Physical Sciences and Mathematics Commons^™

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

Self-Consistency Algorithms, Thaddeus Tarpey

Mathematics and Statistics Faculty Publications

The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.

Applications And Algorithms For Least Trimmed Sum Of Absolute Deviations Regression, Douglas M. Hawkins, David Olive

Articles and Preprints

High breakdown estimation (HBE) addresses the problem of getting reliable parameter estimates in the face of outliers that may be numerous and badly placed. In multiple regression, the standard HBE's have been those defined by the least median of squares (LMS) and the least trimmed squares (LTS) criteria. Both criteria lead to a partitioning of the data set's n cases into two “halves” – the covered “half” of cases are accommodated by the fit, while the uncovered “half”, which is intended to include any outliers, are ignored. In LMS, the criterion is the Chebyshev norm of the residuals of the …

A Hierarchy Of Maps Between Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev_≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev_≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …

Estimating The Probability Of Severe Convective Storms: A Local Perspective For The Central And Northern Plains, Preston W. Leftwich Jr.

NOAA Technical Reports and Related Materials

Summary and Conclusions

A procedure to estimate probabilities of the occurrence of severe convective storms within local areas has been described. Probabilities were based on a simulated climatology and the relative frequency of severe convective events when a selected site was contained within an operational Outlook or Watch. Combined data from five local areas were used to develop a general model for local probabilities within the central and northern Plains region. Attachment of probabilities to specific products placed values within a framework familiar to both forecasters and "end-users." Application of results in an operational scenario demonstrated representative local probabilities and …

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.

Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato

Mathematics, Statistics and Computer Science Faculty Research and Publications

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5<HS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2¹⁰. A modified method is proposed to correct for …

Student Fact Book, Fall 1999, Twenty Third Annual Edition November 1999, 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, 1999.

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Mathematics and Statistics Faculty Publications

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

In this paper, we examine a random version of the lattice point problem.

How Much Justice Hangs In The Balance? A New Look At Hung Jury Rates, Paula Hannaford-Agor, Valerie P. Hans, G. Thomas Munsterman

Cornell Law Faculty Publications

Reports of apparent increases in the number of hung juries in some jurisdictions have caused concern among policy makers. A 1995 report by the California District Attorneys Association cited hung jury rates in 1994 that exceeded 15 percent in some jurisdictions (the rates varied from 3 to 23 percent across the nine counties for which data were available). In 1996, the District of Columbia Superior Court reported a higher-than-expected hung jury rate of 11 percent. Why juries hang at these rates isn't clear, but some commentators have claimed that hung juries are the product of eccentric or nullifying holdout jurors …

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Let D be a smoothly bounded domain in Euclidean space and let X_t be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by X_t, where the average is taken overall starting points in D.

Openness And Monotoneity Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Level Adjusted Exponential Smoothing: A Method For Judgmentally Adjusting Exponential Smoothing Models For Planned Discontinuities, Dan Williams, Don Miller

Publications and Research

Forecasters often make judgmental adjustments to exponential smoothing forecasts to account for the effects of a future planned change. While this approach may produce sound initial forecasts, it can result in diminished accuracy for forecast updates. A proposed technique lets the forecaster include policy change adjustments within an exponential smoothing model. For 20 real data series representing Virginia Medicaid expenses, initial forecasts and forecast updates are developed using the proposed technique and several alternatives, and they are updated through various simulated level shifts. The proposed technique was more accurate than the alternatives in updating forecasts when a shift in level …

Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00

All HMC Faculty Publications and Research

No abstract provided in this article.

Spectral Indications Of Unexpected Contributors To Atmospheric Co2 Variability?, Gary B. Hughes, Robert Gigengack, Haralambos N. Kritikos

Statistics

The frequency spectrum of Northern Hemisphere atmospheric CO₂ concentration shows strong periodicities at 6.2, 1.0 and 0.5 years. The 6.2 year cyclicity has been attributed to non-linear interactions between the annual cycle and the atmospheric pole tide. The yearly signal is linked to terrestrial photosynthesis; phase analysis shows that annual CO₂ minima occur at a lag of approximately 85 days from insolation maxima. Variations in the nominal yearly period occur during times of anomalous anthropogenic CO₂ production. Periodicity at 6 months represents a deviation of the yearly signal from an annual sinusoid. If the yearly signal is …

Shopping For Judges: An Empirical Analysis Of Venue Choice In Large Chapter 11 Reorganizations, Theodore Eisenberg, Lynn M. Lopucki

Cornell Law Faculty Publications

For almost two decades, an embarrassing pattern of forum shopping has been developing in the highly visible world of big-case bankruptcy reorganization. Forum shopping--defined here as the act of filing in a court that does not serve the geographical area of the debtor's corporate headquarters--now occurs in more than half of all big-case bankruptcies. Two jurisdictions have attracted most of the forum shoppers. During the 1980s, when a large portion of the shopping was to New York, the lawyers involved asserted that New York was a natural venue because of its role as the country's financial capital and because so …

Anticommuting Derivations, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.

Improved Feasible Solution Algorithms For High Breakdown Estimation, Douglas M. Hawkins, David J. Olive

Articles and Preprints

High breakdown estimation allows one to get reasonable estimates of the parameters from a sample of data even if that sample is contaminated by large numbers of awkwardly placed outliers. Two particular application areas in which this is of interest are multiple linear regression, and estimation of the location vector and scatter matrix of multivariate data. Standard high breakdown criteria for the regression problem are the least median of squares (LMS) and least trimmed squares (LTS); those for the multivariate location/scatter problem are the minimum volume ellipsoid (MVE) and minimum covariance determinant (MCD). All of these present daunting computational problems. …

Judicial Politics, Death Penalty Appeals, And Case Selection: An Empirical Study, John H. Blume, Theodore Eisenberg

Cornell Law Faculty Publications

Several studies try to explain case outcomes based on the politics of judicial selection methods. Scholars usually hypothesize that judges selected by partisan popular elections are subject to greater political pressure in deciding cases than are other judges. No class of cases seems more amenable to such analysis than death penalty cases. No study, however, accounts both for judicial politics and case selection, the process through which cases are selected for death penalty litigation. Yet, the case selection process cannot be ignored because it yields a set of cases for adjudication that is far from a random selection of cases. …

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan

Mathematics, Statistics and Computer Science Faculty Research and Publications

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …

Kriging Puerto Rico Rainfall, Gary B. Hughes

Statistics

In Earth science research, climatic conditions can have significant effects on dynamic processes. For example, the growth of forests is affected by temperature, rainfall and other climatic variables. However, these climate parameters are rarely measured at the forest stands whose growth is being investigated. The climate conditions are measured at nearby weather stations, though, and it is a common approach to use the weather station data to ‘predict’ the climate at the study site

Judicial Decisionmaking In Federal Products Liability Cases, 1978-1997, Theodore Eisenberg

Cornell Law Faculty Publications

In 1992, Professor James Henderson and I wrote that, throughout the 1980s, a quiet, pro-defendant revolution in products liability had occurred. That revolution was likely largely the product of a "widespread, independent shift in judicial attitudes." It was not discernable in cases tried before juries. The federal data used in that study were available through 1989. Also in 1992, using the same database, Professor Kevin Clermont and I wrote about the surprising relation between plaintiff win rates in judge and jury trials in products liability cases. Plaintiffs prevailed at a higher rate before judges than they did before juries. Comparable …

Nonparametric Estimation Of The Survival Function Based On Censored Data With Additional Observations From The Residual Distribution, Paul Kvam, Harshinder Singh, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

We derive the nonparametric maximum likelihood estimator (NPMLE) of the distribution of the test items using a random, right-censored sample combined with an additional right-censored, residual-lifetime sample in which only lifetimes past a known, fixed time are collected. This framework is suited for samples for which individual test data are combined with left-truncated and randomly censored data from an operating environment. The NPMLE of the survival function using the combined sample is identical to the Kaplan-Meier product-limit estimator only up to the time at which the test items corresponding to the residual sample were known to survive. The limiting distribution …

Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based …

Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh

Department of Math & Statistics Faculty Publications

Standard inference procedures assume a random sample from a population with density f_μ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density f_μ^w(x) that is proportional to w(x)f_μ(x). In this paper, we assume that f_μ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the k^th order …

A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Two popular approaches for efficiency measurement are a non‐stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms.

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.