Constructible Sandwich Cut, 2024 FIU Department of Mathematics

#### Constructible Sandwich Cut, Philip A. Son

*FIU Undergraduate Research Journal*

In mathematical measure theory, the “Ham-Sandwich” theorem states that any n objects in an n-dimensional Euclidean space can be simultaneously divided in half with a single cut by an (n-1)-dimensional hyperplane. While it guarantees its existence, the theorem does not provide a way of finding this halving hyperplane, as it is only an existence result. In this paper, we look at the problem in dimension 2, more in the style of Euclid and the antique Greeks, that is from a constructible point of view, with straight edge and compass. For two arbitrary regions in the plane, there is certainly no …

Identifying Transitions In Plasma With Topological Data Analysis Of Noisy Turbulence, 2024 William & Mary

#### Identifying Transitions In Plasma With Topological Data Analysis Of Noisy Turbulence, Julius Kiewel

*Undergraduate Honors Theses*

Cross-field transport and heat loss in a magnetically confined plasma is determined by turbulence driven by perpendicular (to the magnetic field) pressure gradients. The heat losses from turbulence can make it difficult to maintain the energy density required to reach and maintain the conditions necessary for fusion. Self-organization of turbulence into intermediate scale so-called zonal flows can reduce the radial heat losses, however identifying when the transition occurs and any precursors to the transition is still a challenge. Topological Data Analysis (TDA) is a mathematical method which is used to extract topological features from point cloud and digital data to …

Models Of Functional Redundancy In Ecological Communities, 2024 Clemson University

#### Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa

*All Dissertations*

Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, 2024 East Tennessee State University

#### Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

*Electronic Theses and Dissertations*

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

Rsa Algorithm, 2024 Arkansas Tech University

#### Rsa Algorithm, Evalisbeth Garcia Diazbarriga

*ATU Research Symposium*

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

A Cohomological Perspective To Nonlocal Operators, 2024 University of Nebraska - Lincoln

#### A Cohomological Perspective To Nonlocal Operators, Nicholas White

*Honors Theses*

Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …

Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, 2024 Purdue University

#### Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, Kaeul Lim, Arezoo Ardekani

*Graduate Industrial Research Symposium*

Hyperspectral imaging (HSI) is a promising modality in medicine with many potential applications. This study focuses on developing a label-free lipid nanoparticle characterization method using a convolutional neural network (CNN) analysis of HSI images. The HSI data, hypercube, consists of a series of images acquired at different wavelengths for the same field of view, providing continuous spectra information for each pixel. Three distinct liposome samples were collected for analysis. Advanced image preprocessing and classification methods for HSI data were developed to differentiate liposomes based on their material compositions. Our machine learning-based classification method was able to distinguish different liposome types …

Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, 2024 Bucknell University

#### Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, Lucas Waddell, Warren Adams

*Faculty Journal Articles*

The quadratic assignment problem (QAP) is an extremely challenging NP-hard combinatorial optimization program. Due to its difficulty, a research emphasis has been to identify special cases that are polynomially solvable. Included within this emphasis are instances which are *linearizable*; that is, which can be rewritten as a linear assignment problem having the property that the objective function value is preserved at all feasible solutions. Various known sufficient conditions for identifying linearizable instances have been explained in terms of the continuous relaxation of a weakened version of the level-1 reformulation-linearization-technique (RLT) form that does not enforce nonnegativity on a subset …

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, 2024 Purdue University Fort Wayne

#### Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

*The Journal of Purdue Undergraduate Research*

No abstract provided.

Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, 2024 Illinois State University

#### Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

*Spora: A Journal of Biomathematics*

Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.

Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, 2024 Bowdoin College

#### Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma

*Honors Projects*

Particle swarm optimization (PSO) is a metaheuristic optimization method that finds near- optima by spawning particles which explore within a given search space while exploiting the best candidate solutions of the swarm. PSO algorithms emulate the behavior of, say, a flock of birds or a school of fish, and encapsulate the randomness that is present in natural processes. In this paper, we discuss different initialization schemes and meta-optimizations for PSO, its performances on various multi-minima functions, and the unique intricacies and obstacles that the method faces when attempting to produce images for basins of attraction, which are the sets of …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, 2024 Department of mathematics and engineering physics, faculty of engineering, Mansoura University, Mansoura, Egypt

#### A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

*Mansoura Engineering Journal*

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Penalized Interpolating B-Splines And Their Applications, 2024 Virginia Commonwealth University

#### 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 …

The Precedence-Constrained Quadratic Knapsack Problem, 2024 Bucknell University

#### 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.

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, 2024 Georgia Southern University

#### 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 …

Bringing Gans To Medieval Times: Manuscript Translation Models, 2024 Georgia Southern University

#### 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 …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, 2024 Georgia Southern University

#### 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 …

Reducing Food Scarcity: The Benefits Of Urban Farming, 2023 Brigham Young University

#### 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, 2023 Western University

#### 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, 2023 University of Maine

#### 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.