Physical Sciences and Mathematics Commons^™

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

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.

Envariance As A Symmetry In Quantum Mechanics And Applications To Statistical Mechanics, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal in number to that of the possible outcomes of the experiment. Correlations between the apparatus and environment give rise to a type of selection rule which prohibits the apparatus from appearing in a superposition corresponding to different eigenvalues of the pointer basis of the apparatus. The eigenspaces of this observable form a natural basis for the apparatus …

The Vanishing Discount Method For Stochastic Control: A Linear Programming Approach, Brian Hospital

Theses and Dissertations

Under consideration are convergence results between optimality criteria for two infinite-horizon stochastic control problems: the long-term average problem and the $\alpha$-discounted problem, where $\alpha \in (0,1]$ is a given discount rate. The objects under control are those stochastic processes that arise as (relaxed) solutions to a controlled martingale problem; and such controlled processes, subject to a given budget constraint, comprise the feasible sets for the two stochastic control problems.

In this dissertation, we define and characterize the expected occupation measures associated with each of these stochastic control problems, and then reformulate each problem as an equivalent linear program over a …

Tardys Quantifiers: Extracting Temporal And Reversible Dynamical Symmetries, Nhat Vu Minh Nguyen, Arjendu K. Pattanayak, Andres Aragoneses

2023 Symposium

One of the great challenges in complex and chaotic dynamics is to reveal the details of its underlying determinism. This can be manifest in the form of temporal correlations or structured patterns in the dynamics of a measurable variable. These temporal dynamical structures are sometimes a consequence of hidden global symmetries. Here we identify the temporal (approximate) symmetries of a semiconductor laser with external optical feedback, based on which we define the Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers to evaluate the relevance of specific temporal correlations in a time series. We show that these symmetries are also present in …

A Mathematical Investigation Of Landauer’S Principle, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 Use Of Probability In Quantum Mechanics To Calculate Measurement Outcomes, Hannah E. Collins

CAFE Symposium 2023

The concept of probability can help measure some of the possible outcomes of different experiments in the field of quantum mechanics. Those experiments include Thomas Young's double slit experiment, the Schrödinger equation, the wave function, and the Born Rule, which all make use of probability to predict the placement of certain subatomic particles including photons of light, in the experiments. In this project, the manner in which probability does this is explored in depth.

The Probability Of Miracles, Lewis A. Pummell

CAFE Symposium 2023

An insight into the probability that we will experience a miracle within our lives. This project considers different ways of defining a miracle, and how this impacts how we consider them in our lives. They are paradoxical, and completely subjective - although there are key concepts of probability which will guide opinion.

Looking For Life, Conor C. Grubb

CAFE Symposium 2023

The topic of aliens is not just about conspiracy theories and tinfoil hats, through the years numerous respected scientists have weighed in and put thought into the topic. The Search for Extraterrestrial Intelligence (SETI) is closely tied to the Fermi Paradox and the Drake Equation. The Fermi Paradox considers why humans haven't already interacted with aliens if they exist, and the Drake Equation outlines potential variables that would influence the chances of humanity receiving radio contact from an alien civilization.

The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

Models For Decision-Making - Second Edition, Steven Cosares, Fred Rispoli

Open Educational Resources

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.

We provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use …

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 …

(R1971) Analysis Of Feedback Queueing Model With Differentiated Vacations Under Classical Retrial Policy, Poonam Gupta, Naveen Kumar, Rajni Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical …

Learnfca: A Fuzzy Fca And Probability Based Approach For Learning And Classification, Suraj Ketan Samal

Department of Computer Science and Engineering: Dissertations, Theses, and Student Research

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering.

This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide …

Optimizing Cybersecurity Budgets With Attacksimulation, Alexander Master, George Hamilton, J. Eric Dietz

Faculty Publications

Modern organizations need effective ways to assess cybersecurity risk. Successful cyber attacks can result in data breaches, which may inflict significant loss of money, time, and public trust. Small businesses and non-profit organizations have limited resources to invest in cybersecurity controls and often do not have the in-house expertise to assess their risk. Cyber threat actors also vary in sophistication, motivation, and effectiveness. This paper builds on the previous work of Lerums et al., who presented an AnyLogic model for simulating aspects of a cyber attack and the efficacy of controls in a generic enterprise network. This paper argues that …

Application Of Probabilistic Ranking Systems On Women’S Junior Division Beach Volleyball, Cameron Stewart, Michael Mazel, Bivin Sadler

