Applied Mathematics Commons^™

Automating Defeasible Reasoning In Law With Answer Set Programming, How Khang Lim, Avishkar Mahajar, Martin Strecker, Meng Weng Wong

Centre for Computational Law (2022-2025)

The paper studies defeasible reasoning in rule-based systems, in particular about legal norms and contracts. We identify rule modifiers that specify how rules interact and how they can be overridden. We then define rule transformations that eliminate these modifiers, leading in the end to a translation of rules to formulas. For reasoning with and about rules, we contrast two approaches, one in a classical logic with SMT solvers, which is only briefly sketched, and one using non-monotonic logic with Answer Set Programming solvers, described in more detail.

Could Cultures Determine The Course Of Epidemics And Explain Waves Of Covid-19?, Md Salman Rahman

Theses and Dissertations

Coronavirus Disease (COVID-19), caused by the SARS-CoV-2 virus, is an infectious disease that quickly became a pandemic spreading with different patterns in each country. Travel bans, lockdowns, social distancing, and non-essential business closures caused significant economic disruptions and stalled growth worldwide in the pandemic’s first year. In almost every country, public health officials forced and/or encouraged Nonpharmaceutical Interventions (NPIs) such as contact tracing, social distancing, masks, and quarantine. Human behavioral decision-making regarding social isolation significantly impedes global success in containing the pandemic. This thesis focuses on human behaviors and cultures related to the decision-making of social isolation during the pandemic. …

Relationships Between Covid-19 Infection Rates, Healthcare Access, Socioeconomic Status, And Cultural Diversity, Marghece P. J. Barnes

Boise State University Theses and Dissertations

The COVID-19 pandemic has had a disproportionate impact on racial and ethnic minority groups, with high infection rates throughout those communities. There are a complex set of factors that account for COVID-19 disparities. Focusing on infection and death rates alone without also examining health equity, underestimates the true impact of the pandemic. To gain a more clear understanding of COVID-19’s impact in these communities, we analyzed the relationship between state COVID-19 infection rates with social determinants of health: cultural diversity, health care access, and socioeconomic status. Our approach to identifying this relationship was to estimate infection rates by fitting John …

Evaluation Of Generative Models For Predicting Microstructure Geometries In Laser Powder Bed Fusion Additive Manufacturing, Andy Ramlatchan

Computer Science Theses & Dissertations

In-situ process monitoring for metals additive manufacturing is paramount to the successful build of an object for application in extreme or high stress environments. In selective laser melting additive manufacturing, the process by which a laser melts metal powder during the build will dictate the internal microstructure of that object once the metal cools and solidifies. The difficulty lies in that obtaining enough variety of data to quantify the internal microstructures for the evaluation of its physical properties is problematic, as the laser passes at high speeds over powder grains at a micrometer scale. Imaging the process in-situ is complex …

Utilization Of Finite Element Analysis Techniques For Adolescent Idiopathic Scoliosis Surgical Planning, Michael A. Polanco

Mechanical & Aerospace Engineering Theses & Dissertations

Adolescent Idiopathic Scoliosis, a three-dimensional deformity of the thoracolumbar spine, affects approximately 1-3% of patients ages 10-18. Surgical correction and treatment of the spinal column is a costly and high-risk task that is consistently complicated by factors such as patient-specific spinal deformities, curve flexibility, and surgeon experience. The following dissertation utilizes finite element analysis to develop a cost-effective, building-block approach by which surgical procedures and kinematic evaluations may be investigated. All studies conducted are based off a volumetric, thoracolumbar finite element (FE) model developed from computer-aided design (CAD) anatomy whose components are kinematically validated with in-vitro data. Spinal ligament stiffness …

Bridge Trisections And Classical Knotted Surface Theory, Jason Joseph, Jeffrey Meier, Maggie Miller, Miller Zupan

Department of Mathematics: Faculty Publications

We seek to connect ideas in the theory of bridge trisections with other wellstudied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney–Massey theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of …

Dimension And Ramsey Results In Partially Ordered Sets., Sida Wan

Electronic Theses and Dissertations

In this dissertation, there are two major parts. One is the dimension results on different classes of partially ordered sets. We developed new tools and theorems to solve the bounds on interval orders using different number of lengths. We also discussed the dimension of interval orders that have a representation with interval lengths in a certain range. We further discussed the interval dimension and semi dimension for posets. In the second part, we discussed several related results on the Ramsey theory of grids, the results involve the application of Product Ramsey Theorem and Partition Ramsey Theorem

