a numerical study of inverse heat conduction problems abstract in this paper two boundary element methods a collocation method and a weighted method are employed to solve a one dimensional inverse heat conduction problem ihcp inverse heat conduction problems are well known for being ill posed when numerical methods are directly applied on an ihcp ill conditioned linear systems will be involved we show that the condition numbers for these systems increase as e n where n is the number of the elements we use a couple of tikhonov s regularization methods to stabilize the matrix which is generated by the weighted method an error bound for each method is analyzed finally both methods are implemented and the result for the collocation method with the truncated singular value decomposition method is also shown in this article

an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

estimation of the distribution function of a standardized statistic for estimating the distribution of a standardized statistic the bootstrap estimate is known to be local asymptotic minimax various computational techniques have been developed to improve on the simulation efficiency of uniform resampling the standard monte carlo approach to approximating the bootstrap estimate two new approaches are proposed which give accurate yet simple approximations to the bootstrap estimate the second of the approaches even improves the convergence rate of the simulation error a simulation study examines the performance of these two approaches in comparison with other modified bootstrap estimates

brunn minkowski inequality for multiplicities this is a convex subset of the real vector space p zr in fact it is a convex polytope see br where this polytope is discussed from an algebraic point of view it is known that the total mass of m is a polynomial in m for su ciently large m denote by k its degree and m k m m weak d where d is the lebesgue measure supported on and the density is a piecewise polynomial function we will not use this piecewise polynomiality in this paper recall that a real function f de ned on a convex subset u of a vector space v is called concave if

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

antithetic resampling for the bootstrap summary an antithetic variates method for the bootstrap is proposed and discussed it is applicable quite generally to bias estimation distribution function estimation and quantile estimation for example it is based on an antithetic permutation of the sample which amounts to ranking values of a certain function of the data once this has been done b uniform resampling operations may be immediately converted into 2b effective resampling operations yielding greater statistical efficiency than 2b totally independent resampling operations we show that antithetic resampling leads to positive nonnegligible gains in performance for the same level of labour when compared with ordinary uniform resampling

okounkov bodies and seshadri constants abstract okounkov bodies which are closed convex sets defined for big line bundles have rich information on the line bundles on the other hand seshadri constants are invariants which measure the positivity of line bundles in this paper we prove that okounkov bodies give lower bounds of seshadri constants

identification of an unknown time dependent heat source term from overspecified dirichlet boundary data by conjugate gradient method the inverse problem of identifying the unknown time dependent heat source h t of the variable coefficient heat equation u t k x u x x f x h t with separable sources of the form f x h t from supplementary temperature measurement h t u 0 t at the left end of the rod is investigated the fourier method is employed to illustrate the comparison of spacewise f x and time dependent h t heat source identification problems an explicit formula for the frechet gradient of the cost functional j h u 0 h h l 2 0 t f 2 is derived via the unique solution of the appropriate adjoint problem the conjugate gradient algorithm based on the gradient formula for the cost functional is then proposed for numerical solution of the inverse source problem the algorithm is examined through numerical examples related to reconstruction of continuous and discontinuous heat sources h t when heat is transferred through non homogeneous as well as composite structures numerical analysis of the algorithm applied to the inverse source problem in typical classes of source functions is presented computational results obtained for random noisy output data show how the iteration number of the conjugate gradient algorithm can be estimated based on these results it is shown that this iteration number plays a role of a regularization parameter numerical results illustrate bounds of applicability of the proposed algorithm and also its efficiency and accuracy

on efficient bootstrap simulation summary it is shown that three new efficient bootstrap algorithms are asymptotically equivalent this is done in two ways first asymptotic formulae for variances and mean squared errors are derived and shown to be identical secondly it is demonstrated that two of the methods may be viewed as approximations to the third the three algorithms considered are the balanced bootstrap and the linear approximation method proposed by davison hinkley schechtman 1986 and a centring method proposed by efron in the context of bias estimation it is shown that each reduces the order of magnitude of mean squared error by the factor n 1 where n is sample size these results apply to smooth functions of means

growth of multiplicities of graded families of ideals let r m be a noetherian local ring of dimension d 0 let i in n n be a graded family of m primary ideals in r we examine how far off from a polynomial can the length function lr r in be asymptotically more specifically we show that there exists a constant 0 such that for all n 0 lr r in 1 lr r in nd 1

nonparametric confidence and tolerance regions in canonical variate analysis canonical variate analysis is a much used descriptive multivariate technique for grouped data in which the group means are represented by points in a low typically two dimensional space if inferential use is to be made of the technique some knowledge of the variability of these points under repeated sampling is necessary the traditional approach is to construct confidence or tolerance circles around each point by using approximate asymptotic results based on normal assumptions for the data jackknife and bootstrap resampling schemes are proposed in this paper as a basis for constructing nonparametric regions these regions are compared with the normal based circles on the well known fisher iris data and also by means of a small monte carlo study incorporating nonnormal as well as normal data it is suggested that the normal based circles may often be inappropriate and areas of further investigation are identified

okounkov bodies and restricted volumes along very general curves abstract given a big divisor d on a normal complex projective variety x we show that the restricted volume of d along a very general complete intersection curve c x can be read off from the okounkov body of d with respect to an admissible flag containing c from this we deduce that if two big divisors d 1 and d 2 on x have the same okounkov body with respect to every admissible flag then d 1 and d 2 are numerically equivalent

asymptotic multiplicities of graded families of ideals and linear series abstract we find simple necessary and sufficient conditions on a local ring r of dimension d for the limit lim n l r r i n n d to exist whenever i n is a graded family of m r primary ideals and give a number of applications we also give simple necessary and sufficient conditions on projective schemes over a field k for asymptotic limits of the growth of all graded linear series of a fixed kodaira iitaka dimension to exist

prediction and tolerance intervals with transformation and or weighting we consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and or weighting we consider the case of normally distributed errors and to a lesser extent the nonparametric case in which the error distribution is unknown quantile estimation here follows standard theory although we introduce a simple computational device for likelihood ratio testing and confidence intervals prediction and tolerance intervals are somewhat more difficult to obtain we show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem improved prediction and tolerance intervals are constructed based on resampling techniques in the tolerance interval case a simple analytical correction is introduced we apply these methods to the prediction of automobile stopping distances and salmon production using respectively a he

determining the appropriate sample size for nonparametric tests for location shift for the case in which two independent samples arc to be compared using a nonparametric test for location shift we propose a bootstrap technique for estimating the sample sizes required to achieve a specified power the estimator called boot uses information from a small pilot experiment for the special case of the wilcoxon test a simulation study is conducted to compare boot to two other sample size estimators one method called anpv is based on the assumption that the underlying distribution is normal with a variance estimated from the pilot data the other method called noether adapts the sample size formula of noether for use with a location shift alternative the boot and noether sample size estimators are particularly appropriate for this nonparametric setting because they do not require assumptions about the shape of the underlying continuous probability distribution the simulation study shows that a sample size estimates can have large uncertainty b boot is at least as accurate as an

an stable numerical algorithm for identifying the solution of an inverse problem in this paper we consider an inverse parabolic problem with space dependent coefficient mathematical model of the problem consists a parabolic equation in which the condition is unknown at the one of the boundary and to be determined from an overspecified data measured at an interior point inside the body uniqueness of the solution of under study inverse problem will be shown our concern for the numerical procedure for this inverse problem is based on a finite differences scheme stability conditions for numerical solution to inverse problem are stated the approach of proposed method is approximated the unknown function by a set of chebyshev polynomials where the unknown set of expansion coefficients in unknown function are determined from the minimizing the least squares method some numerical examples will be given in the last section

improvements of jackknife confidence limit methods summary edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method adjustments to the usual jackknife confidence limit formulae are obtained this approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate t approximate confidence limits for the estimand can be found by using a large sample normal approximation for t somewhat curiously little is known about possible improvements to the normal approximation in this context although improvements based on edgeworth expansions are familiar in other problems in this paper we show that edgeworth expansion methods can be applied in the jackknife context numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods efron 1982

global okounkov bodies for bott samelson varieties abstract we use the theory of mori dream spaces to prove that the global okounkov body of a bott samelson variety with respect to a natural flag of subvarieties is rational polyhedral as a corollary okounkov bodies of effective line bundles over schubert varieties are shown to be rational polyhedral in particular it follows that the global okounkov body of a flag variety g b is rational polyhedral as an application we show that the asymptotic behaviour of dimensions of weight spaces in section spaces of line bundles is given by the volume of polytopes

