Statistics and Probability Commons^™

Student Fact Book, Fall 2009, Thirty-Third Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2009.

A Berry-Esseen Theorem For Sample Quantiles Under Weak Dependence, S. N. Lahiri, Shuxia Sun

Mathematics and Statistics Faculty Publications

This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n^-1/2) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n^-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile …

A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng

Mathematics and Statistics Faculty Publications

We present a direct, linear boundary integral equation method for the inverse problem of recovering the Robin coefficient from a single partial boundary measurement of the solution to the Laplace equation.

A Note On The Positive Solutions Of An Inhomogeneous Elliptic Equation On Rn, Yinbin Deng, Yi Li, Fen Yang

Mathematics and Statistics Faculty Publications

This paper is contributed to the elliptic equation

(0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, x∈Rn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than r−m at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.

Periodic Traveling Waves In Sirs Endemic Models, Tong Li, Yi Li, Herbert W. Hethcote

Mathematics and Statistics Faculty Publications

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious …

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.

Student Fact Book, Fall 2008, Thirty-Second Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2008.

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).

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.

Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith

Mathematics and Statistics Faculty Publications

The highly conductive surface layers found in nearly all as-grown or annealed bulk ZnO wafers are studied by temperature-dependent Hall-effect and secondary-ion mass spectroscopy (SIMS) measurements. In this work, we have used annealing in N₂ at 900 degrees C, and forming gas (5% H₂ in N₂) at 600 degrees C, to cause a large enough surface conduction that SIMS measurements can be reliably employed. The increased near-surface donor density, as determined from two-layer Hall-effect modeling, is consistent with an increased near-surface concentration of Al, Ga, and In atoms, resulting from diffusion. There is no evidence for …

Student Fact Book, Fall 2007, Thirty-First Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2007.

Decompositions Of Signed-Graphic Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

Student Fact Book, Fall 2006, Twenty-Ninth Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2006.

Allometric Extension For Multivariate Regression Models, Thaddeus Tarpey, Christopher T. Ivey

Mathematics and Statistics Faculty Publications

In multivariate regression, interest lies on how the response vector depends on a set of covariates. A multivariate regression model is proposed where the covariates explain variation in the response only in the direction of the first principal component axis. This model is not only parsimonious, but it provides an easy interpretation in allometric growth studies where the first principal component of the log-transformed data corresponds to constants of allometric growth. The proposed model naturally generalizes the two–group allometric extension model to the situation where groups differ according to a set of covariates. A bootstrap test for the model is …

Electrical Properties Of Unintentionally Doped Semi-Insulating And Conducting 6h-Sic, William C. Mitchel, W. D. Mitchell, Z. Q. Fang, S. R. Smith, Helen Smith, Igor Khlebnikov, Y. I. Khlebnikov, C. Basceri, C. Balkas

Mathematics and Statistics Faculty Publications

Temperature dependent Hall effect (TDH), low temperature photoluminescence (LTPL), secondary ion mass spectrometry (SIMS), optical admittance spectroscopy (OAS), and thermally stimulated current (TSC) measurements have been made on 6H-SiC grown by the physical vapor transport technique without intentional doping. n- and p-type as well semi-insulating samples were studied to explore the compensation mechanism in semi-insulating high purity SiC. Nitrogen and boron were found from TDH and SIMS measurements to be the dominant impurities that must be compensated to produce semi-insulating properties. The electrical activation energy of the semi-insulating sample determined from the dependence of the resistivity …

Bias Matroids With Unique Graphical Representations, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a 3-connected biased graph Ω with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of Ω is uniquely represented by Ω.

Algebraic Characterizations Of Graph Imbeddability In Surfaces And Pseudosurfaces, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications. The specifications for the pseudosurface are: the number of face-connected components, the number of pinches, the number of crosscaps and handles, and the dimension of the first Z2-homology group. The characterizations are formulated in terms of the existence of a dual graph G ∗ on the same set of edges as G which satisfies algebraic conditions inspired by homology groups and their intersection products.

On Adaptive Testing In Orthogonal Saturated Designs, Daniel T. Voss, Weizhen Wang

Mathematics and Statistics Faculty Publications

Adaptive, size-a step-down tests are provided for the analysis of orthogonal saturated designs. The tests work effectively under effect sparsity, and include as special cases the individual nonadaptive tests of Berk and Picard (1991) and the simultaneous nonadaptive tests of Voss (1988). The approach is similar to that used by Wang and Voss (2003) to construct adaptive confidence intervals, but testing is simpler because one can use the same denominator for all statistics. Step-down tests also have a clear power advantage over simultaneous confidence intervals and analogous single-step tests, as is demonstrated theoretically and assessed via simulation.

Student Fact Book, Fall 2005, Twenty-Ninth Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2005.

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 …

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 …

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.

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 …

Student Fact Book, Fall 2004, Twenty-Eighth Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2004.

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …