Physical Sciences and Mathematics Commons^™

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 …

A Simple Algorithm For Generating A New Two Sample Type-Ii Progressive Censoring With Applications, E. M. Shokr, Rashad Mohamed El-Sagheer, Mahmoud Mansour, H. M. Faied, B. S. El-Desouky

Basic Science Engineering

In this article, we introduce a simple algorithm to generating a new type-II progressive censoring scheme for two samples. It is observed that the proposed algorithm can be applied for any continues probability distribution. Moreover, the description model and necessary assumptions are discussed. In addition, the steps of simple generation algorithm along with programming steps are also constructed on real example. The inference of two Weibull Frechet populations are discussed under the proposed algorithm. Both classical and Bayesian inferential approaches of the distribution parameters are discussed. Furthermore, approximate confidence intervals are constructed based on the asymptotic distribution of the maximum …

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

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 …

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

Electronic Theses and 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

Electronic Theses and 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 …

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)^𝛼/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 …

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

Representation Theory And Its Applications In Physics, Jakub Bystrický

Honors Theses

Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …

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 …

Containing Compounding Container Congestion, Curtis Salinger

CMC Senior Theses

The Covid-19 pandemic caused major disruptions throughout the container shipping supply chain. Professor Dongping Song of Liverpool University wrote a paper discussing the logistical vulnerabilities in the supply chain, including the issue of congestion in ports. This paper examines the Port of Los Angeles from 2018-2021 as it relates to Song’s paper to see how its operations were impacted during the Covid-19 timeframe. It is found that labor shortages, chassis shortages, and change in trade behavior each contributed to the congestion. Unfortunately, the implemented policies were insufficient to bolster the port against sustained challenges and congestion continues to worsen.

Dynamic Nonlinear Gaussian Model For Inferring A Graph Structure On Time Series, Abhinuv Uppal

CMC Senior Theses

In many applications of graph analytics, the optimal graph construction is not always straightforward. I propose a novel algorithm to dynamically infer a graph structure on multiple time series by first imposing a state evolution equation on the graph and deriving the necessary equations to convert it into a maximum likelihood optimization problem. The state evolution equation guarantees that edge weights contain predictive power by construction. After running experiments on simulated data, it appears the required optimization is likely non-convex and does not generally produce results significantly better than randomly tweaking parameters, so it is not feasible to use in …

What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.

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 …

Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King

Honors Projects

This project is an analysis of the effectiveness of five distinct optimization methods in their ability in producing clear images of the basins of attraction, which is the set of initial points that approach the same minimum for a given function. Basin images are similar to contour plots, except that they depict the distinct regions of points--in unique colors--that approach the same minimum. Though distinct in goal, contour plots are useful to basin research in that idealized basin images can be inferred from the steepness levels and location of extrema they depict. Effectiveness of the method changes slightly depending on …

Testing The Efficiency Of The Nfl Betting Market, Ryan Earl Oswald

Honors Program Theses

This paper seeks to investigate the NFL betting market, using statistical and economic tests to challenge the Efficient Market Hypothesis’ claim that it is efficient and no strategy can be expected to make a profit. Specifically, this paper studies the spread, over-under, and money line markets to see if each is efficient on their own and as a collective. In looking to see how these lines can influence the outcomes of each other, this paper finds a number of strategies that were profitable over the timeframe of the data. This shows that the NFL betting market was not completely efficient …

Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier

Theses and Dissertations--Mathematics

We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

Determining Power System Fault Location Using Neural Network Approach, Edward O. Ojini

Theses and Dissertations--Electrical and Computer Engineering

Fault location remains an extremely pivotal feature of the electric power grid as it ensures efficient operation of the grid and prevents large downtimes during fault occurrences. This will ultimately enhance and increase the reliability of the system. Since the invention of the electric grid, many approaches to fault location have been studied and documented. These approaches are still effective and are implemented in present times, and as the power grid becomes even more broadened with new forms of energy generation, transmission, and distribution technologies, continued study on these methods is necessary. This thesis will focus on adopting the artificial …

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 …

Correlation Does Not Imply Correlation: A Thesis On Causal Influence And Simpson’S Paradox, Emily Naitoh

Scripps Senior Theses

In our data-driven world, it has become commonplace to attempt to find
causal relationships. One of the themes of this thesis is to show methods of
determining causation. The second theme follows a saying in mathematics,
"correlation does not imply causation". We will also discuss situations where
correlation does not even imply correlation itself. These cases are described
by Simpson’s paradox in an exploration of different areas of mathematics
and computer coding.

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 …

Colonial Markets, Consumers, And Trade: A Comparative Analysis Of Historic Ceramics From The Bluefields Bay Area, Westmoreland, Jamaica, Lacy Risner

Murray State Theses and Dissertations

The ceramic assemblages from a British colonial settlement in Bluefields Bay, Jamaica, provide a unique window into the market availability, exchange routes, and consumption patterns of the eighteenth century. This study compares the historic ceramics collected from two sites in Bluefields Bay to one another and to other intra-island (Jamaica), intraregional (Lesser Antilles), and international (North America) colonial and postcolonial sites to reveal patterns of individual and global ceramic consumption and distribution in the emergent capitalist networks and markets of the colonial era. Integrating small British colonial sites into the networks of other more extensive studies focusing primarily on plantations …

Online Algorithms With Advice For The 𝒌-Search Problem, Jhoirene B. Clemente, Henry N. Adorna, Proceso L. Fernandez Jr

Department of Information Systems & Computer Science Faculty Publications

In the online search problem, a seller seeks to find the maximum price from a sequence of prices p1, p2,…, pn that is revealed in a piece-wise manner. The bound for all prices is well known in advance with m ≤ pί ≤ M. In the online k-search problem, the seller seeks to find the k maximum out of the n prices. In this paper, we present a tight bound of [Formula Presented] on the advice complexity of optimal online algorithms for online k-search. We also provide online algorithms with advice that use less than the required number of bits …

Efficient Numerical Optimization For Parallel Dynamic Optimal Power Flow Simulation Using Network Geometry, Rylee Sundermann

Electronic Theses and Dissertations

In this work, we present a parallel method for accelerating the multi-period dynamic optimal power flow (DOPF). Our approach involves a distributed-memory parallelization of DOPF time-steps, use of a newly developed parallel primal-dual interior point method, and an iterative Krylov subspace linear solver with a block-Jacobi preconditioning scheme. The parallel primal-dual interior point method has been implemented and distributed in the open-source PETSc library and is currently available. We present the formulation of the DOPF problem, the developed primal dual interior point method solver, the parallel implementation, and results on various multi-core machines. We demonstrate the effectiveness our proposed block-Jacobi …

Smoothed Bounded-Confidence Opinion Dynamics On The Complete Graph, Solomon Valore-Caplan

HMC Senior Theses

We present and analyze a model for how opinions might spread throughout a network of people sharing information. Our model is called the smoothed bounded-confidence model and is inspired by the bounded-confidence model of opinion dynamics proposed by Hegselmann and Krause. In the Hegselmann–Krause model, agents move towards the average opinion of their neighbors. However, an agent only factors a neighbor into the average if their opinions are sufficiently similar. In our model, we replace this binary threshold with a logarithmic weighting function that rewards neighbors with similar opinions and minimizes the effect of dissimilar ones. This weighting function can …

Check Yourself Before You Wrek Yourself: Unpacking And Generalizing Randomized Extended Kaczmarz, William Gilroy

HMC Senior Theses

Linear systems are fundamental in many areas of science and engineering. With the advent of computers there now exist extremely large linear systems that we are interested in. Such linear systems lend themselves to iterative methods. One such method is the family of algorithms called Randomized Kaczmarz methods.
Among this family, there exists a Randomized Kaczmarz variant called Randomized
Extended Kaczmarz which solves for least squares solutions in inconsistent linear systems.
Among Kaczmarz variants, Randomized Extended Kaczmarz is unique in that it modifies input system in a special way to solve for the least squares solution. In this work we …

An Adaptive Hegselmann–Krause Model Of Opinion Dynamics, Phousawanh Peaungvongpakdy

HMC Senior Theses

Models of opinion dynamics have been used to understand how the spread
of information in a population evolves, such as the classical Hegselmann–
Krause model (Hegselmann and Krause, 2002). One extension of the model
has been used to study the impact of media ideology on social media
networks (Brooks and Porter, 2020). In this thesis, we explore various
models of opinions and propose our own model, which is an adaptive
version of the Hegselmann–Krause model. The adaptive version implements
the social phenomenon of homophily—the tendency for like-minded agents to
associate together. This is done by having agents dissolve connections …

An Exploration Of Voting With Partial Orders, Mason Acevedo

HMC Senior Theses

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher

Theses and Dissertations--Mathematics

Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where in silico models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually in silico models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …