Applied Mathematics Commons^™

Cancer Quasispecies And Stem-Like Adaptive Aneuploidy, Domenico Napoletani, M. Signore, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we develop a theoretical frame to understand self-regulation of aneuploidy rate in cancer and stem cells. This is accomplished building upon quasispecies theory, by leaving its formal mathematical structure intact, but by drastically changing the meaning of its objects. In particular, we propose a novel definition of chromosomal master sequence, as a sequence of physically distinct whole or fragmented chromosomes, whose length is taken to be the sum of the copy numbers of each whole or fragmented chromosome. This fundamental change in the functional objects of quasispecies theory allows us to show that previously measured aneuploidy rates …

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 …

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 …

Invisibility: A Mathematical Perspective, Austin G. Gomez

CMC Senior Theses

The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. …

On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov

Articles

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.

Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Articles

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.

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 …

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 …

A Semigroup/Laplace Transform Approach To Approximating Flows, Ladorian Nichele Latin

LSU Doctoral Dissertations

It is well known that all flows in a state space O induce a semigroup of linear operators on an appropriately chosen vector space of functions (observables) from O into a vector space Z (observations). After choosing appropriate continuity assumptions on the flow, the associated semigroup will be strongly continuous and will have a linear, infinitesimal generator A. The purpose of this dissertation is to explore approximation methods for linear semigroups and/or Laplace transform inversion methods in order to reconstruct the flow starting with the linear generator A . In preparing for these investigations, we collect some of the essential …

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 …

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.

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 …

Multiplicity Formulas For Perverse Coherent Sheaves On The Nilpotent Cone, Myron Minn-Thu-Aye

LSU Doctoral Dissertations

Arinkin and Bezrukavnikov have given the construction of the category of equivariant perverse coherent sheaves on the nilpotent cone of a complex reductive algebraic group. Bezrukavnikov has shown that this category is in fact weakly quasi-hereditary with Andersen--Jantzen sheaves playing a role analogous to that of Verma modules in category O for a semi-simple Lie algebra. Our goal is to show that the category of perverse coherent sheaves possesses the added structure of a properly stratified category, and to use this structure to give an effective algorithm to compute multiplicities of simple objects in perverse coherent sheaves. The algorithm is …

Refining The Characterization Of Projective Graphs, Perry K. Iverson

LSU Doctoral Dissertations

Archdeacon showed that the class of graphs embeddable in the projective plane is characterized by a set of 35 excluded minors. Robertson, Seymour and Thomas in an unpublished result found the excluded minors for the class of k-connected graphs embeddable on the projective plane for k = 1,2,3. We give a short proof of that result and then determine the excluded minors for the class of internally 4-connected projective graphs. Hall showed that a 3-connected graph diff_x000B_erent from K5 is planar if and only if it has K3,3 as a minor. We provide two analogous results for projective graphs. For …

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 …

Pressure Poisson Method For The Incompressible Navier-Stokes Equations Using Galerkin Finite Elements, John Cornthwaite

College of Graduate Studies: Theses & Dissertations

In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.

Full Newton Step Interior Point Method For Linear Complementarity Problem Over Symmetric Cones, Andrii Berdnikov

College of Graduate Studies: Theses & Dissertations

In this thesis, we present a new Feasible Interior-Point Method (IPM) for Linear Complementarity Problem (LPC) over Symmetric Cones. The advantage of this method lies in that it uses full Newton-steps, thus, avoiding the calculation of the step size at each iteration. By suitable choice of parameters we prove the global convergence of iterates which always stay in the the central path neighborhood. A global convergence of the method is proved and an upper bound for the number of iterations necessary to find ε-approximate solution of the problem is presented.

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, …