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 …

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.

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.

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.

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.

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.

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.

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.

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 …

The Analysis Of Count Data In A One-Way Layout, Yuhua Wang, Dallas E. Johnson, Linda J . Young

Conference on Applied Statistics in Agriculture

An efficient score statistic for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter is introduced and a new approximation to its distribution is given. The performance of the efficient score statistic using this approximation, the original efficient score statistic approximated by X ² (t -1), the likelihood ratio statistic and four more ANOVA methods based on raw data or transformed data are compared in terms of size and power by using Monte Carlo simulations. The efficient score statistic with its new approximation is recommended. An application is given.

Hydrological Normalization Of Nutrient Deliveries From Agricultural Catchments, Per Stalnacke, Anders Grimvall

Conference on Applied Statistics in Agriculture

Nutrient deliveries from agricultural catchments are strongly influenced by natural fluctuations in water discharge. Hydrological normalization of such data may therefore facilitate estimation of human impact on the environment. In the present study, we compared conventional statistical normalization techniques with a recently proposed, semi-parametric regression technique, which can accommodate time-dependent relationships between nutrient deliveries and water discharge. Case studies of agricultural catchments in Sweden and Norway demonstrated that all of the tested normalization techniques were able to remove a substantial fraction of the interannual variation in nitrogen deliveries, whereas normalization of phosphorus loads was problematic. Semi-parametric regression models were found …

A Computationally Efficient Method For Determining Significance In Interval Mapping Of Quantitative Trait Loci, Dan Nettleton

Conference on Applied Statistics in Agriculture

This paper provides a brief introduction to the mapping of quantitative trait loci (QTL). An example on mapping QTL for root thickness in rice is presented to illustrate popular statistical methods used in QTL mapping. Interval mapping is used in conjunction with permutation testing techniques to detect significant associations between genetic positions and quantitative traits while controlling overall type I error rate. A review of a recent technique that can greatly reduce the computational expense of permutation testing in QTL mapping is discussed. Theory is provided for an extension of recent results that may lead to more powerful methods of …

An Improved Estimator For Assessing The Measure Of Agreement With A Gold Standard, Brent D. Burch, Ian R. Harris, Roy T. St. Laurent

Conference on Applied Statistics in Agriculture

St. Laurent (1998, Biometrics 54, 537-545) developed a measure of agreement for method comparison studies in which an approximate method of measurement is compared to a gold standard method of measurement. The measure of agreement proposed was shown to be related to a population intraclass correlation coefficient. This paper develops a family of estimators for the measure of agreement based on pivotal quantities. A blend of two particular members of the family is suggested as an estimator itself. In general, this estimator outperforms the maximum likelihood estimator in terms of bias and mean-squared error.

Nonlinear Models For Multi-Factor Plant Nutrition Experiments, R. D. Landes, W. W. Stroup, E. T. Paparozzi, M. E. Conley

Conference on Applied Statistics in Agriculture

Plant scientists are interested in measuring plant response to quantitative treatment factors, e.g. amount of nutrient applied. Response surface methods are often used for experiments with multiple quantitative factors. However, in many plant nutrition studies, second-order response surface models result in unacceptable lack of fit. This paper explores multi-factor nonlinear models as an alternative. We have developed multi-factor extensions of Mitscherlich and Gompertz models, and fit them to data from experiments conducted at the University of Nebraska-Lincoln Horticulture department. These data are typical of experiments for which conventional response surface models perform poorly. We propose design selection strategies to facilitate …

Using Isotonic Regression To Improve Estimation In Factorial Experiments With Ordered Factor Levels, Matt Strand, Jim Higgins

Conference on Applied Statistics in Agriculture

In many designed experiments in agriculture and the life sciences, a researcher can anticipate the direction that responses will take when treatments are varied. For example, in a 2-way factorial, a researcher may know that increasing the levels of nitrogen and phosphorus will increase yields of a crop. Classical analysis of variance does not take into account a known ordering among population means. However, it can be shown that by restricting the estimates of means to have the same ordering as the anticipated ordering of population means, a reduction in mean-squared errors of estimators will likely occur, often by more …

Characterizing The Statistical Distribution Of Organic Carbon And Extractable Phosphorus At A Regional Scale, John J. Brejda, David W. Meek, Douglas L. Karlen

Conference on Applied Statistics in Agriculture

Greater awareness of potential environmental problems has created the need to monitor total organic carbon (TOC) and extractable phosphorus (P) concentrations at a regional scale. The probability distribution of these soil properties can have a significant effect on the power of statistical tests and the quality of inferences applied to these properties. The objectives of this study were to: (1) evaluate the probability distribution of TOC and extractable P at the regional scale in three Major Land Resource Areas (MLRA), and (2) identify appropriate transformations that will result in a normal distribution. Both TOC and extractable P were non-normally distributed …

Analysis Of Nuclei Fluorescence Histograms Using Non-Linear Functions Or Wavelets, Susanne Aref, Maria Kocherginsky, Carrie A. Northcott, Lane A. Rayburn

Conference on Applied Statistics in Agriculture

Histograms based on 5,000 nuclei from cells (Chinese hamster ovary cells, bone marrow cells) are used to determine the coefficient of variation (CV) of observations surrounding the highest peak. The cells are subjected to various treatments, for example exposure to herbicides. By eyeballing the histogram, an interval under the highest peak is determined. The CV calculated from the histogram on the eyeballed interval is the response variable in an ANOVA. To avoid the subjectivity of eyeballing the histogram, non-linear functions such as the Gaussian density function can be used to model the histogram. The CV may then be determined from …

On Using Proc Mixed For Longitudinal Data, Walter W. Stroup

Conference on Applied Statistics in Agriculture

PROC MIXED has become a standard tool for analyzing repeated measures data. Its popularity results from a wide choice of correlated error models compared to other software, e.g. PROC GLM. However, PROC MIXED's versatility comes at a price. Users must take care. Problems may result from MIXED defaults. These include: questionable criteria for selecting correlated error models; starting values that may impede REML estimation of covariance components; and biased standard errors and test statistics. Problems may be induced by inadequate design. This paper is a survey of current knowledge about mixed model methods for repeated measures. Examples are presented using …

Modeling The Fate Of Toxic Chemicals In Soils, Anabayan Kessavalou, Anne M. Parkhurst

Conference on Applied Statistics in Agriculture

Studies on the fate of toxic chemicals in soils are often reported with a minimum of descriptive statistics. Use of modeling techniques to describe the kinetics of chemical degradation provides a better understanding of the fate of chemicals in soil systems. When modeling nonlinear systems, assumptions made about the error term greatly influence the parameter estimation. Inappropriate use of linearization and failure to account for autocorrelated errors may result in inaccurate models. Information is also needed about the effects of the magnitude of autocorrelation on parameter estimation. The exponential decay function was chosen to fit the data obtained from a …