constructions in sasakian geometry we first generalize the join construction described previously by the first two authors 4 for quasi regular sasakian einstein orbifolds to the general quasi regular sasakian case this allows for the further construction of specific types of sasakian structures that are preserved under the join operation such as positive negative or null sasakian structures as well as sasakian einstein structures in particular we show that there are families of sasakian einstein structures on certain 7 manifolds homeomorphic to s 2 s 5 we next show how the join construction emerges as a special case of lerman s contact fibre bundle construction 32 in particular when both the base and the fiber of the contact fiber bundle are toric we show that the construction yields a new toric sasakian manifold finally we study toric sasakian manifolds in dimension 5 and show that any simply connected compact oriented 5 manifold with vanishing torsion admits regular toric sasakian structures this is accomplished by explicitly constructing circle bundles over the equivariant blow ups of hirzebruch surfaces

high order asymptotic expansions for robust tests summary this paper provides high order asymptotic expansions for the m ratio and the signedroot m ratio robust test statistics which allow one to compute accurate approximations to significance or critical values using the edgeworth approximation the bartlett correction the variance correction or the saddlepoint approximation specific results are obtained for the linear regression model with the huber m estimator a monte carlo study illustrates the numerical accuracy of these approximations with respect to the usual first order approximations

sasaki einstein manifolds and volume minimisation we study a variational problem whose critical point determines the reeb vector field for a sasaki einstein manifold this extends our previous work on sasakian geometry by lifting the condition that the manifolds are toric we show that the einstein hilbert action restricted to a space of sasakian metrics on a link l in a calabi yau cone x is the volume functional which in fact is a function on the space of reeb vector fields we relate this function both to the duistermaat heckman formula and also to a limit of a certain equivariant index on x that counts holomorphic functions both formulae may be evaluated by localisation this leads to a general formula for the volume function in terms of topological fixed point data as a result we prove that the volume of a sasaki einstein manifold relative to that of the round sphere is always an algebraic number in complex dimension n 3 these results provide via ads cft the geometric counterpart of a maximisation in four dimensional superconformal field theories we also show that our variational problem dynamically sets to zero the futaki invariant of the transverse space the latter being an obstruction to the existence of a kahler einstein metric

a simplex algorithm for piecewise linear programming i derivation and proof the simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise linear objective subject to linear constraints this three part paper develops and analyzes a general computationally practical simplex algorithm for piecewiselinear programming

scalar curvature and stability of toric varieties we define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a kahler metric of constant scalar curvature the main result of the paper goes some way towards verifying this conjecture in the case of toric surfaces we prove that under the stability hypothesis the mabuchi functional is bounded below on invariant metrics and that minimising sequences have a certain convergence property in the reverse direction we give new examples of polarised surfaces which do not admit metrics of constant scalar curvature the proofs use a general framework developed by guillemin and abreu in which invariant kahler metrics correspond to convex functions on the moment polytope of a toric variety this paper is a step towards the solution of the general problem of finding conditions under which a complex projective variety admits a kahler metric of constant scalar curvature the pattern of the answer one expects is that this differential geometric condition should be equivalent to some notion of stability in the sense of geometric invariant theory this expectation is probably now an item of folklore going back to suggestions put forward by yau in the case of kahlereinstein metrics and the many results of tian and others in this case reinforced by a detailed formal picture which makes clear the analogy with the well established relation between the stability of vector bundles and yang mills connections 5 here we begin the investigation of

approximately bayesian inference abstract consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates it is well known that methods of interval estimation that do not correspond to bayesian inference with respect to some prior distribution have some logical difficulties this article proposes a measure of how close a system of interval estimates is to being of bayesian form using this measure several non bayesian methods of interval estimation are analyzed these results are illustrated on several examples

toric geometry sasaki einstein manifolds and a new infinite class of ads cft duals recently an infinite family of explicit sasaki einstein metrics yp q on s2 s3 has been discovered where p and q are two coprime positive integers with q p these give rise to a corresponding family of calabi yau cones which moreover are toric aided by several recent results in toric geometry we show that these are kahler quotients open image in new window namely the vacua of gauged linear sigma models with charges p p p q p q thereby generalising the conifold which is p 1 q 0 we present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold open image in new window for all q p with fixed p we hence find that the yp q manifolds are ads cft dual to an infinite class of open image in new window superconformal field theories arising as ir fixed points of toric quiver gauge theories with gauge group su n 2p as a non trivial example we show that y2 1 is an explicit irregular sasaki einstein metric on the horizon of the complex cone over the first del pezzo surface the dual quiver gauge theory has already been constructed for this case and hence we can predict the exact central charge of this theory at its ir fixed point using the ads cft correspondence the value we obtain is a quadratic irrational number and remarkably agrees with a recent purely field theoretic calculation using a maximisation

obstructions to the existence of sasaki einstein metrics we describe two simple obstructions to the existence of ricci flat kahler cone metrics on isolated gorenstein singularities or equivalently to the existence of sasaki einstein metrics on the links of these singularities in particular this also leads to new obstructions for kahler einstein metrics on fano orbifolds we present several families of hypersurface singularities that are obstructed including 3 fold and 4 fold singularities of ade type that have been studied previously in the physics literature we show that the ads cft dual of one obstruction is that the r charge of a gauge invariant chiral primary operator violates the unitarity bound

the gas transmission problem solved by an extension of the simplex algorithm the problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow pressure relations material balances and pressure bounds the solution method is based on piecewise linear approximations of the nonlinear flow pressure relations the approximated problem is solved by an extension of the simplex method the solution method is tested on real world data and compared with alternative solution methods

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

kahler metrics on toric orbifolds a theorem of e lerman and s tolman generalizing a result of t delzant states that compact symplectic toric orbifolds are classified by their moment polytopes together with a positive integer label attached to each of their facets in this paper we use this result and the existence of global actionangle coordinates to give an effective parametrization of all compatible toric complex structures on a compact symplectic toric orbifold by means of smooth functions on the corresponding moment polytope this is equivalent to parametrizing all toric kahler metrics and generalizes an analogous result for toric manifolds a simple explicit description of interesting families of extremal kahler metrics arising from recent work of r bryant is given as an application of the approach in this paper the fact that in dimension four these metrics are self dual and conformally einstein is also discussed this gives rise in particular to a one parameter family of self dual einstein metrics connecting the well known eguchi hanson and taub nut metrics

a simplex algorithm for piecewise linear programming 11 finiteness feasibility and degeneracy the simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise linear objective subject to linear constraints part i of this paper has developed a general and direct simplex algorithm for piecewise linear programming under convenient assumptions that guarantee a finite number of basic solutions existence of basic feasible solutions and nondegeneracy of all such solutions part ii now shows how these assumptions can be weakened so that they pose no obstacle to effective use of the piecewise linear simplex algorithm the theory of piecewise linear programming is thereby extended and numerous features of linear programming are generalized or are seen in a new light an analysis of the algorithm s computational requirements and a survey of applications will be presented in part iii

a simplex algorithm for piecewise linear fractional programming problems generalizations of the well known simplex method for linear programming are available to solve the piecewise linear programming problem and the linear fractional programming problem in this paper we consider a further generalization of the simplex method to solve piecewise linear fractional programming problems unifying the simplex method for linear programs piecewise linear programs and the linear fractional programs computational results are presented to obtain further insights into the behavior of the algorithm on random test problems

k semistability for irregular sasakian manifolds we introduce a notion of k semistability for sasakian manifolds this extends to the irregular case of the orbifold k semistability of ross thomas our main result is that a sasakian manifold with constant scalar curvature is necessarily k semistable as an application we show how one can recover the volume minimization results of martelli sparks yau and the lichnerowicz obstruction of gauntlett martelli sparks yau from this point of view

improved likelihood ratio statistics for exponential family nonlinear models summary this paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models corrected up to order n 1 where n is the sample size this result generalizes previous work by cordeiro 1983 various general bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed

a simplex algorithm for piecewise linear programming iii computational analysis and application the first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise linear functions subject to linear constraints this concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program the advantages are shown to be implicit in relationships between the linear and piecewise linear algorithms and to be independent of many details of implementation two sets of computational results serve to illustarate these arguments the piecewise linear simplex algorithm is observed to run 2 6 times faster than a comparable linear algorithm not including any additional expense that might be incurred in setting up the equivalent linear program further support for the practical value of a good piecewise linear programming algorithm is provided by a survey of many varied applications

algorithms for network piecewise linear programs a comparative study abstract piecewise linear programming plp is an important area of mathematical programming and concerns the minimisation of a convex separable piecewise linear objective function subject to linear constraints in this paper a subarea of plp called network piecewise linear programming nplp is explored the paper presents four specialised algorithms for nplp strongly feasible primal simplex dual method out of kilter and strongly polynomial cost scaling and their relative efficiency is studied a statistically designed experiment is used to perform a computational comparison of the algorithms the response variable observed in the experiment is the cpu time to solve randomly generated network piecewise linear problems classified according to problem class transportation transshipment and circulation problem size extent of capacitation and number of breakpoints per arc results and conclusions on performance of the algorithms are reported

piecewise linear multicriteria programs the continuous case and its discontinuous generalization in this paper we study piecewise linear multicriteria programs that is multicriteria programs with either a continuous or discontinuous piecewise linear objective function and a polyhedron set constraint we obtain an algebraic representation of a semi closed polyhedron and apply it to show that the image of a semi closed polyhedron under a continuous linear function is always one semi closed polyhedron we establish that the weak pareto solution point set of a piecewise linear multicriteria program is the union of finitely many semi closed polyhedra we propose an algorithm for finding the pareto point set of a continuous piecewise linear bi criteria program and generalize it to the discontinuous case we apply our algorithm to solve the discontinuous bi criteria portfolio selection problem with an l risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy

a symbolic algorithm for studying adjustments to the profile likelihood summary a symbolic algorithm for the derivation of the asymptotic expansion of the maximum likelihood estimate was first introduced by andrews stafford 1993 this algorithm is quite general and can be modified to give asymptotic expansions for the maximum likelihood estimate based on either the conditional modified or adjusted profile likelihoods expansions are obtained quickly with no chance for human clerical error as a result these three adjustments can be easily studied and some new statistical results are obtained bartlett corrections of each adjusted likelihood and asymptotic expansions for the first four moments of the maximum likelihood estimate based on the conditional and adjusted profile likelihoods are derived

symplectic homology of some brieskorn manifolds this paper consists of two parts in the first part we use symplectic homology to distinguish the contact structures on the brieskorn manifolds varsigma 2 ell 2 2 2 which contact homology cannot distinguish this answers a question from kwon and van koert brieskorn manifolds in contact topology preprint 2013 arxiv 1310 0343 in the second part we prove the existence of infinitely many exotic but homotopically trivial exotic contact structures on s 7 distinguished by the mean euler characteristic of s 1 equivariant symplectic homology apart from various connected sum constructions these contact structures can be taken from the brieskorn manifolds varsigma 78k 1 13 6 3 3 we end with some considerations about extending this result to higher dimensions

canonical sasakian metrics let m be a closed manifold of sasaki type a polarization of m is defined by a reeb vector field and for any such polarization we consider the set of all sasakian metrics compatible with it on this space we study the functional given by the square of the l2 norm of the scalar curvature we prove that its critical points or canonical representatives of the polarization are sasakian metrics that are transversally extremal we define a sasaki futaki invariant of the polarization and show that it obstructs the existence of constant scalar curvature representatives for a fixed cr structure of sasaki type we define the sasaki cone of structures compatible with this underlying cr structure and prove that the set of polarizations in it that admit a canonical representative is open we use our results to describe fully the case of the sphere with its standard cr structure showing that each element of its sasaki cone can be represented by a canonical metric we compute their sasaki futaki invariant and use it to describe the canonical metrics that have constant scalar curvature and to prove that only the standard polarization can be represented by a sasaki einstein metric

