Browsing by Department "Mathematics and Statistics"
Now showing items 261-280 of 283
Statistical Inference for High-Dimensional Regularized Huber Regression
(2023-04-18)
With the rapid advancement of technology, the amount of available data for extracting interesting insights and meaningful patterns has grown exponentially, resulting in a significant increase in the dimensionality of ...
Statistical methods for identification of NF-κB related genes and their expression profiles in channel catfish after bacterial infection
(2017-04-16)
Interactions of NF-κB family, IκB family and IKK complex are key components of NF-κB pathway that is essential for many biological processes including innate and adaptive immunity, and inflammation and stress responses. ...
Stochastic Differential Equations: A Dynamical Systems Approach
(2008-05-15)
The relatively new subject of stochastic differential equations has increasing impor-
tance in both theory and applications. The subject draws upon two main sources, prob-
ability/stochastic processes and differential ...
The Stone-Čech Compactification and the Number of Pairwise Nonhomeomorphic Subcontinua of β[0,∞)\[0,∞)
(2014-05-02)
An introduction to the Stone-Čech compactification $\beta X$ of a normal topological space $X$ is given. The method of invariantly embedding linear orders into ultrapowers is used to find $2^{\mathfrak{c}}$ pairwise ...
Structure Theory and a Generalization of the Isomorphism Theorems
(2013-07-10)
A general format in which the mathematical structure of topological spaces, algebraic structures, and graphs can be expressed is described. A generalization of the fundamental homomorphism theorem and the isomorphism ...
A Study of Polya's Enumeration Theorem
(2005-08-15)
The controversial lemma, known most commonly as Burnside's Lemma, is stated and proven. The influential Polya's Enumeration Theorem is stated and proven. Computations using Polya's Enumeration Theorem are discussed and ...
A Study of Regularity and Normality
(2009-04-15)
This paper is a broad overview of the separation axioms, commonly known as the Hausdorff, Regular, and Normal axioms. After a review of basic definitions and lemmas, we proceed to certain examples and theorems dealing ...
A Study of Space-time Fractional SPDE in Bounded Domains
(2023-07-24)
This dissertation considers space-time fractional stochastic heat equation on a regular bounded domain B in R^d, d ⩾ 1 with Dirichlet boundary condition:
∂βt ut(x) = −(−Δ)α2 ut(x) + I1−βt [λσ(ut(x)) ˙W (t, x)] for x ∈ B ...
Study of Stochastic Differential Equation Driven by Time-Changed Levy Noise
(2020-03-24)
This dissertation is composed of two parts. The first part studies stabilities of the solution
of stochastic differential equation (SDE) driven by time-changed L´evy noise in probability,
moment, and path sense. This ...
Survival, Count and Discrete Mixture Models for Analyzing Tumor Latency and Multiplicity in Carcinogenesis and Chemoprevention
(2013-04-09)
Since the chemicals, including Bisphenol A (BPA), Bis(2-ethylhexyl) phthalate (DEHP), have been reported for potential carcinogens separately and genistein is an controversial chemopreventive isoflavone, animal experiment ...
Techniques for Finding Homeomorphisms Between Generalized Inverse Limits
(2016-05-05)
Techniques are presented for finding homeomorphisms between generalized inverse limits, including a generalization of techniques introduced by Smith and Varagona, and a characterization in terms of category theory.
Text and Predictive Analytics; Classification of On-line Customer Opinion Surveys
(2011-11-17)
Thanks to computers and other data storage technologies, today we can easily save and rapid access to enormous amounts of data. According to results a report published by Andrew Harbison & Pearse Ryan, the information ...
THEORY OF HIGH-DIMENSIONAL ℓ1-PENALIZED LOGISTIC REGRESSION
(2023-08-04)
n the setting where sample size n is sufficiently large relative to the number of features p, a classical result is that fitting a logistic model by means of maximum likelihood produces estimates that are approximately ...
Thin-Type Dense Sets and Related Properties
(2010-04-07)
Dense sets in topological spaces may be thought of as those which are ubiquitous. We discuss dense sets in product spaces which also have a thin-type property, making them in some sense rare or spread out. Thin-type ...
Time Dependent Queuing Systems
(2008-12-15)
Using elementary probability theory, we establish limiting probabilities for the queue length of a queuing system whose arrivals follow a nonhomogeneous Poisson process and are served by a single server whose services also ...
Toeplitz Matrices are Unitarily Similar to Symmetric Matrices
(2017-07-25)
We prove that Toeplitz matrices are unitarily similar to complex symmetric matrices.
Moreover, two $n\times n$ unitary matrices that uniformly turn all $n\times n$ Toeplitz matrices via
similarity to complex symmetric ...
Topics in Edge Regular Graphs
(2014-07-24)
A graph, G, is edge-regular with parameters (n,d,lambda) if G is regular of degree d on n vertices and for all u, v in V(G) such that uv is in E(G), the order of the intersection of N(u) and N(v) is lambda, where N(v) ...
Torsionless Modules and Minimal Generating Sets for Ideals of Integral Domains
(2006-08-15)
This is a treatise of relationships between the number of elements necessary to generate the ideals of a domain and the
torsionless modules of that domain. Three types of domains are
identified according to natural ...
Transition Fronts in Time Heterogeneous Bistable Equations with Nonlocal Dispersal: Existence, Regularity, Stability and Uniqueness
(2015-04-30)
This dissertation is devoted to the existence, regularity, stability and uniqueness of transition fronts in nonlocal bistable equations in time heterogeneous media.
Instead of existence, we start our study with ...
Triangle Centers and Kiepert's Hyperbola
(2006-12-15)
In this paper, we discuss the proofs of the primary classical triangle centers and Kiepert's Hyperbola as a solution to Lemoine's Problem. The definitions of terms which will be used throughout the paper are presented. ...