Probability Commons^™

Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen

All Graduate Reports and Creative Projects, Fall 2023 to Present

While often taught in high school and required as part of a college degree, statistics classes are sometimes viewed by students as an obstacle rather than a support for their overall goals. One way to increase student engagement in a statistics course is to use the history of statistics. Within the literature review, the advantages to using the history of statistics are discussed as well as the more extensive research on using the history of mathematics in mathematics courses. Included are instructional strategies for using the context around the development of mathematical ideas in math classrooms which can be extended …

Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg

Industrial Engineering Undergraduate Honors Theses

Each NFL, NBA, and MLB season consists of a regular season, in which teams play a set number of scheduled games and a playoff, in which qualifying teams compete for a championship. At the conclusion of each season, teams are ranked based on their performance throughout the season. This study aims to investigate the ability of each league's season format to accurately rank teams using Monte Carlo simulation. Matches between two teams are simulated by using the team’s assigned strength ranks to calculate a winning probability for each team. The winning probabilities are simulated with different skill values, dictating how …

Stability Of Predator-Prey Model For Worm Attack In Wireless Sensor Networks, Rajeev Kishore, Padam Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose a predator-prey mathematical model for analyzing the dynamical behaviors of the system. This system is an epidemic model, and it is capable of ascertaining the worm's spreading at the initial stage and improving the security of wireless sensor networks. We investigate different fixed points and examine the stability of the projected model.

Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis

Rose-Hulman Undergraduate Mathematics Journal

Dominion is a deck-building card game that simulates competing lords growing their kingdoms. Here we wish to optimize a strategy called Big Money by modeling the game as a Markov chain and utilizing the associated transition matrices to simulate the game. We provide additional analysis of a variation on this strategy known as Big Money Terminal Draw. Our results show that player's should prioritize buying provinces over improving their deck. Furthermore, we derive heuristics to guide a player's decision making for a Big Money Terminal Draw Deck. In particular, we show that buying a second Smithy is always more optimal …

Sensitivity Analysis Of Prior Distributions In Regression Model Estimation, Ayoade I Adewole, Oluwatoyin K. Bodunwa

Al-Bahir Journal for Engineering and Pure Sciences

Bayesian inferences depend solely on specification and accuracy of likelihoods and prior distributions of the observed data. The research delved into Bayesian estimation method of regression models to reduce the impact of some of the problems, posed by convectional method of estimating regression models, such as handling complex models, availability of small sample sizes and inclusion of background information in the estimation procedure. Posterior distributions are based on prior distributions and the data accuracy, which is the fundamental principles of Bayesian statistics to produce accurate final model estimates. Sensitivity analysis is an essential part of mathematical model validation in obtaining …

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

Predicting Superconducting Critical Temperature Using Regression Analysis, Roland Fiagbe

Data Science and Data Mining

This project estimates a regression model to predict the superconducting critical temperature based on variables extracted from the superconductor’s chemical formula. The regression model along with the stepwise variable selection gives a reasonable and good predictive model with a lower prediction error (MSE). Variables extracted based on atomic radius, valence, atomic mass and thermal conductivity appeared to have the most contribution to the predictive model.

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

The Distribution Of The Significance Level, Paul O. Monnu

Electronic Theses and Dissertations

Reporting the p-value is customary when conducting a test of hypothesis or significance. The likelihood of getting a fictitious second sample and presuming the null hypothesis is correct is the p-value. The significance level is a statistic that interests us to investigate. Being a statistic, it has a distribution. For the F-test in a one-way ANOVA and the t-tests for population means, we define the significance level, its observed value, and the observed significance level. It is possible to derive the significance level distribution. The t-test and the F-test are not without controversy. Specifically, we demonstrate that as sample size …

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 …

Ohio Recovery Housing: Resident Risk And Outcomes Assessment, Elyjiah Potter, Bivin Sadler

SMU Data Science Review

Addiction and substance abuse disorder is a significant problem in the United States. Over the past two decades, the United States has faced a boom in substance abuse, which has resulted in an increase in death and disruption of families across the nation. The State of Ohio has been particularly hard hit by the crisis, with overdose rates nearly doubling the national average. Established in the mid 1970’s Sober Living Housing is an alcohol and substance use recovery model emphasizing personal responsibility, sober living, and community support. This model has been adopted by the Ohio Recovery Housing organization, which seeks …

Static And Dynamic State Estimation Applications In Power Systems Protection And Control Engineering, Ibukunoluwa Olayemi Korede

Doctoral Dissertations

The developed methodologies are proposed to serve as support for control centers and fault analysis engineers. These approaches provide a dependable and effective means of pinpointing and resolving faults, which ultimately enhances power grid reliability. The algorithm uses the Least Absolute Value (LAV) method to estimate the augmented states of the PCB, enabling supervisory monitoring of the system. In addition, the application of statistical analysis based on projection statistics of the system Jacobian as a virtual sensor to detect faults on transmission lines. This approach is particularly valuable for detecting anomalies in transmission line data, such as bad data or …

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 …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

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 …

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.