bias correction of two state latent markov process parameter estimates under misclassification a discretely observed two state process may misclassify the state of an unobservable continuous time two state markov process we examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities since maximum likelihood estimators are not available in closed form we provide two alternatives for bias adjusted estimation in the case of large samples the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities for finite samples we provide an approximation based on partial derivatives estimators that are bias adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small simulation studies reveal the effect of misclassification on estimation repeated diagnostic testing data illustrate the approaches

a fast semi discrete kansa method to solve the two dimensional spatiotemporal fractional diffusion equation abstract fractional order diffusion equations fdes extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media real world diffusion can be multi dimensional requiring efficient numerical solvers that can handle long term memory embedded in mass transport to address this challenge a semi discrete kansa method is developed to approximate the two dimensional spatiotemporal fde where the kansa approach first discretizes the fde then the gauss jacobi quadrature rule solves the corresponding matrix and finally the mittag leffler function provides an analytical solution for the resultant time fractional ordinary differential equation numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes applications further show that the numerical method can efficiently solve two dimensional spatiotemporal fde models with either a continuous or discrete mixing measure hence this study provides an efficient and fast computational method for modeling super diffusive sub diffusive and mixed diffusive processes in large two dimensional domains with irregular shapes

a method for calculating meshless finite difference weights an exact method for calculating the finite difference weights for arbitrary distributed points in multiple dimensions is presented the method avoids the numerical ill conditioning associated with a small scale factor by delaying the limiting of 0 the gaussian radial basis function is approximated by a taylor s series expansion in the variable and the resultant matrix equation is solved using the fraction free lu decomposition method

solving time dependent engineering problems with multiquadrics abstract this paper deals with the solution of time dependent problems the multiquadric radial basis function method is formulated with a new approach for transient problems one and two dimensional problems are considered the forward difference and the crank nicolson time marching schemes for parabolic cases are considered the central difference integration method of the newmark family is considered for hyperbolic problems the method proves its accuracy in four numerical examples

a nodal integration and post processing technique based on voronoi diagram for galerkin meshless methods a stabilized nodal integration technique is adopted by adding the square of the residual of the equilibrium equation to the potential energy functional an approach is proposed based on voronoi diagram to evaluate nodal volumes accurately it is a key issue for nodal integration of galerkin meshless methods furthermore as the dual of voronoi diagram the corresponding delaunay triangles are at hand provided voronoi diagram construction is completed a realistic technique is proposed based on background delaunay triangles for post processing of meshless results in the whole domain of interest two elastic stress analysis problems are investigated which demonstrate the approach is realistic versatile and robust

radial spline collocation method for static analysis of beams conventional spline collocation method scm uses equally spaced knots in the computation of approximation however when load distribution geometry material property of structure are discontinuous it will greatly reduce accuracy the goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots applying the concept of radial basis functions rbf the spline function is transformed into radial spline function rsf consequently rsf can conveniently calculate the values for unequally spaced knots so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method rscm in this paper the proposed rscm also can be extended to solve other structural problems such as frame plate shell etc

an explicit material point finite element method for hyper velocity impact in this paper an explicit material point finite element fe method is proposed and a computer code empfe 3d is developed for simulating hyper velocity impact the material domain is discretized by a mesh of finite elements the momentum equations are solved on a predefined computational grid like the material point method in the large deformation zone and on the fe mesh like the traditional fe method elsewhere the grid may be fixed in space or moved in a predefined way the nodes covered by the grid are treated as material particles and the remaining nodes are treated as fe nodes the proposed method yields the same results as the traditional fe method if the grid vanishes on the other hand it yields the same results as the material point method if the grid covers the entire material domain at all time steps the method combines the advantages of eulerian and lagrangian descriptions of motion while eliminates their drawbacks due to element entanglement and numerical dissipation the method is computationally efficient and can be easily implemented in an existing explicit fe code like dyna3d copyright 2005 john wiley sons ltd

a natural neighbour method for linear elastic problems based on fraeijs de veubeke variational principle the natural neighbour method can be considered as belonging to the meshless methods classically the development of this method is based on the virtual work principle in the present paper we use the natural neighbour method for 2d domains starting from the fraeijs de veubeke variational principle and we approximate separately the displacement field the stress field and the strain field the assumed strains and the assumed stresses are constant over each voronoi cell the assumed surface reactions are constant along the edge where the displacements are imposed while the assumed displacements are interpolated by laplace interpolants in the absence of body forces it is shown that the calculation of integrals on the area of the solid domain can be avoided only integrals on the edges of the voronoi cells are necessary on the other hand displacements can be imposed in the average sense on some boundaries of the domain patch tests and some applications in the elastic domain are given in the paper and show the effectiveness of the method copyright 2007 john wiley sons ltd

on unsymmetric collocation by radial basis functions solving partial differential equations by collocation with radial basis functions can be efficiently done by a technique first proposed by kansa in 1990 it rewrites the problem as a generalized interpolation problem and the solution is obtained by solving a possibly large linear system the method has been used successfully in a variety of applications but a proof of nonsingularity of the linear system was still missing this paper shows that a general proof of this fact is impossible however numerical evidence shows that cases of singularity are rare and have to be constructed with quite some effort

likelihood inference for a class of latent markov models under linear hypotheses on the transition probabilities summary for a class of latent markov models for discrete variables having a longitudinal structure we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process for the maximum likelihood estimation of a latent markov model under hypotheses of this type we outline an em algorithm that is based on well known recursions in the hidden markov literature we also show that under certain assumptions the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent markov model against a less stringent linear hypothesis on the transition probabilities of the same model is of x2 type as a particular case we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent markov version which may be used to test the hypothesis of absence of transition between latent states the approach is illustrated through a series of simulations and two applications the first of which is based on educational testing data that have been collected within the national assessment of educational progress 1996 and the second on data concerning the use of marijuana which have been collected within the national youth survey 19761980

a fe meshfree quad4 element based on partition of unity a new 4 node quadrilateral element is developed by combining the shape functions of finite element and meshfree methods the objective is to synergise the attractive features of finite element and meshfree shape functions using the concepts of partition of unity pu methods the shape functions of the well known quad4 element are used for pu and the least square point interpolation for local approximation this enables the proposed element inherit the compatibility properties of finite element method and the quadratic polynomial completeness properties of meshfree methods numerical results for the bench mark problems show that the proposed element has a good tolerance to distorted meshes the element also seems to be free from the linear dependence problem which is known to plague some of the pu based elements

estimation of operating characteristics for dependent diagnostic tests based on latent markov models we describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test log linear models are adopted for the classification distributions conditional on the latent state where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests a marginal likelihood is constructed by marginalizing over a latent two state markov process specific latent processes we consider include a first order markov model a second order markov model and a time nonhomogeneous markov model although the method is described in full generality adaptations to handle missing data are described model diagnostics are considered based on the bootstrap distribution of conditional residuals the methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement

multiquadric method for the numerical solution of a biphasic mixture model a computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model the model includes a set of constitutive equations for the fluid flows through the solid phase a set of momentum equations for stress strain equilibrium and a continuity equation for the solid phase and the fluid phase the numerical method does not require the generation of mesh as in the finite element method and hence gives high flexibility in applying the method to irregular geometry numerical examples are made to compute the solution of the confined compression problem which approximates the nonlinear response of soft hydrated tissues under external loading the numerical results are compared with spilker s penalty finite element method

marginal methods for correlated binary data with misclassified responses misclassification is a longstanding concern in medical research although there has been much research concerning error prone covariates relatively little work has been directed to problems with response variables subject to error in this paper we focus on misclassification in clustered or longitudinal outcomes we propose marginal analysis methods to handle binary responses which are subject to misclassification the proposed methods have several appealing features including simultaneous inference for both marginal mean and association parameters and they can handle misclassified responses for a number of practical scenarios such as the case with a validation subsample or replicates furthermore the proposed methods are robust to model misspecification in a sense that no full distributional assumptions are required numerical studies demonstrate satisfactory performance of the proposed methods under a variety of settings copyright 2011 oxford university press

bayesian modeling of differential gene expression we present a bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects and show how to use the output for choosing lists of genes for further investigation we give empirical evidence that expression level dependent array effects are needed and explore different nonlinear functions as part of our model based approach to normalization the model includes gene specific variances but imposes some necessary shrinkage through a hierarchical structure model criticism via posterior predictive checks is discussed modeling the array effects normalization simultaneously with differential expression gives fewer false positive results to choose a list of genes we propose to combine various criteria for instance fold change and overall expression into a single indicator variable for each gene the posterior distribution of these variables is used to pick the list of genes thereby taking into account uncertainty in parameter estimates in an application to mouse knockout data gene ontology annotations over and underrepresented among the genes on the chosen list are consistent with biological expectations

numerical solution to the unsteady two dimensional schrodinger equation using meshless local boundary integral equation method a meshless local boundary integral equation lbie method is proposed to solve the unsteady two dimensional schrodinger equation the method is based on the lbie with moving least squares mls approximation for the mls approximation nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables a time stepping method is employed to deal with the time derivative an efficient method for dealing with singular domain integrations that appear in the discretized equations is presented finally numerical results are considered for some examples to demonstrate the accuracy efficiency and high rate of convergence of this method copyright 2008 john wiley sons ltd

a local point interpolation method for static and dynamic analysis of thin beams abstract the local point interpolation method lpim is a newly developed truly meshless method based on the idea of meshless local petrov galerkin mlpg approach in this paper a new lpim formulation is proposed to deal with fourth order boundary value and initial value problems for static and dynamic analysis stability free vibration and forced vibration of beams local weak forms are developed using weighted residual method locally in order to introduce the derivatives of the field variable into the interpolation scheme a technique is proposed to construct polynomial interpolation with kronecker delta function property based only on a group of arbitrarily distributed points because the shape functions so obtained possess delta function property the essential boundary conditions can be implemented with ease as in the conventional finite element method fem the validity and efficiency of the present lpim formulation are demonstrated through numerical examples of beams under various loads and boundary conditions

a double boundary collocation hermitian approach for the solution of steady state convection diffusion problems in this article a double boundary collocation approach based on the meshless radial basis function hermitian method symmetric method is proposed and compared with the conventional single collocation in the double boundary collocation approach at the boundary collocation points the boundary condition and the governing partial differential equation are required to be satisfied simultaneously instead of only the boundary condition as required in the single collocation we are able to carry out this type of algorithm due to the robustness of the proposed hermite interpolation scheme in which the resulting matrix will be non singular as long as the partial differential operators applied to each point are linearly independent even if in a single node we impose two different differential conditions the results obtained with this new method are characterized by a higher precision especially for the prediction of the fluxes at the boundaries this is due to the higher order of continuity of the approximation at the boundary points imposed by the double collocation

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

novel adaptive meshfree integration techniques in meshless methods summary we propose two strategies of novel adaptive numerical integration based on mapping techniques for solving the complicated problems of domain integration encountered in meshfree methods several mapping methods are presented in detail that map a complex integration domain to much simpler ones for example squares triangles or circles the techniques described in the paper can be applied to both global and local weak forms and the highly nonlinear meshfree integrands are evaluated with controlled accuracy the necessity of the clumsy procedure of background mesh or cell structures used for integration purpose in existing meshfree methods is avoided and many meshfree methods that require the domain integration can now become truly meshfree various numerical examples in two dimensions are considered to demonstrate the applicability and the effectiveness of the proposed methods and it shows that the accuracy is improved significantly their obtained results are compared with analytical solutions and other approaches and very good agreements are found additionally some three dimensional cases applied by the present methods are also examined copyright 2012 john wiley sons ltd

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

controlling false discoveries in multidimensional directional decisions with applications to gene expression data on ordered categories microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes some common experiments are time course dose response experiments where a tissue or cell line is exposed to different doses and or durations of time to a chemical a goal of such studies is to identify gene expression patterns profiles over the ordered categories this problem can be formulated as a multiple testing problem where for each gene the null hypothesis of no difference between the successive mean gene expressions is tested and further directional decisions are made if it is rejected much of the existing multiple testing procedures are devised for controlling the usual false discovery rate fdr rather than the mixed directional fdr mdfdr the expected proportion of type i and directional errors among all rejections benjamini and yekutieli 2005 journal of the american statistical association 100 71 93 proved that an augmentation of the usual benjamini hochberg bh procedure can control the mdfdr while testing simple null hypotheses against two sided alternatives in terms of one dimensional parameters in this article we consider the problem of controlling the mdfdr involving multidimensional parameters to deal with this problem we develop a procedure extending that of benjamini and yekutieli based on the bonferroni test for each gene a proof is given for its mdfdr control when the underlying test statistics are independent across the genes the results of a simulation study evaluating its performance under independence as well as under dependence of the underlying test statistics across the genes relative to other relevant procedures are reported finally the proposed methodology is applied to a time course microarray data obtained by lobenhofer et al 2002 molecular endocrinology 16 1215 1229 we identified several important cell cycle genes such as dna replication repair gene mcm4 and replication factor subunit c2 which were not identified by the previous analyses of the same data by lobenhofer et al 2002 and peddada et al 2003 bioinformatics 19 834 841 although some of our findings overlap with previous findings we identify several other genes that complement the results of lobenhofer et al 2002

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

fe meshfree quad4 element for free vibration analysis the fe lspim quad4 element which was recently introduced for the static analysis uses new shape functions that combine the meshfree and finite element shape functions so as to synergize the individual strengths of meshfree and finite element methods as a result the element inherits the completeness properties of meshfree shape functions and the compatibility properties of finite element shape functions in this paper the element is extended to free vibration analysis of two dimensional solids typical benchmark problems are solved to test the efficacy of the element the results show that the element gives more accurate solution than the peer elements particularly under distorted mesh

the natural neighbour petrov galerkin method for elasto statics in this paper an efficient and accurate meshless natural neighbour petrov galerkin method nnpg is proposed to solve elasto static problems in two dimensional space this method is derived from the generalized meshless local petrov galerkin method mlpg as a special case in the nnpg the local supported trial functions are constructed based on the non sibsonian interpolation and test functions are taken as the three node triangular fem shape functions the local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub domains these sub domains are constructed with delaunay tessellations and domain integrals are evaluated over included delaunay triangles by using gaussian quadrature scheme as this method combines the advantages of natural neighbour interpolation with petrov galerkin method together no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems copyright 2005 john wiley sons ltd

the partition of unity quadrature in meshless methods summary in dealing with mesh free formulations a major problem is connected to the computation of the quadra tures appearing in the variational principle related to the dierential boundary value problem these integrals require in the standard approach the introduction of background quadrature subcells which somehow make these methods not truly meshless in this paper a new general method for computing denite integrals over arbitrary bounded domains is proposed and it is applied in particular to the evaluation of the discrete weak form of the equilibrium equations in the framework of an augmented lagrangian element free formulation the approach is based on splitting the integrals over the entire domain into the sum of integrals over weight function supports without modifying in any way the variational principle or requiring background quadrature cells the accuracy and computational cost of the technique compared to standard gauss subcells quadrature are discussed copyright 2002 john wiley sons ltd

tail posterior probability for inference in pairwise and multiclass gene expression data we consider the problem of identifying differentially expressed genes in microarray data in a bayesian framework with a noninformative prior distribution on the parameter quantifying differential expression we introduce a new rule tail posterior probability based on the posterior distribution of the standardized difference to identify genes differentially expressed between two conditions and we derive a frequentist estimator of the false discovery rate associated with this rule we compare it to other bayesian rules in the considered settings we show how the tail posterior probability can be extended to testing a compound null hypothesis against a class of specific alternatives in multiclass data

a matrix triangularization algorithm for the polynomial point interpolation method a novel matrix triangularization algorithm mta is proposed to overcome the singularity problem in the point interpolation method pim using the polynomial basis and to ensure stable and reliable construction of pim shape functions the present algorithm is validated using several examples and implemented in the local point interpolation method lpim that is a truly meshfree method based on a local weak form numerical examples demonstrate that lpim using the present mta are very easy to implement and very robust for solving problems of computational mechanics it is shown that pim with the present mta is very effective in constructing shape functions most importantly pim shape functions possess kronecker delta function properties parameters that influence the performance of them are studied in detail the convergence and efficiency of them are thoroughly investigated

iterative solution of systems originating from integral equations and surface interpolation a simple procedure for generating diagonal dominance in certain linear systems is presented and the iterative solution of the transformed systems is discussed the method is presented for systems encountered in the numerical solution of fredholm equations of the first kind with singular kernels and for systems arising in the interpolation of surfaces by certain sets of radial functions in the second case the method provides new sets of basis functions generalizing in some sense the univariate b splines

moving particle finite element method with superconvergence nodal integration formulation and applications abstract a new approach of moving particle finite element method has been developed which is capable to gain a global superconvergence through solving particle kernel function to satisfy high order consistencies the nodal based moving particle finite element method inconjunction with the proposed superconvergence approach provides an optimized combination in numerical accuracy and computation efficiency the three dimensional engineering scale simulations demonstrate that this scheme is robust and capable to handle high speed penetration and dynamic crack propagation with intersonic and supersonic speeds

the effect of conditional dependence on the evaluation of diagnostic tests the accuracy of a new diagnostic test is often determined by comparison with a reference test which also has unknown error rates maximum likelihood estimation of the error rates of both tests is possible if they are simultaneously applied to two populations with different disease prevalences the estimation procedure assumes that the two tests are independent conditional on a subject s true diagnostic status if the tests are conditionally dependent error rates for both tests can be substantially underestimated estimators for the prevalence rates in the two populations can be positively or negatively biased depending on the relative magnitude of the two conditional covariances and the value of the prevalence parameter

using latent class models to characterize and assess relative error in discrete measurements whenever a definitive standard is not available to mark accuracy in a classification process discrete measurement error can be discussed only in relative terms if strong assumptions concerning the underlying discrete processes can be made latent class models allow one to characterize patterns of agreement disagreement among raters while simultaneously producing consensus estimates of prevalence a hypothetical definitive standard serves as the latent factor the discrete data are treated as incomplete and log linear models can be used to parameterize latent class models and extensions of latent class models data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence assess relative error and examine the validity of several traditional assumptions concerning diagnostic reliability latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics

application of radial basis functions to linear and nonlinear structural analysis problems the basic characteristic of the techniques generally known as meshless methods is the attempt to reduce or even to eliminate the need for a discretization at least not in the way normally associated with traditional finite element techniques in the context of numerical solutions for boundary and or initial value problems the interest in meshless methods is relatively new and this is why despite the existence of various applications of meshless techniques to several problems of mechanics as well as to other fields these techniques are still relatively unknown to engineers furthermore and compared to traditional finite elements it may be difficult to understand the physical meaning of the variables involved in the formulations as an attempt to clarify some aspects of the meshless techniques and simultaneously to highlight the ease of use and the ease of implementation of the algorithms applications are made in this work to structural analysis problems the technique used here consists of the definition of a global approximation for a given variable of interest in this case components of the displacement field by means of a superposition of a set of conveniently placed in the domain and on the boundary radial basis functions rbfs in this work various types of one dimensional problems are analyzed ranging from the static linear elastic case free vibration and linear stability analysis for a beam on elastic foundation to physically nonlinear damage models problems to further complement the range of problems analysed the static analysis of a plate on elastic foundation was also addressed several error measures are used to numerically establish the performance of both symmetric and nonsymmetric approaches for several global rbfs the results obtained show that rbf collocation leads to good approximations and very high convergence rates

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

a strictly conservative spatial approximation scheme for the governing engineering and physics equations over irregular regions and inhomogeneously scattered nodes abstract this paper reports the progress made in multiquadrics mq as a spatial approximation scheme for systems of governing equations of engineering and physics by minimizing the spatial truncation errors without excessive refinement although mq is defined over the general n dimensional real space this paper is limited to two spatial dimensions defined over a general non convex irregular region containing inhomogeneously scattered nodes we have developed a strictly conservative interpolation scheme over such irregular regions from which the partial derivative estimates are obtained in addition we developed a non iterative scheme to be used with domain decomposition to ensure derivative continuity over contiguous regions jump discontinuities for shock and material interfaces are likewise treated by appropriate modification of the algorithm we have compared the relative errors of the derivative estimates defined over an irregular region consisting of inhomogeneously scattered nodes obtained by the mq and voronoi mesh schemes the mq relative errors of the derivative estimates are three orders of magnitude better than those obtained from the voronoi mesh method in our previous papers we have shown that mq is superior in its derivative estimates over regular gridded regions we have also used mq to estimate derivatives within a very narrow shock region with similar excellent results while comparing spatial approximation schemes for pde s we found the mq results to be superior in accuracy and were calculated by far fewer operations than standard finite difference schemes other authors have likewise used mq successfully to solve integral equations

how independent are multiple independent diagnostic classifications multiple performances of diagnostic tests are commonly employed in clinical practice and epidemiologic research to assess test reliability to increase sensitivity or specificity or to correct for misclassification bias an assumption almost universally made in this context is the assumption of independence of test results conditional on the true value for dichotomous diagnostic tests for example disease present or absent this assumption is usually not tenable however since there is typically a continuum of the traits that underly diagnosis and individuals in the vicinity of the implicit or explicit diagnostic cutpoint such as the threshold of clinical detectibility are more likely to be misclassified than other individuals this paper assesses the magnitude of the resulting correlation of diagnostic errors as a function of the distribution of the underlying trait the magnitude of the measurement error and the diagnostic threshold it is concluded that errors of diagnostic tests can be strongly correlated even if errors in perception of the underlying trait are independent it is illustrated by numerical examples that such positive correlation of diagnostic errors can substantially inflate commonly employed indices of reliability such as the kappa coefficient

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

a fictitious domain method using equilibrated basis functions for harmonic and bi harmonic problems in physics abstract in this paper we present a new meshless method to solve well known problems in physics and engineering with either constant or variable material properties in 2d space harmonic and bi harmonic problems are considered in this paper the method constructs a set of basis functions called equilibrated basis functions eqbfs through a weighted residual integration over a fictitious domain embedding the main one the bases can satisfy the governing partial differential equations approximately chebyshev polynomials of the first kind are employed to construct the eqbfs and exponential functions are used as the weights in the integrals the parameters of the solution are arranged so that all the integrals can be decomposed into much simpler 1d ones over a normalized intervals this reduces the computational efforts significantly either the eqbfs or the results of the integration process may be stored for further use the validity of the results is examined through an extended patch test a set of physical sample problems with variable non variable material properties as the potential flow over a cylinder steady state heat conduction problems in an anisotropic inhomogeneous functionally graded material potential and stokes flow through a channel of finite width obstructed by periodic cylinders and the bending of thin elastic plates having constant or variable thickness are solved to demonstrate the capabilities of the method as a preliminary study we show that the method may effectively be used in a domain decomposition approach

modelling three dimensional piece wise homogeneous domains using the α shape based natural element method in this paper the application of the natural element method nem to the numerical analysis of two and three dimensional piece wise homogeneous domains is presented the nem differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries the shape based extension of this method nem generalizes this behaviour to non convex domains enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner in the following sections simple and effective algorithms are presented for the construction of shapes in domains composed of various materials examples are presented in two and three dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used copyright 2002 john wiley sons ltd

a mlpg lbie approach in combination with bem abstract the local boundary integral equation lbie approach is a promising meshless method recently proposed as an effective alternative to the boundary element method bem for solving non homogeneous anisotropic and non linear problems since the lbie method utilizes in its weak form fundamental solutions as test functions it can be considered as one of the six meshless local petrov galerkin mlpg methods proposed by atluri and coworkers this explains the use of the initials mlpg lbie in the title of the present paper this work addresses a coupling of a new mlpg lbie method recently proposed by the authors for elastodynamic problems and the bem because both methods conclude to a final system of linear equations expressed in terms of nodal displacement and tractions their combination is accomplished directly with no further transformations as it happens in other mlpg bem formulations as well as in typical hybrid finite element method bem schemes the coupling approach is demonstrated for static and frequency domain elastodynamic problems three representative examples are provided in order to illustrate the achieved accuracy of the proposed here mlpg lbie be methodology

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

boundary knot method for 2d and 3d helmholtz and convection diffusion problems under complicated geometry the boundary knot method bkm of very recent origin is an inherently meshless integration free boundary type radial basis function collocation technique for the numerical discretization of general partial differential equation systems unlike the method of fundamental solutions the use of non singular general solution in the bkm avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain the purpose of this paper is to extend the bkm to solve 2d helmholtz and convection diffusion problems under rather complicated irregular geometry the method is also first applied to 3d problems numerical experiments validate that the bkm can produce highly accurate solutions using a relatively small number of knots for inhomogeneous cases some inner knots are found necessary to guarantee accuracy and stability the stability and convergence of the bkm are numerically illustrated and the completeness issue is also discussed

coupling three field formulation and meshless mixed galerkin methods using radial basis functions in this work we solve the elliptic partial differential equation by coupling the meshless mixed galerkin approximation using radial basis function with the three field domain decomposition method the formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper

conditional inference for predictive agreement we introduce the concept and a measure of predictive agreement tau for two raters classifying items into q categories the measure is based on the linear combination of log odds ratios from 2 x 2 subtables of a q x q cross classification table we show that analysis procedures for this measure and transforms of it can be based on conditional likelihood procedures these procedures are exact which is particularly helpful because of the small tabular cell frequencies which can typically arise with agreement data to illustrate the advantages of the methodology examples of typical agreement data arising from medical studies are considered we demonstrate that the conditional likelihood function portrays the available sample information about tau often more appropriately than the maximum likelihood estimate and an associated standard error we highlight the value of combining information via likelihoods in an example involving 24 2 x 2 tables an example involving three categories is used to illustrate that the methodology for the overall agreement measure can be adapted to examine relative agreement between pairs of categories

a meshless integral method based on regularized boundary integral equation a meshless integral method based on the regularized boundary integral equation is developed and applied to two dimensional linear elasticity the governing integral equation is obtained from the weak form of elasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the method is built on the lbie method proposed by atluri and co workers and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method the most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation the technique is straightforward and efficient and is much simpler and easier compared to other singularity removal techniques a special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy the collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient the natural boundary conditions are incorporated in the system governing equation and require no special handling numerical tests show that the meshless integral method is accurate and robust the effects of weight function support domain sub domain and monomial basis are investigated and discussed

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

least squares collocation meshless method a finite point method least squares collocation meshless method is proposed except for the collocation points which are used to construct the trial functions a number of auxiliary points are also adopted unlike the direct collocation method the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least squares sense the moving least squares interpolant is used to construct the trial functions the computational effort required for the present method is in the same order as that required for the direct collocation while the present method improves the accuracy of solution significantly the proposed method does not require any mesh so that it is a truly meshless method three numerical examples are studied in detail which show that the proposed method possesses high accuracy with low computational effort copyright 2001 john wiley sons ltd

enriching the finite element method with meshfree particles in structural mechanics summary the automatic generation of meshes for the finite element fe method can be an expensive computational burden especially in structural problems with localized stress peaks the use of meshless methods can address such an issue as these techniques do not require the existence of an underlying connection among the particles selected in a general domain this study advances a numerical strategy that blends the fe method with the meshless local petrov galerkin mlpg technique in structural mechanics with the aim at exploiting the most attractive features of each procedure the idea relies on the use of fes to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid adding the meshless particles only where needed avoids the cost of mesh refining or even of re meshing without the prohibitive computational cost of a thoroughly meshfree approach in the present implementation an efficient integration strategy for the computation of the coefficients taking into account the mutual fe mlpg interactions is introduced moreover essential boundary conditions are enforced separately on both fes and meshless particles thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level with no re meshing effort and at a low computational cost this article is protected by copyright all rights reserved

applications of point interpolation method for spatial general shells structures the meshfree point interpolation method pim based on polynomial function is presented for the static analysis of spatial general shell structures the formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible shells based on the cosserat surface the pim technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property hence the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method an improved matrix triangularization algorithm mta is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis it is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non conforming pim npim when the energy principles are used to formulate pim to obtain compatible shape functions the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell based nodal selection is utilized which lead to conforming pim cpim both npim and cpim are evaluated in the paper several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the npim and cpim the phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy the convergences and performances are investigated for both conforming and non conforming pims it is also shown that the npim and cpim with the improved mta are very easy to implement and very efficient in constructing shape functions in comparison with the element free galerkin method

correcting for misclassification for a monotone disease process with an application in dental research motivated by a longitudinal oral health study we evaluate the performance of binary markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence incidences and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature we propose an extension of the simple version of the binary markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers we implemented a bayesian version of the extended model and show that under the settings of our motivating example the parameters can be estimated without any external information finally the analyses of the motivating problem are presented

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

meshless local petrov galerkin method for two dimensional nonlinear water wave problems in this paper the meshless local petrov galerkin mlpg method is extended to dealing with nonlinear water wave problems the formulation is based on general fluid governing equations and a time marching procedure at each time step the boundary value problem for the pressure is solved using the mlpg method and the velocity and position of nodes are updated by numerical integration the newly extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

a note on the sparse representation of discrete integral operators we show how to give sparse matrix representations for a number of integral operators in one and two dimensions typically this results when using a galerkin or a discrete galerkin method related collocation methods using the same basis do not yield sparse representations this suggests that the traditional preference of collocation over galerkin methods be re examined in light of exploiting sparseness in a number of known algorithms

quadrature for meshless methods in this paper we discuss quadrature for meshless methods we present results of two analyses the first of these was developed in 1 and the second was developed in 2 using a simple example we show that a natural quadrature scheme that satisfies no special properties leads to severe inaccuracies in the approximate solution we then show in the first analysis that a simple correction to the stiffness matrix controls the effect of the quadrature in the second analysis we show that if the quadrature scheme satisfies green s formula then the effect of the quadrature is controlled

on the smoothness of positive definite and radial functions we consider positive definite and radial functions after giving general results concerning the smoothness of general positive definite and radial functions we investigate the class of compactly supported positive definite and radial functions where every function consists of a univariate polynomial within its support especially we show that these functions necessarily possess an even number of continuous derivatives finally we provide a general construction technique which we use to construct a new family of compactly supported basis functions of arbitrary smoothness

a meshless multilayer model for a coastal system by radial basis functions abstract a multilayer computational model for simulating three dimensional tidal flows in coastal waters is presented in this paper a truly meshless numerical scheme based on radial basis functions rbfs is employed to obtain an accurate approximation to the solution of the model for computational efficiency in solving large scale problems a noniterative domain decomposition method is combined with the use of the rbfs scheme to smooth the numerical simulation of the advection across each subdomain the commonly used upstream technique is also incorporated finally for numerical verification the proposed multilayer model is successfully used to obtain a stable and convergent simulation of the water flows in the pearl river estuary of the south china sea the numerical approximations exhibit good agreement with the observed tidal and current data

using association models to analyse agreement data two examples two examples demonstrate how one can use association models to analyse agreement data the first example concerns intra rater variability in the classification of sputum cytology slides and the second deals with variability associated with the reporting of passive smoking histories the paper emphasizes models in which one estimates category scores from the data that is models that are not in the log linear family of models such models have use in assessment of category distinguishability and provide insights not easily obtained with log linear models

improved accuracy of multiquadric interpolation using variable shape parameters given n scattered data points we examined the problem of finding n variable multiquadric mq shape parameters or r2 values because the problem of finding the optimal r2 values is a nonlinear one we optimized these parameters numerically by minimizing the root mean square rms errors the resulting r2 values varied over many orders of magnitude we have tested this approach on a number of univariate and bivariate franke s problems and found that the rms error reduction was substantial

local radial point interpolation mlrpi method for solving time fractional diffusion wave equation with damping the purpose of the current investigation is to determine numerical solution of time fractional diffusion wave equation with damping for caputo s fractional derivative of order 1 2 a meshless local radial point interpolation mlrpi scheme based on galerkin weak form is analyzed the reason of choosing mlrpi approach is that it does not require any background integrations cells instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape the unconditional stability and convergence with order o 6 2 are proved where is time stepping also several numerical experiments are illustrated to verify theoretical analysis

log linear modelling of pairwise interobserver agreement on a categorical scale this article uses log linear models to describe pairwise agreement among several raters who classify a sample on a subjective categorical scale the models describe agreement structure simultaneously for second order marginal tables of a multidimensional cross classification of ratings practical difficulties arise in fitting the models because models refer to pairwise marginal tables of a very large and sparse table a standard analysis that treats the marginal tables as independent yields consistent estimates of model parameters but not of the covariance matrix of the estimates we estimate the covariance matrix using the jackknife we apply the models to describe agreement between evaluations made by seven pathologists of carcinoma in situ of the uterine cervix using a five level ordinal scale previous analyses showed differences among the pathologists in their pairwise levels of agreement but we observe near homogeneity in the dependence structure of their ratings

element free method for static and free vibration analysis of spatial thin shell structures the implementation of the element free galerkin method efg for spatial thin shell structures is presented in this paper both static deformation and free vibration analyses are considered the formulation of the discrete system equations starts from the governing equations of stress resultant geometrically exact theory of shear flexible shells moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry discrete system equations are obtained by incorporating these interpolations into the galerkin weak form the formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial thin shell structures for static load analysis essential boundary conditions are enforced through penalty method and lagrange multipliers while boundary conditions for frequency analysis are imposed through a weak form using orthogonal transformation techniques the efg results compare favorably with closed form solutions and that of finite element analyses

bayesian robust inference for differential gene expression in microarrays with multiple samples summary we consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays because of the many steps involved in the experimental process from hybridization to image analysis cdna microarray data often contain outliers for example an outlying data value could occur because of scratches or dust on the surface imperfections in the glass or imperfections in the array production we develop a robust bayesian hierarchical model for testing for differential expression errors are modeled explicitly using a t distribution which accounts for outliers the model includes an exchangeable prior for the variances which allows different variances for the genes but still shrinks extreme empirical variances our model can be used for testing for differentially expressed genes among multiple samples and it can distinguish between the different possible patterns of differential expression when there are three or more samples parameter estimation is carried out using a novel version of markov chain monte carlo that is appropriate when the model puts mass on subspaces of the full parameter space the method is illustrated using two publicly available gene expression data sets we compare our method to six other baseline and commonly used techniques namely the t test the bonferroni adjusted t test significance analysis of microarrays sam efron s empirical bayes and ebarrays in both its lognormal normal and gamma gamma forms in an experiment with hiv data our method performed better than these alternatives on the basis of between replicate agreement and disagreement

a meshfree hermite type radial point interpolation method for kirchhoff plate problems a meshfree computational method is proposed in this paper to solve kirchhoff plate problems of various geometries the deflection of the thin plate is approximated by using a hermite type radial basis function approximation technique the standard galerkin method is adopted to discretize the governing partial differential equations which were derived from using the kirchhoff s plate theory the degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency accuracy and robustness of the method copyright 2005 john wiley sons ltd

implicit boundary method for analysis using uniform b spline basis and structured grid several analysis techniques such as extended finite element method x fem have been developed recently which use structured grid for the analysis implicit boundary method uses implicit equations of the boundary to apply boundary conditions in x fem framework using structured grids solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary in this paper this method is applied for analysis using uniform b spline basis defined over a structured grid solution structures that are c1 or c2 continuous throughout the analysis domain can be constructed using b spline basis functions as a structured grid does not conform to the geometry of the analysis domain the boundaries of the analysis domain are defined independently using equations of the boundary curves surfaces compared with conforming mesh it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted numerical examples are presented to demonstrate the performance of these b spline elements the results are compared with analytical solutions as well as with traditional finite element solutions convergence studies for several examples show that b spline elements provide accurate solutions with fewer elements and nodes compared with traditional fem they also provide continuous stress and strain in the analysis domain thus eliminating the need for smoothing stress strain results copyright 2008 john wiley sons ltd

solving partial differential equations by collocation using radial basis functions after a series of application papers have proven the approach to be numerically effective this paper gives the first theoretical foundation for methods solving partial differential equations by collocation with possibly radial basis functions

free mesh radial basis function collocation approach for the numerical solution of system of multi ion electrolytes the main objective of this work is to show the versatility of an innovative mesh free numerical scheme which allows the solution of the coupled transport equations governing the evolution of a system of multi ion electrolytes by mean of the use of radial basis functions interpolation and a nesting approach the nesting approach is used in order to capture the detail behaviour of the solution near a solid wall i e at the diffusion reaction layer as a numerical example the problem of silver deposition on a rotating disk is analysed the versatility of the proposed numerical scheme is proved by solving the proposed electrochemical phenomena imposing three different kinds of boundary conditions at the solid wall dirichlet neumann and robin the obtained numerical results are compared with simplified analytical approximation of the corresponding problems the effect of the ligand concentration on the others species is considered and a comparison between the obtained concentration profiles for the complex ags2o and ag s2o3 when the concentration of the ligand s2o takes different values is shown copyright 2005 john wiley sons ltd

equilibrium on line method elm for imposition of neumann boundary conditions in the finite point method fpm equilibrium on line method elm for imposition of neumann boundary conditions in the finite point method fpm is presented in contrary to weak form based methods strong form based methods such as the fpm are often unstable and less accurate especially for problems governed by partial differential equations with neumann derivative boundary conditions in this paper a truly meshless approach for imposition of neumann boundary conditions in the fpm is proposed and adopted for 2d elasticity analyses in the proposed method equilibrium on lines on the neumann boundary conditions is satisfied as neumann boundary condition equations numerical studies show that this method for imposition of neumann boundary is simple to implement and computationally efficient and also leads to more stable and accurate results copyright 2006 john wiley sons ltd

meshfree numerical approach based on the finite pointset method for static linear elasticity problems abstract in this work a promising meshfree numerical approach is extended and implemented for the first time in the field of linear static elasticity a real meshfree method the so called finite pointset method fpm is applied and implemented in order to solve the strong classical form of the governing partial differential equations pdes the well known navier cauchy equations fpm numerical performance is demonstrated for several classical and well known studied benchmark problems and comparison with other approaches is also reported numerical results suggest that fpm method is stable with good convergence behavior for 2d linear static elasticity problems

meshless analysis of timoshenko beams based on a locking free formulation and variational approaches abstract a meshless method is developed based on subdomain variational formulations and a local petrov galerkin approximation along with the locking free formulation for the analysis of bending of a thick beam the local point interpolation method is employed to construct both trial and test functions the present method is a truly meshless method based only on a number of randomly located nodes no global background integration mesh is needed no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated problems of thick and thin beams under various loading and boundary conditions are analysed by the proposed method and the numerical results are compared with analytical solutions the contact problem for beam by means of subdomain variational inequalities and the meshless method has also been investigated

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

comparison of variance estimation approaches in a two state markov model for longitudinal data with misclassification we examine the behaviour of the variance covariance parameter estimates in an alternating binary markov model with misclassification transition probabilities specify the state transitions for a process that is not directly observable the state of an observable process which may not correctly classify the state of the unobservable process is obtained at discrete time points misclassification probabilities capture the two types of classification errors variance components of the estimated transition parameters are calculated with three estimation procedures observed information jackknife and bootstrap techniques simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation the three approaches generally provide similar variance estimates for large samples and moderate misclassification in these situations the resampling methods are reasonable alternatives when programming partial derivatives is not appealing with smaller chains or higher misclassification probabilities the bootstrap method appears to be the best choice