Other Applied Mathematics Commons^™

A Novel Correction For The Adjusted Box-Pierce Test, Sidy Danioko, Jianwei Zheng, Kyle Anderson, Alexander Barrett, Cyril S. Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical Box-Pierce and Ljung-Box tests for auto-correlation of residuals possess severe deviations from nominal type I error rates. Previous studies have attempted to address this issue by either revising existing tests or designing new techniques. The Adjusted Box-Pierce achieves the best results with respect to attaining type I error rates closer to nominal values. This research paper proposes a further correction to the adjusted Box-Pierce test that possesses near perfect type I error rates. The approach is based on an inflation of the rejection region for all sample sizes and lags calculated via a linear model applied to simulated …

Cooccurrr - Applying Glcm Analysis Techniques To Non-Image Objects Such As Fitness Landscapes, Steph J. Owen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Empirical And Computational Approaches To Explore The Underlying Neuromodulatory Mechanisms Of Social Status Regulation On Zebrafish Motor Circuits, Sungwoo Ahn, Choongseok Park, Fadi Issa

Biology and Medicine Through Mathematics Conference

No abstract provided.

Age-Dependent Ventilator-Induced Lung Injury, Quintessa Hay, Christopher Grubb, Rebecca L. Heise, Sarah Minucci, Michael S. Valentine, Jennifer Van Mullekom, Angela M. Reynolds

Biology and Medicine Through Mathematics Conference

No abstract provided.

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, 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, 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, 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, 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, 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, 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, Michael Pieper

Honors Program: Senior Projects (Public)

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, 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, 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 …

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, …

An Exploration Of Voting With Partial Orders, Mason Acevedo

HMC Senior Theses

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

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 …

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, 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 …

Containing Compounding Container Congestion, Curtis Salinger

CMC Senior Theses

The Covid-19 pandemic caused major disruptions throughout the container shipping supply chain. Professor Dongping Song of Liverpool University wrote a paper discussing the logistical vulnerabilities in the supply chain, including the issue of congestion in ports. This paper examines the Port of Los Angeles from 2018-2021 as it relates to Song’s paper to see how its operations were impacted during the Covid-19 timeframe. It is found that labor shortages, chassis shortages, and change in trade behavior each contributed to the congestion. Unfortunately, the implemented policies were insufficient to bolster the port against sustained challenges and congestion continues to worsen.