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Edible fruits, such as that of the tomato plant and other vegetable crops, are markedly diverse in shape and size. SUN, one of the major genes controlling the elongated fruit shape of tomato, was positionally cloned and found to encode a member of the IQ67 domain-containing family. We show that the locus arose as a result of an unusual 24.7-kilobase gene(More)
SUMMARY In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where(More)
BACKGROUND Universally accepted landmark stages are necessary to highlight key events in plant reproductive development and to facilitate comparisons among species. Domestication and selection of tomato resulted in many varieties that differ in fruit shape and size. This diversity is useful to unravel underlying molecular and developmental mechanisms that(More)
We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix(More)
Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of the present paper is to propose and analyze two new spectral estimation methods that are based on the sample autocovariances in a nonlinear way. The rate of convergence of the new estimators is quantified, and practical issues such(More)
We establish Nagaev and Rosenthal-type inequalities for dependent random variables. The imposed dependence conditions, which are expressed in terms of functional dependence measures, are directly related to the physical mechanisms of the underlying processes and are easy to work with. Our results are applied to nonlinear time series and kernel density(More)
We consider the maximum deviations of the sample covariances under the contexts of high dimensional data analysis and time series analysis. In the large n (number of observations) and large m (data dimension) paradigm, we show that the maximum deviation of the sample covariances converges in distribution to the extreme value distribution of type I. The(More)
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