A New Sir Model With Mobility., Ciana Applegate

Electronic Theses and Dissertations

In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first …

Cross-Validation For Autoregressive Models., Christina Han

Electronic Theses and Dissertations

There are no set rules for choosing the lag order for autoregressive (AR) time series models. Currently, the most common methods employ AIC or BIC. However, AIC has been proven to be inconsistent and BIC is inefficient. Racine proposed an estimator based on Shao's work which he hypothesized would also be consistent, but left the proof as an open problem. We will show his claim does not follow immediately from Shao. However, Shao offered another consistent method for cross validation of linear models called APCV, and we will show that AR models satisfy Shao's conditions. Thus, APCV is a consistent …

Inexact Fixed-Point Proximity Algorithms For Nonsmooth Convex Optimization, Jin Ren

Mathematics & Statistics Theses & Dissertations

The aim of this dissertation is to develop efficient inexact fixed-point proximity algorithms with convergence guaranteed for nonsmooth convex optimization problems encountered in data science. Nonsmooth convex optimization is one of the core methodologies in data science to acquire knowledge from real-world data and has wide applications in various fields, including signal/image processing, machine learning and distributed computing. In particular, in the context of image reconstruction, compressed sensing and sparse machine learning, either the objective functions or the constraints of the modeling optimization problems are nondifferentiable. Hence, traditional methods such as the gradient descent method and the Newton method are …

Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura

Mathematics & Statistics ETDs

This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of …

Robust Uncertainty Quantification With Analysis Of Error In Standard And Non-Standard Quantities Of Interest, Zachary Stevens

Mathematics & Statistics ETDs

This thesis derives two Uncertainty Quantification (UQ) methods for differential equations that depend on random parameters: (\textbf{i}) error bounds for a computed cumulative distribution function (\textbf{ii}) a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria. Both UQ approaches utilize adjoint-based \textit{a posteriori} error analysis in order to accurately estimate the error in samples of numerically approximated quantities of interest. The adaptive MLMC algorithm developed in this thesis relies on the adjoint-based error analysis to adaptively create meshes and accurately monitor a stopping criteria. This is in contrast to classical MLMC algorithms which employ either a …

Optimal First Order Methods For Reducing Gradient Norm In Unconstrained Convex Smooth Optimization, Yunheng Jiang

All Theses

In this thesis, we focus on convergence performance of first-order methods to compute an $\epsilon$-approximate solution of minimizing convex smooth function $f$ at the $N$-th iteration.

In our introduction of the above research question, we first introduce the gradient descent method with constant step size $h=1/L$. The gradient descent method has a $\mathcal{O}(L^2\|x_0-x^*\|^2/\epsilon)$ convergence with respect to $\|\nabla f(x_N)\|^2$. Next we introduce Nesterov’s accelerated gradient method, which has an $\mathcal{O}(L\|x_0-x^*\|\sqrt{1/\epsilon})$ complexity in terms of $\|\nabla f(x_N)\|^2$. The convergence performance of Nesterov’s accelerated gradient method is much better than that of the gradient descent method but still not optimal. We also …

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova

CODEE Journal

We consider a three-species fish dynamical system in Chesapeake Bay consisting of the Atlantic menhaden as the prey and its two competing predators, the striped bass and the catfish. Building on our previous work in this system, we consider the issue of balancing economic harvesting goals (financial gain for fishermen) with ecological harvesting goals (non-extinction of species). In particular, we investigate the bionomic equilibria, maximum sustainable yield, and the maximum economic yield. Analytical computations and numerical simulations are employed to provide some mathematical guidance on fisheries management policies.

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Mathematics Textbook: Motivation, Experiences, And Didactical Aspect From Authors’ Perspectives, Deepak Basyal, Bhesh Raj Mainali

Mathematics and Statistics

Textbooks play a vital role in the Nepali education system since they are one of the main resources for teaching and learning mathematics. Because of poor physical infrastructure and inadequate educational resources, both teachers and students heavily rely on textbooks. In this regard, this study investigated the mathematics textbook authors' experiences and motivation, and what types of didactical knowledge were utilised while writing textbooks. A convenient yet purposeful sampling method was utilised to select four participants. The data analysis unveiled that each textbook author had different types of motivation and experiences, and only one participant was aware of the ideas …

An Iot Based Worker Safety Helmet Using Cloud Computing Technology, Yuthriya Iddi Khamis, Mahmoud Alawi, Waheed Muhammad Sanya

Tanzania Journal of Engineering and Technology (TJET)

Miner safety and security is a major challenge around the world due to the exposure to toxic gases that are frequently released in underground mines. Miners' health is adversely affected primarily by toxic gases, which endanger the workers' lives. Furthermore, human sensory abilities do not detect these dangerous gases. As a result, this paper proposes a safety monitoring system that includes a temperature sensor, humidity sensor, and gas sensors to detect harmful gases and alert miners to those harmful gases using the smart helmet they wear. These gases are transmitted to the control station via the cloud using Internet of …

Navier-Stokes Equations In One And Two Dimensions, Jon Nerdal

LSU Master's Theses

The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two …