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Articles 1 - 30 of 39
Full-Text Articles in Probability
Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan
Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan
Electrical and Computer Engineering ETDs
Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …
(R2095) On Discrete Hypoexponential Distribution And Integer-Valued Autoregressive Process, K. Krishnakumari, Dais George
(R2095) On Discrete Hypoexponential Distribution And Integer-Valued Autoregressive Process, K. Krishnakumari, Dais George
Applications and Applied Mathematics: An International Journal (AAM)
Discrete distributions provide a substantive contribution in modeling real world frame work. Though a lot of discrete distributions are available in literature, they are inappropriate to model many practical situations. The conventional discrete distributions like geometric, Negative Binomial and Poisson have limited applications in modeling count and lifetime data. This paper introduces a new two parameter discrete distribution namely, discrete hypoexponential distribution by discretizing the well known hypoexponential distribution. Various distributional and structural properties of the proposed distribution are studied. We introduce a first order auto regressive process with the newly proposed distribution as marginal and study the properties. Depending …
(R2098) Dynamic Analysis Of Stochastic Leslie-Gower Biological Predator-Prey Model With Prey Cannibalism, Sada Nand Prasad, Itendra Kumar Universiry Of Delhi, India, Pawan Kumar
(R2098) Dynamic Analysis Of Stochastic Leslie-Gower Biological Predator-Prey Model With Prey Cannibalism, Sada Nand Prasad, Itendra Kumar Universiry Of Delhi, India, Pawan Kumar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the dynamical analysis of a stochastic Leslie–Gower biological predator– prey model. Earlier, the Leslie–Gower model was studied in the context of biological systems, including cases involving cannibalism. In our model, we investigate the dynamic properties of a stochastic Leslie–Gower predator–prey ecological system using the stability of invariant measures on invariant sets, where the invariant measures are shown to be ergodic. We also conduct a threshold analysis to study the stochastic persistence and extinction of species. Stochastic bifurcation is also examined. The theoretical results are supported by numerical simulations and examples. Intra-species competition is considered and …
(R2116) The Novel Garima Distribution Properties And Nuclear Data Application, Murat Aygün, Ayşe Metin Karakaş
(R2116) The Novel Garima Distribution Properties And Nuclear Data Application, Murat Aygün, Ayşe Metin Karakaş
Applications and Applied Mathematics: An International Journal (AAM)
This research introduces a new two-parameter Marshall-Olkin Garima distribution model. The novel model has many sub-models that are useful in modeling real-life data, such as the extended Garima distribution, exponentiated Garima distribution, exponential distribution, Lindley distribution, Kumaraswamy Garima distribution, and normal distribution. The proposed model demonstrates a high level of suitability in modeling both reliability and survival data. It is flexible in accommodating various failures. The quantile function, density shapes, hazard rate functions, and order statistics are a few of the statistical features that have been explored. Maximum likelihood estimation methods were employed to estimate the parameters. Using five data …
(R2117) Cost Optimization Of Queueing System With Differentiated Vacations And Reneging Of Customers, Poonam Gupta, Rajni Gupta
(R2117) Cost Optimization Of Queueing System With Differentiated Vacations And Reneging Of Customers, Poonam Gupta, Rajni Gupta
Applications and Applied Mathematics: An International Journal (AAM)
This manuscript deals with an infinite-capacity queueing system under multiple differentiated working vacations and customers’ impatience. The first vacation is assumed to be a working vacation where the server, instead of being idle, serves the customers at a lower rate. In contrast, the second one is considered a non-working vacation of a different duration. The customers may leave the system at any time due to long delays in service during vacations but, via some convincing mechanisms, they are retained in the system. The operating characteristics of the system are obtained in a steady state. The results obtained are illustrated numerically …
Performance Of Acoustic Telemetry And Space Use Of Pallid Sturgeon In The Lower Platte River, Nebraska, Christopher F. Pullano
Performance Of Acoustic Telemetry And Space Use Of Pallid Sturgeon In The Lower Platte River, Nebraska, Christopher F. Pullano
School of Natural Resources: Dissertations, Theses, and Student Research
Pallid Sturgeon (Scaphirhynchus albus) are centenarian, potamodromous, rheophiles that historically occupied the Missouri River and Mississippi River basins. Listed on the U.S. Endangered Species Act in 1990, population declines are attributed to habitat fragmentation and degradation, as well as overharvest, and hybridization. A knowledge gap exists regarding the extent to which tributaries facilitate key life stages for Pallid Sturgeon. This study evaluated the capacity of acoustic telemetry to monitor the movements of Pallid Sturgeon in a shallow, braided tributary to the Missouri River. The specific objectives were to (1) evaluate the environmental variables influencing the performance of acoustic …
Early Ctdna Kinetics As A Dynamic Biomarker Of Cancer Treatment Response, Aaron Li, Emil Lou, Kevin Leder, Jasmine Foo
Early Ctdna Kinetics As A Dynamic Biomarker Of Cancer Treatment Response, Aaron Li, Emil Lou, Kevin Leder, Jasmine Foo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou
Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou
LSU Doctoral Dissertations
Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …
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 …
Exploring Healthcare Chatbot Information Presentation: Applying Hierarchical Bayesian Regression And Inductive Thematic Analysis In A Mixed Methods Study, Samuel Nelson Koscelny
Exploring Healthcare Chatbot Information Presentation: Applying Hierarchical Bayesian Regression And Inductive Thematic Analysis In A Mixed Methods Study, Samuel Nelson Koscelny
All Theses
High blood pressure, also known as hypertension, significantly increases the risk of heart disease and stroke, which are leading causes of death in the United States. While contributing to over 691,000 deaths in 2021 alone in the United States (U.S.), it also imposes immense economic burden on the healthcare system, costing approximately $131 billion annually. One way to address this issue is for increased self-care behaviors and medication adherence, both of which require sufficient health literacy. Despite the importance of health literacy, 90% of U.S. adults struggle with health-related subjects. Overcoming the issues associated with health literacy requires addressing the …
Simulation Study On Confidence Interval Estimation For Standard Deviation With Non-Normal Distributions, Theophilus Oppong Kyeremeh
Simulation Study On Confidence Interval Estimation For Standard Deviation With Non-Normal Distributions, Theophilus Oppong Kyeremeh
Electronic Theses and Dissertations
This study explores innovative approaches to constructing confidence intervals for the population standard deviation, σ, in non-normal data scenarios. While the sample standard deviation, s, is widely used, its reliability is compromised when dealing with skewed or heavy-tailed distributions and exhibits sensitivity to outliers. Our research addresses these limitations by investigating alternative estimation methods that offer greater robustness and accuracy.
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 …
(R2073) Analysis Of Mmap/Ph(1), Ph(2)/1 Preemptive Priority Queueing Model With Single Vacation, Repair And Impatient Customers, S. Meena, G. Ayyappan
(R2073) Analysis Of Mmap/Ph(1), Ph(2)/1 Preemptive Priority Queueing Model With Single Vacation, Repair And Impatient Customers, S. Meena, G. Ayyappan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we analyse a single server preemptive priority queue with phase-type vacation and repair, feedback, working breakdown, close-down and impatient customers. Customers arrive according to the Marked Markovian Arrival Process and their service time according to Phase-type distribution. If the High Priority customers need feedback, they lose their priority and join the Low Priority queue. At any instant, if the server is broken down, the server provide service with slow mode for that current customer and then the server will go into a repair process. When there are no customers present in both the queues, the server close-down …
(R2081) Analysis Of A Flexible Group Service Map/Ph/1 Queueing Model With Soft Failure And Reneging, S. Kalaiarasi, G. Ayyappan
(R2081) Analysis Of A Flexible Group Service Map/Ph/1 Queueing Model With Soft Failure And Reneging, S. Kalaiarasi, G. Ayyappan
Applications and Applied Mathematics: An International Journal (AAM)
Queueing models where services are offered in groups (or blocks or batches) have shown to be very helpful in real-world applications and these queues have been well studied in the literature. In this paper we see one such group service queueing model with soft failure and reneging; here, by soft failure, we mean an emergency arrival. The arrival process is a Markovian arrival, whereas the emergency arrival follows an exponential distribution. Customers are served in groups ranging in size from 1 to a fixed constant, let’s say N. A batch’s service time is determined by the phase-type distribution that corresponds …
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
CBN Journal of Applied Statistics (JAS)
This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …
Qwixx Strategies Using Simulation And Mcmc Methods, Joshua W. Blank
Qwixx Strategies Using Simulation And Mcmc Methods, Joshua W. Blank
Master's Theses
This study explores optimal strategies for maximizing scores and winning in the popular dice game Qwixx, analyzing both single and multiplayer gameplay scenarios. Through extensive simulations, various strategies were tested and compared, including a scorebased approach that uses a formula tuned by MCMC random walks, and race-to-lock approaches which use absorbing Markov chain qualities of individual score sheet rows to find ways to lock rows as quickly as possible. Results indicate that employing a scorebased strategy, considering gap, count, position, skip, and likelihood scores, significantly improves performance in single player games, while move restrictions based on specific dice roll sums …
Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid
Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid
Master's Theses
Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …
Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif
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
Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey
Biology and Medicine Through Mathematics Conference
No abstract provided.
