Physical Sciences and Mathematics Commons^™

Projective Splitting Methods For Maximal Monotone Mappings In Hilbert Spaces, Oday Hazaimah

Graduate Research Theses & Dissertations

In this dissertation, novel approaches for solving convex nonsmooth optimization, variational inequalities and inclusion problems are studied. The main contributions of the dissertation are given in Chapter 4 and Chapter 5. The two proposed iterations in Chapter 4, Half-Extragradient algorithm (HEG) and its accelerated version, are a natural modification of the classical Extragradient algorithm (EG)

when the composite objective function is a sum of three convex functions. EG evaluates the smooth operator twice per iteration via proximal mappings, and also, it allows larger step sizes. One of the main advantages of the proposed scheme is to avoid evaluating an

extragradient …

Determining Tone Of A Body Of Text, Cole G. Hollant

Senior Projects Spring 2020

We will be looking into emotion detection and manipulation within a body of text based off of Robert Plutchik’s basic emotions. This project encompasses building probabilistic and lexical models, full-stack web development, and dataset creation and application. We will build our models off of Latent Dirichlet Allocation—a grouping model common in natural language processing (nlp) and lexicons compiled through crowdsourcing. User testing is undergone as a means of measuring the effectiveness of our models. We discuss the application of concepts and technologies including MongoDB, REST APIs, containerization, IaaS, and web frontends.

Missing Data Imputation Of High-Resolution Temporal Climate Time Series Data, Eben Afrifa-Yamoah, Ute A. Mueller, S. M. Taylor, A. J. Fisher

Research outputs 2014 to 2021

© 2020 The Authors. Meteorological Applications published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society. Analysis of high-resolution data offers greater opportunity to understand the nature of data variability, behaviours, trends and to detect small changes. Climate studies often require complete time series data which, in the presence of missing data, means imputation must be undertaken. Research on the imputation of high-resolution temporal climate time series data is still at an early phase. In this study, multiple approaches to the imputation of missing values were evaluated, including a structural time series model with Kalman smoothing, …

The Geometry Of The Orthological Triangles, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

Plants and trees grow perpendicular to the plane tangent to the soil surface, at the point of penetration into the soil; in vacuum, the bodies fall perpendicular to the surface of the Earth - in both cases, if the surface is horizontal. Starting from the property of two triangles to be orthological, the two authors have designed this work that seeks to provide an integrative image of elementary geometry by the prism of this "filter". Basically, the property of orthology is the skeleton of the present work, which establishes many connections of some theorems and geometric properties with it. The …

Variational Analysis Of Composite Optimization, Ashkan Mohammadi

Wayne State University Dissertations

The dissertation is devoted to the study of the first- and second-order variational analysis of the composite functions with applications to composite optimization. By considering a fairly general composite optimization problem, our analysis covers numerous classes of optimization problems such as constrained optimization; in particular, nonlinear programming, second-order cone programming and semidefinite programming(SDP). Beside constrained optimization problems our framework covers many important composite optimization problems such as the extended nonlinear programming and eigenvalue optimization problem. In first-order analysis we develop the exact first-order calculus via both subderivative and subdifferential. For the second-order part we develop calculus rules via second-order subderivative …

Nanomagnetic Resonance Imaging (Nano-Mri) Gives Personalized Medicine A New Perspective, Lorenzo Rosa, Jonathan Blackledge, Albert Boretti

Books/Book chapters

This chapter provides a brief overview of molecular imaging techniques and its present and future potential in personalized medicine, with special a focus on the magnetic resonance imaging (MRI) approach. It discusses the current techniques that allow for the in vivo visualization of molecular processes at the nanoscale resolution (nano-MRI). Nano-MRI is progressing rapidly thanks to the work of a very small but extremely brilliant community of experts. This paper is not intended to be a comprehensive review of nano-MRI written for these experts, but rather a concise description of the present achievements for a much broader audience of medical …

The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane

Dissertations, Master's Theses and Master's Reports

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L²(M) → X, U : L²(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that

