Physical Sciences and Mathematics Commons^™

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Reducing Generalization Error In Multiclass Classification Through Factorized Cross Entropy Loss, Oleksandr Horban

CMC Senior Theses

This paper introduces Factorized Cross Entropy Loss, a novel approach to multiclass classification which modifies the standard cross entropy loss by decomposing its weight matrix W into two smaller matrices, U and V, where UV is a low rank approximation of W. Factorized Cross Entropy Loss reduces generalization error from the conventional O( sqrt(k / n) ) to O( sqrt(r / n) ), where k is the number of classes, n is the sample size, and r is the reduced inner dimension of U and V.

Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares

CMC Senior Theses

Shor's Algorithm is an extremely powerful tool, in utilizing this tool it is important to understand how it works and why it works. As well as the vast implications it could have for cryptography

A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, Andrew Calvin Janes

Masters Theses

"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and …

Data Driven And Machine Learning Based Modeling And Predictive Control Of Combustion At Reactivity Controlled Compression Ignition Engines, Behrouz Khoshbakht Irdmousa

Dissertations, Master's Theses and Master's Reports

Reactivity Controlled Compression Ignition (RCCI) engines operates has capacity to provide higher thermal efficiency, lower particular matter (PM), and lower oxides of nitrogen (NOx) emissions compared to conventional diesel combustion (CDC) operation. Achieving these benefits is difficult since real-time optimal control of RCCI engines is challenging during transient operation. To overcome these challenges, data-driven machine learning based control-oriented models are developed in this study. These models are developed based on Linear Parameter-Varying (LPV) modeling approach and input-output based Kernelized Canonical Correlation Analysis (KCCA) approach. The developed dynamic models are used to predict combustion timing (CA50), indicated mean effective pressure (IMEP), …

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …

Robot-Based 3d Printing, Aaron Hoffman

Williams Honors College, Honors Research Projects

Details of a large-format 3D printer created to print experimental materials, test multi-axis print techniques, and quickly print large objects. The printer consists of a 7-axis robotic arm and pellet extruder, which are controlled by a PC. Experimental materials such as recycled polymers or carbon-fiber reinforced materials can be easily tested with the pellet format of the extruder. The printer can perform different printing techniques and can be used to experiment with material properties when using these techniques with different polymers. The print surface is around 5 times larger than the average commercial 3D printer, and the robotic arm provides …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper

Chemistry & Biochemistry Faculty Publications

Surface-enhanced Raman spectroscopy (SERS) is an ultrasensitive spectroscopic technique that generates signal-enhanced fingerprint vibrational spectra of small molecules. However, without rigorous control of SERS substrate active sites, geometry, surface area, or surface functionality, SERS is notoriously irreproducible, complicating the consistent quantitative analysis of small molecules. While evaporatively prepared samples yield significant SERS enhancement resulting in lower detection limits, the distribution of these enhancements along the SERS surface is inherently stochastic. Acquiring spatially resolved SERS spectra of these dried surfaces, we have shown that this enhancement is governed by a power law as a function of analyte concentration. Consequently, by definition, …

Uniform Regularity Estimates For The Stokes System In Perforated Domains, Jamison R. Wallace

Theses and Dissertations--Mathematics

We consider the Stokes equations in an unbounded domain $\omega_{\epsilon,\eta}$ perforated by small obstacles, where $\epsilon$ represents the minimal distance between obstacles and $\eta$ is the ratio between the obstacle size and $\epsilon$. We are able to obtain uniform $W^{1,q}$ estimates for solutions to the Stokes equations in such domains with bounding constants depending explicitly on $\epsilon$ and $\eta$.

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

Theses and Dissertations

We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that …

Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

Theses and Dissertations

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

Electronic Theses and Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

Electronic Theses and Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

Electronic Theses and Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

In this work, based on the theory of barycentric coordinates and simplexes, a linear interpolation method is proposed for modeling and controlling the operation of multiparameter converters. It has been determined that the linear interpolation method minimizes the structural diagram of a computing device, which makes it possible to more accurately determine the metrological characteristics of multiparameter measuring transducers and offer effective methods and means for processing primary measurement information. A theorem has been proven about a linear interpolating polynomial of a function of many variables, which will allow us to judge the property of linearization of multidimensional quantities from …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Adaptation Reshapes The Distribution Of Fitness Effects, Diego Tenoch Morales Lopez

Electronic Thesis and Dissertation Repository

The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these …

Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin

Electronic Theses and Dissertations

This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.

Population Dynamics And Bifurcations In Predator-Prey Systems With Allee Effect, Yanni Zeng

Electronic Thesis and Dissertation Repository

This thesis investigates a series of nonlinear predator-prey systems incorporating the Allee effect using differential equations. The main goal is to determine how the Allee effect affects population dynamics. The stability and bifurcations of the systems are studied with a hierarchical parametric analysis, providing insights into the behavioral changes of the population within the systems. In particular, we focus on the study of the number and distribution of limit cycles (oscillating solutions) and the existence of multiple stable states, which cause complex dynamical behaviors. Moreover, including the prey refuge, we examine how our method benefits the low-density animals and affects …

Tikaram And Chandrakala Dhananjaya: A Collaborative Couple In Mathematics From Nepal, Deepak Basyal, Brigitte Stenhouse

Mathematics and Statistics

Within the history of mathematics and mathematics education in Nepal, Tikaram and Chandrakala Dhananjaya are relatively well-known figures for their two books Śiśubodha Taraṅgiṇī and Līlāvatī. This is despite there being almost no archival or manuscript materials offering a window into their lives: we have no letters, notebooks, diaries, or school records. Rather than focusing on either individual in isolation, in this article we present an argument for considering the Dhananjayas as an analytically indivisible collaborative couple in mathematics. Of the two aforementioned books, one is attributed to Chandrakala and the other to Tikaram; but in fact, both are translations …

High-Performance Computing In Covariant Loop Quantum Gravity, Pietropaolo Frisoni

Electronic Thesis and Dissertation Repository

This Ph.D. thesis presents a compilation of the scientific papers I published over the last three years during my Ph.D. in loop quantum gravity (LQG). First, we comprehensively introduce spinfoam calculations with a practical pedagogical paper. We highlight LQG's unique features and mathematical formalism and emphasize the computational complexities associated with its calculations. The subsequent articles delve into specific aspects of employing high-performance computing (HPC) in LQG research. We discuss the results obtained by applying numerical methods to studying spinfoams' infrared divergences, or ``bubbles''. This research direction is crucial to define the continuum limit of LQG properly. We investigate the …

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

(R2066) New Results Of Ulam Stabilities Of Functional Differential Equations Of First Order Including Multiple Retardations, Merve Şengün, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we pay attention to a functional differential equation (FDE) of first order including N-variable delays. We construct new sufficient conditions in relation to the Hyers-Ulam stability (HUS) and the generalized Hyers-Ulam-Rassias stability (GHURS ) of the FDE of first order including N-variable delays. By using Banach contraction principle (BCP), Picard operator and Gronwall lemma, we confirm two new theorems in relation to the HUS and the GHURS. The results of this study are new and extend, improve some earlier results of the HUS and the GHURS.

(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the convergence of solutions of certain nonlinear system of two differential equations using a suitable Lyapunov functional with sufficient conditions to establish our new result. An example is given to demonstrate the effectiveness of the result obtained and geometric argument to show that the solutions of the system are better rapidly converging under the criteria obtained.

Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, Nhu Thuat Tran, Hady W. Lauw

Research Collection School Of Computing and Information Systems

This article introduces a novel architecture for two objectives recommendation and interpretability in a unified model. We leverage textual content as a source of interpretability in content-aware recommender systems. The goal is to characterize user preferences with a set of human-understandable attributes, each is described by a single word, enabling comprehension of user interests behind item adoptions. This is achieved via a dedicated architecture, which is interpretable by design, involving two components for recommendation and interpretation. In particular, we seek an interpreter, which accepts holistic user’s representation from a recommender to output a set of activated attributes describing user preferences. …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

Electronic Theses and Dissertations

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …