Physical Sciences and Mathematics Commons^™

Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao

All Dissertations

In this dissertation, we address several research problems in statistical inference. We obtain results in the following four directions: linear model selection, minimax estimation of linear functionals, Bayes type estimators for the survival functions based on right censored data, and estimation of survival functions based on doubly censored data.

Effects Of An Inserted Endoscope On Chyme Movement In Small Intestine – A Theoretical Model, V. P. Srivastava

Applications and Applied Mathematics: An International Journal (AAM)

The effects of an inserted endoscope on chyme movement in small intestine (gastrointestinal tract) have been investigated. The flow of chyme is induced by a progressive wave of area contraction along the length of intestinal wall under long wavelength approximation. It is found that the chyme movement is significantly influenced due to the presence of the endoscope. The pressure drop assumes lower values for higher values of the endoscope radius for small flow rates but the property reverses with increasing flow rates. The friction forces at intestinal wall and endoscope possess character similar to the pressure drop for any given …

Fuzzy Efficiency Measure With Fuzzy Production Possibility Set, T. Allahviranloo, F. Hosseinzade Lotfi, M. Adabitabar Firozja

Applications and Applied Mathematics: An International Journal (AAM)

The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. The notion of fuzziness has been introduced to deal with imprecise data. Fuzzy DEA models are made more powerful for applications. This paper develops the measure of efficiencies in input oriented of DMUs by envelopment form in fuzzy production possibility set (FPPS) with constant return to scale.

Statistical Issues In Proteomic Research, Jeffrey S. Morris

Jeffrey S. Morris

No abstract provided.

Bayesian Analysis For Penalized Spline Regression Using Win Bugs, Ciprian M. Crainiceanu, David Ruppert, M.P. Wand

Johns Hopkins University, Dept. of Biostatistics Working Papers

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. MCMC mixing is substantially improved from the previous versions by using low{rank thin{plate splines instead of truncated polynomial basis. Simulation time …

A Lower Estimate For The Norm Of The Kerzman-Stein Operator, Michael Bolt

University Faculty Publications and Creative Works

We establish an elementary lower estimate for the norm of the Kerzman-Stein operator for a smooth, bounded domain. The estimate involves the boundary length and logarithmic capacity. The estimate is tested on model domains for which the norm is known explicitly. It is shown that the estimate is sharp for an annulus and a strip, and is asymptotically sharp for an ellipse and a wedge. © 2007 Rocky Mountain Mathematics Consortium.

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

Age-Structured Population Model With Cannibalism, Mmohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An age-structured population model with cannibalism is investigated. We determine the steady states and study the local asymptotic stability as well as the global stability. The results in this paper generalize previous results.

On The Total Duration Of Negative Surplus Of A Risk Process With Two-Step Premium Function, Pavlina Jordanova

Applications and Applied Mathematics: An International Journal (AAM)

We consider a risk reserve process whose premium rate reduces from c_d to c_u when the reserve comes above some critical value v. In the model of Cramer-Lundberg with initial capital u ≥ 0, we obtain the probability that ruin does not occur before the first up-crossing of level v. When u < v, following H. Gerber and E. Shiu (1997), we derive the probability that starting with initial capital u ruin occurs and the severity of ruin is not bigger than v. Further we express the probability of ruin in the two step premium function model - ψ (u,v), by the last two probabilities. Our assumptions imply that the surplus process will go to infinity almost surely. This entails that the process will stay below zero only temporarily. We derive the distribution of the total duration of negative surplus and obtain its Laplace transform and mean value. As a consequence of these results, under certain conditions in the Model of Cramer-Lundberg we obtain the expected value of the severity of ruin. In the end of the paper we give examples with exponential claim sizes.

Stability Analysis For The Gurtin-Maccamy’S Age-Structured Population Dynamics Model, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of the Gurtin-MacCamy’s age-structured population dynamics model is investigated. We determine the steady states and study their stability. The results in this paper generalize previous results.

On A Class Of Backward Mckean-Vlasov Stochastic Equations In Hilbert Space: Existence And Convergence Properties, Nazim I. Mahmudov, Mark A. Mckibben

Mathematics Faculty Publications

This investigation is devoted to the study of a class of abstract first-order backward McKean-Vlasov stochastic evolution equations in a Hilbert space. Results concerning the existence and uniqueness of solutions and the convergence of an approximating sequence of solutions (and corresponding probability measures) are established. Examples that illustrate the abstract theory are also provided.

A New Family Of Pr Two Channel Filter Banks, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A new family of multidimensional dimensional (MD) perfect reconstruction (PR) two channel filter banks with finite impulse response (FIR) filters induced from systems of biorthogonal MD scaling functions and wavelets are introduced. One of the advantages of this construction is that the biorthogonal scaling functions and wavelets are easy to establish due to the interpolatory property of the scaling functions to start with. The other advantage is that all filters can be centrosymmetric or bi-linear phase. Examples of two dimensional (2D) bi-linear phase PR twochannel FIR filter banks will be demonstrated.

Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski

All HMC Faculty Publications and Research

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …

What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz

Dissertations

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …

Bidimensional Pr Qmf With Fir Filters, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed.

On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, D. N. Riahi

Applications and Applied Mathematics: An International Journal (AAM)

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …

Trends In Uspto Office Actions, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

Loss-Based Estimation With Evolutionary Algorithms And Cross-Validation, David Shilane, Richard H. Liang, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Many statistical inference methods rely upon selection procedures to estimate a parameter of the joint distribution of explanatory and outcome data, such as the regression function. Within the general framework for loss-based estimation of Dudoit and van der Laan, this project proposes an evolutionary algorithm (EA) as a procedure for risk optimization. We also analyze the size of the parameter space for polynomial regression under an interaction constraints along with constraints on either the polynomial or variable degree.

A Stable Algorithm For Flat Radial Basis Functions On A Sphere, Bengt Fornberg, Cecile M. Piret

Cecile M Piret

Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers to general multiobjective problems under a refined version of the subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers (as well as for conventional efficient and weak efficient …

Posterminaries: More Or Less Modern, Alexander H. King

Alexander H. King

It is yet another sign that I am aging. More and more often when young researchers hand me a written report of their research, I find myself criticizing their introductory section: “You need to start your literature survey with the original papers on this topic. Go and read…” followed by a citation to some classic of the learned literature.

Image Reconstruction In Multi-Channel Model Under Gaussian Noise, Veera Holdai, Alexander Korostelev

Mathematics Research Reports

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in N independent channels in Gaussian white noise. In each channel the image and the background intensities are unknown. They define a non-identifiable nuisance "parameter" that slows down the typical minimax rate of convergence. The large sample asymptotics of the minimax risk is found and an asymptotically optimal estimator for boundary function is suggested.

A Hyperbolic Two -Step Model Based Finite Difference Method For Studying Thermal Deformation In A Micro Thin Film Heated By Ultrashort -Pulsed Lasers, Tianchan Niu

Doctoral Dissertations

Heat transport through micro thin films plays a very important role in microtechnology applications. Many microelectronic devices have metal thin films as their key components. Microscale heat transfer is also important for the thermal processing of materials, including laser micromachining, laser patterning, laser synthesis and laser surface hardening. Hence, studying the thermal behavior of thin films is essential for predicting the performance of a microelectronic device or for obtaining the desired microstructure. Recently, it has become very popular to use ultrashort-pulsed lasers in thermal processing, which lasers have pulse durations of the order of subpicoseconds to femtoseconds, and these kinds …

A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker

Department of Mathematics: Faculty Publications

Three types of pseudocodewords for LDPC codes are found in the literature: graph cover pseudocodewords, linear programming pseudocodewords, and computation tree pseudocodewords. In this paper we first review these three notions and known connections between them. We then propose a new decoding rule — universal cover decoding — for LDPC codes. This new decoding rule also has a notion of pseudocodeword attached, and this fourth notion provides a framework in which we can better understand the other three.

Mathematical Analysis Of Pde Systems Which Govern °Uid Structure Interactive Phenomena, George Avalos, Roberto Triggiani

Department of Mathematics: Faculty Publications

In this paper, we review and comment upon recently derived results for time dependent partial differential equation (PDE) models, which have been used to describe the various fluid-structure interactions which occur in nature. For these fluid-structure PDEs, this survey is particularly focused on the authors' results of (i) semigroup wellposedness, (ii) stability, and (iii) backward uniqueness.

Necessary Conditions For Super Minimizers In Constrained Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.

The Apostle Table - Part Iii - Incompetent Endogenous Response Intransitivity, David Randall Jenkins

David Randall Jenkins

The Apostle Table illustrates a New Testament encryption scheme revealed in the Book of Matthew. Specifically, the list of the twelve apostles in Matthew, 10:1-4, points to the Matthew, Chapters 8 and 9, disciple characterizations. The disciples metaphorically characterize the social choice theory aspect of the scripture writers' (ordered relations theory: social choice theory: welfare model) regression. The paper is written in two parts: I. The Exogenous Pressures; and, II. The Endogenous Response. Interestingly, the paper explains why the crucified Jesus could not get off the cross.

Time-Dependent Performance Comparison Of Stochastic Optimization Algorithms, David Shilane, Jarno Martikainen, Seppo Ovaska

U.C. Berkeley Division of Biostatistics Working Paper Series

This paper proposes a statistical methodology for comparing the performance of stochastic optimization algorithms that iteratively generate candidate optima. The fundamental data structure of the results of these algorithms is a time series. Algorithmic differences may be assessed through a procedure of statistical sampling and multiple hypothesis testing of time series data. Shilane et al. propose a general framework for performance comparison of stochastic optimization algorithms that result in a single candidate optimum. This project seeks to extend this framework to assess performance in time series data structures. The proposed methodology analyzes empirical data to determine the generation intervals in …

Automorphic Decompositions Of Graphs, Robert Beeler

All Dissertations

Let G and H be graphs. A G-decomposition D of a graph H is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. It is well known that a graceful labelling (or more generally a rho-valuation) of a graph G induces a cyclic G-decomposition of a complete graph. We will extend these notions to that of a general valuation in a cyclic group. Such valuations yield decompositions of circulant graphs. We will show that every graph has a valuation and hence is a …

The Barycenter Of The Numerical Range Of A Matrix, Sean A. Broughton, Roger G. Lautzenheiser, Thomas Werne

Mathematical Sciences Technical Reports (MSTR)

The numerical range W(A) of an nxn matrix A is the totality of the scalar products <Ax,x> as x varies over all unit vectors in Cⁿ The barycenter (center of mass) of the numerical range is defined geometrically as the center of mass of W(A) considered as a planar lamina with variable density and also as a limit of sample averages (<Ax₁,x₁>+...+<Ax_N,x_N>)/N. Under a wide range the sampling schemes it is shown that the barycenter is the average of the spectrum …