tools for the symbolic computation of asymptotic expansions summary this paper describes a collection of procedures for the systematic computation of asymptotic expansions that are common in statistical theory and practice expansions of functions of sums of independent and identically distributed random variables the procedures permit the expansion of maximum likelihood estimates the associated deviance or drop in likelihood and more general functions of random variables with distributions involving one or more parameters the procedures are illustrated with examples involving general and specific laws much of statistical theory and practice is based on asymptotic expansions many programs are available to assist in the numerical evaluation of such expansions but there is a need for computational tools to assist in their derivation and symbolic evaluation heller 1991 shows how symbolic calculation may be used in a wide variety of statistical problems kendall 1988 1990 gives procedures for the symbolic computation of expressions in the analysis of the diffusion of euclidean shape silverman and young 1987 use computer algebra to evaluate criteria on which the decision to smooth a bootstrap distribution is based young and daniels 1990 apply symbolic computation to evaluate expressions in the assessment of bootstrap bias venables 1985 utilizes symbolic computation heavily to obtain expansions of maximum marginal likelihood estimates most notably fisher s a statistic barndorff nielsen and blasild 1986 describe procedures for the numerical calculation of bartlett factors in cases where cumulants of the likelihood function may be specified most of these references involve the evaluation of complicated formulae in particular cases and not the derivation of the formulae themselves here we give general procedures for both the derivation of formulae and their evaluation in specific cases the derivation of asymptotic expansions is typically a simple but laborious task consider for example the calculation of the expectation of the likelihood ratio test statistic for a one parameter family to order 1 n this may be accomplished in general

reducibility in sasakian geometry the purpose of this paper is to study reducibility properties in sasakian geometry first we give the sasaki version of the de rham decomposition theorem however we need a mild technical assumption on the sasaki automorphism group which includes the toric case next we introduce the concept of it cone reducible and consider s 3 bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2 torus of reeb type in particular we can classify all such sasakian structures up to contact isotopy on s 3 bundles over a riemann surface of genus greater than zero finally we show that in the toric case an extremal sasaki metric on a sasaki join always splits

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

optimal objective function approximation for separable convex quadratic programming we present an optimal piecewise linear approximation method for the objective function of separable convex quadratic programs the method provides guidelines on how many grid points to use and how to position them for a piecewise linear approximation if the error induced by the approximation is to be bounded a priori

hamiltonian 2 forms in kahler geometry ii global classification we present a classification of compact kahler manifolds admitting a hamiltonian 2 form which were classified locally in part i of this work this involves two components of independent interest the first is the notion of a rigid hamiltonian torus action this natural condition for torus actions on a kahler manifold was introduced locally in part i but such actions turn out to be remarkably well behaved globally leading to a fairly explicit classification up to a blow up compact kahler manifolds with a rigid hamiltonian torus action are bundles of toric kahler manifolds the second idea is a special case of toric geometry which we call orthotoric we prove that orthotoric kahler manifolds are diffeomorphic to complex projective space but we extend our analysis to orthotoric orbifolds where the geometry is much richer we thus obtain new examples of kahler einstein 4 orbifolds combining these two themes we prove that compact kahler manifolds with hamiltonian 2 forms are covered by blow downs of projective bundles over kahler products and we describe explicitly how the kahler metrics with a hamiltonian 2 form are parameterized we explain how this provides a context for constructing new examples of extremal kahler metrics in particular a subclass of such metrics which we call weakly bochner flat we also provide a self contained treatment of the theory of compact toric kahler manifolds since we need it and find the existing literature incomplete

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v