Other Applied Mathematics Commons^™

Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

UNO Student Research and Creative Activity Fair

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet …

Parametric Natura Morta, Maria C. Mannone

The Transdisciplinary STEAM+ Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates

Electronic Theses and Dissertations

Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …

On Some Metaphysical Problems Of Many Worlds Interpretation Of Quantum Mechanics, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the socalled quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is : how …

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

Herglotz Functions Of Several Quaternionic Variables, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We first review realizations of Herglotz functions in the unit ball of C^N and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey

Senior Honors Theses

The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To conclude, …

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

Branch Mathematics and Statistics Faculty and Staff Publications

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, Fabrizio Colombo, Jonathan Gantner, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of …

Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King

Electronic Theses and Dissertations

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule M_k outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …

Cayley Graphs Of Groups And Their Applications, Anna Tripi

Graduate Theses/Dissertations

Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the …

Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg

Journal of Pre-College Engineering Education Research (J-PEER)

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews …

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Tropical Algebra, Graph Theory, & Foreign Exchange Arbitrage, Bradley A. Mason

Senior Honors Projects, 2010-2019

We answer the question, given n currencies and k trades, how can a maximal arbitrage opportunity be found and what is its value? To answer this question, we use techniques from graph theory and employ a max-plus algebra (commonly known as tropical algebra). Further, we show how the tropical eigenvalue of a foreign exchange rate matrix relates to arbitrage among the currencies and can be found algorithmically. We finish by employing time series techniques to study the stability of maximal, high-currency arbitrage opportunities.

Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green

Electronic Theses and Dissertations

To determine the function of a protein, we must know its 3-dimensional structure, which can be difficult to ascertain. Currently, predictive models are used to determine the structure of a protein from its sequence, but these models do not always predict the correct structure. To this end we use a nested graph model along with weighted invariants to minimize the errors and improve the accuracy of a predictive model to determine if we have the correct structure for a protein.

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Pattern Recognition In Stock Data, Kathryn Dover

HMC Senior Theses

Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.