Physical Sciences and Mathematics Commons^™

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

Yi Li

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 …

Tea Tasting And Pascal Triangles, Paul Alper, Yongzhi Yang

Humanistic Mathematics Network Journal

No abstract provided.

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 …

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 …

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

Yi Li

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.

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.

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 …

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

Yi Li

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.

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.

Efficient Simulation Via Validation And Application Of An External Analytical Model, Thomas H. Irish

Theses and Dissertations

This research makes significant contributions towards improving the efficiency of simulation studies using an external analytical model. The foundation for this research is the analytical control variate (ACV) method. The ACV method can produce significant variance reduction, but the resulting point estimate may exhibit bias. A Monte Carlo sampling method for resolving the bias problem is developed and demonstrated through a queueing network example. The method requires knowledge of the parameters and approximate distributions of the random variables used to produce the ACV. Often, some of these parameters or distributions are not known. Both parametric and non-parametric alternatives to the …

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.

Gis And Spatial Statistics: Recent Uk Experiences And Developments., Derek Bond

Derek Bond

The uptake and use of GIS in the public sector in the United Kingdom was critically reviewed in a recent paper by Worrall & Bond (1996). Their main conclusion was that the high hopes about the use of GIS that had been prevalent during the late 1980s had failed to materialise. This they argued was due mainly to organisational and implementation issues but also highlighted the lack of effective spatial analysis techniques available to practitioners who have made the heavy investment needed in GIS. In this paper some of the practical developments in spatial analysis that have emerged from the …

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

Yi Li

No abstract provided.

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.

Likely And Unlikely Events In International Security Affairs: An Example From The People's Republic Of China, Ibpp Editor

International Bulletin of Political Psychology

This article describes a human judgment shortfall in international security decision making based on statistical probabilities.

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 …

Survival Versus Years Of Healthy Life; Which Is More Powerful As A Study Outcome?, Paula Diehr

Paula Diehr

Studies of interventions that are intended to improve patients' health are often evaluated with survival as the primary outcome, even when a measure adjusted for quality of survival, such as years of healthy life (YHL), would seem more appropriate. The purpose of this article is to determine whether studies based on survival are more or less powerful than studies based on YHL in clinical trials where either measure might be appropriate. We used data from the Cardiovascular Health Study (CHS) to estimate the sample size that would be needed in studies of 156 different health conditions, for the two outcome …

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 …

The Power Of Structured Designs And Mixed Models In A Real World Experiment, J. C. Galland, G. A. Milliken, D. R. Hyatt, M. Hornback, K. Cudjoe

Conference on Applied Statistics in Agriculture

Justifications usually given for adopting an automated system pertain to a reduction in labor and an improvement in quality control. A manufacturer of a prototype instrument that automated some of the steps for culturing bacteria wanted to compare the automated system to the manual system. The manufacturer wanted to compare the two systems in 1) Total time needed to isolate the target bacteria, 2) Ability to isolate the target bacteria, 3) Amount of interference from background (non-target) bacterial growth, and 1) Extent of cross (sample to sample) contamination.

This paper presents the experimental design used to make these comparisons and …

Investigating Power Of Analysis Of Covariance Methods, James R. Schwenke, J. Mark Donovan

Conference on Applied Statistics in Agriculture

Analysis of covariance is a well-utilized statistical methodology. The procedure involves a series of statistical tests to first construct a most significant analysis model to characterize the effect of the covariate on response. Pairwise comparisons among treatments are then based on the finalized model.

For traditional Normal error assumptions, each step of the process is based on exact statistical tests. However, the series of statistical tests defines a conditional probability scheme with possible multiplicity issues. The question then becomes if the analysis of covariance methodology considered in entirety is able to maintain a nominal level of significance with good power. …

Starting Values For Proc Mixed With Repeated Measures Data, J. C. Recknor, W. W. Stroup

Conference on Applied Statistics in Agriculture

A major advantage of PROC MIXED for repeated measures data is that one could choose from many different correlated error models. However, MIXED uses default starting values that may cause difficulty obtaining REML estimates of the covariance parameters for several of the models available. This can take the form of excessively long run times or even failure to converge. We have written a program to obtain initial covariance parameter estimates that result in greatly improved performance of the REML algorithm. We will use two covariance models frequently of interest in animal health experiments, the first-order ante-dependence model [ANTE(l)] and the …

Analysis Of Genotype-By-Environment Interaction With Ammi Models Using Sas Proc Mixed, Raul E. Macchiavelli, James S. Beaver

Conference on Applied Statistics in Agriculture

Genotype-by-environment (GE) interaction can be analyzed using different approaches. Among these, the additive main effects and multiplicative interaction model yields useful interpretations and can be applied successfully to plant breeding programs. In this paper we review fitting strategies for this model and show how to combine the capabilities of the Mixed and IML procedures in SAS to fit this model. This permits straightforward use of likelihood-based inference in standard and non standard situations like complex experimental designs. The proposed procedures were applied to data from red mottled bean variety trials conducted in the Dominican Republic and Puerto Rico in 9 …