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Articles 1 - 30 of 106
Full-Text Articles in Mathematics
Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal
Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal
Doctoral Dissertations and Master's Theses
Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …
On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis
On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis
LSU Doctoral Dissertations
The Boltzmann equation describes the time evolution of the density function in position-velocity space for a classical particle subjected to possible collisions by other particles in a diluted gas that expands in vacuum for a given initial distribution. While many authors have studied the probabilistic interpretation of the spatially homogeneous Boltzmann equation, there is a dearth of articles on the stochastic framework of the full (that is, spatially inhomogeneous) Boltzmann equation. In this thesis, we examine a stochastic process, developed by S. Albevario, B. Ruediger, and P. Sundar, whose law is a weak solution to a mollified Boltzmann equation. This …
Gompertz Distribution On Time Scales, Wasiu Sule
Gompertz Distribution On Time Scales, Wasiu Sule
Theses, Dissertations and Capstones
We shall investigate Gompertz dynamic equations within the context of time scales calculus, by exploring the mathematical foundations and applications of the Gompertz model, which is commonly used to describe growth phenomena in various fields such as biology and economics. This research seeks to analyze the Gompertz cumulative distribution functions (CDF) and probability density functions (PDF) across different time scales, including the real numbers R and integer multiples hN. Probability techniques will be used to derive the CDF and PDF associated with the Gompertz dynamic equations, and we will examine how varying the time scale impacts the characteristics …
Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan
Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan
Honors Theses
In this thesis, we classify the pointwise behavior of finite-range random walks on finitely generated abelian groups in terms of local limit theorems. Random walks are central objects of research in probability theory, and the theory has found applications in statistics, physics, and even card shuffling. One significant topic in this line of study is random walks on finitely generated groups. Starting from the pioneering work of G. Pólya and H. Kesten, random walks on finitely generated groups have been studied extensively. However, many notable results on the subject (local limit theorems, for example) make assumptions about periodicity and irreducibility …
Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts
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 …
Book Review: How To Expect The Unexpected: The Science Of Making Predictions -- And The Art Of Knowing When Not To By Kit Yates, Mark Huber
Journal of Humanistic Mathematics
Humans think about the future all the time. Prediction is a part of how we prepare for the coming of both good and bad events in our lives. Kit Yates' book, How to expect the unexpected, concentrates primarily on the question of why prediction is difficult, and what mental shortcuts people take in prediction that can lead to incorrect results. Unfortunately, a lack of concern for details and several omissions undermine the quality of the book.
Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu
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 …
Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara
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 …
Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost
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 …
Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine
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.
A Mathematical Investigation Of Landauer’S Principle, Paul Bracken
A Mathematical Investigation Of Landauer’S Principle, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
A minimal mathematical approach is used to state Landauer’s principle in a precise, general way. The results are obtained by means of a rigorous development which is based on the use of quantum statistical mechanics. A mathematical form of the principle results as an equality rather than an inequality. The equality version does imply the original statement of the principle as introduced by Landauer.
The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken
The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The role of dissipation with respect to a microscopic superposition of quantum states is investigated by means of master equations. This has implications for the study of the emergence of classicality from the quantum level. In particular, it illustrates why it is difficult to observe a macroscopic quantum state. The role of the environment is assumed by the measuring apparatus. A pure state is reduced to a mixture in the pointer basis of the system by means of the interaction with the apparatus. It is the intention that this type of analysis will have applications to experiments which are designed …
On A Prior Based On The Wasserstein Information Matrix, Wuchen Li, F. J. Rubio
On A Prior Based On The Wasserstein Information Matrix, Wuchen Li, F. J. Rubio
Faculty Publications
We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information geometry. We present sufficient conditions for the propriety of the posterior distribution for general classes of models. We present a simulation study that shows that the induced posteriors have good frequentist properties.
Efficient Handover Mechanisms For Heterogeneous Networks., Shankar Kumar Ghosh Dr.
Efficient Handover Mechanisms For Heterogeneous Networks., Shankar Kumar Ghosh Dr.
Doctoral Theses
In this thesis, some analytical frameworks have been developed to analyze the effect of different system parameters on handover performances in heterogeneous network (HetNet) and based on such frameworks, some efficient handover algorithms have been proposed. The study starts with an analytical framework to investigate the effect of resource allocation mechanisms, upper layer mobility management protocols (MMPs) and handover decision metrics on user perceived throughput. This analysis reveals that among other factors, handover decision metric plays a crucial role in determining user perceived throughput in HetNet. Subsequently, we develop two handover decision metrics for ultra dense networks (UDN) and unlicensed …
A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman
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 …
A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
Doctoral Theses
Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …
Classroom And Computational Investigations Of Camel Up, Thomas J. Clark
Classroom And Computational Investigations Of Camel Up, Thomas J. Clark
Faculty Work Comprehensive List
Camel Up is a popular board game in which players score points by betting on camels which move randomly via a dice mechanic. The game is available both as a board game [1], as well as an IOS App [2]. Because of the random nature of the camels it is generally difficult to play optimally, but one can nevertheless develop various strategies. Probabilistic knowledge proves helpful in assigning relative value to potential game choices. We discuss how this game can be used to motivate and provide context for learning about the concepts of conditional probability and expected value. Also we …
Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.
Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.
Doctoral Theses
This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …
Irreducibility And Galois Groups Of Random Polynomials, Hanson Hao, Eli Navarro, Henri Stern
Irreducibility And Galois Groups Of Random Polynomials, Hanson Hao, Eli Navarro, Henri Stern
Rose-Hulman Undergraduate Mathematics Journal
In 2015, I. Rivin introduced an effective method to bound the number of irreducible integral polynomials with fixed degree d and height at most N. In this paper, we give a brief summary of this result and discuss the precision of Rivin's arguments for special classes of polynomials. We also give elementary proofs of classic results on Galois groups of cubic trinomials.
Essays In Social Choice Theory., Dipjyoti Majumdar Dr.
Essays In Social Choice Theory., Dipjyoti Majumdar Dr.
Doctoral Theses
The purpose of this thesis is to explore some issues in social choice theory and decision theory. Social choice theory provides the theoretical foundations for the field of public choice and welfare economics. It tries to bring together normative aspects like perspective value judgements and positive aspects, like strategic con- siderations. The second feature which is our focus, is closely related to the problem of providing appropriate incentives to agents, an issue of prime importance in eco- nomics.Consider for example, a set of agents who must elect one among a set of can- didates. These candidates may be physical agents …
Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.
Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.
Doctoral Theses
No abstract provided.
Proving Pairwise Intransitivity In Sets Of Dice, Erika Clary
Proving Pairwise Intransitivity In Sets Of Dice, Erika Clary
Honors Projects
Prior research has been conducted regarding the intransitivity of a set of dice when a single die from a set is rolled against another die from that set and when two of the same dice are rolled against a different pair of two of the same dice. This project examines and proves that an intransitive cycle exists in every set of at least five dice when two different dice are rolled against two other different dice.
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
LSU Doctoral Dissertations
Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit …
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
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 …
Blackjack: The Math Behind The Cards, Hanna Blanchard
Blackjack: The Math Behind The Cards, Hanna Blanchard
Mathematics Senior Capstone Papers
In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities …
Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii
Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii
UNLV Gaming Research & Review Journal
This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting …
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Masters Theses & Specialist Projects
The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …
A Mathematical Analysis Of The Game Of Chess, John C. White
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 …
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Ladies' Night, Robert Dawson
Ladies' Night, Robert Dawson
Journal of Humanistic Mathematics
"Lady" Jane is an expert at her racket. The Joint Statistical Meetings are in Vegas, and she reckons it's payday. But she's taking on the professionals.