develops Next-Generation Democratic Cyber Statecraft (NG-DCS), a unified strategic doctrine for democratic governments to contest the cognitive domain against authoritarian adversaries. Drawing on twenty-six years of cross-national panel data (1999–2024) spanning 213 countries, game-theoretic modeling, and qualitative case analysis, the paper establishes three interconnected empirical and theoretical foundations. First, cross-national OLS regression across 160+ countries demonstrates that regime type is the dominant structural determinant of internet freedom (R²=0.615, β=2.513, p< 0.001), explaining more than twice the variance attributable to per-capita wealth (R²=0.268). Democratic governance, not economic development, produces open digital environments. Second, a two-way fixed effects (TWFE) difference-in-differences study exploiting government-ordered internet shutdowns as discrete policy interventions finds that digital restrictions causally degrade V-Dem governance quality by 0.21–0.38 standard deviations (p< 0.001 across all specifications). Treatment effects are immediate (β=−0.302 at k=0) and persist through five post-treatment years (β=−0.246 at k=+5), indicating structural rather than transitory governance damage. Parallel trends validation (p=0.352) and Callaway–Sant’Anna heterogeneity-robust estimation (ATT=−0.230, SE=0.077) support causal identification. Instrumental variable triangulation (2SLS β=−0.949, p=0.005) confirms that simultaneity was attenuating, not inflating, the primary estimates. Third, formal game-theoretic analysis reveals that the current U.S.–adversary equilibrium is (Restrain, Escalate)—the risk-dominant but Pareto-inferior outcome of a Stag Hunt structure. China, Russia, North Korea, and Venezuela each occupy structurally distinct positions (Stackelberg commitment, asymmetric two-level, autarky, and reactive trigger, respectively), requiring differentiated doctrinal responses rather than a uniform strategic playbook. Generative AI and algorithmic governance are shown to accelerate cognitive vulnerability by collapsing influence operation costs and exploiting engagement-optimized platform architectures that systematically degrade deliberative capacity in democratic populations.

Efficacy Analysis In Clinical Trials: A Comprehensive Review Of Statistical And Machine Learning Approaches, Dhrubajyoti Ghosh, Samhita Pal

Faculty Articles

Efficacy testing is a cornerstone of clinical trials, ensuring that medical interventions achieve their intended therapeutic effects. Over the decades, a wide range of statistical methodologies have been developed to address the complexities of clinical trial data, including parametric, nonparametric, Bayesian, and machine learning approaches. Parametric methods, such as t-tests, ANOVA, and LMMs, have traditionally been the foundation of efficacy testing due to their efficiency under well-defined assumptions. Nonparametric techniques, including the Friedman test, Brunner-Munzel test, and modern extensions like nparLD, have emerged as robust alternatives, particularly for skewed, ordinal, or non-normal data. Bayesian methodologies have enabled the incorporation of …

Bayesball : A Comprehensive Framework For Predicting Ucl Injury, Brady M. Pinter, Will Best Ph.D.

SPARK Symposium Presentations

Ulnar Collateral Ligament (UCL) reconstruction, commonly referred to as Tommy John Surgery, has seen a significant rise among Major League Baseball (MLB) pitchers, prompting growing interest in identifying the mechanical and performance-based factors that contribute to injury risk. While previous studies have examined these relationships using traditional frequentist approaches separately, this study combines multiple different model techniques to present a broad framework for finding significant predictors of UCL Surgery. These models include Lasso and Ridge Regression,  Principal Component Regression (PCR) , Partial Least Squares Regression (PLS) , Random Forest, Multiple Linear Regression, and a Bayesian Statistical Model. Using these models, …

Implementing A Clustering Framework On Distributional Bee Data, Roheel Nawaz

Research and Creativity Symposium

Understanding spatial patterns in biodiversity is important for identifying how ecological communities are structured across landscapes. Clustering methods provide a useful way to detect non-random species distributions and reveal potential environmental or geographic influences. In this study, we applied a clustering framework to a large long-term bee abundance dataset from the Mid-Atlantic United States to evaluate community structure across regions of Maryland, Delaware, and Washington, D.C.

The dataset included over 1,100 sites and more than 3,000 transects. Because sampling methods were not fully standardized, abundance data were converted to presence/absence and analyzed using the Jaccard index to measure site similarity. …