Dna Self-Assembly Of Trapezohedral Graphs,
2023
California State University - San Bernardino
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Electronic Theses, Projects, and Dissertations
Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …
Mathematics Behind Machine Learning,
2023
California State University, San Bernardino
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 …
Stability Of Cauchy's Equation On Δ+.,
2023
University of Louisville
Stability Of Cauchy's Equation On Δ+., Holden Wells
Electronic Theses and Dissertations
The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …
Null Space Removal In Finite Element Discretizations,
2023
Clemson University
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 …
Waste Treatment Facility Location For Hotel Chains,
2023
Universidad de Las Palmas de Gran Canaria
Waste Treatment Facility Location For Hotel Chains, Dolores R. Santos-Peñate, Rafael R. Suárez-Vega, Carmen Florido De La Nuez
ITSA 2022 Gran Canaria - 9th Biennial Conference: Corporate Entrepreneurship and Global Tourism Strategies After Covid 19
Tourism generates huge amounts of waste. About half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. We consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. An optimization model is applied to locate the facilities and allocate the waste and products, and several scenarios are analysed. The study shows that, …
Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis,
2023
California Polytechnic State University, San Luis Obispo
Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis, Jackie Driscoll
Master's Theses
Pluripotent stem cells have been observed to segregate into Turing-like patterns during the early stages of Dox-inducible hiPSC differentiation. In this thesis, we de- velop a tool to quantify the tortuosity in the patterns formed by colonies of pluripo- tent stem cells using methods from topological data analysis. We use clustering techniques and the mapper algorithm to create simplicial complexes representing samples of cells and detail a method of evaluating the tortuosity of these complexes. We use the resulting persistence landscapes and their associated norms to evaluate experimental data and simulated data from an agent based model. This thesis finds …
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods,
2023
The University of Southern Mississippi
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 …
An Lp-Based Characterization Of Solvable Qap Instances With Chess-Board And Graded Structures,
2023
Francis Marion University
An Lp-Based Characterization Of Solvable Qap Instances With Chess-Board And Graded Structures, Lucas Waddell, Jerry Phillips, Tianzhu Liu, Swarup Dhar
Faculty Journal Articles
The quadratic assignment problem (QAP) is perhaps the most widely studied nonlinear combinatorial optimization problem. It has many applications in various fields, yet has proven to be extremely difficult to solve. This difficulty has motivated researchers to identify special objective function structures that permit an optimal solution to be found efficiently. Previous work has shown that certain such structures can be explained in terms of a mixed 0-1 linear reformulation of the QAP known as the level-1 reformulation-linearization-technique (RLT) form. Specifically, the objective function structures were shown to ensure that a binary optimal extreme point solution exists to the continuous …
Relative Efficacy Of Resource Constrained Forward And Backward Contact Tracing In An Open Population,
2023
Virginia Commonwealth University
Relative Efficacy Of Resource Constrained Forward And Backward Contact Tracing In An Open Population, Nicholas Roberts
Biology and Medicine Through Mathematics Conference
No abstract provided.
Machine Learning In Finances,
2023
CUNY New York City College of Technology
Machine Learning In Finances, Elma Kastrat, Akinyemi Apampa, Satyanand Singh
Publications and Research
In our study we work on an optimization of an appropriate stock portfolio base on available information. Our work takes into consideration the average return and any associated risk. We produce an investment strategy that predictively allows a portfolio to grow with high yields.
Creating The Optimal Wedding Seating Chart,
2023
University of Nebraska at Omaha
Creating The Optimal Wedding Seating Chart, Madison Lane
Theses/Capstones/Creative Projects
The purpose of this project is to develop an effective seating arrangement for a wedding reception that enhances the comfort of guests. The ultimate aim is to create a harmonious and enjoyable atmosphere for all attendees. To achieve this, an integer program was designed to optimize the seating arrangement for the author’s upcoming wedding on May 27th, 2023. To ensure accuracy and feasibility, actual feedback was gathered from the guests to evaluate their compatibility and preferences. The proposed seating chart optimization not only addresses the placement of guests but also determines the number of tables required for the reception. The …
Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks,
2023
University of Missouri-St. Louis
Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks, Adam Wagenknecht
Dissertations
Convolutional Neural Networks (CNNs) have become one of the most commonly used tools for performing image classification. Unfortunately, as with most machine learning algorithms, CNNs suffer from a lack of interpretability. CNNs are trained by using a training data set and a loss function to tune a set of parameters known as the layer weights. This tuning process is based on the classical method of gradient descent, but it relies on a strong stochastic component, which makes the weight behavior during training difficult to understand. However, since CNNs are governed largely by the weights that make up each of the …
Project Based Learning,
2023
Johnson County Community College
Project Based Learning, Christopher Imm
Sabbatical Projects
Project-based learning (PBL) is a pedagogy which encourages students to be actively involved in their learning process through gaining information to solve real-world problems with projects. In areas of STEM education, PBL can supplement the traditional classroom lecture, where students have a predominantly passive role in the learning process. Through practical activities, interactive discussions, independent reflection and/or team cooperation, students achieve the desired learning outcomes.
Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment,
2023
Southern Methodist University
Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans
Mathematics Theses and Dissertations
For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …
Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow,
2023
Southern Methodist University
Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami
Mathematics Theses and Dissertations
When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. …
Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience,
2023
University of Nebraska at Omaha
Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner
UNO Student Research and Creative Activity Fair
Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …
An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence,
2023
Old Dominion University
An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu
OUR Journal: ODU Undergraduate Research Journal
This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …
Quantum Computing And Its Applications In Healthcare,
2023
Old Dominion University
Quantum Computing And Its Applications In Healthcare, Vu Giang
OUR Journal: ODU Undergraduate Research Journal
This paper serves as a review of the state of quantum computing and its application in healthcare. The various avenues for how quantum computing can be applied to healthcare is discussed here along with the conversation about the limitations of the technology. With more and more efforts put into the development of these computers, its future is promising with the endeavors of furthering healthcare and various other industries.
Novel Architectures And Optimization Algorithms For Training Neural Networks And Applications,
2023
University of Kentucky
Novel Architectures And Optimization Algorithms For Training Neural Networks And Applications, Vasily I. Zadorozhnyy
Theses and Dissertations--Mathematics
The two main areas of Deep Learning are Unsupervised and Supervised Learning. Unsupervised Learning studies a class of data processing problems in which only descriptions of objects are known, without label information. Generative Adversarial Networks (GANs) have become among the most widely used unsupervised neural net models. GAN combines two neural nets, generative and discriminative, that work simultaneously. We introduce a new family of discriminator loss functions that adopts a weighted sum of real and fake parts, which we call adaptive weighted loss functions. Using the gradient information, we can adaptively choose weights to train a discriminator in the direction …
Swarm Intelligence For Solving Some Nonlinear Differential Equations,
2023
Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Egypt
Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly
Mansoura Engineering Journal
The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …
