Digital Commons Network^™

Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa

All Dissertations

Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …

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 …

Spotting K-Tricaps In Spot It!, Jenarah Skyara Lara

Senior Projects Spring 2023

The card game “SPOT IT!” consists of 55 cards, with 8 symbols appearing on each card. Every pair of cards has exactly one symbol in common, and the goal of the game is to be the first person to find this symbol. An alternate way to play the game is to find sets of 3 cards that have the same symbol in common. We will use combinatorics, probability, and finite projective geometry to analyze the structure of the game. The game “SPOT IT!” can be viewed as the projective plane of order 7. However, we can construct a similar game …

A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman

USF Tampa Graduate Theses and Dissertations

The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …

Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal

Doctoral Dissertations

Deep learning (DL) has emerged as the leading paradigm for predictive modeling in a variety of domains, especially those involving large volumes of high-dimensional spatio-temporal data such as images and text. With the rise of big data in scientific and engineering problems, there is now considerable interest in the research and development of DL for scientific applications. The scientific domain, however, poses unique challenges for DL, including special emphasis on interpretability and robustness. In particular, a priority of the Department of Energy (DOE) is the research and development of probabilistic ML methods that are robust to overfitting and offer reliable …

Using Modern Portfolio Theory To Analyze Virgil's Aeneid (Or Any Other Poem), David Patterson

Master's Theses

This paper demonstrates that it is possible to use mathematics to study literature as it has been used to study the social sciences. By focusing on mathematically defining economic and literary terms, it can be shown that the underlying mathematical structure behind key concepts in economics and literature are analogous. This opens the possibility of applying economic models in literature. Specifically, it is demonstrated that the economic mathematical model of modern portfolio theory can answer long standing questions around the Roman epic Aeneid by Virgil. The poet died before completing his poem. The relative completeness of the books of the …

Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond

Graduate College Dissertations and Theses

With the rise of social media, researchers have become increasingly interested in understanding how individuals inform, influence, and interact with others in their social network and how the network mediates the flow of information. Previous research on information flow has primarily used models of contagion to study the adoption of a technology, propagation of purchase recommendations, or virality of online activity. Social (or "complex") contagions spread differently than biological ("simple") contagions. A limitation when researchers validate contagion models is that they neglect much of the massive amounts of data now available through online social networks. Here we model a recently …

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …

Paper Structure Formation Simulation, Tyler R. Seekins

Electronic Theses and Dissertations

On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Quantifying The Effect Of The Shift In Major League Baseball, Christopher John Hawke Jr.

Senior Projects Spring 2017

Baseball is a very strategic and abstract game, but the baseball world is strangely obsessed with statistics. Modern mainstream statisticians often study offensive data, such as batting average or on-base percentage, in order to evaluate player performance. However, this project observes the game from the opposite perspective: the defensive side of the game. In hopes of analyzing the game from a more concrete perspective, countless mathemeticians - most famously, Bill James - have developed numerous statistical models based on real life data of Major League Baseball (MLB) players. Large numbers of metrics go into these models, but what this project …

The Survival Probability Of Beneficial De Novo Mutations In Budding Viruses, With An Emphasis On Influenza A Viral Dynamics, Jennifer Ns Reid

Electronic Thesis and Dissertation Repository

A deterministic model is developed of the within-host dynamics of a budding virus, and coupled with a detailed life-history model using a branching process approach to follow the fate of de novo beneficial mutations affecting five life-history traits: clearance, attachment, eclipse, budding, and cell death. Although the model can be generalized for any given budding virus, our work was done with a major emphasis on the early stages of infection with influenza A virus in human populations. The branching process was then interleaved with a stochastic process describing the disease transmission of this virus. These techniques allowed us to predict …

Thinking Poker Through Game Theory, Damian Palafox

Electronic Theses, Projects, and Dissertations

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be …

A Logistic Regression And Markov Chain Model For The Prediction Of Nation-State Violent Conflicts And Transitions, Nicholas Shallcross

Theses and Dissertations

Using open source data, this research formulates and constructs a suite of statistical models that predict future transitions into and out of violent conflict and forecasts the regional and global incidences of violent conflict over a ten-year time horizon. A total of thirty predictor variables are tested and evaluated for inclusion in twelve conditional logistic regression models, which calculate the probability that a nation will transition from its current conflict state, either In Conflict or Not in Conflict, to a new state in the following year. These probabilities are then used to construct a series of nation-specific Markov chain models …

Random Walks On Random Lattices And Their Applications, Ryan Tyler White

Theses and Dissertations

This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.

Calibrated Probabilistic Quantitative Precipitation Forecasts Based On The Mrf Ensemble, Frederick Anthony Eckel

Theses and Dissertations

Probabilistic quantitative precipitation forecasts (PQPF) based on the medium range forecast (MRF) ensemble are currently in operational use below their full potential quality (i.e., accuracy and reliability). This unfulfilled potential is due to the MRF ensemble being adversely affected by systematic errors which arise from an imperfect model and less than ideal ensemble initial perturbations. This thesis sought to construct a calibration to account for these systematic errors and thus produce higher quality PQPF. Systematic errors were explored with the use of the verification rank histogram, which tracks the performance of the ensemble. The information in these histograms was then …

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.