Applied Mathematics Commons^™

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu

Theses and Dissertations--Mathematics

We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

Theses and Dissertations--Mechanical and Aerospace Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is …

Autonomous Quadrotor Collision Avoidance And Destination Seeking In A Gps-Denied Environment, Thomas C. Kirven

Theses and Dissertations--Mechanical and Aerospace Engineering

This thesis presents a real-time autonomous guidance and control method for a quadrotor in a GPS-denied environment. The quadrotor autonomously seeks a destination while it avoids obstacles whose shape and position are initially unknown. We implement the obstacle avoidance and destination seeking methods using off-the-shelf sensors, including a vision-sensing camera. The vision-sensing camera detects the positions of points on the surface of obstacles. We use this obstacle position data and a potential-field method to generate velocity commands. We present a backstepping controller that uses the velocity commands to generate the quadrotor's control inputs. In indoor experiments, we demonstrate that the …

Asymptotic Formulae For Restricted Unimodal Sequences, Richard Alexander Frnka

LSU Doctoral Dissertations

Additive enumeration problems, such as counting the number of integer partitions, lie at the intersection of various branches of mathematics including combinatorics, number theory, and analysis. Extending partitions to integer unimodal sequences has also yielded interesting combinatorial results and asymptotic formulae, which form the subject of this thesis. Much like the important work of Hardy and Ramanujan proving the asymptotic formula for the partition function, Auluck and Wright gave similar formulas for unimodal sequences. Following the circle method of Wright, we provide the asymptotic expansion for unimodal sequences with odd parts. This is then generalized to a two-parameter family of …

On Braids, Branched Covers And Transverse Invariants, Jose Hector Ceniceros

LSU Doctoral Dissertations

In this work, we present a brief survey of knot theory supported by contact 3-manifolds. We focus on transverse knots and explore different ways of studying transverse knots. We define a new family of transverse invariants, this is accomplished by considering $n$-fold cyclic branched covers branched along a transverse knot and we then extend the definition of the BRAID invariant $t$ defined in cite{BVV} to the lift of the transverse knot. We call the new invariant the lift of the BRAID invariant and denote it by $t_n$. We then go on to show that $t_n$ satisfies a comultiplication formula and …

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

Eigenvector Centrality: Illustrations Supporting The Utility Of Extracting More Than One Eigenvector To Obtain Additional Insights Into Networks And Interdependent Structures, Dawn Iacobucci, Rebecca Mcbride, Deidre L. Popovich

University Faculty Publications and Creative Works

Among the many centrality indices used to detect structures of actors’ positions in networks is the use of the first eigenvector of an adjacency matrix that captures the connections among the actors. This research considers the seeming pervasive current practice of using only the first eigenvector. It is shows that, as in other statistical applications of eigenvectors, subsequent vectors can also contain illuminating information. Several small examples, and Freeman’s EIES network, are used to illustrate that while the first eigenvector is certainly informative, the second (and subsequent) eigenvector(s) can also be equally tractable and informative.

Long And Short-Range Air Navigation On Spherical Earth, Nihad E. Daidzic

International Journal of Aviation, Aeronautics, and Aerospace

Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route validation. …

Family-Based Association Studies Of Autism In Boys Via Facial-Feature Clusters, Luke Andrew Settles

Masters Theses

"Autism spectrum disorder (ASD) refers to a set of developmental disorders with varied attributes. Due to its substantial heterogeneity in terms of behavioral and clinical phenotypes, it is challenging to discern the genetic biomarkers behind ASD, even though the disease is known to be genetic in nature. This serves as a motivation to detect relationships between single nucleotide polymorphisms (SNPs) and a causal autism disease susceptibility locus (DSL) within more homogeneous subgroups. Recently, clinically meaningful subclassifications of ASD have been discovered utilizing facial features of prepubescent boys. Therefore, through the employment of data from 44 prepubertal Caucasian boys with ASD …

The Pantograph Equation In Quantum Calculus, Thomas Griebel

Masters Theses

"In this thesis, the pantograph equation in quantum calculus is investigated. The pantograph equation is a famous delay differential equation that has been known since 1971. Till the present day, the continuous and the discrete cases of the pantograph equation are well studied. This thesis deals with different pantograph equations in quantum calculus. An explicit solution representation and the exponential behavior of solutions of a pantograph equation are proved. Furthermore, several pantograph equations regarding asymptotic stability are considered. In fact, conditions for the asymptotic stability of the zero solution are derived and subsequently illustrated by examples. Moreover, an explicit solution …

End-To-End Molecular Communication Channels In Cell Metabolism: An Information Theoretic Study, Zahmeeth Sayed Sakkaff, Jennie L. Catlett, Mikaela Cashman, Massimiliano Pierobon, Nicole R. Buan, Myra B. Cohen, Christine A. Kelley

Department of Biochemistry: Faculty Publications

The opportunity to control and fine-tune the behavior of biological cells is a fascinating possibility for many diverse disciplines, ranging from medicine and ecology, to chemical industry and space exploration. While synthetic biology is providing novel tools to reprogram cell behavior from their genetic code, many challenges need to be solved before it can become a true engineering discipline, such as reliability, safety assurance, reproducibility and stability. This paper aims to understand the limits in the controllability of the behavior of a natural (non-engineered) biological cell. In particular, the focus is on cell metabolism, and its natural regulation mechanisms, and …

P-Union And P-Intersection Of Neutrosophic Cubic Sets, Florentin Smarandache, Young Bae Jun, Chang Su Kim

Branch Mathematics and Statistics Faculty and Staff Publications

Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.

Plithogeny, Plithogenic Set, Logic, Probability, And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce for the first time, as generalization of dialectics and neutrosophy, the philosophical concept called plithogeny. And as its derivatives: the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics), plithogenic probability (as generalization of classical, imprecise, and neutrosophic probabilities), and plithogenic statistics (as generalization of classical, and neutrosophic statistics).

Plithogeny is the genesis or origination, creation, formation, development, and evolution of new entities from dynamics and organic fusions of contradictory and/or neutrals and/or non-contradictory multiple old entities.

Plithogenic …

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (Second Extended And Improved), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:

— Neutrosophic Duplets and the Neutrosophic Duplet Structures;

— Neutrosophic Multisets (as an extension of the classical multisets);

— Neutrosophic Spherical Numbers;

— Neutrosophic Overnumbers / Undernumbers / Offnumbers;

— Neutrosophic Indeterminacy of Second Type;

— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);

— Neutrosophic Triplet Loop;

— Neutrosophic Triplet …

Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Neutrosophic Operational Research - Vol. 1, Florentin Smarandache, Mohamed Abdel Basset, Yongquan Zhou

Branch Mathematics and Statistics Faculty and Staff Publications

This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It is concerned with the …

Complex Valued Graphs For Soft Computing, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …

Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.

Branch Mathematics and Statistics Faculty and Staff Publications

The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can …

Special Types Of Bipolar Single Valued Neutrosophic Graphs, Ali Hassan, Muhammad Aslam Malik, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

Paving The Randomized Gauss-Seidel, Wei Wu

Scripps Senior Theses

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix …

Compressive Vector Reconstruction: Hypothesis For Blind Image Deconvolution, Alonso Orea Amador

Open Access Theses & Dissertations

Alternative imaging devices propose to acquire and compress images simultaneously. These devices are based on the compressive sensing (CS) theory. A reduction in the measurement required for reconstruction without a post-compression sub-system allows imaging devices to become simpler, smaller, and cheaper. In this research, we propose a new algorithm to compress and reconstruct blurred images for CS imaging devices. Blur effect in images is common due to relative motion, lens, limited aperture dimensions, lack of focus, and/or atmospheric turbulence. Our intention is to compress a blurred image with CS techniques and then reconstruct a blur-free version using the proposed algorithm. …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …

Joint Hierarchical Models For Sparsely Sampled High-Dimensional Lidar And Forest Variables, Andrew O. Finley, Sudipto Banerjee, Yuzhen Zhou, Bruce D. Cook, Chad Babcock

United States National Aeronautics and Space Administration: Publications

Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for above ground biomass (AGB) and LiDAR signals. The processbased framework offers richness in inferential capabilities, e.g., inference on the entire underlying processes instead of estimates only at pre-specified points. Key challenges we obviate include misalignment between the …

An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield

Department of Mathematics: Faculty Publications

Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …

Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner

CMC Senior Theses

Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour …

Cyclic Codes And Cyclic Lattices, Scott Maislin

CMC Senior Theses

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two …

Daily Traffic Flow Pattern Recognition By Spectral Clustering, Matthew Aven

CMC Senior Theses

This paper explores the potential applications of existing spectral clustering algorithms to real life problems through experiments on existing road traffic data. The analysis begins with an overview of previous unsupervised machine learning techniques and constructs an effective spectral clustering algorithm that demonstrates the analytical power of the method. The paper focuses on the spectral embedding method’s ability to project non-linearly separable, high dimensional data into a more manageable space that allows for accurate clustering. The key step in this method involves solving a normalized eigenvector problem in order to construct an optimal representation of the original data.

While this …

A Wasserstein Gradient Flow Approach To Poisson-Nernst-Planck Equations, David Kinderlehrer, Leinard Monsaingeon, Xiang Xu

Mathematics & Statistics Faculty Publications

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial …