Statistics and Probability Commons^™

Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If u_α(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that lim_α→0αu_α(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.

A Survey On Intrusion Detection Approaches, A Murali M. Rao

International Conference on Information and Communication Technologies

Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Usages of computer network services are tremendously increasing day by day and at the same time intruders are also playing a major role to deny network services, compromising the crucial services for Email, FTP and Web. Realizing the importance of the problem due to intrusions, many researchers have taken up research in this area and have proposed several solutions. It has come to a stage to take a stock of the research results and project a comprehensive view so …

Specific Ige Response To Purified And Recombinant Allergens In Latex Allergy, Viswanath P. Kurup, Gordon L. Sussman, Hoong Y. Yeang, Nancy Elms, Heimo Breiteneder, Siti Am Arif, Kevin J. Kelly, Naveen K. Bansal, Jordan N. Fink

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

In recent years, allergy to natural rubber latex has emerged as a major allergy among certain occupational groups and patients with underlying diseases. The sensitization and development of latex allergy has been attributed to exposure to products containing residual latex proteins. Although improved manufacturing procedures resulted in a considerable reduction of new cases, the potential risk for some patient groups is still great. In addition the prevalent cross-reactivity of latex proteins with other food allergens poses a major concern. A number of purified allergens and a few commercial kits are currently available, but no concerted effort was undertaken to …

Investigation Of Laser Beam Induced Current Techniques For Heterojunction Photodiode Characterization, Weifu Fang, David A. Redfern, Kazufumi Ito, G. Bahir, Charles A. Musca, John M. Dell, Lorenzo Faraone

Mathematics and Statistics Faculty Publications

A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P-n HgCdTe heterojunction photodiode structures. In particular, the question of …

Good Measures On Cantor Space, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U): U is clopen} of the unit interval. It is a topological invariant for the measure. For the class of good measures, it is a complete invariant. A full, nonatomic measure μ is good if whenever U, V are clopen sets with μ(U) < μ(V), there exists W a clopen subset of V such that μ(W) = μ(U). These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, G δ conjugacy class. ©2004 American Mathematical Society.

Computational Optical Biopsy, Yi Li, Ming Jiang, Ge Wang

Mathematics and Statistics Faculty Publications

Optical molecular imaging is based on fluorescence or bioluminescence, and hindered by photon scattering in the tissue, especially in patient studies. Here we propose a computational optical biopsy (COB) approach to localize and quantify a light source deep inside a subject. In contrast to existing optical biopsy techniques, our scheme is to collect optical signals directly from a region of interest along one or multiple biopsy paths in a subject, and then compute features of an underlying light source distribution. In this paper, we formulate this inverse problem in the framework of diffusion approximation, demonstrate the solution uniqueness properties in …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …

Statistical Analysis Of Longitudinal And Multivariate Discrete Data, Deepak Mav

Mathematics & Statistics Theses & Dissertations

Correlated multivariate Poisson and binary variables occur naturally in medical, biological and epidemiological longitudinal studies. Modeling and simulating such variables is difficult because the correlations are restricted by the marginal means via Fréchet bounds in a complicated way. In this dissertation we will first discuss partially specified models and methods for estimating the regression and correlation parameters. We derive the asymptotic distributions of these parameter estimates. Using simulations based on extensions of the algorithm due to Sim (1993, Journal of Statistical Computation and Simulation, 47, pp. 1–10), we study the performance of these estimates using infeasibility, coverage probabilities of the …

A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin

Mathematics and Statistics Faculty Research & Creative Works

Many efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.

Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to …

Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.

Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness and extremality results.

Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.

A Quasilinearization Approach For Two Point Nonlinear Boundary Value Problems On Time Scales, Elvan Akin, Ferhan Atici. Merdivenci

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Microarray Data From A Statistician’S Point Of View, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

Stability Properties Of Linear Volterra Integrodifferential Equations With Nonlinear Perturbation, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

A Lyapunov functional is employed to obtain conditions that guarantee stability, uniform stability and uniform asymptotic stability of the zero solution of a scalar linear Volterra integrodifferential equation with nonlinear perturbation.

Boundedness And Stability In Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam, Ernest Yankson

Mathematics Faculty Publications

In this paper we study stability and boundedness of the nonlinear difference equation

x(t+1)=a(t)x(t)+c(t)Δx(t−g(t))+q(x(t),x(t−g(t))).

In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.

On Cographic Matroids And Signed-Graphic Matroids, Dan Slilaty

Mathematics and Statistics Faculty Publications

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-planar graphs, then the cographic matroids of G1, . . . , G29 are among the forbidden minors for the class of bias matroids …

Estimating Load-Sharing Properties In A Dynamic Reliability System, Paul H. Kvam, Edsel A. Peña

Department of Math & Statistics Faculty Publications

An estimator for the load-share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (˙) and failure rate r (˙). In an equal load-share model, after the first of k components fails, failure rates for the remaining components change from r (t) to γ1r (t), then to γ2r (t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline …

Mapping Properties Of Co-Existentially Closed Continua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A continuous surjection between compacta is called co-existential if it is the second of two maps whose composition is a standard ultracopower projection. A continuum is called co-existentially closed if it is only a co-existential image of other continua. This notion is not only an exact dual of Abraham Robinson's existentially closed structures in model theory, it also parallels the definition of other classes of continua defined by what kinds of continuous images they can be. In this paper we continue our study of co-existentially closed continua, especially how they (and related continua) behave in certain mapping situations.

A Genetic Algorithm Hybrid For Constructing Optimal Response Surface Designs, David Drain, W. Matthew Carlyle, Douglas C. Montgomery, Connie Borror, Christine Anderson-Cook

Mathematics and Statistics Faculty Research & Creative Works

Hybrid heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective, and simple heuristics like simulated annealing fail to find good solutions. One such heuristic hybrid is GASA (genetic algorithm-simulated annealing), developed to take advantage of the exploratory power of the genetic algorithm, while utilizing the local optimum exploitive properties of simulated annealing. the successful application of this method is demonstrated in a difficult design problem with multiple optimization criteria in an irregularly shaped design region. Copyright © 2004 John Wiley & Sons, Ltd.

Infinite Prandtl Number Limit Of Rayleigh-Bénard Convection, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer. © 2004 Wiley Periodicals, Inc.

Random Walks On The Torus With Several Generators, Timothy Prescott '02, Francis E. Su

All HMC Faculty Publications and Research

Given n vectors {_i} ∈ [0, 1)^d, consider a random walk on the d-dimensional torus ^d = ℝ^d/ℤ^d generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*^k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*^k) ≥ C₁k^−n/2, where C₁ = C(n, d) is …

Modulation Of Airway Inflammation By Immunostimulatory Cpg Oligodeoxynucleotides In A Murine Model Of Allergic Aspergillosis, Banani Banerjee, Kevin J. Kelly, Jordan N. Fink, James D. Henderson Jr., Naveen K. Bansal, Viswanath P. Kurup

Mathematics, Statistics and Computer Science Faculty Research and Publications

Allergic aspergillosis is a Th2 T-lymphocyte-mediated pulmonary complication in patients with atopic asthma and cystic fibrosis. Therefore, any therapeutic strategy that selectively inhibits Th2 T-cell activation may be useful in downregulating allergic lung inflammation in asthma. In the present study, we developed a CpG oligodeoxynucleotide (ODN)-based immune intervention of allergic inflammation in a mouse model of allergic aspergillosis. Four different groups of mice were used in a short-term immunization protocol. Three experimental groups of animals (groups 1 to 3) were sensitized with Aspergillus fumigatus antigens. Animals in group 1 were immunized with A. fumigatus antigen alone, while those in group …

Deadline Analysis Of Interrupt-Driven Software, Dennis Brylow, Jens Palsberg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Real-time, reactive, and embedded systems are increasingly used throughout society (e.g., flight control, railway signaling, vehicle management, medical devices, and many others). For real-time, interrupt-driven software, timely interrupt handling is part of correctness. It is vital for software verification in such systems to check that all specified deadlines for interrupt handling are met. Such verification is a daunting task because of the large number of different possible interrupt arrival scenarios. For example, for a Z86-based microcontroller, there can be up to six interrupt sources and each interrupt can arrive during any clock cycle. Verification of such systems has traditionally relied …

Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …

Large Prandtl Number Behavior Of The Boussinesq System Of Rayleigh-Bénard Convection, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We establish the validity of the infinite Prandtl number model as an approximation of the Boussinesq system at large Prandtl number on finite and infinite time interval, as well as in some statistical sense. © 2004 Elsevier Ltd. All rights reserved.

Oscillation Of Symplectic Dynamic Systems, Martin Bohner, Ondřej Došlý

Mathematics and Statistics Faculty Research & Creative Works

We investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. the unperturbed system is supposed to be Non oscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well. © Australian Mathematical Society 2004.

Sub-Supersolution Method For Quasilinear Parabolic Variational Inequalities, Siegfried Carl, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about a systematic attempt to apply the sub-supersolution method to parabolic variational inequalities. We define appropriate concepts of sub-supersolutions and derive existence, comparison, and extremity results for such inequalities.