Exchangeability And A Model Of Biological Evolution, Renee Haddad
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.
Capturing Higher-Order Relationships Through Information Decomposition, Aobo Lyu
Capturing Higher-Order Relationships Through Information Decomposition, Aobo Lyu
McKelvey School of Engineering Graduate Student Theses & Dissertations
Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion. Specifically, Shannon's mutual information does not capture fine-grained interactions between those three variables, resulting in limited insights in complex systems. To capture these fine-grained higher-order interactions among variables, Williams and Beer proposed a framework called Partial Information Decomposition (PID) to decompose this mutual information to information atoms, called unique, redundant, and synergistic, and proposed several operational axioms that these atoms must satisfy. This conceptual …
Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg
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 …
Evaluating Novel Approaches For Improving Anadromous Fish Passage In Coastal Rivers, Aaron Bunch
Evaluating Novel Approaches For Improving Anadromous Fish Passage In Coastal Rivers, Aaron Bunch
All Dissertations
Few of the world's rivers remain free-flowing for over 1000 km, significantly impacting anadromous fish populations due to dam-induced habitat fragmentation. Three partial migration barriers (low-head dams) on North Carolina's Cape Fear River (USA)—lock and dam 1 (LD1), lock and dam 2 (LD2), and lock and dam 3 (LD3)—impact American shad Alosa sapidissima, Atlantic sturgeon Acipenser oxyrinchus oxyrinchus, and striped bass Morone saxatilis populations. Mitigation strategies to pass fish upstream have included conservation locking, nature-like fishway construction, and environmental flows (e-flows). This study introduced a novel e-flow (dam submergence flow), tested acoustic double-tagging techniques for tracking American …
Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen
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 …
Uconn Baseball Reliever Lane Optimization Tool, Jason Bartholomew
Uconn Baseball Reliever Lane Optimization Tool, Jason Bartholomew
Honors Scholar Theses
The building of a tool to be utilized by UConn’s Division I baseball team that will generate a game plan for when different relievers should be used against different parts of the opponent’s lineup to achieve the lowest total expected value of runs allowed for the remainder of the game based on game situations and matchup probabilities. The tool will also examine and determine situations that may be vital enough to the outcome of the game to bring in a better reliever normally saved for later in the game.
Latent Classification Of Multi-Model Non-Homogeneous Continuous-Time Markov Chains, Joonha Chang
Latent Classification Of Multi-Model Non-Homogeneous Continuous-Time Markov Chains, Joonha Chang
Dissertations and Theses (Open Access)
The continuous-time Markov chain (CTMC) model and latent clustering models are commonly used to study longitudinal measures of categorical outcomes. Because of its simple but powerful Markovian property, CTMC models have been widely used in medical and public health researches. Due to limitations in the standard CTMC model, there have been some studies on non-homogeneous continuous-time Markov chain (NH-CTMC) that utilized time-dependent rates, but the progresses have been limited. NH-CTMC can be more powerful than CTMC by its default nature of time-dependent rate that can be fitted to a wider range of applications in medical studies. In this study, we …
Stability Of Predator-Prey Model For Worm Attack In Wireless Sensor Networks, Rajeev Kishore, Padam Singh
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
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
Sensitivity Analysis Of Prior Distributions In Regression Model Estimation, Ayoade I Adewole, Oluwatoyin K. Bodunwa
Al-Bahir
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 …
Predicting Superconducting Critical Temperature Using Regression Analysis, Roland Fiagbe
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.