SMU Data Science Review

Women’s beach volleyball is one of the fastest growing collegiate sports today. The increase in popularity has come with an increase in valuable scholarship opportunities across the country. With thousands of athletes to sort through, college scouts depend on websites that aggregate tournament results and rank players nationally. This project partnered with the company Volleyball Life, who is the current market leader in the ranking space of junior beach volleyball players. Utilizing the tournament information provided by Volleyball Life, this study explored replacements to the current ranking systems, which are designed to aggregate player points from recent tournament placements. Three …

The Role Of Surprise In Guessing Games, Justin Carpender

Honors Program Theses and Projects

In this thesis we will study the connection between game structure, surprise, and guessing strategies for these first two versions of a word guessing game. Our analysis will have three levels: one, a basic understanding of language and letter probabilities and the creation of programs that seek to use the structure of a game to efficiently guess words; two, an introduction of mathematical background and Information Theory; three, an analysis of the games and their corresponding guesses via a creative use of the key ideas of Information Theory, particularly, the concepts of surprise and entropy.

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

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 Probabilistic Perspective Of Human-Machine Interaction, Mustafa Canan, Mustafa Demir, Samuel Kovacic

Engineering Management & Systems Engineering Faculty Publications

Human-machine interaction (HMI) has become an essential part of the daily routine in organizations. Although the machines are designed with state-of-the-art Artificial Intelligence applications, they are limited in their ability to mimic human behavior. The human-human interaction occurs between two or more humans; when a machine replaces a human, the interaction dynamics are not the same. The results indicate that a machine that interacts with a human can increase the mental uncertainty that a human experiences. Developments in decision sciences indicate that using quantum probability theory (QPT) improves the understanding of human decision-making than merely using classical probability theory (CPT). …

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. …

A Computational Study Of Genotype-Phenotype Mutation Patterns, Kamaludin Dingle, Omar Tawfik, Ahmed Aldabagh

Undergraduate Research Symposium

Understanding properties of genotype-phenotype maps is important for understanding biology and evolution. In this project we make a computational study of the statistical effects of genetic mutations, in particular computing the probabilities of each phenotype transitioning to any other phenotype. We also investigate the importance of the local phenotypic environment of a single genotype, and its role in determining mutation transition probabilities. We use HP protein folding, RNA structure, and a simplified GRN matrix model to study these questions.

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 …

The Foundations Of Inference And Its Application To Fundamental Physics, Nicholas Matthew Carrara

Legacy Theses & Dissertations (2009 - 2024)

This thesis concerns the foundations of inference – probability theory,entropic inference, information geometry, etc. – and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM) [21, 22, 41, 53, 56–61, 150–153, 165, 195, 196, 268]. The first half of this thesis, chapters 2-6, concern the development of the inference framework. We begin in chapter 2 by discussing de- ductive inference, which involves formal logic and it’s role in access- ing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can’t address situations in which we have incomplete information. This necessitates a …

Optimizing Percentile Matching, Joshua Megchelsen

Pence-Boyce STEM Student Scholarship

Point estimation is a technique used in statistics to estimate unknown parameters in populations of data by using samples of data from that population. Percentile matching is a method of point estimation that selects one piece of data from a sample and assumes that the percentile that piece of data represents in the sample is equal to that same percentile’s theoretical value in the population. That assumption is then used to project what the unknown parameter is. The fundamental question our research sought to answer was which percentile should be matched from the sample to the population to produce the …

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

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.

Monty Hall Meets Game Theory, Jamie Lynn Dobson

Honors Projects

I explored the Monty Hall game scenario and how to calculate the chances of winning by staying or switching doors using a probability and game theory approach. I also calculated how these chances change when there are 4, 5,..., n doors.

Markov Model Composition Of Balinese Reyong Norot Improvisations, Taylor Flanagan, Robert Rovetti

Honors Thesis

Markov models are mathematical structures that model the transition between possible states based on the probability of moving from one state to any other. Thus, given a distribution of starting points, the model produces a chain of states that are visited in sequence. Such models have been used extensively to generate music based on probabilities, as sequences of states can represent sequences of notes and rhythms. While music generation is a common application of Markov models, most existing work attempts to reconstruct the musical style of classical Western composers. In this thesis, we produce a series of Markov chains that …

Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.

Doctoral Theses

No abstract provided.