Probability Commons^™

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, …

(R2133) Analysis Of A Bulk Queue With Balking, Adaptive Overloading Service, Multiple Vacation, Inspection And Rework, S. Karpagam, R. Lokesh

Applications and Applied Mathematics: An International Journal (AAM)

We consider a queueing system that utilizes a single server to manage product flow through bulk and overload service modes, depending on queue length. Balking occurs when the queue length reaches ‘N’. After completion of service, products undergo quality inspection, with defective products sent for rework based on specific probabilities. If the product is non-defective, the server continues processing until the queue length exceeds a certain threshold; beyond this point, the server is either routed back to bulk service or directed to an overload service. Also, the server goes into a vacation mode when the queue size is below a …

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

Effective Wordle Heuristics, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.

Using Automotive Lidar To Reduce The Energy Consumption Of An Ego Autonomous Vehicle, Logan P. Schexnaydre

Dissertations, Master's Theses and Master's Reports

There is significant potential to reduce the energy consumption of the transportation sector through autonomous vehicles. Prior work on autonomous vehicle energy efficiency focuses on the whole system or the control subsystem. Yet, the sensing and processing components, which have direct and indirect effects on net energy use, are less explored. This dissertation fills this gap by modeling and evaluating these effects for lidar sensors, which provide high-resolution spatial data at the cost of high power and processing demands. I apply lidar to the energy-saving tasks of automated vehicle following and road surface profiling. For automated vehicle following, I model …

Beyond The Lace Index: Benchmarking Machine Learning Architectures And Explaining 30-Day Hospital Readmission Risk With Shap Analysis, Carl E. Hughes Iii

Williams Honors College, Honors Research Projects

Unplanned 30-day hospital readmission remains a fundamental challenge in US healthcare, associated with increased risk to patient recovery and representing an estimated $52.4 billion in annual expenses (Beauvais et al., 2022). While the rigorously validated LACE index serves as the clinical standard for readmission modeling, its linear structure and four explanatory variables lack the complexity to capture the high-dimensional and interactive nature of patient risk. This study utilizes an admission granularity level cohort of the MIMIC-IV database to develop and compare machine learning architectures against the baseline LACE index. Due to the imbalanced prevalence of readmission, the penalized logistic regression, …

The Excess Path Length Distribution: A Stochastic Model For Sample-Based Path Planners, Chaz B. Cornwall

Dissertations, Master's Theses and Master's Reports

Through random sampling, sample-based path planners enable autonomous agents to quickly find paths without human intervention. However, due to the paths' randomness, sample-based path planners currently require additional verification, partially nullifying agents' ability to act autonomously. I set out to characterize this uncertainty so humans know what to expect from these path planners and know how to alter the path planner to desired specifications. To ensure the results are theoretical as well as practical, I first create a stochastic model of path length uncertainty using the trade-off between sampling time and optimality. By leveraging this model, my proposed algorithm reduces …

All Games Have Equilibria, Arthur Paul Pedersen, M. Ali Khan, Maxwell B. Stinchcombe

Publications and Research

Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same …

Swimming In Uncertainty: Filling Data Gaps And Providing An Educational Platform For Beach Water Quality At Tybee Island, Georgia, Lukas Roberson

College of Graduate Studies: Theses & Dissertations

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Swimming in beaches water contaminated with high levels of bacteria can make you sick. Current monitoring at the public beaches on Tybee Island consists of weekly monitoring and enumeration of fecal indicator bacteria that takes 24 hours for results. If the number of bacteria exceed regulatory limits, a public health advisory is issued, and affected waters are retested until …

(R2131) Analysis Of Map/Ph/1 Retrial Inventory Queueing System With Constant Retrial Rate, Bernoulli Vacation, Breakdown, Delayed Repair, Balking, (S, S) Policy And Emergency Replenishment, G. Ayyappan, M. Thilakavathy

Applications and Applied Mathematics: An International Journal (AAM)

A single server retrial queueing-inventory model is investigated in this study. In Bernoulli vacation, after providing service to the customer, the server may opt to avail vacation or start the service to subsequent customer. During the busy period, breakdown and balking may occur. The inventory is replenished to an (s, S) policy and the replenishing time is assumed to adopt an exponential distribution. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. We integrate the emergency replenishment into the system to ensure customer satisfaction. For our …

(R2120) Flexible Group Service Map/Ph/1 Queueing Model With Working Vacation And Optional Service, G. Ayyappan, S. Kalaiarasi

Applications and Applied Mathematics: An International Journal (AAM)

There are many uses of queues, where services are provided in groups; these types of queues are widely studied in the literature. In this paper we examine a particular queueing model wherein the services are provided in groups and the group size may be less than or equal to the size initially fixed. The arrival follows a Markovian arrival process. The service time of each individual customer follows phase type distribution. The maximum of each customer’s individual service time within a group is defined as the group’s service time. At the service completion moment if there are fewer customers than …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

Syntax-Enhanced Boundary-Aware Named Entity Recognition Model, Chuanming Yu, Bin Deng, Zhengang Zhang

Journal of Scientific Information Research

[Purpose/significance] This study addresses the issue of inadequate perception of entity boundaries in traditional character-level modeling-based named entity recognition models by integrating syntax information containing entity boundary features into the task using a multi-head graph attention network with dense connections. This integration enhances the effectiveness of named entity recognition.