a remark on the alexandrov fenchel inequality abstract in this article we give a complex geometric proof of the alexandrov fenchel inequality without using toric compactifications the idea is to use the legendre transform and develop the brascamp lieb proof of the prekopa theorem new ingredients in our proof include an integration of timorin s mixed hodge riemann bilinear relation and a mixed norm version of hormander s l 2 estimate which also implies a non compact version of the khovanski teissier inequality

local positivity in terms of newton okounkov bodies abstract in recent years the study of newton okounkov bodies on normal varieties has become a central subject in the asymptotic theory of linear series after its introduction by lazarsfeld musta and kaveh khovanskii one reason for this is that they encode all numerical equivalence information of divisor classes by work of jow at the same time they can be seen as local positivity invariants and kuronya lozovanu have studied them in depth from this point of view we determine what information is encoded by the set of all newton okounkov bodies of a big divisor with respect to flags centered at a fixed point of a surface by showing that it determines and is determined by the numerical equivalence class of the divisor up to negative components in the zariski decomposition that do not go through the fixed point

finite volume method for solving a one dimensional parabolic inverse problem in this paper finite volume method is used to solve a one dimensional parabolic inverse problem with source term and neumann boundary conditions for the first time some advantages of this approach are developing difference schemes and maintaining certain properties of the physics of the problems especially for the treatment of the source term and the unknown boundary conditions numerical results show that our method is more effective

conditional bootstrap methods in the mean shift model summary bootstrap methods are not inherently conditional but they can be made so by appropri ate stratification of the simulated samples which bootstrap produces we show how stratification can work in a bootstrap analysis of mean shift in nile river flow data the results are compared with both parametric and semiparametric likelihood analyses the paper ends with some general remarks on conditional bootstraps bootstrap methods efron 1982 are simulation methods for assessing frequency properties of statistical analyses the simulation model being that which is fitted to the actual data often the simulation involves monte carlo rather than theoretical evaluation unfortunately the bootstrap as usually described is inherently unconditional rubin s 1981 discussion bears on this point however if the bootstrap simulation results can be properly stratified then it is possible to estimate relevant conditional probabilities stratification can sometimes be effected in the model itself as when fixing the values of sample sizes or explanatory variables otherwise one must run the unconditional bootstrap and stratify its output in the present paper we illustrate the latter situation in the analysis of a mean shift model section 2 describes the application and its analysis by parametric methods sections 3 and 4 produce alternative bootstrap analyses the first of which uses the stratification of an unconditional monte carlo simulation the second bootstrap analysis involves estimation of a likelihood function the final section contains some brief general remarks about conditional bootstraps

augmented base loci and restricted volumes on normal varieties we extend to normal projective varieties defined over an arbitrary algebraically closed field a result of ein lazarsfeld musta nakamaye and popa characterizing the augmented base locus aka non ample locus of a line bundle on a smooth projective complex variety as the union of subvarieties on which the restricted volume vanishes we also give a proof of the folklore fact that the complement of the augmented base locus is the largest open subset on which the kodaira map defined by large and divisible multiples of the line bundle is an isomorphism

arithmetic linear series with base conditions in this note we study the volume of arithmetic linear series with base conditions as an application we consider the problem of zariski decompositions on arithmetic varieties

estimating the power of the two sample wilcoxon test for location shift summary traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution the distribution shape however may be unknown this paper describes a bootstrap method for using observed data or pilot data to approximate the power no assumptions need be made about the shape of the underlying continuous probability distribution simulation evidence shows that when applied to the wilcoxon two sample test for location shift the suggested method is reliable the evidence also shows that it is more accurate than a benchmark traditional approach the bootstrap method is applied to a real data example the analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift

improvements on cross validation the 632 bootstrap method abstract a training set of data has been used to construct a rule for predicting future responses what is the error rate of this rule this is an important question both for comparing models and for assessing a final selected model the traditional answer to this question is given by cross validation the cross validation estimate of prediction error is nearly unbiased but can be highly variable here we discuss bootstrap estimates of prediction error which can be thought of as smoothed versions of cross validation we show that a particular bootstrap method the 632 rule substantially outperforms cross validation in a catalog of 24 simulation experiments besides providing point estimates we also consider estimating the variability of an error rate estimate all of the results here are nonparametric and apply to any possible prediction rule however we study only classification problems with 0 1 loss in detail our simulations include smooth prediction rules like fisher s linear discriminant fun

vanishing sequences and okounkov bodies we define and study the vanishing sequence along a real valuation of sections of a line bundle on a normal projective variety building on previous work of the first author with huayi chen we prove an equidistribution result for vanishing sequences of large powers of a big line bundle and study the limit measure in particular the latter is described in terms of restricted volumes for divisorial valuations we also show on an example that the associated concave function on the okounkov body can be discontinuous at boundary points

filtrations and test configurations we introduce a strengthening of k stability based on filtrations of the homogeneous coordinate ring this allows for considering certain limits of families of test configurations which arise naturally in several settings we prove that if a manifold with no automorphisms admits a csck metric then it satisfies this stronger stability notion we also discuss the relation with the birational transformations in the definition of b stability

bootstrap confidence regions for directional data abstract methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p dimensional unit vector x with an arbitrary unimodal distribution on the p sphere the approach of this article differs from that of other authors in that it is based on pivotal statistics a general pivotal method is introduced that produces a wide variety of confidence regions on general p dimensional spheres included are confidence cones and likelihood based regions it can readily be modified to incorporate extra assumptions about the underlying distribution such as rotational symmetry the general method leads to confidence pictures which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces an application is given to a sample of spherical cross bed measurements the methods extend to the case where x has random length and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions

on importance resampling for the bootstrap summary we introduce an empirical method of importance resampling which does not require analytical calculation of the resampling probabilities our method can easily be used as part of a general algorithm for monte carlo calculation of bootstrap confidence intervals and hypothesis tests it produces consistent efficient and unbiased monte carlo approximations we also present a very general but elementary account of importance resampling which shows that even optimal importance resampling cannot improve on uniform resampling for calculating bootstrap estimates of bias variance skewness and related quantities this result demonstrates a major difference between importance resampling and other approaches to efficient bootstrap simulation such as balanced resampling and antithetic resampling which produce significant improvements in efficiency for a wide range of problems involving the bootstrap

incorporating covariates into standard line transect analyses summary an implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line heterogeneity in detection probabilities is commonly minimized using stratification but this may be precluded by small sample sizes we develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach small sample size properties of estimators are examined via simulations as an example the method is applied to eastern tropical pacific dolphin sightings data

more efficient bootstrap computations abstract this article concerns computational methods for the bootstrap that are more efficient than the straightforward monte carlo methods usually used the bootstrap is considered in its simplest form in a one sample nonparametric problem where the goal is to estimate the bias or variance of some statistic by bootstrap sampling or to set approximate confidence intervals for a parameter of interest in terms of various percentiles of the bootstrap distribution the methods of this article can in favorable situations reduce the necessary number of bootstrap replications manyfold moreover simple diagnostics are available to see whether or not any particular case is accessible to these methods

thresholds valuations and k stability abstract let x be a normal complex projective variety with at worst klt singularities and l a big line bundle on x we use valuations to study the log canonical threshold of l as well as another invariant the stability threshold the latter generalizes a notion by fujita and odaka and can be used to characterize when a q fano variety is k semistable or uniformly k stable it can also be used to generalize volume bounds due to fujita and liu the two thresholds can be written as infima of certain functionals on the space of valuations on x when l is ample we prove that these infima are attained in the toric case toric valuations achieve these infima and we obtain simple expressions for the two thresholds in terms of the moment polytope of l

an inverse heat conduction problem with a nonlinear source term abstract in this paper the nonlinear problem of an inhomogeneous heat equation with linear boundary conditions will be considered the surface heat flux history of a heated conducting body will be identified the approach of the proposed method is to approximate the unknown function using linear polynomial pieces which are determined consecutively from the solution of the minimization problem on the basis of overspecified data some numerical examples will also be presented

okounkov bodies and toric degenerations let vardelta be the okounkov body of a divisor d on a projective variety x we describe a geometric criterion for vardelta to be a lattice polytope and show that in this situation x admits a flat degeneration to the corresponding toric variety this degeneration is functorial in an appropriate sense

model selection in estimating equations summary model selection is a necessary step in many practical regression analyses but for methods based on estimating equations such as the quasi likelihood and generalized estimating equation gee approaches there seem to be few well studied model selection techniques in this article we propose a new model selection criterion that minimizes the expected predictive bias epb of estimating equations a bootstrap smoothed cross validation bcv estimate of epb is presented and its performance is assessed via simulation for overdispersed generalized linear models for illustration the method is applied to a real data set taken from a study of the development of ewe embryos

