Generating A Dataset For Comparing Linear Vs. Non-Linear Prediction Methods In Education Research, 2022 Loyola Marymount University

#### Generating A Dataset For Comparing Linear Vs. Non-Linear Prediction Methods In Education Research, Jack Mauro, Elena Martinez, Anna Bargagliotti

*Honors Thesis*

Machine learning is often used to build predictive models by extracting patterns from large data sets. Such techniques are increasingly being utilized to predict outcomes in the social sciences. One such application is predicting student success. Machine learning can be applied to predicting student acceptance and success in academia. Using these tools for education-related data analysis, may enable the evaluation of programs, resources and curriculum. Currently, research is needed to examine application, admissions, and retention data in order to address equity in college computer science programs. However, most student-level data sets contain sensitive data that cannot be made public. To …

Data And Algorithmic Modeling Approaches To Count Data, 2022 Murray State University

#### Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack

*Honors College Theses*

Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as …

Advancements In Gaussian Process Learning For Uncertainty Quantification, 2022 Clemson University

#### Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

*All Dissertations*

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, 2022 Southwestern Oklahoma State University

#### Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri

*Student Research*

- Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level.
- Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population.
- Here, we have examined the behavior of a measles-like disease[2] that is characterized by a non-constant transmission rate.

Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, 2022 Embry-Riddle Aeronautical University

#### Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, Joshua Sonderegger

*Doctoral Dissertations and Master's Theses*

The landing and reusability of space vehicles is one of the driving forces into renewed interest in space utilization. For missions to planetary surfaces, this soft landing has been most commonly accomplished with parachutes. However, in spite of their simplicity, they are susceptible to parachute drift. This parachute drift makes it very difficult to predict where the vehicle will land, especially in a dense and windy atmosphere such as Earth. Instead, recent focus has been put into developing a powered landing through gimbaled thrust. This gimbaled thrust output is dependent on robust path planning and controls algorithms. Being able to …

Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, 2022 University of South Carolina

#### Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor

*Senior Theses*

Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …

On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, 2022 Dortmund University of Applied Sciences and Arts

#### On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias

*Spora: A Journal of Biomathematics*

This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, 2022 University of Nebraska - Lincoln

#### Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

*Honors Theses*

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, 2022 Western Carolina University

#### An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias

*Spora: A Journal of Biomathematics*

In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact at least three distinct mathematical models attributed to the 1954 paper. In this study, we examine this important paper and the mathematical derivation of their model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.

Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, 2022 Dickinson College

#### Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, Richard Forrester, Lucas Waddell

*Faculty Journal Articles*

The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately …

Optimizing Pension Outcomes Using Target Volatility Investment Concept, 2022 Bentley University

#### Optimizing Pension Outcomes Using Target Volatility Investment Concept, Zefeng Bai

*2022*

The target volatility strategy is a very popular investment concept in financial marketplace. For my dissertation, I focus on studying the target volatility investment concept in application to pension accumulation as well as decumulation stages. Additionally, I extend a basic target volatility strategy by introducing trading boundaries to its asset allocation mechanism. My dissertation study follows a three-paper format.

In paper one, we propose a new pension strategy that aims at improving the protection of a long-term pension plan in volatile market conditions. Over a hypothetical twenty-year pension scheme, we show that our newly proposed strategy, which attaches a target …

An Exploration In Health Analytics: Pediatric Burns, Care Policy Assessment And Interrupted Time Series, 2022 Bentley University

#### An Exploration In Health Analytics: Pediatric Burns, Care Policy Assessment And Interrupted Time Series, Chao Wang

*2022*

Healthcare systems globally face multiple challenges in the face of population growth and changes in disease pathology. With regard to the rising demand of the healthcare and the global threats of the pandemic, the medical datasets can be trained further to develop preventive methods. Meanwhile, policy reforms of health systems could be a critical aspect to deal with the public crisis and concerns. However, two basic problems must be addressed first: identification of key factors on a priority basis and evaluation of changes.

Thus, the paper presents a series of trials on the application of data analytics to health-related problems, …

Mathematical Models Of Infection Prevention Programs In Hospital Settings, 2022 Virginia Commonwealth University

#### Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan

*Theses and Dissertations*

Hospitals play a vital role in providing for the healthcare needs of a community. Patients can develop hospital-acquired infections (HAIs) during their hospitalization due to exposure to foreign bacteria, viruses, and fungi. Infection prevention programs target and reduce HAIs, but implementing the infection prevention programs often comes with a cost. The goal of my research is to use mathematical models to quantify the impact of infection prevention programs on cases of HAIs and total healthcare costs. First, I use a Markov chain model to quantify how one infection prevention program reduces general HAIs in the hospital. Then, I calculate the …

Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, 2022 Bowdoin College

#### Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King

*Honors Projects*

This project is an analysis of the effectiveness of five distinct optimization methods in their ability in producing clear images of the basins of attraction, which is the set of initial points that approach the same minimum for a given function. Basin images are similar to contour plots, except that they depict the distinct regions of points--in unique colors--that approach the same minimum. Though distinct in goal, contour plots are useful to basin research in that idealized basin images can be inferred from the steepness levels and location of extrema they depict. Effectiveness of the method changes slightly depending on …

Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, 2022 Bowdoin College

#### Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah

*Honors Projects*

The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. …

Representation Theory And Its Applications In Physics, 2022 Colby College

#### Representation Theory And Its Applications In Physics, Jakub Bystrický

*Honors Theses*

Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …

Dynamic Nonlinear Gaussian Model For Inferring A Graph Structure On Time Series, 2022 Claremont Colleges

#### Dynamic Nonlinear Gaussian Model For Inferring A Graph Structure On Time Series, Abhinuv Uppal

*CMC Senior Theses*

In many applications of graph analytics, the optimal graph construction is not always straightforward. I propose a novel algorithm to dynamically infer a graph structure on multiple time series by first imposing a state evolution equation on the graph and deriving the necessary equations to convert it into a maximum likelihood optimization problem. The state evolution equation guarantees that edge weights contain predictive power by construction. After running experiments on simulated data, it appears the required optimization is likely non-convex and does not generally produce results significantly better than randomly tweaking parameters, so it is not feasible to use in …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, 2022 Georgia Southern University

#### Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

*Electronic Theses and Dissertations*

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Eeg Signals Classification Using Lstm-Based Models And Majority Logic, 2022 Georgia Southern University

#### Eeg Signals Classification Using Lstm-Based Models And Majority Logic, James A. Orgeron

*Electronic Theses and Dissertations*

The study of elecroencephalograms (EEGs) has gained enormous interest in the last decade with the increase of computational power and availability of EEG signals collected from various human activities or produced during medical tests. The applicability of analyzing EEG signals ranges from helping impaired people communicate or move (using appropriate medical equipment) to understanding people's feelings and detecting diseases.

We proposed new methodology and models for analyzing and classifying EEG signals collected from individuals observing visual stimuli. Our models rely on powerful Long-Short Term Memory (LSTM) Neural Network models, which are currently the state of the art models for performing …

Decoding Cyclic Codes Via Gröbner Bases, 2022 Colby College

#### Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

*Honors Theses*

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …