Mathematics Commons^™

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed

Articles and Preprints

In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.

Control Of Error Rates In Adaptive Analysis Of Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level 1 - α.

Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests …

Canonical Thurston Obstructions, Kevin M. Pilgrim

Mathematics and Statistics Faculty Research & Creative Works

We refine Douady and Hubbard's proof of Thurston's topological characterization of rational functions by proving the following theorem. Let f: S2→S2 be a branched covering with finite postcritical set Pf and hyperbolic orbifold. Let Γc denote the set of all homotopy classes γ of nonperipheral, simple closed curves in S2-Pf such that the length of the unique geodesic homotopic to γ tends to zero under iteration of the Thurston map induced by f on Teichmüller space. Then either Γc is empty, and f is equivalent to a rational function, or else Γc is a Thurston obstruction. © 2001 Academic Press.

Branching Exponent Heterogeneity And Wall Shear Stress Distribution In Vascular Trees, Kelly Lynn Karau, Gary S. Krenz, Christopher A. Dawson

Mathematics, Statistics and Computer Science Faculty Research and Publications

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D ₁)^z = (D ₂)^z + (D ₃)^z; D ₁ is the parent vessel diameter and D ₂ and D ₃ are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance …

Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su

All HMC Faculty Publications and Research

We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin²(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.

A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X).

Boundary Layers In Channel Flow With Injection And Suction, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

We present a rigorous result regarding the boundary layer associated with the incompressible Newtonian channel flow with injection and suction. © 2000 Elsevier Science Ltd. All rights reserved.

A Coin Flipping Game With Non Transitive Odds, Stacy Jurgens

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Residual Properties And Almost Equicontinuity, Ethan Akin, Eli Glasner

Mathematics and Statistics Faculty Research & Creative Works

A property P of a compact dynamical system (X, f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjective inverse limits. Many transitivity properties are residual. Weak disjointness from all property P systems is a residual property provided P is a residual property stronger than transitivity. Here two systems are weakly disjoint when their product is transitive. Our main result says that for an almost equicontinuous system (X, f) with associated monothetic group Λ, (X, f) is weakly disjoint from all P systems if the only P systems upon which Λ acts are …

Heckman's Methodology For Correcting Selectivity Bias : An Application To Road Crash Costs, Margaret Giles

Research outputs pre 2011

Aggregate road crash costs are traditionally determined using average costs applied to incidence figures found in Police-notified crash data. Such data only comprise a non-random sample of the true population of road crashes, the bias being due to the existence of crashes that are not notified to the Police. The traditional approach is to label the Police-notified sample as 'non-random' thereby casting a cloud over data analyses using this sample. Heckman however viewed similar problems as 'omitted variables' problems in that the exclusion of some observations in a systematic manner (so-called selectivity bias) has inadvertently introduced the need for an …

On The Evolution Of Probability-Weighting Function And Its Impact On Gambling, Steven Li, Yun Hsing Cheung

Research outputs pre 2011

It is well known that individuals treat losses and gains differently and there exists non-linearity in probability. The asymmetry between gains and losses is highlighted by the reflection effect. The non-linearity in probability is described by the curvature of the probability-weighting function. This paper studies the evolution of the probability-weighting function. It is assumed that the probability weighting for an individual follows a mean-reverting stochastic process. The Monte Carlo simulation technique is employed to study the evolution of the weighting function. The evolution of the probability- weighting function implies that an individual does not treat gains or losses consistently over …

Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.

Analysis Of A Non-Replicated Split-Split Plot Experiment, Emily Simmons Sim

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

A major obstacle in the analysis of experimental data, in many situations, is the lack of "true" or "complete" replication. In some disciplines, researchers are very aware of the importance of replication and the methods for correctly replicating an experiment. In other subject areas, however, researchers are less aware of what it means to properly replicate an experiment. Due to this lack of awareness, many non-replicated experiments are carried out every year. For many of these non-replicated experiments, there is no satisfactory statistical analysis.

The subject of this report is the analysis of two non-replicated experiments in environmental engineering. First, …

Power Connector, Stephen L. Clark, Joseph B. Shuey, Jose L. Ortega, John B. Brown Iii

Mathematics and Statistics Faculty Research & Creative Works

A pair of mating connectors includes a receptacle having an insulative housing and at least one conductive receptacle contact with a pair of spaced walls forming a plug contact receiving space. The plug connector has an insulative housing and at least one conductive contact having a pair of spaced walls which converge to form a projection engageable in the plug receiving space of the receptacle contact. In each case, the spaced walls are joined by a bridging structure that unites the walls. The plug and receptacle contacts are retained in the respective housings by engagement of opposed lateral edge portions …

Commuting Self-Adjoint Extensions Of Symmetric Operators Defined From The Partial Derivatives, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂x_j):j=1,...,d} with domain C^∞_c(Ω) where the self-adjointness is defined relative to L²(Ω), and Ω is a given open subset of R^d.

The Expected Wet Period Of Finite Dam With Exponential Inputs, Eui Yong Lee, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for the expected hitting time of either 0 or V and a new expression for the distribution of the number of overflows during the wet period, both without the use of complex analysis.

A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao

Mathematics and Statistics Faculty Publications

An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative behaviour of solutions.

Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes

Mathematics and Statistics Faculty Research & Creative Works

For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.

Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.

A Census Of Rational Maps, Eva Brezin, Rosemary Byrne, Joshua Levy, Kevin M. Pilgrim, Kelly Plummer

Mathematics and Statistics Faculty Research & Creative Works

We discuss the general combinatorial, topological, algebraic, and dynamical issues underlying the enumeration of postcritically finite rational functions, regarded as holomorphic dynamical systems on the Riemann sphere. We present findings from our creation of a census of all degree two and three hyperbolic nonpolynomial maps with four or fewer postcritical points. Our data is tabulated in detail at. © 1999 American Mathematical Society.

Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia

Doctoral Dissertations

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.

A Rational Solution To Cootie, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

No abstract provided in this article.

Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski

Mathematics and Statistics Faculty Research & Creative Works

It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.

Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a two-parameter family of piecewise linear unimodal bonding maps. This investigation focuses on the parameter values at the boundary between a hereditarily decomposable inverse limit and an inverse limit containing an indecomposable continuum. © 1999 American Mathematical Society.

Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.

A Leveque-Type Lower Bound For Discrepancy, Francis E. Su

All HMC Faculty Publications and Research

A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVeque. An analogous bound is proved for discrepancy on R^k / Z^k. These are discussed in the more general context of the discrepancy of probablity measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.