T = Um_σV ^†,

with m_σ : L²(M ) → L²(M ) defined by m_σ(f ) = σf for all f …

Sub-Sampled Matrix Approximations, Joy Azzam

Dissertations, Master's Theses and Master's Reports

Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate a matrix A with an appropriate embedding of the data sampled. This work introduces a novel family of randomized iterative algorithms which use significantly less data per iteration than current methods by sampling input and output spaces simultaneously. The data footprint of the algorithms can be tuned (independent of the underlying matrix dimension) to available hardware. Proof is given for the convergence of the algorithms, which are referred to as sub-sampled, in terms of numerically tested …

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …

Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam

Honors Projects

In light of concerns about climate change, there is interest in how sustainable management can maintain the resilience of ecosystems. We use flow-kick dynamical systems to model ecosystems subject to a constant kick occurring every τ time units. We classify the stability of flow-kick equilibria to determine which management strategies result in desirable long-term characteristics. To classify the stability of a flow-kick equilibrium, we classify the linearization of the time-τ map given by the time-τ map of the variational equation about the equilibrium trajectory. Since the variational equation is a non-autonomous linear differential equation, we conjecture that the asymptotic stability …

Swimming Of Motile Gyrotactic Microorganisms And Nanoparticles In Blood Flow Through Anisotropically Tapered Arteries, M. M. Bhatti, M. Marin, A. Zeeshan, R. Ellahi, Sara I. Abdelsalam

Basic Science Engineering

In the present article, we have presented a theoretical study on the swimming of migratory gyrotactic microorganisms in a non-Newtonian blood-based nanofluid via an anisotropically narrowing artery. Sutterby fluid model is used in order to understand the rheology of the blood as a non-Newtonian fluid model. This fluid pattern has the ability to show Newtonian and non-Newtonian features. The mathematical formulation is performed via continuity, temperature, motile microorganism, momentum, and concentration equation. The series solutions are obtained using the perturbation scheme up to the third-order approximation. The resulting solutions are discussed with the help of graphs for all the leading …

Adverse Effects Of A Hybrid Nanofluid In A Wavy Non-Uniform Annulus With Convective Boundary Conditions, H. Sadaf, Sara I. Abdelsalam

Basic Science Engineering

The presented investigation theoretically studies the physical characteristics of a two-dimensional incompressible hybrid nanofluid in a non-uniform annulus where the boundaries are flexible. A mixed convective peristaltic mechanism is implemented to model blood-based nanofluids using two different nanoparticles (Ag + Al2O3). Convective boundary conditions are employed and different forms of nanoparticles are discussed (bricks, cylinders and platelets). The problem is shortened by engaging a lubrication method. Exact expressions for the temperature of cumulative heat source/sink standards, hemodynamic velocity, pressure gradient and streamlines of different shapes of nanoparticles are obtained. Special cases of pure blood and the Al2O3 nanofluid of our …

Editorial: Recent Trends In Computational Fluid Dynamics, M. M. Bhatti, M. Marin, A. Zeeshan, Sara I. Abdelsalam

Basic Science Engineering

No abstract provided.

Zero-Inflated Longitudinal Mixture Model For Stochastic Radiographic Lung Compositional Change Following Radiotherapy Of Lung Cancer, Viviana A. Rodríguez Romero

Theses and Dissertations

Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture …

Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins

Electronic Theses and Dissertations

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …

Modeling The Evolution Of Barrier Islands, Greg Robson

Theses and Dissertations

Barrier islands form off the shore of many coastal areas and serve as the first line of defense, protecting littoral communities against storms. To study the effects that climate change has on barrier islands, we use a cellular model of wind erosion, surface dynamics, beach dynamics, marsh dynamics, and vegetation development. We will show the inhibition of movement when vegetation is present.

Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives, Sachin Munshi

Legacy Theses & Dissertations (2009 - 2024)

Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.

Increasing Performance Of Classifiers For Ssvep-Based Brain-Computer Interfaces Using Extension Methods, Ethan Douglas Webster

Legacy Theses & Dissertations (2009 - 2024)

Brain-computer interfaces (BCI) provide an alternative communication method that does not require standard physical mediums (speech, typing, etc.). These systems have been implemented to provide additional communication and control options for people with certain motor disabilities. Classification is an important part of BCI systems and consists of inferring user commands from brain activity. Supervised classification methods often achieve higher accuracy, but unsupervised classification methods are useful when training is not practical for the user. This thesis focuses on unsupervised classification algorithms used for a BCI speller application and presents extensions for two existing classifiers that improve classification accuracy and thus …

