Numerical Analysis and Computation Commons^™

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …

A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams, Md Rafi As Sadeq Ibn Emran

Masters Theses & Specialist Projects

The one-dimensional Partial Differential Equation (PDE) model of the wave equation, which describes wave dynamics of a wide-range of controlled mechanical systems, with a state feedback controller at its boundary is known to have exponentially stable solutions. Moreover, it is also reported that the several model reductions of the wave equation by the standard Finite Differences and Finite Elements approximations suffer from the lack of exponential stability (and exact observability without a state feedback controller) uniformly as the discretization parameter tends to zero. This is due to the loss of a uniform gap among the high-frequency eigenvalues as the discretization …

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Departmental Research

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla

Physics Theses & Dissertations

This experiment investigates the deep virtual production of both σ− and ρ− mesons, with a particular focus on the microscopic structure of the σ mesons. While the ρ meson is an ordinary qq¯ pair, the σ meson is composed of not only the typical qq¯ pair, making it a topic of controversy for nearly six decades. Although the existence of the σ− meson is now well established, its microscopic structure remains poorly understood. The primary objective of this thesis is to contribute to the understanding of the σ meson by analyzing its deep virtual production. The main focus of this …

Flow Dynamics In Cardiovascular Devices: A Comprehensive Review, Venant Niyonkuru, Bosco Jean Ndayishimiye Dr, Anicet Barthélemy Sibomana

Digital Journal of Clinical Medicine

This review explores flow dynamics in cardiovascular devices, focusing on fundamental fluid mechanics principles and normal blood flow patterns. It discusses the role of different structures in maintaining flow dynamics and the importance of stents, heart valves, artificial hearts, and ventricular assist devices in cardiovascular interventions. The review emphasizes the need for optimized designs and further research to enhance knowledge of flow dynamics in cardiovascular devices, advancing the field and improving patient care in cardiovascular interventions.

Mathematics Behind Machine Learning, Rim Hammoud

Electronic Theses, Projects, and Dissertations

Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …

Null Space Removal In Finite Element Discretizations, Pengfei Jia

All Theses

Partial differential equations are frequently utilized in the mathematical formulation of physical problems. Boundary conditions need to be applied in order to obtain the unique solution to such problems. However, some types of boundary conditions do not lead to unique solutions because the continuous problem has a null space. In this thesis, we will discuss how to solve such problems effectively. We first review the foundation of all three problems and prove that Laplace problem, linear elasticity problem and Stokes problem can be well posed if we restrict the test and trial space in the continuous and discrete finite element …

She Is An Expert In This Research Field: The Signal Of Recent Publications' Relevance, Gil Zeevi, Osnat Mokryn

Northeast Journal of Complex Systems (NEJCS)

Assessing the expertise of researchers has garnered increased interest recently. This heightened focus arises from the growing emphasis on interdisciplinary science and the subsequent need to form expert teams. When forming these teams, the coordinators need to assess expertise in fields that are often very different from theirs. The conventional reliance on signals of success, prestige, and academic impact can unintentionally perpetuate biases within the assessment process. This traditional approach favors senior researchers and those affiliated with prestigious institutions, potentially overlooking talented individuals from underrepresented backgrounds or institutions. This paper addresses the challenge of determining expertise by proposing a methodology …

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofsky, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Assessment On Usage Of The Library Website Resources By Students In The Information Studies Programme At The University Of Dar Es Salaam, Hosea N. Mungwabi

Tanzania Journal of Engineering and Technology (TJET)

The study investigated students' usage of electronic resources available on the UDSM Library's website. Specifically, the study determined whether information studies students were aware of the electronic resources, how frequently they used them, and whether their demographic characteristics influenced their usage. The study also examined the students' satisfaction with the functional and non functional attributes of the website resources. A mixed-methods research design combining both qualitative and quantitative data collection methods was used. The sample consisted of 118 student respondents who were selected using a stratified random sampling technique. The data were collected through questionnaires and interviews with class representatives …

Deep Learning Model Compression Techniques: Advances, Opportunities, And Perspective, Hubert Msuya

Tanzania Journal of Engineering and Technology (TJET)

Recently, deep learning (DL) models have excelled in a wide range of fields. All of these successes are built on intricate DL models. The hundreds of millions or even billions of parameters and high-performance computing graphical processing units or tensor processing units are largely responsible for their achievement. DL model integration into real-time devices with tight latency limitations, limited memory, and power-constrained requirements is the key driving force behind investigation of DL model compression techniques. Also, there is an increase in data availability that encourages multimodal fusion in DL models to boost the models' predictive accuracy. In order to create …

Performance Evaluation Of Full Array, Sub-Array And Overlapped Sub-Array Hybrid Beamforming Architectures For Massive Mimo Systems, Godwin Mruma Gadiel

Tanzania Journal of Engineering and Technology (TJET)

The technological advancement in wireless communication, promises high data rate for end users. This has led to the possibility of smart cities, inter connected vehicles, and virtual reality applications. One of the recent technologies in wireless communication is massive MIMO where large number of antennas are deployed at the transmitter or receiver. This is possible due to the use of mmWave in wireless communication. With massive MIMO, beamforming technique can be employed in the communication system. Beamforming is the ability of communication system to direct power to the intended users and to cancel power at non-intended users and thus significantly …

Said-Ball Polynomials For Solving Linear Systems Of Ordinary Differential Equations, Mubark Al-Subaai Dr., Ahmes Saleh Kherd

Emirates Journal for Engineering Research

Said-Ball polynomials with collocation method are used to numerically solve a system of linear ordinary differential equations. The matrix forms of Said-Ball polynomials of the solution, derivatives, and conditions are done. The linear system of ordinary differential equations with appropriate conditions is reduced to the linear algebraic equations system with unknown Said-Ball coefficients. Solving the resulting system determines the coefficients of Said-Ball polynomials. By Substituting these values in the polynomial, we get the problem's exact and approximate solutions. The obtaining numerical results show the proposed method's accuracy and reliability when compared with the other works and exact solutions

Temporality-Induced Chaos In The Kuramoto Model, Keanu Mason Rock, Hamza Dirie, Sean P. Cornelius

Northeast Journal of Complex Systems (NEJCS)

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in …

Extending The Spectral Difference Method With Divergence Cleaning (Sddc) To The Hall Mhd Equations, Russell J. Hankey, Kuangxu Chen, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is …

Using Medicare Claims To Estimate Risk-Adjusted Performance Of Pennsylvania Trauma Centers, Alexis M Zebrowski, Phillipe Loher, David G Buckler, Isidore Rigoutsos, Brendan G Carr, Douglas J Wiebe

Computational Medicine Center Faculty Papers

Trauma centers use registry data to benchmark performance using a standardized risk adjustment model. Our objective was to utilize national claims to develop a risk adjustment model applicable across all hospitals, regardless of designation or registry participation. Patients from 2013-14 Pennsylvania Trauma Outcomes Study (PTOS) registry data were probabilistically matched to Medicare claims using demographic and injury characteristics. Pairwise comparisons established facility linkages and matching was then repeated within facilities to link records. Registry models were estimated using GLM and compared with five claims-based LASSO models: demographics, clinical characteristics, diagnosis codes, procedures codes, and combined demographics/clinical characteristics. Area under the …

(R1951) Numerical Solution For A Class Of Nonlinear Emden-Fowler Equations By Exponential Collocation Method, Mohammad Aslefallah, Saeid Abbasbandy, Şuayip Yüzbaşi

Applications and Applied Mathematics: An International Journal (AAM)

In this research, exponential approximation is used to solve a class of nonlinear Emden-Fowler equations. This method is based on the matrix forms of exponential functions and their derivatives using collocation points. To demonstrate the usefulness of the method, we apply it to some different problems. The numerical approximate solutions are compared with available (existing) exact (analytical) solutions to show the accuracy of the proposed method. The method has been checked with several examples to show its validity and reliability. The reported examples illustrate that the method is reasonably efficient and accurate.

(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

Distributed Control Of Servicing Satellite Fleet Using Horizon Simulation Framework, Scott Plantenga

Master's Theses

On-orbit satellite servicing is critical to maximizing space utilization and sustainability and is of growing interest for commercial, civil, and defense applications. Reliance on astronauts or anchored robotic arms for the servicing of next-generation large, complex space structures operating beyond Low Earth Orbit is impractical. Substantial literature has investigated the mission design and analysis of robotic servicing missions that utilize a single servicing satellite to approach and service a single target satellite. This motivates the present research to investigate a fleet of servicing satellites performing several operations for a large, central space structure.

This research leverages a distributed control approach, …

Domain Decomposition Methods For Linear And Non-Linear Elliptic Problems, Tadanaga Takahashi

Dissertations

The primary purpose of this dissertation is to expand upon the circle of domain decomposition methods (DDM) which are algorithms that reformulate a boundary value problem in terms of multiple localized problems on subdomains. The first project involves expanding upon DDMs in a relatively mature field: the Helmholtz equation for wave scattering applications. The proposed method is an adaptation of a continuous cross-point Finite Element Non-overlapping DDM algorithm. The usual unbounded computational domain is truncated and then the near-field wave pattern is solved with a parallelized finite element method. Several improvements over the standard transmission operator are discussed in this …

Covid-19 In Casinos: Analysis Of Covid-19 Contamination And Spread With Economic Impact Assessment, Anastasia (Stasi) D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Abstract:

The COVID-19 pandemic caused tremendous disruption for casinos, with the virus causing various lengths of shutdowns, capacity restrictions, and social distancing strategies such as machine removals or section closures. Although most of the world has now eased off these measures, it is important to review lessons learned to understand, and better prepare for similar circumstances in the future. We present Monte Carlo slot floor simulation software customized to simulate players spreading COVID-19 on the slot floor. We simulate the amount of touch surface contamination; the number of potential surface contact exposure events per day, and a proximity exposures statistic …

Stochastic Gradient Descent Method For A Parameter Identification Problem In Elasticity Imaging, Basca Jadamba

Biology and Medicine Through Mathematics Conference

No abstract provided.

Variational And Adaptive Non-Local Image Denoising Using Edge Detection And K − Means Clustering, Shiraz Mujahid

Theses and Dissertations

With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of …

Spectral Multistep Methods For The Scalable Simulation Of Time-Dependent Phenomena, Bailey Rester

Dissertations

Krylov subspace spectral (KSS) methods are high-order accurate, one-step explicit time-stepping methods for partial differential equations (PDEs) that also possess stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE, using techniques developed by Golub and Meurant for approximating bilinear forms involving matrix functions. As a result, KSS methods scale effectively to higher spatial resolution.

This dissertation will present spectral multistep methods, explicit and implicit, designed through the combination of KSS methods and Adams methods. This combination allows spectral multistep methods …

Brief Review: Low Frequency Event Charts (G-Charts) In Healthcare, James Espinosa, David Ho, Alan Lucerna, Henry Schuitema

Rowan-Virtua Research Day

The ability to determine if a change in a system is actually an improvement—or worsening in function—is one of the essential desiderata of quality improvement efforts. There are many ways to look at the issue. A special problem occurs when the event being studied is low frequency by nature. By way of example, patient falls in a given hospital or division of a hospital may occur in a way that is low frequency—yet each event is important. Process engineering has developed an approach to low frequency events. Part of this approach may involve specialized charts that look at the “time-between-events”—as …

Advancements In Fluid Simulation Through Enhanced Conservation Schemes, Sean Ingimarson

All Dissertations

To better understand and solve problems involving the natural phenomenon of fluid and air flows, one must understand the Navier-Stokes equations. Branching several different fields including engineering, chemistry, physics, etc., these are among the most important equations in mathematics. However, these equations do not have analytic solutions save for trivial solutions. Hence researchers have striven to make advancements in varieties of numerical models and simulations. With many variations of numerical models of the Navier-Stokes equations, many lose important physical meaningfulness. In particular, many finite element schemes do not conserve energy, momentum, or angular momentum. In this thesis, we will study …

Modeling, Simulation And Control Of Microrobots For The Microfactory., Zhong Yang

Electronic Theses and Dissertations

Future assembly technologies will involve higher levels of automation in order to satisfy increased microscale or nanoscale precision requirements. Traditionally, assembly using a top-down robotic approach has been well-studied and applied to the microelectronics and MEMS industries, but less so in nanotechnology. With the boom of nanotechnology since the 1990s, newly designed products with new materials, coatings, and nanoparticles are gradually entering everyone’s lives, while the industry has grown into a billion-dollar volume worldwide. Traditionally, nanotechnology products are assembled using bottom-up methods, such as self-assembly, rather than top-down robotic assembly. This is due to considerations of volume handling of large …

Mathematical Modeling Of Egain Droplets Sliding Down An Inclined Plane, Shawn Koohy, Kathryn Massey, Luis Schneegans, Megan Vezzetti, Keith Hillaire, Souradip Chattopadhyay, Jessie Chen, Carmen Lee, Karen Daniels

Undergraduate Research Symposium

Eutectic Gallium-Indium (EGaIn) is a room-temperature liquid metal alloy that dramatically changes its surface tension and dynamics under an applied electric field. EGaIn has been used heavily in soft electronics engineering due to its high conductivity, malleability, and safety. However, the absence of mathematical modeling in the current literature makes its behavior difficult to understand and predict. In this study, we present a one-dimensional lubrication model for the dynamics of an EGaIn droplet moving along an inclined plane. Our model incorporates essential physical effects and parameters including oxidation, capillary action, diffusion, gravity, and Marangoni effects. In particular, we incorporate effects …