zero one schubert polynomials we prove that if sigma in s m is a pattern of w in s n then we can express the schubert polynomial mathfrak s w as a monomial times mathfrak s sigma in reindexed variables plus a polynomial with nonnegative coefficients this implies that the set of permutations whose schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment using magyar s orthodontia we characterize this class by a list of twelve avoided patterns we also give other equivalent conditions on mathfrak s w being zero one in this case the schubert polynomial mathfrak s w is equal to the integer point transform of a generalized permutahedron

a continuum of relative equilibria in the five body problem abstract it is generally believed that the set of relative equilibria equivalence classes in the newtonian n body problem for a given set of positive masses is finite however the result has only been proven for n 3 and remains a difficult open question for n 4 a wintner princeton math ser 5 215 princeton university press princeton nj 1941 s smale mathematical intelligencer 20 1998 7 15 we demonstrate that the condition for the masses being positive is a necessary one by finding a continuum of relative equilibria in the five body problem which unfortunately includes one negative mass this family persists in similar potential functions including the logarithmic potential used to describe the motion of point vortices in a plane of fluid

rotopulsators of the curved n body problem we consider the n body problem in spaces of constant curvature and study its rotopulsators i e solutions for which the configuration of the bodies rotates and changes size during the motion rotopulsators fall naturally into five groups positive elliptic positive elliptic elliptic negative elliptic negative hyperbolic and negative elliptic hyperbolic depending on the nature and number of their rotations and on whether they occur in spaces of positive or negative curvature after obtaining existence criteria for each type of rotopulsator we derive their conservation laws we further deal with the existence and uniqueness of some classes of rotopulsators in the 2 and 3 body case and prove two general results about the qualitative behaviour of rotopulsators more precisely for positive curvature we show that there is no foliation of the 3 sphere with clifford tori such that the motion of each body is confined to some clifford torus for negative curvature a similar result is proved relative to foliations of the hyperbolic 3 sphere with hyperbolic cylinders

on measuring sensitivity to parametric model misspecification summary in settings where parametric inference is inconsistent under model misspecification the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models to make the comparison tractable large sample and small misspecification approximations are employed the ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of sensitivity to model misspecification the maximum ratio over a family of correct distributions is determined as a measure of worst case sensitivity as well the distribution producing this maximum can be examined to see how a particular combination of a parametric family and estimand is susceptible to model misspecifications statisticians recognize that in reality no models are really correct in many parametric situations model misspecifications give rise to asymptotically inconsistent estimators of parameters the goal of this work is to quantify how bad an estimator can be relative to the degree of model misspecification the rationale for such an investigation is that misleading inferences arise when a bad answer is produced from an only mildly misspecified model we are less concerned about bad inferences arising from grossly misspecified models as such models are likely to be screened out by diagnostic checks we quantify the sensitivity of a parametric family and estimand to model misspecifications by comparing the kullback leibler kl divergence between correct and misspecified inferences with the kl divergence between correct and misspecified models more specifically the divergence between inferences can be based on either sampling distributions of maximum likelihood estimators or posterior distributions for tractability local approx imations to the kl divergence are employed in a somewhat similar spirit to cook 1986 the maximum ratio of approximate divergences over a class of correct models can be com puted as a worst case measure of sensitivity to misspecifications as well the correct model achieving the maximum can be examined to gain insight into the kind of departures from the model which are damaging this methodology is described fully in the next section then section 3 details an application to some common parametric models for survival data the paper concludes with a discussion in section 4 some technical comments are relegated to appendix a and appendix b

regular cell complexes in total positivity fomin and shapiro conjectured that the link of the identity in the bruhat stratification of the totally nonnegative real part of the unipotent radical of a borel subgroup in a semisimple simply connected algebraic group defined and split over mathbb r is a regular cw complex homeomorphic to a ball the main result of this paper is a proof of this conjecture this completes the solution of the question of bernstein of identifying regular cw complexes arising naturally from representation theory having the lower intervals of bruhat order as their closure posets a key ingredient is a new criterion for determining whether a finite cw complex is regular with respect to a choice of characteristic maps it most naturally applies to images of maps from regular cw complexes and is based on an interplay of combinatorics of the closure poset with codimension one topology

