Applied Mathematics Commons^™

Extra Structures On Three-Dimensional Cobordisms, Xuanye Wang

LSU Doctoral Dissertations

A Topological Quantum Field Theory (TQFT) is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2 + 1-cobordism category is built from manifolds which are equipped with an extra structure such as a p1-structure, or an extended manifold structure. In chapter 1, we perform the universal construction of [3] on a cobordism category without this extra structure and show that the resulting quantization functor assigns an infinite dimensional vector space to the torus. In chapter …

Mixed Categories, Formality For The Nilpotent Cone, And A Derived Springer Correspondence, Laura Joy Rider

LSU Doctoral Dissertations

Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer perverse sheaf and the derived category of di_x000B_erential graded modules over a dg-ring related to the Weyl group

A Characterization Of Almost All Minimal Not Nearly Planar Graphs, Kwang Ju Choi

LSU Doctoral Dissertations

In this dissertation, we study nearly planar graphs, that is, graphs that are edgeless or have an edge whose deletion results in a planar graph. We show that all but finitely many graphs that are not nearly planar and do not contain one particular graph have a well-understood structure based on large Möbius ladders.

Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang

LSU Doctoral Dissertations

In this work, using higher algebraic K-theory, we provide an answer to the following question asked by Green-Griffiths in [13]: Can one define the Bloch-Gersten-Quillen sequence G_j on infinitesimal neighborhoods X_j so that Ker(G₁ &rarr G₀)= TG₀, Here TG₀ should be the Cousin resolution of TK_m(O_X) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of G_j is discussed in chapter 3, following [8] and [18]. The main theorems are theorem5.2.5, theorem 5.2.6 and theorem …

Clustering Methods And Their Applications To Adolescent Healthcare Data, Morgan Mayer-Jochimsen

Scripps Senior Theses

Clustering is a mathematical method of data analysis which identifies trends in data by efficiently separating data into a specified number of clusters so is incredibly useful and widely applicable for questions of interrelatedness of data. Two methods of clustering are considered here. K-means clustering defines clusters in relation to the centroid, or center, of a cluster. Spectral clustering establishes connections between all of the data points to be clustered, then eliminates those connections that link dissimilar points. This is represented as an eigenvector problem where the solution is given by the eigenvectors of the Normalized Graph Laplacian. Spectral clustering …

Stability Of Large Flocks: An Example, J. J. P. Veerman, F. M. Tangerman

Mathematics and Statistics Faculty Publications and Presentations

The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then …

Applications Of Fourier Analysis To Audio Signal Processing: An Investigation Of Chord Detection Algorithms, Nathan Lenssen

CMC Senior Theses

The discrete Fourier transform has become an essential tool in the analysis of digital signals. Applications have become widespread since the discovery of the Fast Fourier Transform and the rise of personal computers. The field of digital signal processing is an exciting intersection of mathematics, statistics, and electrical engineering. In this study we aim to gain understanding of the mathematics behind algorithms that can extract chord information from recorded music. We investigate basic music theory, introduce and derive the discrete Fourier transform, and apply Fourier analysis to audio files to extract spectral data.

Uncertainty Quantification Of Film Cooling Effectiveness In Gas Turbines, Hessam Babaee

LSU Master's Theses

In this study the effect of uncertainty of velocity ratio on jet in crossflow and particual- rly film cooling performance is studied. Direct numerical simulations have been combined with a stochastic collocation approach where the parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) method. Velocity ratio serves as a bifurcation parameter in a jet in a crossflow and the dynamical system is shown to have several bifurcations. As a result of the bifurcations, the target functional is observed to have low-regularity with respect to the paramteric space. In that sense, ME-gPC is particularly effective in discretizing the parametric …

Statistical Classification Problems In Assessment Of Teachers, Xuan Wang

LSU Master's Theses

Classification and regression trees form an important and indispensable tool in data analysis and classification problems. Class trees are described in detail with examples. The method is applied to a data set pertaining to evaluation of teachers. In addition, two other classification methods, bagging and AdaBoost are explained. These methods improve existing classifiers to nearly optimal classifiers.

