Mathematics Commons^™

Study On Port Service Capacity Along The 21st Century Maritime Silk Road : Taking Container Ports As An Example, Rujin Fu

World Maritime University Dissertations

No abstract provided.

Analysis Of Syndrome-Based Iterative Decoder Failure Of Qldpc Codes, Kirsten D. Morris, Tefjol Pllaha, Christine A. Kelley

Department of Mathematics: Faculty Publications

Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code’s graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets are subsets of codeword coordinates that, when initially in error, lead to decoding failure in a trapping set. In this paper we examine the failure inducing sets of QLDPC codes under syndrome-based iterative decoding, and their connection to absorbing sets in classical LDPC codes.

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

Here Comes The Strain: Analyzing Defensive Pass Rush In American Football With Player Tracking Data, Quang Nguyen, Ronald Yurko, Gregory J. Matthews

Mathematics and Statistics: Faculty Publications and Other Works

In American football, a pass rush is an attempt by the defensive team to disrupt the offense and prevent the quarterback (QB) from completing a pass. Existing metrics for assessing pass rush performance are either discrete-time quantities or based on subjective judgment. Using player tracking data, we propose STRAIN, a novel metric for evaluating pass rushers in the National Football League (NFL) at the continuous-time within-play level. Inspired by the concept of strain rate in materials science, STRAIN is a simple and interpretable means for measuring defensive pressure in football. It is a directly-observed statistic as a function of two …

The Spectrum Of Nim-Values For Achievement Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics Faculty Publications

We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is {0, 1, 2, 3, 4}. This positively answers two conjectures from a previous paper by the last two authors.

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

One Formula For Non-Prime Numbers: Motivations And Characteristics, Mahmoud Mansour, Kamal Hassan Prof.

Basic Science Engineering

Primes are essential for computer encryption and cryptography, as they are fundamental units of whole numbers and are of the highest importance due to their mathematical qualities. However, identifying a pattern of primes is not easy. Thinking in a different way may get benefits, by considering the opposite side of the problem which means focusing on non-prime numbers. Recently, researchers introduced, the pattern of non-primes in two maximal sets while in this paper, non-primes are presented in one formula. Getting one-way formula for non-primes may pave the way for further applications based on the idea of primes.

Bifurcation From Infinity With Oscillatory Nonlinearity For Neumann Problems, M. Chhetri, Nsoki Mavinga, R. Pardo

Mathematics & Statistics Faculty Works

We consider a sublinear perturbation of an elliptic eigenvalue problem with Neumann boundary condition. We give sufficient conditions on the nonlinear perturbation which guarantee that the unbounded continuum, bifurcating from infinity at the first eigenvalue, contains an unbounded sequence of turning points as well as an unbounded sequence of resonant solutions. We prove our result by using bifurcation theory combined with a careful analysis of the oscillatory behavior of the continuum near the bifurcation point.

Topological Data Analysis Of Convolutional Neural Networks Using Depthwise Separable Convolutions, Eliot Courtois

Dissertations

In this dissertation, we present our contribution to a growing body of work combining the fields of Topological Data Analysis (TDA) and machine learning. The object of our analysis is the Convolutional Neural Network, or CNN, a predictive model with a large number of parameters organized using a grid-like geometry. This geometry is engineered to resemble patches of pixels in an image, and thus CNNs are a conventional choice for an image-classifying model.

CNNs belong to a larger class of neural network models, which, starting at a random initialization state, undergo a gradual fitting (or training) process, often a …

Computation Of The Basic Reproduction Numbers For Reaction-Diffusion Epidemic Models, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We consider a class of k-dimensional reaction-diusion epidemic models (k = 1; 2; • • • ) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.

Topological Comparison Of Some Dimension Reduction Methods Using Persistent Homology On Eeg Data, Eddy Kwessi

Mathematics Faculty Research

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used in dimension reduction such as isometric feature mapping, Laplacian Eigenmaps, fast independent component analysis, kernel ridge regression, and t-distributed stochastic neighbor embedding. We then give a brief overview of some of the topological notions used in topological data analysis, such as barcodes, persistent homology, and Wasserstein distance. Theoretically, when these methods are applied on a data set, they can be interpreted differently. From EEG data embedded into a manifold of high dimension, …

The Rayleigh–Bénard Problem For Water With Maximum Density Effects, Mahanthesh Basavarajappa, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Linear stability and weakly nonlinear stability analyses are developed for Rayleigh–Bénard convection in water near 3.98 °C subject to isothermal boundary conditions. The density–temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, and cubic terms. The continuity equation, the Navier–Stokes momentum equation, the equation of state, and the energy equation constitute the governing system. Linear stability analysis is used to investigate how the maximum density property of water affects the onset of convective instability and the choice of unstable wave number for four different types of boundary conditions. Then, a weakly nonlinear stability study is …

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Pull-Push Method: A New Approach To Edge-Isoperimetric Problems, Sergei L. Bezrukov, Nikola Kuzmanovski, Jounglag Lim

Department of Mathematics: Faculty Publications

We prove a generalization of the Ahlswede-Cai local-global principle. A new technique to handle edge-isoperimetric problems is introduced which we call the pull-push method. Our main result includes all previously published results in this area as special cases with the only exception of the edge-isoperimetric problem for grids. With this we partially answer a question of Harper on local-global principles. We also describe a strategy for further generalization of our results so that the case of grids would be covered, which would completely settle Harper’s question.

An Extension Of The Complex–Real (C–R) Calculus To The Bicomplex Setting, With Applications, Daniel Alpay, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we extend notions of complex ℂ−ℝ-calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.

Asymptotics And Sign Patterns For Coefficients In Expansions Of Habiro Elements, Ankush Goswami, Abhash Kumar Jha, Byungchan Kim, Robert Osburn

School of Mathematical & Statistical Sciences Faculty Publications

We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich–Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier’s result on asymptotics for the Fishburn numbers.

Platonism, De Re, And (Philosophy Of) Mathematical Practice, Marco Panza

MPP Published Research

The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the …

Effect Of Total Population, Population Density And Weighted Population Density On The Spread Of Covid-19 In Malaysia, Hui Shan Wong, Md Zobaer Hasan, Omar Sharif, Azizur Rahman

School of Mathematical & Statistical Sciences Faculty Publications

Since November 2019, most countries across the globe have suffered from the disastrous consequences of the Covid-19 pandemic which redefined every aspect of human life. Given the inevitable spread and transmission of the virus, it is critical to acknowledge the factors that catalyse transmission of the disease. This research investigates the relation of the external demographic parameters such as total population, population density and weighted population density on the spread of Covid-19 in Malaysia. Pearson correlation and simple linear regression were utilized to identify the relation between the population-related variables and the spread of Covid-19 in Malaysia using data from …

Catalan Numbers As Discrepancies For A Family Of Substitutions On Infinite Alphabets, Dirk Frettlöh, Alexey Garber, Neil Mañibo

School of Mathematical & Statistical Sciences Faculty Publications

In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. While for both settings the leading term of the tile counting function is exponential (and guided by the inflation factor), the behaviour of the second-order term is strikingly different. For the finite setting, it is known that the second term is also exponential or exponential times a polynomial. We exhibit a large family of examples where the second term is at least exponential in n divided by half-integer powers of n, where …

When Are The Natural Embeddings Of Classical Invariant Rings Pure?, Melvin Hochster, Jack Jeffries, Vaibhav Pandey, Anurag K. Singh

Department of Mathematics: Faculty Publications

Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical representations as inWeyl’s book: For the general linear group, consider a direct sum of copies of the standard representation and copies of the dual; in the other cases, take copies of the standard representation. The invariant rings in the respective cases are determinantal rings, rings defined by Pfaffians of alternating matrices, symmetric determinantal rings and the Plücker coordinate rings of Grassmannians; …