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Articles 1 - 14 of 14
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Approximation By Bernstein Polynomials At The Point Of Discontinuity, Jie Ling Liang
Approximation By Bernstein Polynomials At The Point Of Discontinuity, Jie Ling Liang
HIM 1990-2015
Chlodovsky showed that if x0 is a point of discontinuity of the first kind of the function f, then the Bernstein polynomials Bn(f, x0) converge to the average of the one-sided limits on the right and on the left of the function f at the point x0. In 2009, Telyakovskii in (5) extended the asymptotic formulas for the deviations of the Bernstein polynomials from the differentiable functions at the first-kind discontinuity points of the highest derivatives of even order and demonstrated the same result fails for the odd order case. Then in 2010, Tonkov in (6) found the right formulation …
Estimation For The Cox Model With Various Types Of Censored Data, Tonya Riddlesworth
Estimation For The Cox Model With Various Types Of Censored Data, Tonya Riddlesworth
Electronic Theses and Dissertations
In survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) F[subscript n](t,z) for joint distribution function F[sub 0](t,z) of survival time T and covariate Z, where T is subject to right censoring, noting …
Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman
Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman
Electronic Theses and Dissertations
The energy of a graph began with German physicist, Erich H¨uckel’s 1931 paper, Quantenttheoretische Beitr¨age zum Benzolproblem. His work developed a method for computing the binding energy of the π-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n × n matrix used in solving Schr¨odinger’s eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total π-electron energy. The criteria …
Prediction Of Survival Of Early Stages Lung Cancer Patients Based On Er Beta Cellular Expressions And Epidemiological Data, Evgeny Martinenko
Prediction Of Survival Of Early Stages Lung Cancer Patients Based On Er Beta Cellular Expressions And Epidemiological Data, Evgeny Martinenko
Electronic Theses and Dissertations
We attempted a mathematical model for expected prognosis of lung cancer patients based on a multivariate analysis of the values of ER-interacting proteins (ERbeta) and a membrane bound, glycosylated phosphoprotein MUC1), and patients clinical data recorded at the time of initial surgery. We demonstrate that, even with the limited sample size available to use, combination of clinical and biochemical data (in particular, associated with ERbeta and MUC1) allows to predict survival of lung cancer patients with about 80% accuracy while prediction on the basis of clinical data only gives about 70% accuracy. The present work can be viewed as a …
Bayesian Model Selection For Classification With Possibly Large Number Of Groups, Justin Kyle Davis
Bayesian Model Selection For Classification With Possibly Large Number Of Groups, Justin Kyle Davis
Electronic Theses and Dissertations
The purpose of the present dissertation is to study model selection techniques which are specifically designed for classification of high-dimensional data with a large number of classes. To the best of our knowledge, this problem has never been studied in depth previously. We assume that the number of components p is much larger than the number of samples n, and that only few of those p components are useful for subsequent classification. In what follows, we introduce two Bayesian models which use two different approaches to the problem: one which discards components which have “almost constant” values (Model 1) and …
Price Discovery In The U.S. Bond Market Trading Strategies And The Cost Of Liquidity, Haimei Shao
Price Discovery In The U.S. Bond Market Trading Strategies And The Cost Of Liquidity, Haimei Shao
Electronic Theses and Dissertations
The world bond market is nearly twice as large as the equity market. The goal of this dissertation is to study the dynamics of bond price. Among the liquidity risk, interest rate risk and default risk, this dissertation will focus on the liquidity risk and trading strategy. Under the mathematical frame of stochastic control, we model price setting in U.S. bond markets where dealers have multiple instruments to smooth inventory imbalances. The difficulty in obtaining the optimal trading strategy is that the optimal strategy and value function depend on each other, and the corresponding HJB equation is nonlinear. To solve …
Fractal Spectral Measures In Two Dimensions, Beng Oscar Alrud
Fractal Spectral Measures In Two Dimensions, Beng Oscar Alrud
Electronic Theses and Dissertations
We study spectral properties for invariant measures associated to affine iterated function systems. We present various conditions under which the existence of a Hadamard pair implies the existence of a spectrum for the fractal measure. This solves a conjecture proposed by Dorin Dutkay and Palle Jorgensen, in several special cases in dimension 2.
Algebraic Aspects Of (Bio) Nano-Chemical Reaction Networks And Bifurcations In Various Dynamical Systems, Teng Chen
Electronic Theses and Dissertations
The dynamics of (bio) chemical reaction networks have been studied by different methods. Among these methods, the chemical reaction network theory has been proven to successfully predicate important qualitative properties, such as the existence of the steady state and the asymptotic behavior of the steady state. However, a constructive approach to the steady state locus has not been presented. In this thesis, with the help of toric geometry, we propose a generic strategy towards this question. This theory is applied to (bio)nano particle configurations. We also investigate Hopf bifurcation surfaces of various dynamical systems.
Iteratively Reweighted Least Squares Minimization With Prior Information A New Approach, Dmitriy Popov
Iteratively Reweighted Least Squares Minimization With Prior Information A New Approach, Dmitriy Popov
Electronic Theses and Dissertations
Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of …
Analytic & Numerical Study Of A Vortex Motion Equation, Daniel Bueller
Analytic & Numerical Study Of A Vortex Motion Equation, Daniel Bueller
Electronic Theses and Dissertations
A nonlinear second order differential equation related to vortex motion is derived. This equation is analyzed using various numerical and analytical techniques including finding approximate solutions using a perturbative approach.
Convergence Of The Mean Shift Algorithm And Its Generalizations, Ting Hu
Convergence Of The Mean Shift Algorithm And Its Generalizations, Ting Hu
Electronic Theses and Dissertations
Mean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has been rigorously proved only very recently, but with strong assumptions. In this thesis, the method of mean shift is …
Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii
Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii
Electronic Theses and Dissertations
Defensive alliances are a way of using graphs to model the defense of resources (people, buildings, countries, etc.) against attacks where the number of potential attackers against each resource is known. The initial study of defensive alliances focused on questions of minimal defensive alliances in a graph and the minimum possible size of a defensive alliance in a graph, but in order to apply defensive alliances in modeling real-world situations, additional considerations are important. In particular, since each vertex in a defensive alliance represents some real-world object that has a cost associated with remaining in the defensive alliance, it is …
Exploring Confidence Intervals In The Case Of Binomial And Hypergeometric Distributions, Irene Mojica
Exploring Confidence Intervals In The Case Of Binomial And Hypergeometric Distributions, Irene Mojica
Electronic Theses and Dissertations
The objective of this thesis is to examine one of the most fundamental and yet important methodologies used in statistical practice, interval estimation of the probability of success in a binomial distribution. The textbook confidence interval for this problem is known as the Wald interval as it comes from the Wald large sample test for the binomial case. It is generally acknowledged that the actual coverage probability of the standard interval is poor for values of p near 0 or 1. Moreover, recently it has been documented that the coverage properties of the standard interval can be inconsistent even if …
Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith
Electronic Theses and Dissertations
In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in …