Skein Theory And Topological Quantum Field Theory, Xuanting Cai

LSU Doctoral Dissertations

Skein modules arise naturally when mathematicians try to generalize the Jones polynomial of knots. In the first part of this work, we study properties of skein modules. The Temperley-Lieb algebra and some of its generalizations are skein modules. We construct a bases for these skein modules. With this basis, we are able to compute some gram determinants of bilinear forms on these skein modules. Also we use this basis to prove that the Mahler measures of colored Jones polynomial of a sequence of knots converges to the Mahler measure of some two variable polynomial. The topological quantum field theory constructed …

Mathematical Modelling Of Internal Heat Recovery In Flash Tank Heat Exchanger Cascades, Andrei Korobeinikov, John E. Mccarthy, Emma Mooney, Krum Semkov, James Varghese

Mathematics Faculty Research

Flash tank evaporation combined with a condensing heat exchanger can be used when heat exchange is required between two streams and where at least one of these streams is difficult to handle (tends severely to scale, foul, causing blockages). To increase the efficiency of heat exchange, a cascade of these units in series can be used. Heat transfer relationships in such a cascade are very complex due to their interconnectivity, thus the impact of any changes proposed is difficult to predict. Moreover, the distribution of loads and driving forces in different stages and the number of designed stages faces tradeoffs …

Group Developed Weighing Matrices, K. T. Arasu, Jeffrey R. Hollon

Mathematics and Statistics Faculty Publications

A weighing matrix is a square matrix whose entries are 1, 0 or −1, such that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be devel- oped by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into …

Sampling From The Hardcore Process, William C. Dodds

CMC Senior Theses

Partially Recursive Acceptance Rejection (PRAR) and bounding chains used in conjunction with coupling from the past (CFTP) are two perfect simulation protocols which can be used to sample from a variety of unnormalized target distributions. This paper first examines and then implements these two protocols to sample from the hardcore gas process. We empirically determine the subset of the hardcore process's parameters for which these two algorithms run in polynomial time. Comparing the efficiency of these two algorithms, we find that PRAR runs much faster for small values of the hardcore process's parameter whereas the bounding chain approach is vastly …

Immersed Finite Element Method For Interface Problems With Algebraic Multigrid Solver, Wenqiang Feng

Masters Theses

"This thesis is to discuss the bilinear and 2D linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. In contrast to the body-fitting mesh restriction of the traditional finite element methods or finite difference methods for interface problems, a number of numerical methods based on structured meshes independent of the interface have been developed. When these methods are applied to the real world applications, we often need to solve the corresponding large scale linear systems many times, which demands efficient solvers. The algebraic multigrid (AMG) method is a natural choice …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

Large Deviations For Stochastic Navier-Stokes Equations With Nonlinear Viscosities, Ming Tao

LSU Doctoral Dissertations

In this work, a Wentzell-Freidlin type large deviation principle is established for the two-dimensional stochastic Navier-Stokes equations (SNSE's) with nonlinear viscosities. We fi_x000C_rst prove the existence and uniqueness of solutions to the two-dimensionalstochastic Navier-Stokes equations with nonlinear viscosities using the martingale problem argument and the method of monotonicity. By the results of Varadhan and Bryc, the large deviation principle (LDP) is equivalent to the Laplace-Varadhan principle (LVP) if the underlying space is Polish. Then using the stochastic control and weak convergence approach developed by Budhiraja and Dupuis, the Laplace-Varadhan principle for solutions of stochastic Navier-Stokesequations is obtained in appropriate function …

Application Of Helmholtz/Hodge Decomposition To Finite Element Methods For Two-Dimensional Maxwell's Equations, Zhe Nan

LSU Doctoral Dissertations

In this work we apply the two-dimensional Helmholtz/Hodge decomposition to develop new finite element schemes for two-dimensional Maxwell's equations. We begin with the introduction of Maxwell's equations and a brief survey of finite element methods for Maxwell's equations. Then we review the related fundamentals in Chapter 2. In Chapter 3, we discuss the related vector function spaces and the Helmholtz/Hodge decomposition which are used in Chapter 4 and 5. The new results in this dissertation are presented in Chapter 4 and Chapter 5. In Chapter 4, we propose a new numerical approach for two-dimensional Maxwell's equations that is based on …

Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman

Senior Independent Study Theses

This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …

Subset Non Associative Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time we introduce the notion of subset non associative semirings. It is pertinent to keep on record that study of non associative semirings is meager and books on this specific topic is still rare. Authors have recently introduced the notion of subset algebraic structures. The maximum algebraic structure enjoyed by subsets with two binary operations is just a semifield and semiring, even if a ring or a field is used. In case semigroups or groups are used still the algebraic structure of the subset is only a semigroup. To construct a subset non associative …

Subset Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of groupoids is meager and we have recently introduced the new notion of subset groupoids and have studied them. It is interesting to keep on record that interval groupoids have been studied by us in 2010. Further when the subsets of a loop are taken they also form only a subset groupoid and not a subset loop. Thus we do not have the concept of subset interval loop they only form a subset interval groupoid. Special elements like subset interval zero divisors, subset interval idempotents and subset interval units are studied. Concept of subset interval groupoid homomorphism is …

Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of subsets and giving algebraic structure to these subsets of a set started in the mid 18th century by George Boole. The first systematic presentation of Boolean algebra emerged in 1860s in papers written by William Jevons and Charles Sanders Peirce. Thus we see if P(X) denotes the collection of all subsets of the set X, then P(X) under the op erations of union and intersection is a Boolean algebra. Next the subsets of a set was used in the construction of topological spaces. We in this book consider subsets of a semigroup or a group or a …

Fuzzy Analysis Of School Dropouts And Their Life After, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved. A school dropout can be a child labourer, a rag picker or a social miscreant or be in police custody or be in a rehabilitation home if he/she is a runaway. …

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

Lattice Boltzmann Simulations Of Thermal Convective Flows In Two Dimensions, Jia Wang, Donghai Wang, Pierre Lallemand, Li-Shi Luo

Mathematics & Statistics Faculty Publications

In this paper we study the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model for incompressible thermo-hydrodynamics with the Boussinesq approximation. We use the MRT thermal LBE (TLBE) to simulate the following two flows in two dimensions: the square cavity with differentially heated vertical walls and the Rayleigh-Benard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra = 10³-10⁶, and the Prandtl number Pr = 0.71; and for the Rayleigh-Benard convection in a rectangle, Ra = 2 ^. 10³, 10 …

Post-Pareto Optimality Methods For The Analysis Of Large Pareto Sets In Multi-Objective Optimization, Victor Manuel Carrillo

Open Access Theses & Dissertations

Multiple objective optimization involves the simultaneous optimization of more than one, possibly conflicting, objectives. Multiple objective optimization problems arise in a variety of real-world applications. In general, the main difference between single and multi-objective optimization is that in multi-objective optimization there is usually no single optimal solution, but a set of equally good alternatives with different trade-offs, also known as Pareto-optimal solutions. There are two general approaches to solve multiple objective optimization problems: mathematical methods and meta-heuristic methods. The first approach involves the aggregation of the attributes into a linear combination of the objective functions, also known as scalarization. The …

Automatic Elucidation Of Gpi Molecular Structures With Grid Computing Technology, Juan Clemente Aguilar Bonavides

Open Access Theses & Dissertations

Glycosylphosphatidylinositol (GPI)-anchored proteins are involved in many biological processes and are of medical importance. The identification and analysis of the entire collection of free and protein-linked GPIs within an organism (i.e., GPIomics) requires highly sensitive instruments. At present, liquid chromatography-tandem mass spectrometry (LC-MS/MS or -MSⁿ) is the most efficient laboratory technique for these tasks. As a typical MSⁿ experiment produces hundreds of thousands of spectra, the data analysis creates a major bottleneck in high-throughput GPIomic projects. Yet, no computational tool for characterizing the chemical structures of GPI is available to date. We propose a library-search algorithm to …

Modeling The Human Gait Phases Using Granular Computing, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Gait analysis is applied for the provision of diagnosis, evaluation, and for the design of therapeutic intervention for subjects suffering from neurological disorders. The benefits accruing from gait analysis are well established. People with neurological disorders like mild traumatic brain injury, Cerebral Palsy and Multiple Sclerosis, suffer associated functional gait problems. The symptoms and sign of these gait deficits are different from subject to subject and even for the same subject at different stage of the disease. Identifying these gait related abnormalities helps in the treatment planning and rehabilitation process.

The dynamic behavior of gait parameters is cyclic and the …

A Block Operator Splitting Method For Heterogeneous Multiscale Poroelasticity, Paul M. Delgado

Open Access Theses & Dissertations

Traditional models of poroelastic deformation in porous media assume relatively homogeneous material properties such that macroscopic constitutive relations lead to accurate results. Many realistic applications involve heterogeneous material properties whose oscillatory nature require multiscale methods to balance accuracy and efficiency in computation.

The current study develops a multiscale method for poroelastic deformation based on a fixed point iteration based operator splitting method and a heterogeneous multiscale method using finite volume and direct stiffness methods. To characterize the convergence

of the operator splitting method, we use a numerical root finding algorithm to determine a threshold surface in a non-dimensional parameter space …

Functional Data Analysis To Guide A Conditional Likelihood Regression In A Case-Crossover Study Investigating Whether Social Characteristics Modify The Health Effects Of Air Pollution, Juana Maribel Herrera Hernandez

Open Access Theses & Dissertations

In this study we are focused on exploring whether social characteristics modify the relationship between air pollution and hospitalizations due to asthma or chronic pulmonary obstructive disease (COPD) in El Paso, Tx. The case-crossover design with conditional regression analysis was used, here the controls and the case are the same subject at different

times and has the advantage of removing confounding by permanently confounding factors. Social characteristics are included in the models as interactions with the pollutants, variables included are age, sex, ethnicity and insurance status as indicator for the socio-economic status. The pollutant's lags were chosen using the historical …

A Convex Optimization Algorithm For Sparse Representation And Applications In Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. Any test sample is represented in an overcomplete dictionary with the training sample as base elements. A given test sample can be expressed as a linear combination of only those training …