overdetermined systems of equations on toric spherical and other algebraic varieties abstract let e 1 e k be a collection of linear series on an irreducible algebraic variety x over c which is not assumed to be complete or affine that is e i h 0 x l i is a finite dimensional subspace of the space of regular sections of line bundles l i such a collection is called overdetermined if the generic system s 1 s k 0 with s i e i does not have any roots on x in this paper we study consistent systems which are given by an overdetermined collection of linear series generalizing the notion of a resultant hypersurface we define a consistency variety r i 1 k e i as the closure of the set of all systems which have at least one common root and study general properties of zero sets z s of a generic consistent system s r then in the case of equivariant linear series on spherical homogeneous spaces we provide a strategy for computing discrete invariants of such generic non empty set z s for equivariant linear series on the torus c n this strategy provides explicit calculations and generalizes the theory of newton polyhedra

estimating erosion risk on forest lands using improved methods of discriminant analysis a population of 638 timber harvest areas in northwestern california was sampled for data related to the occurrence of critical amounts of erosion 153 m3 within 0 81 ha separate analyses were done for forest roads and logged areas linear discriminant functions were computed in each analysis to contrast site conditions at critical plots with randomly selected controls bootstrapping was used extensively in the development and testing of the equations in estimating prediction bias and in placing confidence limits around parameters and posterior probabilities the resulting three variable equations had classification accuracy corrected for prediction bias of 77 7 for road plots and 69 2 for logged area plots the use of linear discriminant functions facilitates the explicit consideration of erosion risk when planning land disturbing activities

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

minkowski decomposition of okounkov bodies on surfaces abstract we prove that the okounkov body of a big divisor with respect to a general flag on a smooth projective surface whose pseudo effective cone is rational polyhedral decomposes as the minkowski sum of finitely many simplices and line segments arising as okounkov bodies of nef divisors

residual minimization least squares method for inverse heat conduction abstract a numerical method is systematically developed for resolving an inverse heat conduction problem in the presence of noisy discrete data this paper illustrates the effect of imposing constraints on the unknown function of interest a volterra integral equation of the first kind is derived and used as the starting point for residual minimization least squares methodology symbolic manipulation is exploited for purposes of augmenting the computational methodology preliminary indications suggest that the imposition of physical constraints on the system drastically reduces the level of mathematical sophistication needed for accurately approximating the unknown function of interest these constraints are actually available in many design studies or from models which are derived by physical processes

generalised information criteria in model selection summary the problem of evaluating the goodness of statistical models is investigated from an information theoretic point of view information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data the proposed criteria are applied to the evaluation of models estimated by maximum likelihood robust penalised likelihood bayes procedures etc we also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

newton okounkov bodies semigroups of integral points graded algebras and intersection theory generalizing the notion of newton polytope we dene the newtonokounkov body respectively for semigroups of integral points graded algebras and linear series on varieties we prove that any semigroup in the lattice z n is asymptotically approximated by the semigroup of all the points in a sublattice and lying in a convex cone applying this we obtain several results we show that for a large class of graded algebras the hilbert functions have polynomial growth and their growth coecients satisfy a brunn minkowski type inequality we prove analogues of the fujita approximation theorem for semigroups of integral points and graded algebras which imply a generalization of this theorem for arbitrary linear series applications to intersection theory include a far reaching generalization of the kushnirenko theorem from newton polytope theory and a new version of the hodge inequality we also give elementary proofs of the alexandrov fenchel inequality in convex geometry and its analogue in algebraic geometry

mixed multiplicities of divisorial filtrations abstract suppose that r is an excellent local domain with maximal ideal m r the theory of multiplicities and mixed multiplicities of m r primary ideals extends to possibly non noetherian filtrations of r by m r primary ideals and many of the classical theorems for m r primary ideals continue to hold for filtrations the celebrated theorems involving inequalities continue to hold for filtrations but the good conclusions that hold in the case of equality for m r primary ideals do not hold for filtrations in this article we consider multiplicities and mixed multiplicities of r by m r primary divisorial filtrations we show that some important theorems on equalities of multiplicities and mixed multiplicities of m r primary ideals that are not true in general for filtrations are true for divisorial filtrations we prove that a theorem of rees showing that if there is an inclusion of m r primary ideals i i with the same multiplicity then i and i have the same integral closure also holds for divisorial filtrations this theorem does not hold for arbitrary filtrations the classical minkowski inequalities for m r primary ideals i 1 and i 2 hold quite generally for filtrations if r has dimension two and there is equality in the minkowski inequalities then teissier and rees and sharp have shown that there are powers i 1 a and i 2 b that have the same integral closure this theorem does not hold for arbitrary filtrations the teissier rees sharp theorem has been extended by katz to m r primary ideals in arbitrary dimension we show that the teissier rees sharp theorem does hold for divisorial filtrations in an excellent local domain of dimension two we also show that the mixed multiplicities of divisorial filtrations are anti positive intersection products on a suitable normal scheme x birationally dominating r when r is an algebraic local domain essentially of finite type over a field

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

performance of balanced bootstrap resampling in distribution function and quantile problems it is shown that balanced resampling improves on ordinary uniform resampling when employed to estimate distribution functions or quantiles but that the improvement is not by an order of magnitude as happens in problems such as bias estimation maximum improvement occurs at the centre of the distribution where performance increases by 175 the increase is only 16 at the 2 5 and 97 5 quantiles in general the improvement is by the factor 1 2 1 1 where is the standard normal distribution function and

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

double bootstrap methods that use a single double bootstrap simulation we show that when the double bootstrap is used to improve performance of bootstrap methods for bias correction techniques based on using a single double bootstrap sample for each single bootstrap sample can be particularly effective in particular they produce third order accuracy for much less computational expense than is required by conventional double bootstrap methods however this improved level of performance is not available for the single double bootstrap methods that have been suggested to construct confidence intervals or distribution estimators

convex bodies appearing as okounkov bodies of divisors abstract based on the work of okounkov okounkov 1996 15 2003 16 lazarsfeld and musta 2009 13 and kaveh and khovanskii preprint 10 have independently associated a convex body called the okounkov body to a big divisor on a smooth projective variety with respect to a complete flag in this paper we consider the following question what can be said about the set of convex bodies that appear as okounkov bodies we show first that the set of convex bodies appearing as okounkov bodies of big line bundles on smooth projective varieties with respect to admissible flags is countable we then give a complete characterisation of the set of convex bodies that arise as okounkov bodies of r divisors on smooth projective surfaces such okounkov bodies are always polygons satisfying certain combinatorial criteria finally we construct two examples of non polyhedral okounkov bodies in the first one the variety we deal with is fano and the line bundle is ample in the second one we find a mori dream space variety such that under small perturbations of the flag the okounkov body remains non polyhedral

integrable systems toric degenerations and okounkov bodies let x be a smooth projective variety of dimension n over mathbb c equipped with a very ample hermitian line bundle mathcal l in the first part of the paper we show that if there exists a toric degeneration of x satisfying some natural hypotheses which are satisfied in many settings then there exists a surjective continuous map from x to the special fiber x 0 which is a symplectomorphism on an open dense subset u from this we are then able to construct a completely integrable system on x in the sense of symplectic geometry more precisely we construct a collection of real valued functions h 1 ldots h n on x which are continuous on all of x smooth on an open dense subset u of x and pairwise poisson commute on u moreover our integrable system in fact generates a hamiltonian torus action on u in the second part we show that the toric degenerations arising in the theory of newton okounkov bodies satisfy all the hypotheses of the first part of the paper in this case the image of the moment map mu h 1 ldots h n x rightarrow mathbb r n is precisely the newton okounkov body delta delta r v associated to the homogeneous coordinate ring r of x and an appropriate choice of a valuation v on r our main technical tools come from algebraic geometry differential kahler geometry and analysis specifically we use the gradient hamiltonian vector field and a subtle generalization of the famous ojasiewicz gradient inequality for real valued analytic functions since our construction is valid for a large class of projective varieties x this manuscript provides a rich source of new examples of integrable systems we discuss concrete examples including elliptic curves flag varieties of arbitrary connected complex reductive groups spherical varieties and weight varieties

balanced design of bootstrap simulations summary davison et al 1986 have shown that finite bootstrap simulations can be improved by forcing balance in the aggregate of simulated data sets their methods yield first order balance which principally affects bootstrap estimation of bias here we extend the methodology to second order balance which principally affects bootstrap estimation of variance the particular techniques involve latin square and balanced incomplete block designs numerical examples are given to illustrate both the positive and the negative features of the balanced simulations

