nonlinear manifold learning for meshfree finite deformation thin shell analysis calculations on general point set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges the absence of a mesh makes it nontrivial to decide if two neighboring points in the three dimensional embedding are nearby or rather far apart on the manifold furthermore the topology of surfaces is generally not that of an open two dimensional set ruling out global parametrizations we propose a general and simple numerical method analogous to the mathematical theory of manifolds in which the point set surface is described by a set of overlapping charts forming a complete atlas we proceed in four steps 1 partitioning of the node set into subregions of trivial topology 2 automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods 3 parametrization of the surface using smooth meshfree here maximum entropy approximants and 4 gluing together the patch representations by means of a partition of unity each patch may be viewed as a meshfree macro element we exemplify the generality flexibility and accuracy of the proposed approach by numerically approximating the geometrically nonlinear kirchhoff love theory of thin shells we analyze standard benchmark tests as well as point set surfaces of complex geometry and topology

a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

on the estimation of the curvatures and bending rigidity of membrane networks via a local maximum entropy approach we present a meshfree method for the curvature estimation of membrane networks based on the local maximum entropy approach recently presented in 1 a continuum regularization of the network is carried out by balancing the maximization of the information entropy corresponding to the nodal data with the minimization of the total width of the shape functions the accuracy and convergence properties of the given curvature prediction procedure are assessed through numerical applications to benchmark problems which include coarse grained molecular dynamics simulations of the fluctuations of red blood cell membranes 2 3 we also provide an energetic discrete to continuum approach to the prediction of the zero temperature bending rigidity of membrane networks which is based on the integration of the local curvature estimates the local maximum entropy approach is easily applicable to the continuum regularization of fluctuating membranes and the prediction of membrane and bending elasticities of molecular dynamics models

nonlinear superposition formulae of the ito equation and a model equation for shallow water waves nonlinear superposition formulae of the ito equation and a model equation for shallow water waves are proved under certain conditions some particular solutions of the ito equation are obtained as an illustrative application of the obtained nonlinear superposition formula

a locking free meshfree method for the simulation of shear deformable plates based on a mixed variational formulation abstract the problem of shear locking in the thin plate limit is a well known issue that must be overcome when discretising the reissner mindlin plate equations in this paper we present a shear locking free method utilising meshfree maximum entropy basis functions and rotated raviart thomas nedelec elements within a mixed variational formulation the formulation draws upon well known techniques in the finite element literature due to the inherent properties of the maximum entropy basis functions our method allows for the direct imposition of dirichlet essential boundary conditions in contrast to methods based on moving least squares basis functions we present benchmark problems that demonstrate the accuracy and performance of the proposed method

enhanced local maximum entropy approximation for stable meshfree simulations abstract we introduce an improved meshfree approximation scheme which is based on the local maximum entropy strategy as a compromise between shape function locality and entropy in an information theoretical sense the improved version is specifically designed for severe finite deformation and offers significantly enhanced stability as opposed to the original formulation this is achieved by i formulating the quasistatic mechanical boundary value problem in a suitable updated lagrangian setting ii introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability iii spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency iv truncating shape functions at interfaces in order to stably represent multi component systems like composites or polycrystals the new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy as compared to exact solutions and where applicable finite element simulations and efficiency importantly the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes as shown for stable simulations of e g the inhomogeneous extension of a hyperelastic block up to 100 or the torsion of a hyperelastic cube by 200 both in an updated lagrangian setting and without the need for remeshing

some results on the caudrey dodd gibbon kotera sawada equation in this paper a hierarchy of bilinear caudrey dodd gibbon kotera sawada equations with a unified structure is proposed a nonlinear superposition formula for the cdgks equation is proved under certain conditions a backlund transformation for a higher order cdgks equation is presented

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

convergence analysis of meshfree approximation schemes this work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the local maximum entropy lme scheme as a particular example we provide conditions for the convergence in sobolev spaces of schemes that are n consistent in the sense of exactly reproducing polynomials of degree less than or equal to n 1 and whose basis functions are of rapid decay the convergence of the lme in w 1 p loc follows as a direct application of the general theory the analysis shows that the convergence order is linear in h a measure of the density of the point set the analysis also shows how to parameterize the lme scheme for optimal convergence because of the convex approximation property of lme its behavior near the boundary is singular and requires additional analysis for the particular case of polyhedral domains we show that away from a small singular part of the boundary any sobolev function can be approximated by means of the lme scheme with the aid of a capacity argument we further obtain approximation results with truncated lme basis functions in h1 and for spatial dimension d 2

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

symbolic computation and families of jacobi elliptic function solutions of the 2 1 dimensional nizhnik novikov veselov equation in this paper with the aid of the symbolic computation we have improved the extended f expansion method in chaos solitons and fractals 22 2004 111 and proposed the further improved f expansion method by this method we have gotten many new exact solutions which we have never seen before within our knowledge of the 2 1 dimensional nizhnik novikov veselov equations in addition the solutions we get are more general than the solutions the extended f expansion method gets at the same time our method is more convenient than the method in chaos solitons and fractals 18 2003 299 309 and the solutions we get are more abundant than the solutions in h q zh appl math e notes 1 2001 139 in other word the solutions in h q zh appl math e notes 1 2001 139 are part of our solutions our method can also apply to other partial differential equations and also get many new exact solutions

nonlinear superposition formula of the novikov veselov equation a nonlinear superposition formula of the novikov veselov equation is proved under certain conditions some particular solutions of the novikov veselov equation are given as an illustrative application of the obtained result

a higher order method based on local maximum entropy approximation we present here a generalization of local maximum entropy max ent approximation for high orders of consistency i e quadratic cubic the method is based upon the application of the de boor s algorithm to the standard linear local max ent approximation the resulting approximation possesses some interesting properties such as non negativity smoothness exact interpolation on the boundary and variation diminishing no gibbs effect the resulting structure has many similarities with b spline surfaces but without the tensor product structure typical of that approximation examples are provided of its use in the framework of a galerkin method showing the potential of the proposed method in solving boundary value problems copyright 2010 john wiley sons ltd

derivatives of maximum entropy basis functions on the boundary theory and computations summary in this paper we obtain explicit expressions to evaluate the derivatives of maximum entropy max ent basis function on the boundary of a convex domain in the max ent formulation the basis functions are obtained by maximizing a concave functional subjected to linear constraints reproducing conditions in doing so it is found that the lagrange multipliers blow up when x and the expressions for the derivatives of the max ent basis functions in are of an indeterminate form for points on we appeal to l hopital s rule to derive expressions to determine the derivatives of the basis functions we consider the shannon entropy functional and the relative entropy functional with different choices of the prior weight function the first order derivatives of all basis functions are bounded in contrast on an irregular grid with a certain nodal spacing some of the second derivatives of the basis functions are unbounded on the boundary necessary and sufficient conditions on the priors to obtain bounded lagrange multipliers are established optimal convergence rates for fourth order problems are demonstrated for a galerkin approach with a quadratically complete partition of unity enriched max ent approximation copyright 2013 john wiley sons ltd

a lil type result for the product limit estimator let x1 x2 xn be i i d r v s with p x u f u and y1 y2 yn be i i d p y u g u where both f and g are unknown continuous survival functions for i 1 2 n set i 1 if xi yi and 0 if xi yi and zi min itxi yi one way to estimate f from the observations zi i i l n is by means of the product limit p l estimator fn kaplan meier 1958 6

strong approximations of some biometric estimates under random censorship the empirical distribution function has been widely used as an estimator for the distribution function of the elements of a random sample it is not however appropriate when the observations are incomplete this is the case for example when the observations have been randomly censored on the right in the latter case the so called product limit estimate of kaplan and meier 16 has been generally accepted as a substitute for the empirical distribution function and it possesses many of the same properties cf meier 19 developing the corresponding statement of efron 8 weak convergence over a finite interval of the kaplan meier product limit estimate to a gaussian process when there is censorship on the right has been obtained by breslow and crowley 3 cf also meier 19 breslow and crowley obtained their result via the limiting distribution of the closely related cumulative hazard process under random censorship a generalisation of the efron breslow crowley theorem was formulated by yang 24 for the case when censorship on the right is performed by more competing risks these results have numerous statistical applications in areas such as medical follow up studies life testing actuarial sciences and demography koziol and green 18 have computed tables for the limiting distribution of the cram6r von mises statistic based on the kaplan meier product limit estimate under a specific random censorship model a point will be stressed in this paper however that by a certain transformation which seems to have escaped many researchers attention and is due to efron 8 it is always possible to obtain the standard wiener process in the limit the distributions of many functionals of which are well known this transformation was only recently used in a stimulating note by gillespie and fisher 14 to construct asymptotic confidence bands for the unknown distribution function in the kaplan meier model a general scheme of random censorship can be defined in the following way let x be a real random variable with distribution function f t

a backlund transformation and nonlinear superposition formula of a higher order ito equation in this paper we present a backlund transformation for a higher order ito equation and prove a nonlinear superposition formula under certain conditions therefore the integrability of the higher order ito equation is confirmed

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

deriving the continuity of maximum entropy basis functions via variational analysis in this paper we prove the continuity of maximum entropy basis functions using variational analysis techniques the use of information theoretic variational principles to derive basis functions is a recent development in this setting data approximation is viewed as an inductive inference problem with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints for a set of distinct nodes x i i 1 n in mathbb r d the convex approximation of a function u x is u h x sum i 1 n p i x u i where p i i 1 n are nonnegative basis functions and u h x must reproduce affine functions sum i 1 n p i x 1 sum i 1 n p i x x i x given these constraints we compute p i x by minimizing the relative entropy functional kullback leibler distance d p m sum i 1 n p i x ln p i x m i x where m i x is a known prior weight function distribution to prove the continuity of the basis functions we appeal to the theory of epiconvergence

rational solutions of integrable equations via nonlinear superposition formulae in this paper a method is developed to obtain rational solutions of integrable equations which include kdv boussinesq kp ito 1 1 dimensional cdgks ramani and 2 1 dimensional cdgks equations the key step that we use to find rational solutions of these equations is the use of nonlinear superposition formulae all these rational solutions obtained for each equation are connected by a backlund transformation which enables us to find other new solutions through the nonlinear superposition of rational solutions and other known solutions

a mesh free convex approximation scheme for kohn sham density functional theory density functional theory developed by hohenberg kohn and sham is a widely accepted reliable ab initio method we present a non periodic real space mesh free convex approximation scheme for kohn sham density functional theory we rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme we show the utility of the approximation scheme in performing both all electron and pseudopotential calculations the results of which are in good agreement with literature

the rate of strong uniform consistency for the product limit estimator the maximal deviation of the product limit estimate from the estimated distribution function is investigated as a consequence of a functional law of the iterated logarithm the log log law is proved for this deviation on appropriate half lines with the precise constants this result implies that the log log law need not hold in general for the maximal deviation on the whole line then a general asymptotic order of magnitude is determined for the latter deviation this order depends on the joint behaviour of the censoring and censored distributions in a well defined way corresponding to specific joint behaviours several limsup results are deduced as consequence including all the previously known log log type laws in improved form the results are also extended to the variable censoring model

functional limit laws for the increments of kaplan meier product limit processes and applications we prove functional limit laws for the increment functions of empirical processes based upon randomly right censored data the increment sizes we consider are classified into different classes covering the whole possible spectrum we apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions in particular we treat the case of kernel density and hazard rate estimators

improved robustness for nearly incompressible large deformation meshfree simulations on delaunay tessellations abstract a displacement based galerkin meshfree method for large deformation analysis of nearly incompressible elastic solids is presented nodal discretization of the domain is defined by a delaunay tessellation three node triangles and four node tetrahedra which is used to form the meshfree basis functions and to numerically integrate the weak form integrals in the proposed approach for nearly incompressible solids a volume averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes the nodal dilatational constraint is then projected onto the linear approximation space the displacement field is constructed on the linear space and enriched with bubble like meshfree basis functions for stability the new procedure leads to a displacement based formulation that is similar to f bar methodologies in finite elements and isogeometric analysis we adopt maximum entropy meshfree basis functions and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions the nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly incompressible large deformation analysis on delaunay meshes

decay mode solution of the two dimensional kdv equation and the generalized backlund transformation we consider the generalization of the customary backlund transform bt for the two dimensional 2d kdv equation ut 6uux uxxx x 3 2uyy 0 with being constant a nonlinear superposition formula has been obtained and it is shown that the present generalized bt can produce multiple soliton multiple decay mode solutions

central limit theorems for l_p distances of kernel estimators of densities under random censorship a sequence of independent nonnegative random variables with common distribution function f is censored on the right by another sequence of independent identically distributed random variables these two sequences are also assumed to be independent we estimate the density function f of f by a sequence of kernel estimators f n t int infty infty k t x h n d hat f n x h n where h n is a sequence of numbers k is kernel density function and hat f n is the product limit estimator of f we prove central limit theorems for int t 0 f n t f t p d mu t 1 leq p infty 0 t leq infty where mu is a measure on the borel sets of the real line the result is tested in monte carlo trials and applied for goodness of fit

asymptotics for a censored generalized linear model with unknown link function for censored response variable against projected co variable a generalized linear model with an unknown link function can cover almost all existing models under censorship its special cases include the accelerated failure time model with censored data such a model in the uncensored case is called the single index model in econometrics in this paper we systematically study the asymptotic properties we derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter we also obtain the optimal convergence rate of an estimator of the unknown link function in the model

semiparametric analysis of survival data with left truncation and dependent right censoring summary studies of chronic life threatening diseases often involve both mortality and morbidity in observational studies the data may also be subject to administrative left truncation and right censoring because mortality and morbidity may be correlated and mortality may censor morbidity the lynden bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the nonterminal event we propose a semiparametric estimator for this survival function based on a joint model for the two time to event variables which utilizes the gamma frailty specification in the region of the observable data first we develop a novel estimator for the gamma frailty parameter under left truncation using this estimator we then derive a closed form estimator for the marginal distribution of the nonterminal event the large sample properties of the estimators are established via asymptotic theory the methodology performs well with moderate sample sizes both in simulations and in an analysis of data from a diabetes registry

chain of the backlund transformation for the kdv equation we study the chain of the backlund transformation bt by the example of the kdv equation the previously obtained chain of the bt kdv modified kdv mkdv second mkdv has been extended one step further to the third mkdv case from this lowest order example the structure of infinity of the chain process has been foreseen

estimating a distribution function with truncated and censored data a minor modification of the product limit estimator is proposed for estimating a distribution function not necessarily continuous when the data are subject to either truncation or censoring or to both by independent but not necessarily identically distributed truncation censoring variables making use of martingale integral representations and empirical process theory uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function numerical results are also given to illustrate the usefulness of the modification particularly in the context of truncated data

nonlinear superposition formulae for the differential difference analogue of the kdv equation and two dimensional toda equation in this paper nonlinear superposition formulae of the differential difference analogue of the kdv equation and two dimensional toda equation are proved rigorously some particular solutions of the differential difference analogue of the kdv equation are given as an illustrative application of the obtained result

overview and construction of meshfree basis functions from moving least squares to entropy approximants in this paper an overview of the construction of meshfree basis functions is presented with particular emphasis on moving least squares approximants natural neighbour based polygonal interpolants and entropy approximants the use of information theoretic variational principles to derive approximation schemes is a recent development in this setting data approximation is viewed as an inductive inference problem with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints the maximization minimization of the shannon jaynes entropy functional relative entropy functional is used to unify the construction of globally and locally supported convex approximation schemes a java applet is used to visualize the meshfree basis functions and comparisons and links between different meshfree approximation schemes are presented copyright 2006 john wiley sons ltd

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

local maximum entropy approximation schemes a seamless bridge between finite elements and meshfree methods we present a one parameter family of approximation schemes which we refer to as local maximum entropy approximation schemes that bridges continuously two important limits delaunay triangulation and maximum entropy max ent statistical inference local max ent approximation schemes represent a compromise in the sense of pareto optimality between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width local max ent approximation schemes are entirely defined by the node set and the domain of analysis and the shape functions are positive interpolate affine functions exactly and have a weak kronecker delta property at the boundary local max ent approximation may be regarded as a regularization or thermalization of delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation local max ent approximation schemes can be taken as a convenient basis for the numerical solution of pdes in the style of meshfree galerkin methods in test cases characterized by smooth solutions we find that the accuracy of local max ent approximation schemes is vastly superior to that of finite elements

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

high order maximum entropy collocation methods abstract this paper considers the approximation of partial differential equations with a point collocation framework based on high order local maximum entropy schemes holmes in this approach smooth basis functions are computed through an optimization procedure and the strong form of the problem is directly imposed at the collocation points reducing significantly the computational times with respect to the galerkin formulation furthermore such a method is truly meshfree since no background integration grid is necessary the validity of holmes collocation is verified with supportive numerical examples where the expected convergence rates are obtained this includes the approximation of pdes on domains bounded by implicit and explicit nurbs curves illustrating a direct integration between geometric modeling and numerical analysis

estimation of the truncation probability in the random truncation model under random truncation a pair of independent random variables x and y is observable only if x is larger than y the resulting model is the conditional probability distribution h x y p x x y y for the truncation probability p x y a proper estimate is not the sample proportion but n g n s df n s where f n and g n are product limit estimates of the distribution functions f and g of x and y respectivly we obtain a much simpler representation n for n with this the strong consistency an iid representation and hence asymptotic normality and a lil for the estimate are established the results are true for arbitrary f and g the continuity restriction on f and g often imposed in the literature is not necessary furthermore the representation n of n facilitates the establishment of the strong law for the product limit estimates f n and g n

thin shell analysis from scattered points with maximum entropy approximants this is the accepted version of the following article millan d rosolen a and arroyo m 2011 thin shell analysis from scattered points with maximum entropy approximants int j numer meth engng 85 723 751 doi 10 1002 nme 2992 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 2992 abstract

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

improved implementation and robustness study of the x fem for stress analysis around cracks numerical crack propagation schemes were augmented in an elegant manner by the x fem method the use of special tip enrichment functions as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh which is of industrial interest especially when a numerical model for crack propagation is desired this paper improves the implementation of the x fem method for stress analysis around cracks in three ways first the enrichment strategy is revisited the conventional approach uses a topological enrichment only the elements touching the front are enriched we suggest a geometrical enrichment in which a given domain size is enriched the improvements obtained with this enrichment are discussed second the conditioning of the x fem both for topological and geometrical enrichments is studied a preconditioner is introduced so that off the shelf iterative solver packages can be used and perform as well on x fem matrices as on standard fem matrices the preconditioner uses a local nodal cholesky based decomposition third the numerical integration scheme to build the x fem stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme a 2d benchmark problem is designed to show the improvements and the robustness

volume averaged nodal projection method for nearly incompressible elasticity using meshfree and bubble basis functions we present a displacement based galerkin meshfree method for the analysis of nearly incompressible linear elastic solids where low order simplicial tessellations i e 3 node triangular or 4 node tetrahedral meshes are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions in this approach a volume averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower order than the approximation space for the displacement field resulting in a locking free method the stability of the method is provided via bubble like basis functions because the notion of an element or cell is not present in the computation of the meshfree basis functions such low order tessellations can be used regardless of the order of the approximation spaces desired first and second order meshfree basis functions are chosen as a particular case in the proposed method numerical examples are provided in two and three dimensions to demonstrate the robustness of the method its ability to avoid volumetric locking in the nearly incompressible regime and its improved performance when compared to the mini finite element scheme on the simplicial mesh

conservation laws lie symmetry and painleve analysis of the variable coefficients nnv equation in this paper with symbolic computation lie symmetry analysis painleve test conservation laws and similarity solutions for the generalized 2 1 dimensional variable coefficients nizhnik novikov veselov vcnnv equation are studied firstly we derive the group classifications and the corresponding symmetry reductions via lie group method then some new variable separation solutions with lie symmetry properties are discussed and integrable conditions of such system are determined via the painleve analysis at last some new infinite time dependent conservation laws are derived base on the new conservation theorem proved by ibragimov

on the optimum support size in meshfree methods a variational adaptivity approach with maximum entropy approximants we present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle the method is based on a variational approach and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters here those defining the support size of each basis function we consider local maximum entropy approximation schemes which exhibit smooth basis functions with respect to both space and the discretization parameters the node location and the locality parameters we illustrate by the poisson linear and non linear elasticity problems the effectivity of the method which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions copyright 2009 john wiley sons ltd

smooth second order non negative meshfree approximants selected by maximum entropy we present a family of approximation schemes which we refer to as second order maximum entropy max ent approximation schemes that extends the first order local max ent approximation schemes to second order consistency this method retains the fundamental properties of first order max ent schemes namely the shape functions are smooth non negative and satisfy a weak kronecker delta property at the boundary this last property makes the imposition of essential boundary conditions in the numerical solution of partial differential equations trivial the evaluation of the shape functions is not explicit but it is very efficient and robust to our knowledge the proposed method is the first higher order scheme for function approximation from unstructured data in arbitrary dimensions with non negative shape functions as a consequence the approximants exhibit variation diminishing properties as well as an excellent behavior in structural vibrations problems as compared with the lagrange finite elements mls based meshfree methods and even b spline approximations as shown through numerical experiments when compared with usual mls based second order meshfree methods the shape functions presented here are much easier to integrate in a galerkin approach as illustrated by the standard benchmark problems