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman

Mathematics Faculty Publications

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …

Modeling Gene Expression With Differential Equations, Madison Kuduk

Capstone Showcase

Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam

Electronic Theses and Dissertations

The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …

Association Rules Patterns Discovery From Mixed Data, Welendawa Acharige Charith A. Elson

Electronic Theses and Dissertations

Finding Association Rules has been a popular unsupervised learning technique for dis covering interesting patterns in commercial data for well over two decades. The method seeks groups of data attributes and their values where their probability density of these attributesattherespectivevaluesismaximized. Therearecurrentlywell-establishedmeth ods for tackling this problem for data with categorical (discrete) attributes. However, for the cases of data with continuous variables, the techniques are largely focusing on cate gorizing continuous variables into intervals of interest and then relying on the categorical data methods to address the problem. We address the problem of finding association rules patterns in mixed data by …

Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, David Rushing Dewhurst

Graduate College Dissertations and Theses

A sociotechnical system is a collection of humans and algorithms that interact under the partial supervision of a decentralized controller. These systems often display in- tricate dynamics and can be characterized by their unique emergent behavior. In this work, we describe, analyze, and model aspects of three distinct classes of sociotech- nical systems: financial markets, social media platforms, and elections. Though our work is diverse in subject matter content, it is unified though the study of evolution- and adaptation-driven change in social systems and the development of methods used to infer this change.

We first analyze evolutionary financial market microstructure …

Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond

Graduate College Dissertations and Theses

With the rise of social media, researchers have become increasingly interested in understanding how individuals inform, influence, and interact with others in their social network and how the network mediates the flow of information. Previous research on information flow has primarily used models of contagion to study the adoption of a technology, propagation of purchase recommendations, or virality of online activity. Social (or "complex") contagions spread differently than biological ("simple") contagions. A limitation when researchers validate contagion models is that they neglect much of the massive amounts of data now available through online social networks. Here we model a recently …

Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp

Senior Independent Study Theses

As the human population continues increasing rapidly and climate change accelerates, resource depletion is becoming an international problem. Community-based natural resource management (CBNRM) has been suggested as a method to conserve resources while simultaneously empowering traditionally marginalized communities. Because classical equation-based modeling methods fail to capture the complexity of CBNRM, Agent-Based Modeling (ABM) has emerged as a primary method of modeling these systems. In this investigation, we conduct a sensitivity analysis and thorough evaluation of an existing ABM of community forest management. We then modify the original model by providing a new enforcement mechanism that improves the validity of both …

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …

Exploration And Implementation Of Neural Ordinary Differential Equations, Long Huu Nguyen, Andy Malinsky

Capstone Showcase

Neural ordinary differential equations (ODEs) have recently emerged as a novel ap- proach to deep learning, leveraging the knowledge of two previously separate domains, neural networks and differential equations. In this paper, we first examine the back- ground and lay the foundation for traditional artificial neural networks. We then present neural ODEs from a rigorous mathematical perspective, and explore their advantages and trade-offs compared to traditional neural nets.

Applications Of Ornstein-Uhlenbeck Type Stochastic Differential Equations, Osei Kofi Tweneboah

Open Access Theses & Dissertations

In this Dissertation, we show with plausible arguments that the Stochastic Differential Equations (SDEs) arising on the superposition and coupling system of independent Ornstein-Uhlenbeck process is a new method available in modern literature that takes the properties and behavior of the data into consideration when performing the statistical analysis of the time series.

The time series to be analyzed is thought of as a source of fluctuations, and thus we need a model that takes this behavior into consideration when performing such analysis. Most of the standard methods fail to take into account the physical behavior of the time series, …

Higher Accuracy Methods For Fluid Flows In Various Applications: Theory And Implementation, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on several topics related to Defect-deferred correction (DDC) method applying to CFD problems. First, we want to improve the error due to temporal discretization for the problem of two convection dominated convection-diffusion problems, coupled across a joint interface. This serves as a step towards investigating an atmosphere-ocean coupling problem with the interface condition that allows for the exchange of energies between the domains.

The main diffuculty is to decouple the problem in an unconditionally stable way for using legacy code for subdomains. To overcome the issue, we apply the Deferred Correction (DC) method. The DC method …