Numerical Analysis and Computation Commons^™

Understanding The Dynamics Of Human Reliance And Trust On Automation, Carlos E. Bustamante Orellana, Lucero Rodriguez Rodriguez, Jordy Cevallos Chavez, Yun Kang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modelling And Simulation Using An Efficient Pinns Algorithm To Understand Spread Of Infection In Enclosed Spaces, Long Nguyen, Arkaprovo Ghosal, Rudra Nagalia, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Impact Of Fungicide Treatment On The Dynamics Of Cocoa Black Pod Disease, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model For Understanding The Spread Of Covid-19 In Saudi Arabia With Access To Vaccination, Maha Alshabrawi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

Towards Cnl-Based Verbalization Of Computational Contracts, Inari Listenmaa, Maryam Hanafiah, Regina Cheong, Andreas Kallberg

Centre for Computational Law (2022-2025)

We present a CNL, which is a component of L4, a domain-specific programming language for drafting laws and contracts. Along with formal verification, L4’s core functionalities include natural language generation. We present the NLG pipeline and an interactive process for ambiguity resolution.

On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

Principal Component Analysis (PCA) is a commonly used technique that uses the correlation structure of the original variables to reduce the dimensionality of the data. This reduction is achieved by considering only the first few principal components for a subsequent analysis. The usual inclusion criterion is defined by the proportion of the total variance of the principal components exceeding a predetermined threshold. We show that in certain classification problems, even extremely high inclusion threshold can negatively impact the classification accuracy. The omission of small variance principal components can severely diminish the performance of the models. We noticed this phenomenon in …

Fast Multipole Methods For Wave And Charge Source Interactions In Layered Media And Deep Neural Network Algorithms For High-Dimensional Pdes, Wenzhong Zhang

Mathematics Theses and Dissertations

In this dissertation, we develop fast algorithms for large scale numerical computations, including the fast multipole method (FMM) in layered media, and the forward-backward stochastic differential equation (FBSDE) based deep neural network (DNN) algorithms for high-dimensional parabolic partial differential equations (PDEs), addressing the issues of real-world challenging computational problems in various computation scenarios.

We develop the FMM in layered media, by first studying analytical and numerical properties of the Green's functions in layered media for the 2-D and 3-D Helmholtz equation, the linearized Poisson--Boltzmann equation, the Laplace's equation, and the tensor Green's functions for the time-harmonic Maxwell's equations and the …

A Fast Method For Computing Volume Potentials In The Galerkin Boundary Element Method In 3d Geometries, Sasan Mohyaddin

Mathematics Theses and Dissertations

We discuss how the Fast Multipole Method (FMM) applied to a boundary concentrated mesh can be used to evaluate volume potentials that arise in the boundary element method. If $h$ is the meshwidth near the boundary, then the algorithm can compute the potential in nearly $\Ord(h^{-2})$ operations while maintaining an $\Ord(h^p)$ convergence of the error. The effectiveness of the algorithms are demonstrated by solving boundary integral equations of the Poisson equation.

Ensemble Data Fitting For Bathymetric Models Informed By Nominal Data, Samantha Zambo

Dissertations

Due to the difficulty and expense of collecting bathymetric data, modeling is the primary tool to produce detailed maps of the ocean floor. Current modeling practices typically utilize only one interpolator; the industry standard is splines-in-tension.

In this dissertation we introduce a new nominal-informed ensemble interpolator designed to improve modeling accuracy in regions of sparse data. The method is guided by a priori domain knowledge provided by artificially intelligent classifiers. We recast such geomorphological classifications, such as ‘seamount’ or ‘ridge’, as nominal data which we utilize as foundational shapes in an expanded ordinary least squares regression-based algorithm. To our knowledge …

Multilateration Index., Chip Lynch

Electronic Theses and Dissertations

We present an alternative method for pre-processing and storing point data, particularly for Geospatial points, by storing multilateration distances to fixed points rather than coordinates such as Latitude and Longitude. We explore the use of this data to improve query performance for some distance related queries such as nearest neighbor and query-within-radius (i.e. “find all points in a set P within distance d of query point q”). Further, we discuss the problem of “Network Adequacy” common to medical and communications businesses, to analyze questions such as “are at least 90% of patients living within 50 miles of a covered emergency …

Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Changes in the spatial distribution of vegetation respond to variations in the production and transportation mechanisms of seeds at different locations subject to heterogeneities, often because of soil characteristics. In semi-arid environments, the competition for water and nutrients pushes the superficial plant’s roots to obtain scarce resources at long ranges. In this report, we assume that vegetation biomass interacts with itself in two different ways, facilitation and inhibition, depending on the relative distances. We present a 1-dimensional Integro-difference model to represent and study the emergence of patterns in the distribution of vegetation.

A Deep Ensemble Method For Multi-Agent Reinforcement Learning: A Case Study On Air Traffic Control, Supriyo Ghosh, Sean Laguna, Laura Wynter, Laura Wynter, Hasan Poonawala

Research Collection School Of Computing and Information Systems

Reinforcement learning (RL), a promising framework for data-driven decision making in an uncertain environment, has successfully been applied in many real-world operation and control problems. However, the application of RL in a large-scale decentralized multi-agent environment remains a challenging problem due to the partial observability and limited communications between agents. In this paper, we develop a model-based kernel RL approach and a model-free deep RL approach for learning a decentralized, shared policy among homogeneous agents. By leveraging the strengths of both these methods, we further propose a novel deep ensemble multi-agent reinforcement learning (MARL) method that efficiently learns to arbitrate …

A Modified Preconditioned Conjugate Gradient Method For Approximating The Scattering Amplitude, Samson Ayo

Master's Theses

In this thesis, we look at an iterative method for approximating the scattering amplitude that involves solving two linear systems: a forward system Ax=b and an adjoint system A^Ty=g. Once these two systems are solved, the scattering amplitude, defined by g^Tx=y^Tb is easily obtained.

We derive a conjugate gradient-like iteration for a nonsymmetric saddle point matrix that is constructed to have a real positive spectrum. We investigate the use of Schur Complement preconditioners with block-diagonal factorization to speed up the convergence of our method and compare …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Socio-Technical Perspective For Electronic Tax Information System In Tanzania, Lucas Ngowi, Ellen Kalinga

Tanzania Journal of Engineering and Technology (TJET)

Socio-technical systems theory has rarely been used by system architects in setting up computing systems. However, the role of socio-technical concepts in computing, which is becoming social in nature, has made the concepts more relevant and commercial. Tax information systems are examples of such systems because they are influenced by external variables such as the political environment, technological trends, and social environment, introducing complexity in their deployment and determining the type of e-services and their delivery to a diverse group of people. It was observed that in Tanzania there is resistance, reluctance and minimal use of electronic tax system because …

Fully Coupled Internal Radiative Heat Transfer For The 3d Material Response Of Heat Shield, Raghava S. C. Davuluri, Rui Fu, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

The radiative transfer equation (RTE) is strongly coupled to the material response code KATS. A P-1 approximation model of RTE is used to account for radiation heat transfer within the material. First, the verification of the RTE model is performed by comparing the numerical and analytical solutions. Next, the coupling scheme is validated by comparing the temperature profiles of pure conduction and conduction coupled with radiative emission. The validation study is conducted on Marschall et al. cases (radiant heating, arc-jet heating, and space shuttle entry), 3D Block, 2D IsoQ sample, and Stardust Return Capsule. The validation results agree well for …

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …