Applied Mathematics Commons^™

Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong

Dissertations and Theses

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass …

Analyzing Multistationarity In A Model Of A Dual Phosphorylation Network, Killian Kearney Anderson

Graduate Research Theses & Dissertations

Otero-Muras, Banga, and Alonso in [18] state biological reaction systems exhibit multistationarity, a system with at least two positive steady states. According to Otero-Muras,Banga, and Alonso in [18], initial conditions within the system, however, dictate the number of stable states in that system. Furthermore, multistationarity is an important componenet present in biological reaction systems that manage cellular responses [18]. Signal pathways regulating cell maturation, cell replication, and cell death rely on such systems [18]. Given the importance of multistationarity in biological reaction systems, it is necessary to construct a mathematical model, one in which multistationarity will be configured. More importantly, …

Counterexample To Eremenko's Conjecture, Paradise Low

Graduate Research Theses & Dissertations

Eremenko’s Conjecture is a long-standing problem in complex dynamics that asks whetherevery connected component of the set of escaping points of a transcendental entire function is unbounded. It was finally proven false in a paper by Mart ́ı-Pete, Lasse Rempe, and James Waterman that constructs a counterexample to the conjecture. This thesis seeks to pro- vide a background on Eremenko’s Conjecture, discuss the partial results surrounding it, and explain the construction of the counterexample in Mart ́ı-Pete, et al.’s paper.

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

On Implementing And Testing The Rsa Algorithm, Kien Trung Le

Senior Independent Study Theses

In this work, we give a comprehensive introduction to the RSA cryptosystem, implement it in Java, and compare it empirically to three other RSA implementations. We start by giving an overview of the field of cryptography, from its primitives to the composite constructs used in the field. Then, the paper presents a basic version of the RSA algorithm. With this information in mind, we discuss several problems with this basic conception of RSA, including its speed and some potential attacks that have been attempted. Then, we discuss possible improvements that can make RSA runs faster and more secure. On the …

Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee

UNF Graduate Theses and Dissertations

We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …

Interpretable Design Of Reservoir Computing Networks Using Realization Theory, Wei Miao, Vignesh Narayanan, Jr-Shin Li

Publications

The reservoir computing networks (RCNs) have been successfully employed as a tool in learning and complex decision-making tasks. Despite their efficiency and low training cost, practical applications of RCNs rely heavily on empirical design. In this article, we develop an algorithm to design RCNs using the realization theory of linear dynamical systems. In particular, we introduce the notion of α-stable realization and provide an efficient approach to prune the size of a linear RCN without deteriorating the training accuracy. Furthermore, we derive a necessary and sufficient condition on the irreducibility of the number of hidden nodes in linear RCNs based …

Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan

Theses and Dissertations

Hospitals play a vital role in providing for the healthcare needs of a community. Patients can develop hospital-acquired infections (HAIs) during their hospitalization due to exposure to foreign bacteria, viruses, and fungi. Infection prevention programs target and reduce HAIs, but implementing the infection prevention programs often comes with a cost. The goal of my research is to use mathematical models to quantify the impact of infection prevention programs on cases of HAIs and total healthcare costs. First, I use a Markov chain model to quantify how one infection prevention program reduces general HAIs in the hospital. Then, I calculate the …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Scientific Breakdown Of A Ferromagnetic Nanofluid In Hemodynamics: Enhanced Therapeutic Approach, M. M. Bhatti, Sara Abdelsalam

Basic Science Engineering

In this article, we examine the mechanism of cobalt and tantalum nanoparticles through a hybrid fluid model. The nanofluid is propagating through an anisotropically tapered artery with three different configurations; converging, diverging and non-tapered. To examine the rheology of the blood we have incorporated a Williamson fluid model which reveals both Newtonian and non-Newtonian effects. Mathematical and physical formulations are derived using the Lubrication approach for continuity, momentum and energy equations. The impact of magnetic field, porosity and viscous dissipation are also taken into the proposed formulation. A perturbation approach is used to determine the solutions of the formulated nonlinear …

On Behavioral Response Of Ciliated Cervical Canal On The Development Of Electroosmotic Forces In Spermatic Fluid, Sara I. Abdelsalam, A. Z. Zaher

Basic Science Engineering

The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to selfpropulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure …

Computational Framework Of Magnetized Mgo–Ni/Water-Based Stagnation Nanoflow Past An Elastic Stretching Surface: Application In Solar Energy Coatings, M, M. Bhatti, O. A. Bég, Sara Abdelsalam

Basic Science Engineering

In this article, motivated by novel nanofluid solar energy coating systems, a mathematical model of hybrid magnesium oxide (MgO) and nickel (Ni) nanofluid magnetohydrodynamic (MHD) stagnation point flow impinging on a porous elastic stretching surface in a porous medium is developed. The hybrid nanofluid is electrically conducted, and a magnetic Reynolds number is sufficiently large enough to invoke an induced magnetic field. A Darcy model is adopted for the isotropic, homogenous porous medium. The boundary conditions account for the impacts of the velocity slip and thermal slip. Heat generation (source)/absorption (sink) and also viscous dissipation effects are included. The mathematical …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Eeg Signals Classification Using Lstm-Based Models And Majority Logic, James A. Orgeron

College of Graduate Studies: Theses & Dissertations

The study of elecroencephalograms (EEGs) has gained enormous interest in the last decade with the increase of computational power and availability of EEG signals collected from various human activities or produced during medical tests. The applicability of analyzing EEG signals ranges from helping impaired people communicate or move (using appropriate medical equipment) to understanding people's feelings and detecting diseases.

We proposed new methodology and models for analyzing and classifying EEG signals collected from individuals observing visual stimuli. Our models rely on powerful Long-Short Term Memory (LSTM) Neural Network models, which are currently the state of the art models for performing …

Variational Data Assimilation For Two Interface Problems, Xuejian Li

Doctoral Dissertations

“Variational data assimilation (VDA) is a process that uses optimization techniques to determine an initial condition of a dynamical system such that its evolution best fits the observed data. In this dissertation, we develop and analyze the variational data assimilation method with finite element discretization for two interface problems, including the Parabolic Interface equation and the Stokes-Darcy equation with the Beavers-Joseph interface condition. By using Tikhonov regularization and formulating the VDA into an optimization problem, we establish the existence, uniqueness and stability of the optimal solution for each concerned case. Based on weak formulations of the Parabolic Interface equation and …

Data-Driven Modeling And Simulations Of Seismic Waves, Yixuan Wu

Doctoral Dissertations

"In recent decades, nonlocal models have been proved to be very effective in the study of complex processes and multiscale phenomena arising in many fields, such as quantum mechanics, geophysics, and cardiac electrophysiology. The fractional Laplacian(−Δ)^��/2 can be reviewed as nonlocal generalization of the classical Laplacian which has been widely used for the description of memory and hereditary properties of various material and process. However, the nonlocality property of fractional Laplacian introduces challenges in mathematical analysis and computation. Compared to the classical Laplacian, existing numerical methods for the fractional Laplacian still remain limited. The objectives of this research are …

Several Problems In Nonlinear Schrödinger Equations, Tim Van Hoose

Masters Theses

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.

Continuous And Discrete Models For Optimal Harvesting In Fisheries, Nagham Abbas Al Qubbanchee

Masters Theses

"This work focuses on the logistic growth model, where the Gordon-Schaefer model is considered in continuous time. We view the Gordon-Schaefer model as a bioeconomic equation involved in the fishing business, considering biological rates, carrying capacity, and total marginal costs and revenues. In [25], the authors illustrate the analytical solution of the Schaefer model using the integration by parts method and two theorems. The theorems have many assumptions with many different strategies. Due to the nature of the problem, the optimal control system involves many equations and functions, such as the second root of the equation. We concentrate on Theorem …

Horizontal Air Mass: Solutions For Fermi Questions, November 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Camouflaged Poisoning Attack On Graph Neural Networks, Chao Jiang, Yi He, Richard Chapman, Hongyi Wu

Computer Science Faculty Publications

Graph neural networks (GNNs) have enabled the automation of many web applications that entail node classification on graphs, such as scam detection in social media and event prediction in service networks. Nevertheless, recent studies revealed that the GNNs are vulnerable to adversarial attacks, where feeding GNNs with poisoned data at training time can lead them to yield catastrophically devastative test accuracy. This finding heats up the frontier of attacks and defenses against GNNs. However, the prior studies mainly posit that the adversaries can enjoy free access to manipulate the original graph, while obtaining such access could be too costly in …