convergence of the finite difference scheme for a general class of the spatial segregation of reaction diffusion systems abstract in this work we prove convergence of the finite difference scheme for equations of stationary states of a general class of the spatial segregation of reaction diffusion systems with m 2 components more precisely we show that the numerical solution u h l given by the difference scheme converges to the l t h component u l when the mesh size h tends to zero provided u l c 2 for every l 1 2 m in particular our proof provides convergence of a difference scheme for the multi phase obstacle problem

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

batalin vilkovisky formalism and integration theory on manifolds the correspondence between the bv formalism and integration theory on supermanifolds is established an explicit formula for the density on a lagrangian surface in a superspace provided with an odd symplectic structure and a volume form is proposed

geometry of batalin vilkovisky quantization the geometry ofp manifolds odd symplectic manifolds andsp manifolds p manifolds provided with a volume element is studied a complete classification of these manifolds is given this classification is used to prove some results about batalin vilkovisky procedure of quantization in particular to obtain a very general result about gauge independence of this procedure

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

isomorphisms between the batalin vilkovisky antibracket and the poisson bracket one may introduce at least three different lie algebras in any lagrangian field theory i the lie algebra of local brst cohomology classes equipped with the odd batalin vilkovisky antibracket which has attracted considerable interest recently ii the lie algebra of local conserved currents equipped with the dickey bracket and iii the lie algebra of conserved integrated charges equipped with the poisson bracket we show in this paper that the subalgebra of i in ghost number 1 and the other two algebras are isomorphic for a field theory without gauge invariance we also prove that in the presence of a gauge freedom ii is still isomorphic to the subalgebra of i in ghost number 1 while iii is isomorphic to the quotient of ii by the ideal of currents without charge in ghost number different from 1 a more detailed analysis of the local brst cohomology classes in the hamiltonian formalism allows one to prove an isomorphism theorem between the antibracket and the extended poisson bracke

direct estimation of the index coefficient in a single index model single index modeling is widely applied in for example econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models by such modeling the statistical analysis usually focuses on estimating the index coefficients the average derivative estimator ade of the index vector is based on the fact that the average gradient of a single index function f x t is proportional to the index vector unfortunately a straightforward application of this idea meets the so called curse of dimensionality problem if the dimensionality d of the model is larger than 2 however prior information about the vector can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative the method proposed in this paper consists of such iterative improvements of the original ade the whole procedure requires at most 2 log n iterations and the resulting estimator is n consistent under relatively mild assumptions on the model independently of the dimensionality d

gauge symmetries of the master action in the batalin vilkovisky formalism we study the geometry of the lagrangian batalin vilkovisky bv theory on an antisymplectic manifold we show that gauge symmetries of the bv theory are essentially the symmetries of an even symplectic structure on the stationary surface of the master action

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

becchi rouet stora tyutin formalism and zero locus reduction in the becchi rouet stora tyutin brst quantization of gauge theories the zero locus zq of the brst differential q carries an anti bracket whose parity is opposite to that of the fundamental bracket observables of the brst theory are in a 1 1 correspondence with casimir functions of the bracket on zq for any constrained dynamical system with the phase space n0 and the constraint surface we prove its equivalence to the constrained system on the bfv extended phase space with the constraint surface given by zq reduction to the zero locus of the differential gives rise to relations between bracket operations and differentials arising in different complexes the gerstenhaber schouten berezin kirillov and sklyanin brackets the equation ensuring the existence of a nilpotent vector field on the reduced manifold can be the classical yang baxter equation we also generalize our constructions to the bi qp manifolds which from the brst theory viewpoint correspond to the brst anti brst symmetric quantiza

penalized spline estimation for partially linear single index models single index models are potentially important tools for multivariate nonparametric regression they generalize linear regression by replacing the linear combination 0tx with a nonparametric component 0 0tx where 0 is an unknown univariate link function by reducing the dimensionality from that of a general covariate vector x to a univariate index 0tx single index models avoid the so called curse of dimensionality we propose penalized spline p spline estimation of 0 in partially linear single index models where the mean function has the form 0 0tx 0tz the p spline approach offers a number of advantages over other fitting methods for single index models all parameters in the p spline single index model can be estimated simultaneously by penalized nonlinear least squares as a direct least squares fitting method our approach is rapid and computationally stable standard nonlinear least squares software can be used moreover joint inference for 0 0 and 0 is possible by

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

geometry of superspace with even and odd brackets the geometry of the superspace provided by two arbitrary poisson brackets of different gradings is studied it will be shown that the group of transformations that preserve these two brackets is finite dimensional

notes on conformal invariance of gauge fields in lagrangian gauge systems the vector space of global reducibility parameters forms a module under the lie algebra of symmetries of the action since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action this fact can be used to constrain the latter when knowing the former we apply this strategy and its generalization for the non lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields this scheme allows one to show that in terms of potentials massless higher spin gauge fields in minkowski space and partially massless pm fields in a ds space are not conformal for spin strictly greater than one while in terms of curvatures maximal depth pm fields in four dimensions are also not conformal unlike the closely related but less constrained maximal depth fradkin tseytlin fields

closing and abelizing operatorial gauge algebra generated by first class constraints a canonical transformation of operators of relativistic phase space is constructed which abelizes the basis of the operator valued gauge algebra of first class constraints the new operators of contraints commute among themselves the new hamiltonian commutes with the constraints dynamics of the new operators is physically equivalent to the initial one

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

background independent algebraic structures in closed string field theory we construct a batalin vilkovisky bv algebra on moduli spaces of riemann surfaces this algebra is background independent in that it makes no reference to a state space of a conformal field theory conformal theories define a homomorphism of this algebra to the bv algebra of string functionals the construction begins with a graded commutative free associative algebrac built from the vector space whose elements are orientable subspaces of moduli spaces of punctured riemann surfaces the typical element here is a surface with several connected components the operation of sewing two punctures with a full twist is shown to be an odd second order derivation that squares to zero it follows thatc is a batalin vilkovisky algebra we introduce the odd operator where is the boundary operator it is seen thatc and that consistent closed string vertices define a cohomology class of this cohomology class is used to construct a lie algebra on a quotient space ofc this lie algebra gives a manifestly background independent description of a subalgebra of the closed string gauge algebra

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

adapting for the missing link we consider the fitting of generalized linear models in wich the link function is assumed to be unknown and propose the following computational method first estimate regression coefficients using the canonical link then estimate the link via a kernel smoother treating the direction in the predictor space determined by the regression coefficients as known then reestimate the direction using the estimated link and alternate between these two steps we show that under fairly general conditions n 1 2 consistent estimates of the direction are obtained a small monte carlo study is presented

hamiltonian brst and batalin vilkovisky formalisms for second quantization of gauge theories gauge theories that have been first quantized using the hamiltonian brst operator formalism are described as classical hamiltonian brst systems with a brst charge of the form open image in new window and with natural ghost and parity degrees for all fields the associated proper solution of the classical batalin vilkovisky master equation is constructed from first principles both of these formulations can be used as starting points for second quantization in the case of time reparametrization invariant systems the relation to the standard open image in new window master action is established

semiclassical approximation in batalin vilkovisky formalism the geometry of supermanifolds provided with aq structure i e with an odd vector fieldq satisfying q q 0 ap structure odd symplectic structure and ans structure volume element or with various combinations of these structures is studied the results are applied to the analysis of the batalin vilkovisky approach to the quantization of gauge theories in particular the semiclassical approximation in this approach is expressed in terms of reidemeister torsion

spline based tests in survival analysis this paper examines a method for testing hypotheses on covariate effects in a proportional hazards model and also on how effects change over time in regression analysis of survival data the technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models the basic idea is to formulate a flexible parametric alternative using fixed knot splines together with a penalty function that penalizes noisy alternatives more than smooth ones to focus the power of the tests toward smooth alternatives the test statistics are the analogs of ordinary likelihood based statistics only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log likelihood large sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases numerical results suggest these approximations may be adequate with moderate sized samples

miscellanea on the optimal amount of smoothing in penalised spline regression summary the optimal amount of smoothing in penalised spline regression is investigated in particular a simple closed form approximation to the optimal smoothing parameter is derived comparisons with its exact counterpart show it to be a useful starting point for measuring the optimal amount of smoothing in penalised spline regression it also lends itself to the development of quick and simple rules for automatic smoothing parameter selection