Local Limit Theorems On Finitely Generated Abelian Groups,
2025
Colby College
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 …
Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems,
2024
University of New Mexico
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,
2024
St. Thomas College, Palai
(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,
2024
Universiry of Delhi
(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,
2024
Bitlis Eren University, Turkey
(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,
2024
I.B. (PG) College, India
(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,
2024
University of Nebraska-Lincoln
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,
2024
University of Minnesota - Twin Cities
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,
2024
Louisiana State University and Agricultural and Mechanical College
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,
2024
CUNY Graduate Center
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,
2024
Clemson University
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,
2024
Stephen F. Austin State University
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,
2024
New York University
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,
2024
Puducherry Technological University
(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,
2024
Puducherry Technological University
(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 …
Qwixx Strategies Using Simulation And Mcmc Methods,
2024
California Polytechnic State University, San Luis Obispo
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 …
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery,
2024
Federal Inland Revenue Service, Abuja, FCT
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 …
Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats,
2024
California Polytechnic State University, San Luis Obispo
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,
2024
INRAE, CNRS, Université de Tours, PRC, 37380, Nouzilly, France
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,
2024
Columbia University
Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey
Biology and Medicine Through Mathematics Conference
No abstract provided.