distribution estimation using concomitants of order statistics with application to monte carlo simulation for the bootstrap we show that a simulation method suggestted by efron for approximating bootstrap distributions is closely related to tecniques based on concomitants of order statistics and develop its asymptotic properties from that viewpoint we prove that the method produces monte carlo approximations with variance and mean squared error decreasing like b 1 n 1 2 where b denotes the number of simulations and n equals the sample size therefore efron s method can be a competitor with techniques such as balanced resampling importance resampling and antithetic resampling where variance and mean squared error decrease like b 1 with no significant contribution from sample size

quantifying precision of mark recapture estimates using the bootstrap and related methods summary bootstrap techniques yield variance estimates under any model for which parameter estimates can be calculated and are useful in cases where analytic variances are not available in closed form or are available only if more restrictive assumptions are made here the application of bootstrap techniques to mark recapture models is discussed the approach also allows generation of robust confidence intervals which extend beyond the permissible parameter range only if the mark recapture model itself allows out of range parameter estimates if an animal population is assumed to be closed i e no death birth or migration two further methods of obtaining confidence limits for population size are suggested the first is based on a robbins monro search for each limit and the second applies the concept of a randomisation or permutation test in the absence of nuisance parameters both methods are exact apart from monte carlo variation and the limitations imposed by a discrete distribution for the second if all possible permutations are enumerated monte carlo variation is eliminated

generic vanishing in characteristic p 0 and the characterization of ordinary abelian varieties we prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of kawamata s theorems a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the albanese map when the frobenius stable kodaira dimension is zero

local okounkov bodies and limits in prime characteristic this article is concerned with the asymptotic behavior of certain sequences of ideals in rings of prime characteristic these sequences which we call p families of ideals are ubiquitous in prime characteristic commutative algebra e g they occur naturally in the theories of tight closure hilbert kunz multiplicity and f signature we associate to each p family of ideals an object in euclidean space that is analogous to the newton okounkov body of a graded family of ideals which we call a p body generalizing the methods used to establish volume formulas for the hilbert kunz multiplicity and f signature of semigroup rings we relate the volume of a p body to a certain asymptotic invariant determined by the corresponding p family of ideals we apply these methods to obtain new existence results for limits in positive characteristic an analogue of the brunn minkowski theorem for hilbert kunz multiplicity and a uniformity result concerning the positivity of a p family

asymptotic base loci via okounkov bodies abstract an okounkov body is a convex subset of euclidean space associated to a divisor on a smooth projective variety with respect to an admissible flag in this paper we recover the asymptotic base loci from the okounkov bodies by studying various asymptotic invariants such as the asymptotic valuations and the moving seshadri constants consequently we obtain the nefness and ampleness criteria of divisors in terms of the okounkov bodies furthermore we compute the divisorial zariski decomposition by the okounkov bodies and find upper and lower bounds for moving seshadri constants given by the size of simplexes contained in the okounkov bodies

identification of time dependent source terms and control parameters in parabolic equations from overspecified boundary data abstract this paper presents a semigroup approach for inverse source problems for the abstract heat equation when the measured output data is given in subject to the integral overspecification over the spatial domain the existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed such representation permits the derivation of sufficient conditions for the uniqueness of the solution also an approximation method based on the optimal homotopy analysis method oham is designed and the error estimates are discussed using graphical analysis moreover we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data the proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations the accuracy and stability of the method are discussed and compared with several finite difference techniques computational results show efficiency and high accuracy of the proposed algorithm

the bootstrap to smooth or not to smooth summary the bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals consideration of an example the estimation of the standard error in the variance stabilized sample correlation coefficient elucidates previously published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics finally the various approximations used are vindicated by a simulation study

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test

numerical solution of inverse heat conduction problem with nonstationary measurements the inverse heat conduction problem involves the calculation of surface heat flux and or temperature histories from transient measured temperatures inside solid in this paper the temperature is not specified at x 0 in an inverse heat conduction problem we choose an additional moving boundary condition this problem may be subdivided into two separate problems one of these problems is a moving boundary problem which is solved exactly by means of fundamental solution of heat equation the second problem is an inverse moving boundary problem which is solved with the residual minimization least squares method by using numerical examples we show the accuracy of our method