phase space structure and regularization of manev type problems phase space structure and regularization of manev type problems florin diacu a vasile mioc b cristina stoica c a department of mathematics and statistics university of victoria victoria canada v8w 3p4 b astronomical institute of the romanian academy astronomical observatory cluj napoca str cire silor 19 3400 cluj napoca romania c institute for gravitation and space sciences laboratory for gravitation str mendeleev 21 25 bucharest romania

toric degeneration of schubert varieties and gelfand tsetlin polytopes this note constructs the flat toric degeneration of the manifold fln of flags in cn due to gonciulea and lakshmibai transform groups 1 3 1996 215 as an explicit git quotient of the grobner degeneration due to knutson and miller grobner geometry of schubert polynomials ann math 2 to appear this implies that schubert varieties degenerate to reduced unions of toric varieties associated to faces indexed by rc graphs reduced pipe dreams in the gelfand tsetlin polytope our explicit description of the toric degeneration of fln provides a simple explanation of how gelfand tsetlin decompositions for irreducible polynomial representations of gln arise via geometric quantization

saari s conjecture for the collinear n body problem in 1970 don saari conjectured that the only solutions of the newtonian n body problem that have constant moment of inertia are the relative equilibria we prove this conjecture in the collinear case for any potential that involves only the mutual distances furthermore in the case of homogeneous potentials we show that the only collinear and non zero angular momentum solutions are homographic motions with central configurations

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

triple collision in the quasi homogeneous collinear three body problem abstract we generalize and improve the result of f diacu j differential equations 128 1996 58 77 concerning the dynamics of three points particles moving on the line under the influence of a quasihomogeneous potential w u v where u and v are homogeneous functions of degree a and b respectively for b 2 we found a set of positive measure of collision orbits that do not tend to form asymptotically a central configuration

local sensitivity approximations for selectivity bias summary observational data analysis is often based on tacit assumptions of ignorability or randomness the paper develops a general approach to local sensitivity analysis for selectivity bias which aims to study the sensitivity of inference to small departures from such assumptions if m is a model assuming ignorability we surround m by a small neighbourhood at defined in the sense of kullback leibler divergence and then compare the inference for models in iv with that for m interpretable bounds for such differences are developed applications to missing data and to observational comparisons are discussed local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems

on the anisotropic manev problem we consider the manev potential given by the sum between the inverse and the inverse square of the distance in an anisotropic space i e such that the force acts differently in each direction using mcgehee coordinates we blow up the collision singularity paste a collision manifold to the phase space study the flow on and near the collision manifold and find a positive measure set of collision orbits besides frontal homothetic frontal nonhomothetic and spiraling collisions and ejections we put into the evidence the surprising class of oscillatory collision and ejection orbits using the infinity manifold we further tackle capture and escape solutions in the zero energy case by finding the connection orbits between equilibria and or cycles at impact and at infinity we describe a large class of capture collision and ejection escape solutions

monte carlo em for missing covariates in parametric regression models we propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates we allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 we extend this method t o continuous or mixed categorical and continuous covariates and for arbitrary parametric regression models by adapting a monte carlo version of the em algorithm as discussed by wei and tanner 1990 journal of the american statistical association85 699 704 in addition we discuss the gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log concave the log concavity property of the conditional distributions will facilitate a straightforward implementation of the gibbs sampler via the adaptive rejection algorithm of gilks and wild 1992 applied statistics41 337 348 we assume the model for the response given the covariates is an arbitrary parametric regression model such as a generalized linear model a parametric survival model or a nonlinear model we model the marginal distribution of the covariates as a product of one dimensional conditional distributions this allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the e step we present examples involving both simulated and real data

central configurations and total collisions for quasihomogeneous n body problems abstract we consider n body problems given by potentials of the form r a r b with a b constants 0 a b to analyze the dynamics of the problem we first prove some properties related to central configurations including a generalization of moulton s theorem then we obtain several qualitative properties for collision and near collision orbits in the manev type case a 1 at the end we point out some new relationships between central configurations relative equilibria and homothetic solutions

schubert polynomials and the nilcoxeter algebra abstract schubert polynomials were introduced and extensively developed by lascoux and schutzenberger after an earlier less combinatorial version had been considered by bernstein gelfand and gelfand and demazure we give a new development of the theory of schubert polynomials based on formal computations in the algebra of operators u1 u2 satisfying the relations u2i 0 uiuj ujui if i j 2 and uiui 1ui ui 1uiui 1 we call this algebra the nilcoxeter algebra of the symmetric group s n our development leads to simple proofs of many standard results in particular a symmetry of the stable schubert polynomials fw b an explicit combinatorial formula for schubert polynomials due to billey jockusch and stanley c the cauchy formula for schubert polynomials and d a formula of macdonald for s w 1 1 our main new result is a proof of a conjectured q analogue of d due to macdonald which gives a formula for s w 1 q q2

on the singularities of the curved n body problem we study singularities of the n body problem in spaces of constant curvature and generalize certain results due to painleve weierstrass and sundman for positive curvature some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projection a property that offers a new method of approaching the problem in this par ticular case

schubert polynomials and classes of hessenberg varieties abstract regular semisimple hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory numerical analysis representation theory algebraic geometry and combinatorics we give a giambelli formula expressing the classes of regular semisimple hessenberg varieties in terms of chern classes in fact we show that the cohomology class of each regular semisimple hessenberg variety is the specialization of a certain double schubert polynomial giving a natural geometric interpretation to such specializations we also decompose such classes in terms of the schubert basis for the cohomology ring of the flag variety the coefficients obtained are nonnegative and we give closed combinatorial formulas for the coefficients in many cases we introduce a closely related family of schemes called regular nilpotent hessenberg schemes and use our results to determine when such schemes are reduced

merging multiple longitudinal studies with study specific missing covariates a joint estimating function approach merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power this article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics such as different follow up schedules and study specific missing covariates e g covariates observed in some studies but missing in other studies the presence of study specific missing covariates presents great statistical methodology challenge in data merging and analysis we propose a joint estimating function approach to addressing this challenge in which a novel nonparametric estimating function constructed via splines based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates under mild regularity conditions we show that the proposed estimator is consistent and asymptotically normal we evaluate finite sample performances of the proposed method through simulation studies in comparison to the conventional multiple imputation approach our method exhibits smaller estimation bias we provide an illustrative data analysis using longitudinal cohorts collected in mexico city to assess the effect of lead exposures on children s somatic growth

nakayama automorphism and rigidity of dual reflection group coactions abstract we study homological properties and rigidity of group coactions on artin schelter regular algebras

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

local influence for incomplete data models this paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data the idea is to utilize cook s approach to the conditional expectation of the complete data log likelihood function in the em algorithm it is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods an application to the generalized linear mixed model is investigated some illustrative artificial and real examples are presented

subword complexes in coxeter groups abstract let be a coxeter system an ordered list of elements in and an element in determine a subword complex as introduced in knutson and miller ann of math 2 2003 to appear subword complexes are demonstrated here to be homeomorphic to balls or spheres and their hilbert series are shown to reflect combinatorial properties of reduced expressions in coxeter groups two formulae for double grothendieck polynomials one of which appeared in fomin and kirillov proceedings of the sixth conference in formal power series and algebraic combinatorics dimacs 1994 pp 183 190 are recovered in the context of simplicial topology for subword complexes some open questions related to subword complexes are presented

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

affine stanley symmetric functions we define a new family inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of generating functions for w inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i which are affine analogues of stanley symmetric functions we establish basic properties of these functions including symmetry dominance and conjugation we conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine schur functions as applications we show how affine stanley symmetric functions generalize the dual of the k schur functions of lapointe lascoux and morse as well as the cylindric schur functions of postnikov conjecturally affine stanley symmetric functions should be related to the cohomology of the affine flag variety

finiteness of central configurations of five bodies in the plane we prove there are finitely many isometry classes of planar central configurations also called relative equilibria in the newtonian 5 body problem except perhaps if the 5 tuple of positive masses belongs to a given codimension 2 subvariety of the mass space

grothendieck polynomials via permutation patterns and chains in the bruhat order we give new formulas for grothendieck polynomials of two types one type expresses any specialization of a grothendieck polynomial in at least two sets of variables as a linear combination of products of grothendieck polynomials in each set of variables with coefficients schubert structure constants for grothendieck polynomials the other type is in terms of chains in the bruhat order we compare this second type to other constructions of grothendieck polynomials within the more general context of double grothendieck polynomials and the closely related h polynomials our methods are based upon the geometry of permutation patterns

