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Full-Text Articles in Probability

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts Sep 2024

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …


Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu Jun 2024

Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of n≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight …


Exchangeability And A Model Of Biological Evolution, Renee Haddad May 2024

Exchangeability And A Model Of Biological Evolution, Renee Haddad

Honors Scholar Theses

A sequence of random variables (RVs) is exchangeable if its distribution is invariant under permutations. For example, every sequence of independent and identically distributed (IID) RVs is exchangeable. The main result on exchangeable sequences of random variables is de Finetti's theorem, which identifies exchangeable sequences as conditionally IID. In this thesis, we explore exchangeability, provide an elementary proof of de Finetti's theorem, and present two applications: the classical Polya's urn model and a toy model for biological evolution.


Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis Feb 2024

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 …


Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara Jan 2024

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 …


Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe Jan 2024

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 …


Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen Jan 2024

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 …