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Selected AbstractsEstimation of P -value of MAX test with double triangle diagram for 2 × 3 SNP case-control tablesGENETIC EPIDEMIOLOGY, Issue 6 2010Katsura Hirosawa Abstract Single nucle otide polymorphisms (SNPs) are the most popular markers in genetic epidemiology. Multiple tests have been applied to evaluate genetic effect of SNPs, such as Pearson's test with two degrees of freedom, three tests with one degree of freedom (,2 tests for dominant and recessive modes and Cockran-Armitage trend test for additive mode) as well as MAX3 test and MAX test, which are combination of four tests mentioned earlier. Because MAX test is a combination of Pearson's test of two degrees of freedom and two tests of one degree of freedom, the probability density function (pdf) of MAX statistics does not match pdf of ,2 distribution of either one or two degrees of freedom. In order to calculate P -value of MAX test, we introduced a new diagram, Double Triangle Diagram, which was an extension of de Finetti diagram in population genetics which characterized all of the tests for 2 × 3 tables. In the diagram the contour lines of MAX statistics were consisted of elliptic curves and two tangent lines to the ellipses in the space. We normalized the ellipses into regular circles and expressed P -value of MAX test in an integral form. Although a part of the integral was not analytically solvable, it was calculable with arbitrary accuracy by dividing the area under pdf into finite rectangles. We confirmed that P -values from our method took uniform distribution from 0 to 1 in three example marginal count sets and concluded that our method was appropriate to give P -value of MAX test for 2 × 3 tables. Genet. Epidemiol. 34:543,551, 2010. © 2010 Wiley-Liss, Inc. [source] Oral premalignant lesions: is a biopsy reliable?JOURNAL OF ORAL PATHOLOGY & MEDICINE, Issue 5 2007P. Holmstrup Abstract Purpose:, The purpose of the present retrospective study was to learn whether a biopsy of oral premalignant lesions, leukoplakia and erythroplakia, shows histopathological findings representative of the whole surgically removed lesion. Moreover, to see whether histopathological characteristics of the whole lesion are significant for future malignant development after surgery. Materials and methods:, A total of 101 lesions in 96 patients were included, 42 lesions (41%) being homogenous and 50 (50%) non-homogenous leukoplakias, whereas nine (9%) were erythroplakias. The lesions were biopsied and subsequently surgically removed on the average of 10.4 months after biopsy. Surgical specimens were examined in two or more step sections distributed throughout the specimen. The histological findings of the biopsies were compared with those of the whole lesions. After surgical intervention the patients were followed (mean 6.8 years, range: 1.5,18.6), and new biopsies taken in case of recurrences. Smokers (73%) were encouraged to quit smoking and candidal infections were treated. The possible influence of different variables on the risk of malignant development was estimated by means of logistic regression analysis. Results:, Histological examination of the whole lesions showed that seven lesions (7%) harboured a carcinoma and 70 lesions (69%) showed a degree of epithelial dysplasia or carcinoma in situ. Eleven lesions (12%) developed carcinoma after a mean follow-up period of 7.5 years. A comparison of the degree of dysplasia in the biopsies with that of the whole lesion demonstrated variation with concurrent diagnosis in 49% of the lesions and in 79% after inclusion of lesions with one degree up or down the scale of epithelial dysplasia. Conclusion:, The estimated odds ratio showed that none of the associated variables including presence of any degree of epithelial dysplasia in the whole lesion, site, demarcation and smoking had influence on the risk of malignant development. [source] Non-standard finite difference schemes for multi-dimensional second-order systems in non-smooth mechanicsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007Yves Dumont Abstract This work is an extension of the paper (Proc. R. Soc. London 2005; 461A:1927,1950) to impact oscillators with more than one degree of freedom. Given the complex and even chaotic behaviour of these non-smooth mechanical systems, it is essential to incorporate their qualitative physical properties, such as the impact law and the frequencies of the systems, into the envisaged numerical methods if the latter is to be reliable. Based on this strategy, we design several non-standard finite difference schemes. Apart from their excellent error bounds and unconditional stability, the schemes are analysed for their efficiency to preserve some important physical properties of the systems including, among others, the conservation of energy between consecutive impact times, the periodicity of the motion and the boundedness of the solutions. Numerical simulations that support the theory are provided. Copyright © 2006 John Wiley & Sons, Ltd. [source] Constructive model predictive control for constrained nonlinear systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2008De-Feng He Abstract This paper develops a new model predictive control (MPC) design for stabilization of continuous-time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting ,decay rate' of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd. [source] Variable Selection and Model Choice in Geoadditive Regression ModelsBIOMETRICS, Issue 2 2009Thomas Kneib Summary Model choice and variable selection are issues of major concern in practical regression analyses, arising in many biometric applications such as habitat suitability analyses, where the aim is to identify the influence of potentially many environmental conditions on certain species. We describe regression models for breeding bird communities that facilitate both model choice and variable selection, by a boosting algorithm that works within a class of geoadditive regression models comprising spatial effects, nonparametric effects of continuous covariates, interaction surfaces, and varying coefficients. The major modeling components are penalized splines and their bivariate tensor product extensions. All smooth model terms are represented as the sum of a parametric component and a smooth component with one degree of freedom to obtain a fair comparison between the model terms. A generic representation of the geoadditive model allows us to devise a general boosting algorithm that automatically performs model choice and variable selection. [source] | ||||||||||