new approach to study splines by blossoming method and application to the construction of a bivariate c 1 quartic quasi interpolant this work is a contribution in the approximation theory for studying and analyzing piecewise polynomial functions splines which uses the blossoming approach some existing results in the literature are reformulated such as the smoothness conditions between polynomials of a spline by using the affinity property of the blossom some definitions of sub splines are proposed which can be very useful in the study and the construction of splines such as macro elements or quasi interpolants as an application of the proposed results a c 1 quartic spline quasi interpolant with optimal approximation order is defined without using any mask for smoothness or b spline basis numerical results are presented and compared with other methods given in the literature

a general method for constructing quasi interpolants from b splines a general method for constructing quasi interpolation operators based on b splines is developed given a b spline f in r s s 1 normalized by i z email protected i 1 the classical structure q f email protected i z email protected i f i for a quasi interpolation operator q is considered a minimization problem is derived from an estimate of the quasi interpolation error associated with q when lf is a linear combination of values of f at points in some neighbourhood of the support of f or a linear combination of values of f and some of its derivatives at some points in this set or a linear combination of weighted mean values of the function to be approximated that linear functional is defined to produce a quasi interpolant exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates of f the solution of that minimization problem is characterized in terms of specific splines which do not depend on l but only on f

on characteristic classes of determinantal cremona transformations we compute the multidegrees and the segre numbers of general determinantal cremona transformations with generically reduced base scheme by specializing to the standard cremona transformation and computing its segre class via mixed volumes of rational polytopes

near minimally normed spline quasi interpolants on uniform partitions spline quasi interpolants qis are local approximating operators for functions or discrete data we consider the construction of discrete and integral spline qis on uniform partitions of the real line having small infinity norms we call them near minimally normed qis they are exact on polynomial spaces and minimize a simple upper bound of their infinity norms we give precise results for cubic and quintic qis also the qi error is considered as well as the advantage that these qis present when approximating functions with isolated discontinuities

modeling overdispersion heterogeneity in differential expression analysis using mixtures next generation sequencing technologies now constitute a method of choice to measure gene expression data to analyze are read counts commonly modeled using negative binomial distributions a relevant issue associated with this probabilistic framework is the reliable estimation of the overdispersion parameter reinforced by the limited number of replicates generally observable for each gene many strategies have been proposed to estimate this parameter but when differential analysis is the purpose they often result in procedures based on plug in estimates and we show here that this discrepancy between the estimation framework and the testing framework can lead to uncontrolled type i errors instead we propose a mixture model that allows each gene to share information with other genes that exhibit similar variability three consistent statistical tests are developed for differential expression analysis we show through a wide simulation study that the proposed method improves the sensitivity of detecting differentially expressed genes with respect to the common procedures since it reaches the nominal value for the type i error while keeping elevate discriminative power between differentially and not differentially expressed genes the method is finally illustrated on prostate cancer rna seq data

minimizing the quasi interpolation error for bivariate discrete quasi interpolants we define a class of discrete quasi interpolants based on bivariate box splines by imposing the exactness on a space of polynomials of total degree depending on the box spline and minimizing a constant appearing in the leading term of an appropriate quasi interpolation error estimate we give some c 1 quadratic and c 2 quartic examples and compare them with other well known quasi interpolants

effortless quasi interpolation in hierarchical spaces we present a general and simple procedure to construct quasi interpolants in hierarchical spaces such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement the proposed hierarchical quasi interpolants are described in terms of the so called truncated hierarchical basis assuming a quasi interpolant is selected for each space associated with a particular level in the hierarchy the hierarchical quasi interpolants are obtained without any additional manipulation the main properties like polynomial reproduction of the quasi interpolants selected at each level are locally preserved in the hierarchical construction we show how to construct hierarchical local projectors and the local approximation order of the underling hierarchical space is also investigated the presentation is detailed for the truncated hierarchical b spline basis and we discuss its extension to a more general framework

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

quasi interpolants associated with h splines on a three direction mesh h splines are b splines with regular hexagonal supports on a three direction mesh of the plane this family contains in particular classical box splines which are convolution powers of the piecewise affine pyramid in this paper we construct discrete or integral qua si interpolants having the best possible approximation order for the smooth functions the construction is based on properties of hexagonal sequences and associated difference operators and of discrete laplacian schemes

special birational transformations of projective spaces abstract extending some results of crauder and katz and ein and shepherd barron on special cremona transformations we study birational transformations of p r onto a prime fano manifold such that the base locus x p r is smooth irreducible and reduced the main results are a complete classification when x has either dimension 1 and 2 or codimension 2 partial results are also obtained when x has dimension 3

near best quasi interpolants associated with h splines on a three direction mesh spline quasi interpolants with optimal approximation orders and small norms are useful in several applications in this paper we construct the so called near best discrete and integral quasi interpolants based on h splines i e b splines with regular hexagonal supports on the uniform three directional mesh of the plane these quasi interpolants are obtained so as to be exact on some space of polynomials and to minimize an upper bound of their infinite norms which depend on a finite number of free parameters we show that this problem has always a solution which is not unique in general concrete examples of these types of quasi interpolants are given in the two last sections

translates of multivarlate splines abstract we study spaces generated by translations of a fixed function over lattice points we provide some new algebraic and approximation properties for these spaces which show their applicability for finite element analysis

superconvergent trivariate quadratic spline quasi interpolants on worsey piper split in this paper we use normalized trivariate worsey piper b splines recently constructed by sbibih et al 2012 and the method proposed in sbibih et al 2013 to give a new representation of worsey piper hermite interpolant of any piecewise polynomial of class at least c 1 over the worsey piper split in terms of its polar forms using this representation we construct several superconvergent discrete quasi interpolants the construction that we present in this work is a generalization of the one presented in sbibih et al 2012 with other properties

quasi interpolation by c1 quartic splines on type 1 triangulations abstract in this paper we construct two new families of c 1 quartic quasi interpolating splines on type 1 triangulations approximating regularly distributed data the splines are directly determined by setting their bernstein bezier coefficients to appropriate combinations of the given data values instead of defining the approximating splines as linear combinations of compactly supported bivariate spanning functions and do not use prescribed derivatives at any point of the domain the quasi interpolation operators provided by the proposed schemes interpolate the data values at the vertices of the triangulation reproduce cubic polynomials and yield approximation order four for smooth functions we also propose some numerical tests that confirm the theoretical results

on near best discrete quasi interpolation on a four directional mesh spline quasi interpolants are practical and effective approximation operators in this paper we construct qis with optimal approximation orders and small infinity norms called near best discrete quasi interpolants which are based on w splines i e b splines with octagonal supports on the uniform four directional mesh of the plane these quasi interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters we show that this problem has always a solution in general nonunique concrete examples of such quasi interpolants are given in the last section

on the construction of trivariate near best quasi interpolants based on c 2 quartic splines on type 6 tetrahedral partitions the construction of new quasi interpolants qis having optimal approximation order and small infinity norm and based on a trivariate c 2 quartic box spline is addressed in this paper these quasi interpolants called near best qis are obtained in order to be exact on the space of cubic polynomials and to minimize an upper bound of their infinity norm which depends on a finite number of free parameters in a tetrahedral sequence defining the coefficients of the qis we show that this problem has always a unique solution which is explicitly given we also prove that the sequence of the resulting near best quasi interpolants converges in the infinity norm to the schoenberg operator

superconvergent local quasi interpolants based on special multivariate quadratic spline space over a refined quadrangulation abstract in this paper we first recall some results concerning the construction and the properties of quadratic b splines over a refinement of a quadrangulation of a planar domain introduced recently by lamnii et al then we introduce the b spline representation of hermite interpolant in the special space s 2 1 0 of any polynomial or any piecewise polynomial over refined quadrangulation of after that we use this b representation for constructing several superconvergent discrete quasi interpolants the new results that we present in this paper are an improvement and a generalization of those developed in the above cited paper

fieller s theorem the likelihood and the delta method this note discusses the direct likelihood estimation of ratio parameters the method is based on the use of nonlinear regression models from the exponential family the variances of the maximum likelihood estimates are identical with values obtained from the corresponding generalized linear models and the delta method bishop fienberg and holland discrete multivariate analysis theory and practice cambridge massachusetts mit press 1975 but are easier to calculate the approach is illustrated by means of a number of examples including a rather complex logistic regression model we also discuss the connection between confidence intervals obtained from fieller s theorem and large sample intervals obtained from the information matrix we conclude from this comparison and from the examples that direct maximum likelihood estimation of ratios offers a useful alternative to traditional methods based on linear models especially for complex data sets

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

construction of spherical spline quasi interpolants based on blossoming a general theory of quasi interpolants based on quadratic spherical powell sabin splines on spherical triangulations of a sphere like surface s is developed by using polar forms as application various families of discrete and differential quasi interpolants reproducing quadratic spherical bezier bernstein polynomials or the whole space of the spherical powell sabin quadratic splines of class c 1 are presented

weak fano threefolds obtained by blowing up a space curve and construction of sarkisov links we characterise smooth curves in p3 whose blow up produces a threefold with anticanonical divisor big and nef these are curves c of degree d and genus g lying on a smooth quartic such that i 4d