on weak crossed products frobenius algebras and the weak bruhat ordering abstract the weak crossed product algebra was studied first by haile larson and sweedler amer j math 105 1983 689 they gave interesting properties for such an algebra one of which is that if a f is a weak crossed product induced by a weak 2 cocycle f defined on a galois group g gal k f and h is the inertial subgroup of g then a f has a wedderburn splitting that is a f b j where j is the radical of a f and b is a k h central simple algebra the purpose of this paper is to give the necessary and sufficient condition for a weak crossed product to be frobenius and to describe an algorithm for constructing lower subtractive graphs from a finite group g and a generating set s a special case of this construction is the so called weak bruhat ordering on a coxeter group g s we show that the nilcoxeter algebra associated to g s is a special case of the restricted algebra associated to a lower subtractive graph

the center of the affine niltemperley lieb algebra we give a description of the center of the affine niltemperley lieb algebra based on a certain grading of the algebra and on a faithful representation of it on fermionic particle configurations we present a normal form for monomials hence construct a basis of the algebra and use this basis to show that the affine niltemperley lieb algebra is finitely generated over its center as an application we obtain a natural embedding of the affine niltemperley lieb algebra on n generators into the affine niltemperley lieb algebra on n 1 generators

skew divided difference operators in the nichols algebra associated to a finite coxeter group abstract let w s be a finite coxeter system with root system r and with set of positive roots r for r v w w we denote by w and w v the divided difference operators and skew divided difference operators acting on the coinvariant algebra of w generalizing the work of liu 15 we prove that w v can be written as a polynomial with nonnegative coefficients in where r in fact we prove the stronger and analogous statement in the nichols woronowicz algebra model for schubert calculus on w after bazlov 4 we draw consequences of this theorem on saturated chains in the bruhat order and partially treat the question when w v can be written as a monomial in where r in an appendix we study related combinatorics on shuffle elements and bruhat intervals of length two

schubert polynomials and quiver formulas fulton s universal schubert polynomials f3 represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a permutation the quiver formula of buch and fulton bf expresses these polynomials as an integer linear combination of products of schur determinants we present a positive nonrecursive combinatorial formula for the coefficients our result is applied to obtain new expansions for the schubert polynomials of lascoux and schutzenberger ls1 and explicit giambelli formulas in the classical and quantum cohomology ring of any partial flag variety

schubert polynomials slide polynomials stanley symmetric functions and quasi yamanouchi pipe dreams abstract we introduce two new bases for polynomials that lift monomial and fundamental quasisymmetric functions to the full polynomial ring by defining a new condition on pipe dreams called quasi yamanouchi we give a positive combinatorial rule for expanding schubert polynomials into these new bases that parallels the expansion of schur functions into fundamental quasisymmetric functions as a result we obtain a refinement of the stable limits of schubert polynomials to stanley symmetric functions we also give combinatorial rules for the positive structure constants of these bases that generalize the quasi shuffle product and shuffle product respectively we use this to give a littlewood richardson rule for expanding a product of schubert polynomials into fundamental slide polynomials and to give formulas for products of stanley symmetric functions in terms of schubert structure constants

finiteness of relative equilibria of the four body problem we show that the number of relative equilibria of the newtonian four body problem is finite up to symmetry in fact we show that this number is always between 32 and 8472 the proof is based on symbolic and exact integer computations which are carried out by computer

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

the global flow of the manev problem the manev problem a two body problem given by a potential of the form a r b r2 where r is the distance between particles and a b are positive constants comprises several important physical models having its roots in research done by isaac newton we provide its analytic solution then completely describe its global flow using mcgehee coordinates and topological methods and offer the physical interpretation of all solutions we prove that if the energy constant is negative the orbits are generically precessional ellipses except for a zero measure set of initial data for which they are ellipses for zero energy the orbits are precessional parabolas and for positive energy they are precessional hyperbolas in all these cases the set of initial data leading to collisions has positive measure

near collision dynamics for particle systems with quasihomogeneous potentials abstract we study collision and ejection orbits of 3 particle systems having the potential w u v where u and v are homogeneous functions of degree a and b respectively with 1 a b we show that for b 2 collision and ejection orbits tend to form asymptotically a central configuration for the case b 2 which corresponds to maneff s gravitational law we find a set of collision and ejection orbits reaching the triple collision manifold without asymptotic phase this set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions

skew schubert functions and the pieri formula for flag manifolds we show the equivalence of the pieri formula for flag manifolds with certain identities among the structure constants for the schubert basis of the polynomial ring this gives new proofs of both the pieri formula and of these identities a key step is the association of a symmetric function to a finite poset with labeled hasse diagram satisfying a symmetry condition this gives a unified definition of skew schur functions stanley symmetric functions and skew schubert functions defined here we also use algebraic geometry to show the coefficient of a monomial in a schubert polynomial counts certain chains in the bruhat order obtainng a combinatorial chain construction of schubert polynomials

inference for non random samples observational data are often analysed as if they had resulted from a controlled study and yet the tacit assumption of randomness can be crucial for the validity of inference we take some simple statistical models and supplement them by adding a parameter which reflects the degree of non randomness in the sample for a randomized study is known to be 0 we examine the profile log likelihood for and the sensitivity of inference to small non zero values of particular models cover the analysis of survey data with item non response the paired comparison t test and two group comparisons using observational data with covariates some practical examples are discussed allowing for sampling bias increases the uncertainty of estimation and weakens the significance of treatment effects sometimes substantially so

schubert polynomials for the affine grassmannian let g be a complex simply connected simple group and k a maximal compact subgroup let f c t denote the field of formal laurent series and o c t the ring of formal power series the quotient qr g f g 0 is known as the affine grassmannian of g it is known that qr is homotopy equivalent to the space of based loops k into the compact group k see 9 30 the multiplication on qk endows the homology h qr and cohomology h qr with structures of dual hopf algebras these hopf algebras were first identified by bott 4 another descrip tion is given by ginzburg 10 which we shall not use the bruhat decomposition of g f induces a stratification of qr by schubert cells ilw indexed by grassman nian elements w of the affine weyl group waffwe denote by aw g h qr and aw g h qr the schubert classes in homology and cohomology when g sl n c bott identifies h qr and h qr with a subring an and a quotient an of the ring of symmetric functions our main theorem theorem 7 1 identifies the schubert classes aw g qr and aw g h qr as explicit symmet ric functions under this isomorphism these symmetric functions are combinatori ally defined in homology the aw g h qr are represented by lascoux lapointe morse s fc schur functions sw x g an and in cohomology the aw g h qr are represented by the dual fc schur functions or affine schur functions fw x g an see 21 24 17 our theorem was originally conjectured by mark shimozono the conjecture was made explicit in the cohomology case by jennifer morse kostant and kumar 14 studied the topology of homogeneous spaces for arbi trary kac moody groups and in particular calculated the structure constants of h qr in the schubert basis using the algebraic construction of the nilhecke ring our connection between the topology and the combinatorics proceeds via the study of three subalgebras of the nilhecke ring the first subalgebra is the nilcoxeter al gebra ao which is the algebra generated by the divided difference operators the second algebra is a certain centralizer algebra aaff s which we call the peterson subalgebra peterson 28 constructs an isomorphism j from the t equivariant ho mology hr qr of the affine grassmannian to z ff s the third algebra b is a combinatorially defined subalgebra of a0 which we call the affine fomin stanley

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

local influence measure of zero inflated generalized poisson mixture regression models in many practical applications count data often exhibit greater or less variability than allowed by the equality of mean and variance referred to as overdispersion underdispersion and there are several reasons that may lead to the overdispersion underdispersion such as zero inflation and mixture moreover if the count data are distributed as a generalized poisson or a negative binomial distribution that accommodates extra variation not explained by a simple poisson or a binomial model then the dispersion occurs too in this paper we deal with a class of two component zero inflated generalized poisson mixture regression models to fit such data and propose a local influence measure procedure for model comparison and statistical diagnostics at first we formally develop a general model framework that unifies zero inflation mixture as well as overdispersion underdispersion simultaneously and then we mainly investigate two types of perturbation schemes the global and individual perturbation schemes for perturbing various model assumptions and detecting influential observations also we obtain the corresponding local influence measures our method is novel for count data analysis and can be used to explore these essential issues such as zero inflation mixture and dispersion related to zero inflated generalized poisson mixture models on the basis of the results of model comparison we could further conduct the sensitivity analysis of perturbation as well as hypothesis test with more accuracy finally we employ here a simulation study and a real example to illustrate the proposed local influence measures copyright 2012 john wiley sons ltd

a tableau formula for eta polynomials we use the pieri and giambelli formulas of buch et al invent math 178 345 405 2009 j reine angew 2013 and the calculus of raising operators developed in buch et al a giambelli formula for isotropic grassmannians arxiv 0811 2781 2008 and tamvakis j reine angew math 652 207 244 2011 to prove a tableau formula for the eta polynomials of buch et al j reine angew 2013 and the stanley symmetric functions which correspond to grassmannian elements of the weyl group widetilde w n of type text d n we define the skew elements of widetilde w n and exhibit a bijection between the set of reduced words for any skew w in widetilde w n and a set of certain standard typed tableaux on a skew shape lambda mu associated to w

existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi homogeneous n body problems and the curved n body problem we prove that if for relative equilibrium solutions of a generalisation of quasi homogeneous n body problems the masses and rotation are given then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero we furthermore prove that the set of such relative equilibria is compact and prove related results for n body problems in spaces of constant gaussian curvature

local influence for generalized linear models with missing covariates in the analysis of missing data sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions in this article we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data we examine two types of perturbation schemes the single case and global perturbation schemes for perturbing various assumptions in this setting we show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation we also develop several local influence measures to identify influential points and test model misspecification simulation studies are conducted to evaluate our methods and real datasets are analyzed to illustrate the use of our local influence measures

schubert polynomials for the classical groups the task of a theory of schubert polynomials is to produce explicit representatives for schubert classes in the cohomology ring of a flag variety and to do so in a manner that is as natural as possible from a combinatorial point of view to explain more fully let us review a special case the schubert calculus for grassmannians where one asks for the number of linear spaces of given dimension satisfying certain geometric conditions a typical problem is to find the number of lines meeting four given lines in general position in 3 space answer below for each of the four given lines the set of lines meeting it is a schubert variety in the grassmannian and we want the number of intersection points of these four subvarieties in the modem solution of this problem the schubert varieties induce canonical elements of the cohomology ring of the grassmannian called schubert classes the product of these schubert classes is the class of a point times the number of intersection points counted with appropriate multiplicities this reformulation of the problem though one of the great achievements of algebraic geometry is only part of a solution it remains to give a concrete model for the cohomology ring that makes explicit computation with schubert classes possible as it happens the cohomology rings of grassmannians can be identified with quotients of a polynomial ring so that schubert classes correspond to schur functions intersection numbers such as we are considering then turn out to be littlewood richardson coefficients for example the answer to our four lines 4 problem is the coefficient of the schur function s 2 2 in the product s 1 x or 2 for an extended treatment and history of the subject see 10 11 18 the identification of schur functions as schubert polynomials for grassmannians is a consequence of a more general and now highly developed theory of schubert polynomials for the flag varieties of the special linear groups sl n c the starting point for this more general theory is a construction of

a conditional model for incomplete covariates in parametric regression models summary incomplete covariate data arise in many data sets when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 this method requires the estimation of many nuisance parameters for the distribution of the covariates unfortunately in data sets when the percentage of missing data is high and the missing covariate patterns are highly non monotone the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest we propose a conditional model for the covariate distribution that has several modelling advantages for the e step and provides a reduction in the number of nuisance parameters thus providing more stable estimates in finite samples we present a clinical trials example with six covariates five of which have some missing values

maximum likelihood methods for cure rate models with missing covariates we propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction in which the covariates are allowed to be missing we allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions we propose a novel em algorithm for maximum likelihood estimation and derive standard errors by using louis s formula louis 1982 journal of the royal statistical society series b 44 226 233 computational techniques using the monte carlo em algorithm are discussed and implemented a real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology

noncommutative schubert calculus and grothendieck polynomials abstract in this paper we extend the work of fomin and greene on noncommutative schur functions by defining noncommutative analogs of schubert polynomials if the variables satisfy certain relations essentially the same as those needed in the theory of noncommutative schur functions we prove a pieri type formula and a cauchy identity for our noncommutative polynomials our results imply the conjecture of fomin and kirillov concerning the expansion of an arbitrary grothendieck polynomial in the basis of schubert polynomials we also present a combinatorial interpretation for the coefficients of the expansion we conclude with some open problems related to it