on the rate of uniform convergence of the product limit estimator strong and weak laws by approximating the classical product limit estimator of a distribution function with an average of iid random variables we derive sufficient and necessary conditions for the rate of both strong and weak uniform convergence of the product limit estimator over the whole line these findings somehow fill a longstanding gap in the asymptotic theory of survival analysis the result suggests a natural way of estimating the rate of convergent we also prove a related conjecture raised by gill and discuss its application to the construction of a confidence interval for a survival function near the endpoint

repeated confidence intervals for the median survival time summary we describe methods for the construction of a confidence interval for median survival time based on right censored data these methods are extended to the construction of repeated confidence intervals for the median based on accumulating data here the overall probability that all intervals contain the true median is guaranteed at a fixed level the use of repeated confidence intervals for median survival time in post marketing surveillance is discussed a confidence interval for median survival time provides a useful summary of the survival experience of a group of patients if confidence intervals are calculated repeatedly as data accumulates the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly jennison turnbull 1984 have proposed methods for calculating repeated confidence intervals appropriate to such situations similar ideas have also been discussed by lai 1984 in 2 we propose a new form of single sample nonparametric confidence interval this interval has asymptotically correct coverage probability and monte carlo simulations suggest it is superior to its competitors for small sample sizes repeated confidence intervals for the median are presented in 3 and their stnall sample size performance is assessed by monte carlo simulation an example of their use is given in 4 all the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time

maximum entropy methods for time harmonic acoustics abstract this paper explores the application of maximum entropy methods max ent to time harmonic acoustic problems max ent basis functions are mesh free approximants that are constructed observing an equivalence between basis functions and discrete probability distributions and applying jaynes s maximum entropy principle they are c continuous and therefore they are particularly suited for the resolution of helmholtz problems where classical finite element methods show a poor accuracy in the high frequency region in addition it was recently shown that max ent approximants can be blended with isogeometric basis functions on the boundary of the domain this preserves the correct representation of the boundary like in isogeometric analysis with the advantage that the discretization of the interior of the domain is straightforward in this paper the max ent mathematical formulation is reviewed and then some numerical applications are studied including a 2d car cavity geometry defined by b spline curves in all cases if the same nodal discretization is used finite elements results are significantly improved

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

information flux method a meshfree maximum entropy petrov galerkin method including stabilised finite element methods an information flux method incorporating a novel approach to stable methods is proposed the method may be considered as a meshfree petrov galerkin approximation scheme with basis functions based on the principle of maximum entropy the two goals of accuracy and stability are distinctly assigned to solution and weighting functions respectively it is emphasised that stability can be ensured if the weighting functions are chosen such that they resemble the information flux of the underlying physical problem in this study the proposed method is applied to convection dominated convection diffusion problems a seamless transition of the proposed method to stabilised finite element methods is demonstrated for increasing locality of the basis functions in one dimension for lower localities a superior convergence behaviour can be shown compared to stabilised finite elements the method is presented and discussed for the general multi dimensional case with numerical results shown for one and two dimensional problems

nonparametric estimation with left truncated semicompeting risks data summary nonparametric estimators for competing risks data can be applied to semicompeting risks data a type of multi state data where a terminating event may censor a non terminating event after forcing the data into the competing risks format complications may arise with left truncation of the terminating event where the competing risks analysis naively truncates the nonterminating event using the left truncation time for the terminating event which may lead to large efficiency losses we propose nonparametric estimators which use all semicompeting risks information and do not require artificial truncation the uniform consistency and weak convergence of the estimators are established and variance estimators are provided simulation studies and an analysis of a diabetes registry demonstrate large efficiency gains over the naive estimators

meshfree co rotational formulation for two dimensional continua in this paper a meshfree co rotational formulation for two dimensional continua is proposed in a co rotational formulation the motion of a body is separated into rigid motion and strain producing deformation traditionally this has been done in the setting of finite elements for beams and shell type elements in the present work every node in a meshfree discretized domain has its own co rotating coordinate system three key ingredients are established in order to apply the co rotational formulation i the relationship between global and local variables ii the angle of rotation of a typical co rotating coordinate system and iii a variationally consistent tangent stiffness matrix an algorithm for the co rotational formulation based on load control is provided maximum entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations numerical examples are presented to demonstrate the validity of the meshfree co rotational formulation copyright 2009 john wiley sons ltd

optimal transportation meshfree approximation schemes for fluid and plastic flows we develop an optimal transportation meshfree otm method for simulating general solid and fluid flows including fluid structure interaction the method combines concepts from optimal transportation theory with material point sampling and max ent meshfree interpolation the proposed otm method generalizes the benamou brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior the otm method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities the otm method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems we illustrate the range and scope of the method by means of two examples of application the bouncing of a gas filled balloon off a rigid wall and the classical taylor anvil benchmark test extended to the hypervelocity range

stable generalized finite element method sgfem abstract the generalized finite element method gfem is a partition of unity method pum where the trial space of standard finite element method fem is augmented with non polynomial shape functions with compact support these shape functions which are also known as the enrichments mimic the local behavior of the unknown solution of the underlying variational problem gfem has been successfully used to solve a variety of problems with complicated features and microstructure however the stiffness matrix of gfem is badly conditioned much worse compared to the standard fem and there could be a severe loss of accuracy in the computed solution of the associated linear system in this paper we address this issue and propose a modification of the gfem referred to as the stable gfem sgfem we show that sgfem retains the excellent convergence properties of gfem does not require a ramp function in the presence of blending elements and the conditioning of the associated stiffness matrix is not worse than that of the standard fem moreover sgfem is very robust with respect to the parameters of the enrichments we show these features of sgfem on several examples

second order convex maximum entropy approximants with applications to high order pde we present a new approach for second order maximum entropy max ent meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non uniform node sets and prescribes robustly feasible constraints for the entropy maximization program defining the approximants we examine the performance of the proposed approximation scheme in the numerical solution by a direct galerkin method of a number of partial differential equations pdes including structural vibrations elliptic second order pdes and fourth order pdes for kirchhoff love thin shells and for a phase field model describing the mechanics of biomembranes the examples highlight the ability of the method to deal with non uniform node distributions and the high accuracy of the solutions surprisingly the first order meshfree max ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples even in the higher order pdes

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

meshfree enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids abstract this paper presents a meshfree enriched finite element formulation for triangular and tetrahedral elements in the analysis of two and three dimensional compressible and nearly incompressible solids the new formulation is first established in two dimensional case by introducing a meshfree approximation into a linear triangular finite element with an enriched node the interpolation functions of the four noded triangular element are constructed by the meshfree convex approximations and are completed to a polynomial of degree one the reference mapping using the constructed interpolation functions is shown to be invertible everywhere in the element and the global element area is proven to be conserved under a standard three point integration rule the triangular element formulation is extendable to the tetrahedral element in three dimensional case to provide a locking free analysis for the nearly incompressible materials an area weighted strain smoothing is developed in conjunction with the enriched interpolation functions to yield a discrete divergence free property at the integration point the resultant element formulation with strain smoothing is shown to pass the patch test to introduce the smoothed strain into galerkin formulation a modified hu washizu variational principle is adopted to formulate the discrete equations since the kronecker delta property in element interpolation is held along the element boundary using meshfree convex approximation boundary conditions can be treated in a standard way several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method

new exact solutions to the 2 1 dimensional ito equation extended homoclinic test technique exact soliton solutions to the 2 1 dimensional ito equation are studied based on the idea of extended homoclinic test and bilinear method some explicit solutions such as triangle function solutions soliton solutions doubly periodic wave solutions and periodic solitary wave solutions are obtained it shows that the 2 1 dimensional ito equation has richer solutions besides the elastic interactions of the solutions and their corresponding physical meaning are discussed

functional laws of the iterated logarithm for the product limit estimator of a distribution function under random censorship or truncation functional laws of the iterated logarithm are established for a modified version of the classical product limit estimator of a distribution function when the data are subject to random censorship or truncation making use of stochastic integral representations and empirical process theory strong approximations involving i i d continuous parameter martingales are developed for the product limit estimator and these strong approximations are then applied to derive the functional laws