Statistics and Probability Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Integrating Machine Learning Methods For Medical Diagnosis, Jazmin Quezada

Open Access Theses & Dissertations

Abstract:The rapid advancement of machine learning techniques has revolutionized the field of medical diagnosis by offering powerful tools to analyze complex data sets and make accurate predictions. In this proposed method, we present a novel approach that integrates machine learning and optimization models to enhance the accuracy of medical diagnoses. Our method focuses on fine-tuning and optimizing the parameters of machine learning algorithms commonly used in medical diagnosis, such as logistic regression, support vector machines, and neural networks. By employing optimization techniques, we systematically explore the parameter space of these algorithms to discover the most optimal configurations. Moreover, by representing …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

University of New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

Langevin Dynamic Models For Smfret Dynamic Shift, David Frost, Keisha Cook Dr, Hugo Sanabria Dr

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine

Rose-Hulman Undergraduate Mathematics Journal

We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson

Journal of Humanistic Mathematics

In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.

Math And Democracy, Kimberly A. Roth, Erika L. Ward

Journal of Humanistic Mathematics

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …

Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan

Mathematics & Statistics ETDs

In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. …

An Interval-Valued Random Forests, Paul Gaona Partida

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.

For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial …

Stressor: An R Package For Benchmarking Machine Learning Models, Samuel A. Haycock

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many discipline specific researchers need a way to quickly compare the accuracy of their predictive models to other alternatives. However, many of these researchers are not experienced with multiple programming languages. Python has recently been the leader in machine learning functionality, which includes the PyCaret library that allows users to develop high-performing machine learning models with only a few lines of code. The goal of the stressor package is to help users of the R programming language access the advantages of PyCaret without having to learn Python. This allows the user to leverage R’s powerful data analysis workflows, while simultaneously …

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions, David Lund, Xiaoming He, Daoru Frank Han

Mathematics and Statistics Faculty Research & Creative Works

This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. …

Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov

Mathematics & Statistics ETDs

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.

As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …

On Maximum Likelihood Estimators For A Jump-Type Affine Diffusion Two-Factor Model, Jiaming Yin Mr.

Major Papers

We consider a jump-type two-factor affine diffusion model driven by a subordinator in the context of continuous time observations. We study the asymptotic properties of the maximum likelihood estimator (MLE) for the drift parameters. In particular, we prove the strong consistency and the asymptotic normality of MLE in the subcritical case. We also present some numerical illustrations to confirm the theoretical results. The main difficulty of this major paper consists in proving the ergodicity of the model in the subcritical case and deriving the limiting behavior of the process.

Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya

Mathematics and Statistics Faculty Research & Creative Works

In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.

Vallée-Poussin Theorem For Equations With Caputo Fractional Derivative, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the functional differential equation (^CD_a^α+x)(t) + ^mΣ_i=0 (T_ix(ⁱ))(t) = f(t); t 2 [a; b]; with Caputo fractional derivative ^CD_a^α+ is studied. The operators Ti act from the space of continuous to the space of essentially bounded functions. They can be operators with deviations (delayed and advanced), integral operators and their various linear combinations and superpositions. Such equations could appear in various applications and in the study of systems of, for example, two fractional differential equations, when one of the components can be …

(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …

Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata

Mathematics and Statistics Faculty Research & Creative Works

We Consider the One-Dimensional Nonlinear Schrödinger Equation with an Attractive Delta Potential and Mass-Supercritical Nonlinearity. This Equation Admits a One-Parameter Family of Solitary Wave Solutions in Both the Focusing and Defocusing Cases. We Establish Asymptotic Stability for All Solitary Waves Satisfying a Suitable Spectral Condition, Namely, that the Linearized Operator Around the Solitary Wave Has a Two-Dimensional Generalized Kernel and No Other Eigenvalues or Resonances. in Particular, We Extend Our Previous Result [35] Beyond the Regime of Small Solitary Waves and Extend the Results of [19, 29] from Orbital to Asymptotic Stability for a Suitable Family of Solitary Waves.

Modeling And A Domain Decomposition Method With Finite Element Discretization For Coupled Dual-Porosity Flow And Navier–Stokes Flow, Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We First Propose and Analyze a Steady State Dual-Porosity-Navier–Stokes Model, Which Describes Both Dual-Porosity Flow and Free Flow (Governed by Navier–Stokes Equation) Coupled through Four Interface Conditions, Including the Beavers–Joseph Interface Condition. Then We Propose a Domain Decomposition Method for Efficiently Solving Such a Large Complex System. Robin Boundary Conditions Are Used to Decouple the Dual-Porosity Equations from the Navier–Stokes Equations in the Coupled System. based on the Two Decoupled Sub-Problems, a Parallel Robin-Robin Domain Decomposition Method is Constructed and Then Discretized by Finite Elements. We Analyze the Convergence of the Domain Decomposition Method with the Finite …

On Colorings And Orientations Of Signed Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.

A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign

Faculty Publications

This research paper focuses on quaternion neural networks (QNNs) - a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. Previous studies have shown that QNNs outperform real-valued neural networks in basic tasks and have potential in high-dimensional problem spaces. However, research on QNNs has been fragmented, with contributions from different mathematical and engineering domains leading to unintentional overlap in QNN literature. This work aims to unify existing research by evaluating four distinct QNN backpropagation algorithms, including the novel GHR-calculus backpropagation algorithm, and providing concise, scalable implementations of each algorithm using a …

A Survey On Online Matching And Ad Allocation, Ryan Lee

Theses

One of the classical problems in graph theory is matching. Given an undirected graph, find a matching which is a set of edges without common vertices. In 1990s, Richard Karp, Umesh Vazirani, and Vijay Vazirani would be the first computer scientists to use matchings for online algorithms [8]. In our domain, an online algorithm operates in the online setting where a bipartite graph is given. On one side of the graph there is a set of advertisers and on the other side we have a set of impressions. During the online phase, multiple impressions will arrive and the objective of …

An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors

Honors Theses

We investigate the use of Google’s PageRank algorithm to rank sports teams. The PageRank algorithm is used in web searches to return a list of the websites that are of most interest to the user. The structure of the NCAA FBS football schedule is used to construct a network with a similar structure to the world wide web. Parallels are drawn between pages that are linked in the world wide web with the results of a contest between two sports teams. The teams under consideration here are the members of the 2021 Football Bowl Subdivision. We achieve a total ordering …

Movie Recommender System Using Matrix Factorization, Roland Fiagbe

Data Science and Data Mining

Recommendation systems are a popular and beneficial field that can help people make informed decisions automatically. This technique assists users in selecting relevant information from an overwhelming amount of available data. When it comes to movie recommendations, two common methods are collaborative filtering, which compares similarities between users, and content-based filtering, which takes a user’s specific preferences into account. However, our study focuses on the collaborative filtering approach, specifically matrix factorization. Various similarity metrics are used to identify user similarities for recommendation purposes. Our project aims to predict movie ratings for unwatched movies using the MovieLens rating dataset. We developed …

Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez

Student Scholar Symposium Abstracts and Posters

The reason why I am interested in Formula One is that my friend showed me what Formula One was all about. It became interesting to see the action of the sport, including the battles the drivers have during the race and how fast they go through a corner. Also, when qualifying comes around, they push their car to the absolute limit to gain a few seconds off their opponents. The drivers only in the top 10 receive points from the winner getting 25 points, the last driver in the top 10 getting 1 point, and those below the top ten …