[Method/process] This study proposes a Syntax-enhanced Boundary-aware Named Entity Recognition Model (SynBNER), which utilizes BERT for text semantic representation and integrates syntax information using a dense-connected graph attention network. This integration incorporates implicit entity boundary information from syntax information into word representations, thereby enhancing the model's entity boundary perception capability.

[Result/conclusion] …

Expressive And Interpretable User Engagement Prediction Using Multivariate Survival Processes, Akshay Aravamudan

Theses and Dissertations

The ability to characterize how information diffuses online is of paramount importance to stakeholders that are interested in tasks such as proposing solutions for mitigating and countering dis/misinformation, predicting user engagement of content in social media, planning marketing campaigns to roll-out products and planning dissemination of political campaign messaging among others. One such facet of learning the dynamics of information diffusion is the ability to predict user engagement or the popularity of a single piece of information as it spreads through an online medium. Existing works in this regard mainly either obfuscate user level information or utilize frameworks that are …

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 …

Optimizing Decision-Making In A Cerebral Palsy Model Using Reinforcement Learning, Richard Ampah

Pitzer Senior Theses

This study presents an original interdisciplinary investigation into how reinforcement learning (RL) can model motor and cognitive defects and potentially improve motor and cognitive functions in individuals with cerebral palsy (CP), a non-progressive neurological disorder that impairs movement and adaptability. Integrating computational neuroscience and machine learning, the research applies policy gradient methods and Markov Decision Processes (MDPs) to simulate adaptive learning in agents with and without CP-related constraints.

The central aim is to compare the cumulative rewards of optimal policies, derived from value iteration, and human-like learning policies using the REINFORCE algorithm, both with and without the Bellman baseline. The …

Action This Day: The Mathematics And Machinations That Bested The German Enigma, Jonah Weinbaum

Dartmouth College Master’s Theses

This thesis presents a comprehensive and chronological overview of cryptographic techniques designed to break Enigma, beginning in 1932 and culminating in the creation of the Turing-Welchman Bombe. We discuss the mathematical theory and electromechanical implements used to decode one of history's greatest ciphers.

Reexamining the Bombe through the lens of modern group theory, we critique Alan Turing's estimation of the number of "stops" that the Bombe produces for various plaintext-ciphertext pairing structures. To address its limitations, we introduce a new framework for estimating the number of stops by extending John Dixon's theorem concerning the probability that uniformly distributed elements of …

(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

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 …

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 …

(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

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

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 …

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 …

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.

Judging Our New Judges: Why We Must Remove Artificial Intelligence From Our Courtrooms Now, Kieran Duffy Newcomb

Honors Theses and Capstones

In this paper, I explore some of the ways in which artificial intelligence might enhance the sentencing process through recidivism prediction technology. Notably, this technology can increase the accuracy of risk predictions and the speed with which sentencing decisions are reached. I then show, however, that the recidivism prediction technology is likely to turn into what data scientist Cathy O’Neil calls a Weapon of Math Destruction. The potential harmfulness of this technology is due not to the inherent nature of the technology, but the symbiotic relationship it will have with our already harmful criminal justice system. I argue that the …

Optimizing Sports Outcome Prediction Through Feature Engineering And Machine Learning, Vitor S. Freitas

Graduate Theses/Dissertations

The challenge of predicting the outcome of a team game lies in the high complexity and dynamics of the sports data. This thesis focuses on the aspect of using feature engineering and the genetic algorithm to predict the winner and the score of various sports events. Generally, it deals with how machine learning algorithms are combined with state-of-the-art feature engineering techniques in sports datasets derived from various sports disciplines. In this thesis, five different machine learning models have been applied, classification and regression trees (CART), random forest (RF), stochastic gradient boosting (SGB), eXtreme gradient boosting (XGBoost), and extreme learning machine …

Disentangling Cyclic Causality: An Instance-Based Framework For Causal Discovery, Chase A. Yakaboski

Dartmouth College Ph.D Dissertations

Correlation does not imply causation" is one of the fundamental principles taught in science, emphasizing that associations between variables do not necessarily indicate causality. Yet, over the past three decades, extensive research has begun to challenge this perspective by developing sophisticated methods to differentiate causal from correlative relationships. This research suggests that correlations often involve a blend of confounded and causal interactions, which, given certain assumptions, can be disentangled to uncover actionable insights and deepen our understanding of physical, biological, and societal systems.

Accurately discovering causal relationships from data amidst cyclic dynamics remains a challenging open problem in causality research. …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …