Mathematics Commons^™

A Trust-Based Secure Service Discovery (Tssd) Model For Pervasive Computing, Sheikh Iqbal Ahamed, Moushumi Sharmin

Mathematics, Statistics and Computer Science Faculty Research and Publications

To cope with the challenges posed by device capacity and capability, and also the nature of ad hoc networks, a Service discovery model is needed that can resolve security and privacy issues with simple solutions. The use of complex algorithms and powerful fixed infrastructure is infeasible due to the volatile nature of pervasive environment and tiny pervasive devices. In this paper, we present a trust-based secure Service discovery model, TSSD (trust-based secure service discovery) for a truly pervasive environment. Our model is a hybrid one that allows both secure and non-secure discovery of services. This model allows Service discovery and …

A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as …

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …

Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li

Yi Li

In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.

Ubi-App: A Ubiquitous Application For Universal Access From Handheld Devices, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Universal access from a handheld device (such as a PDA, cell phone) at any time or anywhere is now a reality. Ubicomp Assistant (UA) (Sharmin et al. in Proceedings of the 21st annual ACM symposium on applied computing (ACM SAC 2006), Dijon, France, pp 1013–1017, 2006) is an integral service of MARKS (Sharmin et al. in Proceedings of the third international conference on information technology: new generations (ITNG 2006), Las Vegas, Nevada, USA, pp 306–313, 2006). It is a middleware developed for handheld devices, and has been designed to accommodate different types of users (e.g., education, healthcare, marketing, or business). …

Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li

Mathematics and Statistics Faculty Publications

In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.

A Poisson-Like Model Of Sub-Clinical Signs From The Examination Of Healthy Aging Subjects, Stephen Merrill, Barbara Myklebust, Joel B. Myklebust, Norman Reynolds, Edmund Duthie

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background and aims: Our studies of the standard neurological examination on 66 middle-aged (50–64 yrs) and elderly subjects (65–84 yrs) demonstrate that healthy elders have neurological deficits (or “signs”) that are not associated with specific known neurological disease. The purpose of the current study is to describe this loss of neurological function in healthy aging subjects as seen through accumulated subclinical neurological signs present.

Methods: Logistic regression is applied to the data on each of six signs. Parameters determined are used to describe the distribution of first occurrence times for each sign. The results are then used to construct a …

Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …

The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Biologists hypothesize that thousands of micro-scale hairs found on bat wings function as a network of air-flow sensors as part of a biological feedback flow control loop. In this work, we investigate hair-cell sensors as a means of detecting flow features in an unsteady separating flow over a cylinder. Individual hair-cell sensors were modeled using an Euler-Bernoulli beam equation forced by the fluid flow. When multiple sensor simulations are combined into an array of hair-cells, the response is shown to detect the onset and span of flow reversal, the upstream movement of the point of zero wall shear-stress, and the …

Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number to infinity. We study asymptotic behavior of stationary statistical solutions, or in-variant measures, to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the invariant measures of the Boussinesq system for Rayleigh-Bénard convection converge …

Architecture And Implementation Of A Trust Model For Pervasive Applications, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Sailaja Bulusu, Mehrab Monjur

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collaborative effort to share resources is a significant feature of pervasive computing environments. To achieve secure service discovery and sharing, and to distinguish between malevolent and benevolent entities, trust models must be defined. It is critical to estimate a device's initial trust value because of the transient nature of pervasive smart space; however, most of the prior research work on trust models for pervasive applications used the notion of constant initial trust assignment. In this paper, we design and implement a trust model called DIRT. We categorize services in different security levels and depending on the service requester's context information, …

The Weak Euler Scheme For Stochastic Delay Equations, Evelyn Buckwar, Rachel Kuske, Salah-Eldin A. Mohammed, Tony Shardlow

Articles and Preprints

We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

The Signed-Graphic Representations Of Wheels And Whirls, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.

Connectivity In Frame Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).

Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene

Publications and Research

A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …

An Impregnable Lightweight Device Discovery (Ildd) Model For The Pervasive Computing Environment Of Enterprise Applications, Munirul H. Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

The worldwide use of handheld devices (personal digital assistants, cell phones, etc.) with wireless connectivity will reach 2.6 billion units this year and 4 billion by 2010. More specifically, these handheld devices have become an integral part of industrial applications. These devices form pervasive ad hoc wireless networks that aide in industry applications. However, pervasive computing is susceptible and vulnerable to malicious active and passive snoopers. This is due to the unavoidable interdevice dependency, as well as a common shared medium, very transitory connectivity, and the absence of a fixed trust infrastructure. In order to ensure security and privacy in …

Quasigeometric Distributions And Extra Inning Baseball Games, Darren B. Glass, Philip J. Lowry

Math Faculty Publications

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and …

An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene

Publications and Research

Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.

Octahedral Dice, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be given …

A Comparison Of Different Methods For Predicting Cancer Mortality Counts At The State Level, Corinne Wilson

Virginia Journal of Science

Cancer is a major health issue in the United States. Reliable estimates of yearly cancer mortality counts are essential for resourcing and planning. The American Cancer Society has used several methods of forecasting to estimate the future cancer burden and researchers are continually working to develop new methods with improved performance. There have been studies comparing different models for predicting the US cancer mortality counts. This study explores and compares several different models for cancer mortality count predictions at the state level, principally for the state of Virginia. Results of the comparisons appear to show the final improved model to …

Maximum Likelihood Estimation Methodology Comparison For The Three-Parameter Weibull Distribution With Applications To Offshore Oil Spills In The Gulf Of Mexico, William V. Harper, Thomas R. James, Ted G. Eschenbach, Leigh Slauson

Mathematics Faculty Scholarship

Maximum Likelihood estimation of the two-parameter Weibull distribution is straightforward; however, there are multiple methods for maximum likelihood estimation of the three-parameter Weibull. This paper presents an evaluation of these methods using four data sets including oil spill data from the Gulf of Mexico. Highlighted are fairly major differences in the estimated parameters between nine statistical packages. A VBA routine has been developed allowing practitioners to implement three-parameter Weibull maximum likelihood estimate within Excel. The code and support documentation are available free at http:faculty.otterbein.edu/WHarper.

Molecular Targets Of 2,3,7,8-Tetrachlorodibenzo-P-Dioxin (Tcdd) Within The Zebrafish Ovary: Insights Into Tcdd-Induced Endocrine Disruption And Reproductive Toxicity, Tisha C. King Heiden, Craig Struble, Matthew L. Rise, Martin J. Hessner, Reinhold J. Hutz, Michael J. Carvan Iii

Mathematics, Statistics and Computer Science Faculty Research and Publications

TCDD is a reproductive toxicant and endocrine disruptor, yet the mechanisms by which it causes these reproductive alterations are not fully understood. In order to provide additional insight into the molecular mechanisms that underlie TCDD's reproductive toxicity, we assessed TCDD-induced transcriptional changes in the ovary as they relate to previously described impacts on serum estradiol concentrations and altered follicular development in zebrafish. In silico computational approaches were used to correlate candidate regulatory motifs with observed changes in gene expression. Our data suggest that TCDD inhibits follicle maturation via attenuated gonadotropin responsiveness and/or depressed estradiol biosynthesis, and that interference of estrogen-regulated …

Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.

On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …

Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.

Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam

Department of Math & Statistics Faculty Publications

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …

Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.