Numerical Analysis and Computation Commons^™

Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods, Eva Lynn Greenman

Dissertations

The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in Perona-Malik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning …

Optimal Analytical Methods For High Accuracy Cardiac Disease Classification And Treatment Based On Ecg Data, Jianwei Zheng

Computational and Data Sciences (PhD) Dissertations

This work constitutes six projects. In the first project, a newly inaugurated research database for 12-lead electrocardiogram signals was created under the auspices of Chapman University and Shaoxing People's Hospital (Shaoxing Hospital Zhejiang University School of Medicine). This database aims to enable the scientific community in conducting new studies on arrhythmia and other cardiovascular conditions. In the second project, we created a new 12-lead ECG database under the auspices of Chapman University and Ningbo First Hospital of Zhejiang University that aims to provide high quality data enabling detection of the distinctions between idiopathic ventricular arrhythmia from right ventricular outflow tract …

Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai

Mathematical Sciences Spring Lecture Series

There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …

Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai

Mathematical Sciences Spring Lecture Series

We consider solving system of nonlinear algebraic equations arising from the discretization of partial differential equations. Inexact Newton is a popular technique for such problems. When the nonlinearities in the system are well-balanced, Newton's method works well, but when a small number of nonlinear functions in the system are much more nonlinear than the others, Newton may converge slowly or even stagnate. In such a situation, we introduce some nonlinear preconditioners to balance the nonlinearities in the system. The preconditioners are often constructed using a combination of some domain decomposition methods and nonlinear elimination methods. For the nonlinearly preconditioned problem, …

Netsci High: Bringing Agency To Diverse Teens Through The Science Of Connected Systems, Stephen M. Uzzo, Catherine B. Cramer, Hiroki Sayama, Russell Faux

Northeast Journal of Complex Systems (NEJCS)

This paper follows NetSci High, a decade-long initiative to inspire teams of teenage researchers to develop, execute and disseminate original research in network science. The project introduced high school students to the computer-based analysis of networks, and instilled in the participants the habits of mind to deepen inquiry in connected systems and statistics, and to sustain interest in continuing to study and pursue careers in fields involving network analysis. Goals of NetSci High ranged from proximal learning outcomes (e.g., increasing high school student competencies in computing and improving student attitudes toward computing) to highly distal (e.g., preparing students for 21st …

Lecture 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow

Mathematical Sciences Spring Lecture Series

Iterative methods for the solution of linear systems of equations – such as stationary, semi-iterative, and Krylov subspace methods – are classical methods taught in numerical analysis courses, but adapting these methods to run efficiently at large-scale on high-performance computers is challenging and a constantly evolving topic. Preconditioners – necessary to aid the convergence of iterative methods – come in many forms, from algebraic to physics-based, are regularly being developed for linear systems from different classes of problems, and similarly are evolving with high-performance computers. This lecture will cover the background and some recent developments on iterative methods and preconditioning …

Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman

Mathematical Sciences Spring Lecture Series

Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.

Analysis Of Boundary Observability Of Strongly Coupled One-Dimensional Wave Equations With Mixed Boundary Conditions, Wilson Dennis Horner

Masters Theses & Specialist Projects

*see note below

In control theory, the time it takes to receive a signal after it is sent is referred to as the observation time. For certain types of materials, the observation time to receive a wave signal differs depending on a variety of factors, such as material density, flexibility, speed of the wave propagation, etc. Suppose we have a strongly coupled system of two wave equations describing the longitudinal vibrations on a piezoelectric beam of length L. These two wave equations have non-identical wave propagation speeds c1 and c2. First, we prove the exact observability inequality with the optimal …

Modeling Covid-19 Infection Rates Using Sir And Arima Models, Janelle Domantay, Ilya Pivavaruk, Victor Taksheyev

Undergraduate Research Symposium Posters

With the onset of the COVID-19 pandemic, it has become of increasing interest to both monitor and predict the growth of its infection rates. In order to analyze the accuracy of epidemiological prediction, we consider two different models for prediction, the Susceptible Infected and Removed (SIR), and Autoregressive Integrated Moving Average (ARIMA) models. Using a dataset of Clark County COVID-19 infections, we create various ARIMA and SIR models that attempt to predict the progression of COVID-19 infections whilst comparing these predictions to the dataset. We observed that the ARIMA model performed more accurately overall, having a much lower Root Mean …

Flocc: From Agent-Based Models To Interactive Simulations On The Web, Scott Donaldson

Northeast Journal of Complex Systems (NEJCS)

Agent-based modeling (ABM) is a computational technique wherein systems are represented through the actions and interactions of many individual entities (‘agents’) over time. ABM often attempts to elucidate the unpredictable, high-level behavior of systems through the predictable, low-level behavior of actors within the system. There are currently few software or frameworks for ABM that allow modelers to design and build interactive models on the web, for a wide audience as well as a scientifically literate audience well-versed in complexity, models, and simulations. Flocc is a novel framework for agent-based modeling written in JavaScript, the lingua franca programming language of the …

Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt

Northeast Journal of Complex Systems (NEJCS)

The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are …

Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model, Edison E. Chukwuemeka

LSU Master's Theses

Liquid crystal models with the capability of capturing defects has been one of the main focus in modeling the behavior of such phase mathematically. A uni-axially constrained Landau-de Gennes one-constant model, which has this capability was modeled using three minimization schemes - standard gradient descent, Nesterov accelerated gradient descent, and heavy-ball accelerated gradient descent. The uni-axially constrained Landau-de Gennes energy is discretized using finite element method and the performance of the minimization schemes are measured using the classical gradient descent scheme as the baseline. The numerical experiments conducted indicated that the accelerated gradient descent schemes improved the convergence rate and …

Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren

Northeast Journal of Complex Systems (NEJCS)

The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our …

Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev

Dissertations, Theses, and Capstone Projects

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.

We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number …

Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

The following sections are included:

• Present State of Computational Modelling in Fluorescence Nanoscopy

• Recent Contributions to Computational Modelling in Fluorescence Nanoscopy

• Outlook on Computational Modelling in Fluorescence Nanoscopy

• Acknowledgments

• References

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Numerical Reconstruction Of Spalled Particle Trajectories In An Arc-Jet Environment, Raghava S. C. Davuluri, Sean C. C. Bailey, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

To evaluate the effects of spallation on ablative material, it is necessary to evaluate the mass loss. To do so, a Lagrangian particle trajectory code is used to reconstruct trajectories that match the experimental data for all kinematic parameters. The results from spallation experiments conducted at the NASA HYMETS facility over a wedge sample were used. A data-driven adaptive methodology was used to adapts the ejection parameters until the numerical trajectory matches the experimental data. The preliminary reconstruction results show that the size of the particles seemed to be correlated with the location of the ejection event. The size of …

Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

HMC Senior Theses

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.

Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez

HMC Senior Theses

Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …

Common Unit Conversions For Irrigation, Dean E. Eisenhauer, Derrel L. Martin, Derek M. Heeren, Glenn J. Hoffman

Open Learning Resources, General/Selected

A fact sheet that includes common unit conversions for irrigation in international system of units (SI) and United States customary system of units (USCS).

Includes units for: length, area, volume, flow, weight and mass, pressure, crop yield, temperature, and the United States public land survey system.