Probability Commons^™

A Compact Representation Of Oscillatory Limits Via Asymptotic Value Distributions, Ibrahim Arnous, Eric M. Rodarte, Chirag Kumar

Discovery Day - Daytona Beach

Classical limits describe asymptotic behavior through convergence to a single value, but many important oscillatory functions do not converge in this sense. Standard examples such as sin(𝑥) as 𝑥→∞ and sin(1/x) as x→0 instead display stable distributions of values over time. This project examines how such behavior can be described using a measure-theoretic framework, particularly through occupation measures and, in sequence-based settings, Young measures. The objective is to present this perspective in a clear and accessible way while introducing the Ansatz representation, a compact notation for recording the support and density of an asymptotic value distribution when the limiting measure …

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Criticality In A Heterogeneous Neutron Transport Rod Model, Samuel Kaleb Crowford

All Graduate Reports and Creative Projects, Fall 2023 to Present

This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the …

(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, …

(R2072) A Method To Sample From Transition Densities Of Diffusion Processes With Unknown Densities, Yasin Kikabi, Juma Kasozi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and …

(R2133) Analysis Of A Bulk Queue With Balking, Adaptive Overloading Service, Multiple Vacation, Inspection And Rework, S. Karpagam, R. Lokesh

Applications and Applied Mathematics: An International Journal (AAM)

We consider a queueing system that utilizes a single server to manage product flow through bulk and overload service modes, depending on queue length. Balking occurs when the queue length reaches ‘N’. After completion of service, products undergo quality inspection, with defective products sent for rework based on specific probabilities. If the product is non-defective, the server continues processing until the queue length exceeds a certain threshold; beyond this point, the server is either routed back to bulk service or directed to an overload service. Also, the server goes into a vacation mode when the queue size is below a …

Scaling Limits Of Critical Observables Through The High Dimensional Incipient Infinite Cluster, Pranav Chinmay

Dissertations, Theses, and Capstone Projects

We give a general construction of the incipient infinite cluster in high dimensional percolation, and use it as a decoupling tool to rigorize geometric heuristics for analyzing the asymptotics of observables at criticality. Examples include demonstrating the limiting distribution of the chemical distance and full-strength asymptotics for k-point functions, which constitute foundational inputs for scaling limit results associated to critical clusters.

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

A Modified Maximum Likelihood Estimation Algorithm For Modeling Threshold Exceedances With The Generalized Pareto Distribution, Jeffrey Harkness

UNLV Theses, Dissertations, Professional Papers, and Capstones

A modified maximum likelihood estimation (MLE) algorithm is proposed for modeling threshold exceedances with the generalized Pareto distribution (GPD). The algorithm addresses multiple issues with an approach originally published in the Journal Computational Statistics and Data Analysis (Castillo and Serra, 2015). The modified algorithm is intended to be comparatively simple to understand and implement, accurate in the handling of boundary conditions, relatively fast and reliable for most data sets, and relatively easy to transfer between computer languages by leveraging existing optimization routines.

A reproducibility study of work in recent literature published in the journal Extremes (Belzile, et al., 2023) is …

A Statistical Analysis Of Current And Future Hurricane Activity In The North Indian Ocean, Basil Lund

2026 Symposium

A hurricane is defined as a tropical storm with winds sustained at 74 mph or greater. I examined major (category 3 and above) hurricane activity over the North Indian Ocean from the years 1972-2019 as reported by Colorado State University Hurricane Forecast Archive. Using RStudio, I conducted a binomial analysis of the CSU dataset to calculate probabilities of zero to ten years with one or more major North Indian Ocean hurricanes in the next decade. I conducted a geometric analysis to determine probabilities associated with waiting periods for the next year with a major hurricane, as well as a Poisson …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

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 …

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, …

Selecting Without Replacement From A Population Of Bands Of Serially Connected Objects, James E. Marengo, Dominick Banasik, Joseph Voelkel, David L. Farnsworth

Articles

The sampling procedure from a finite population of objects that are serially attached into bands is described and analyzed. One object is randomly selected and removed at a time, which results in that object’s band being broken into two bands or shortened by one object. The main result gives the probability of choosing an object that is part of a band of serially connected objects of any specified size at each stage of the selection process.

Effective Wordle Heuristics, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.

A Mechanistic Model Of The Wash Shuffle And Monte Carlo Exploration Of Its Impact On Card Shuffling In Texas Hold’Em, Michael A. Alexeev, Peter B. Chi

UNLV Gaming Research & Review Journal

In casino games using a standard deck of cards, a wash shuffle is sometimes performed prior to the rest of the card shuffling procedure. Unlike other methods of shuffling, the wash shuffle has not yet been well studied. To this end, we first develop a mechanistic model of the wash shuffle based on our observation of how cards tend to move when a wash shuffle is being performed. Then, we use this model to simulate the card shuffling procedure used in casino poker rooms, and explore the resulting impact on where the cards are dealt in the context of Texas …

Cash Or Crash: Return To Player Percentages And Expected Value Of Crash Games, Robert H. Scott Iii, Mikhail M. Sher, Jonathan Daigle

UNLV Gaming Research & Review Journal

Crash games are a new type of casino game offered on some online gambling sites. The first crash game was created by the online cryptocurrency casino Bustabit. Other cryptocurrency casinos started offering their own versions of crash games. Now mainstream online casinos have developed their own crash games—notably Rocket by DraftKings. Crash games are easy to learn and play. They offer the opportunity to increase your bet by many hundreds of multiples—though, as we show when deriving expected values, these outcomes are rare. In this paper, we study the history of crash games and calculate theoretical values of crash game …

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

Inhomogeneous Branching Random Walks: Incorporating Genealogy And Density Effects, Lauren Ajax, Beatrice Durham, Pratima Hebbar, Cade Johnston, Jiayi Zhang

Spora: A Journal of Biomathematics

We introduce a novel framework using inhomogeneous branching random walks (BRWs) to model biological processes, specifically by introducing genealogy-dependence in branching rates and displacement distributions to model bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such asymptotics are of independent mathematical interest and are crucial in understanding the emergence of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined …

Statistical Quality Control: A Bayesian Framework, Jakia Jaber Tunal

College of Graduate Studies: Theses & Dissertations

In many industries, it is important to assess whether a machine or system is operating within acceptable limits or has gone out of control. This project applies Bayesian statistics to monitor a process over time and detect changes in its behavior. First, initial data are collected to understand the system’s typical performance and to form a starting prior distribution. As new observations arrive over time, the prior is updated through Bayesian inference, combining past information with incoming data. This iterative updating creates a continuous monitoring framework that adapts as more evidence becomes available. When the updated results suggest that the …