dose response signal detection under model uncertainty we investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty when several competing regression models are available to describe the dose response relationship the proposed approach uses the complete structure of the regression models but does not require knowledge of the parameters of the competing models standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters however for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values we thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on gaussian processes the new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations

a finite element method for the simulation of strong and weak discontinuities in solid mechanics in this paper we introduce and analyze a finite element method for elasticity problems with interfaces the method allows for discontinuities internal to the elements in the approximation across the interface we propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code for the case of linear elasticity we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh we present numerical examples for the linear case as well as for contact and crack propagation model problems

an explicit dynamics extended finite element method part 2 element by element stable explicit explicit dynamic scheme abstract this paper presents a general explicit time integration scheme for dynamics simulations using the extended finite element method with standard critical time step we use the generalized mass lumping technique proposed in part i of this paper this technique allows us to consider arbitrary enrichment functions in the x fem for explicit dynamics simulations in this second part the proposed approach allows the use of standard finite elements critical time step estimates for that purpose we develop a classical element by element strategy that couples the standard central difference scheme with the unconditionally stable explicit scheme proposed by chang s y chang an explicit method with improved stability property int j numer methods engrg 77 8 2008 1100 1120 this scheme coupled with x fem allows us to recover fe critical time steps independently of the enrichment functions considered furthermore a study of the stability property of this new explicit scheme is proposed in the x fem framework both with fixed enrichments and evolving enrichments with time some examples illustrate the good properties of the new explicit numerical time scheme and some applications to dynamics crack growth are given

a rigorous and unified mass lumping scheme for higher order elements abstract in dynamic analysis with explicit time integration schemes a lumped mass matrix lmm is preferable because lmm can avoid solving the large scale simultaneous algebraic equations mathematically rigorous mass lumping schemes such as the mass lumping by nodal quadrature and the row sum technique are applicable to only linear or bilinear elements for higher order elements such as 8 node serendipity elements the diagonal scaling procedure is the only lumping method that can be recommended to generate positive definite diagonal element mass matrices unfortunately there is no mathematical theory in support of this approach this study proposes a general mass lumping scheme applicable to higher order elements where the virtual work of initial force is integrated over the problem domain that is viewed as the manifold covered by the finite element patches by a series of numerical experiments both free and forced vibration problems it is suggested that even in the implicit time integration scheme the consistent mass matrix cmm can be superseded by the proposed lmm furthermore the proposed lmm has much stronger adaptability to distorted meshes

cracking node method for dynamic fracture with finite elements a new method for modeling discrete cracks based on the extended finite element method is described in the method the growth of the actual crack is tracked and approximated with contiguous discrete crack segments that lie on finite element nodes and span only two adjacent elements the method can deal with complicated fracture patterns because it needs no explicit representation of the topology of the actual crack path a set of effective rules for injection of crack segments is presented so that fracture behavior beginning from arbitrary crack nucleations to macroscopic crack propagation is seamlessly modeled the effectiveness of the method is demonstrated with several dynamic fracture problems that involve complicated crack patterns such as fragmentation and crack branching copyright 2008 john wiley sons ltd

admissibility of the lidelihood ratio test when the parameter space is restricted under the alternative this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example the likelihood ratio lr test is shown to be admissible and to maximize power against alternatives that are arbitrarily distant from the null hypothesis exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

combining multiple comparisons and modeling techniques in dose response studies the analysis of data from dose response studies has long been divided according to two major strategies multiple comparison procedures and model based approaches model based approaches assume a functional relationship between the response and the dose taken as a quantitative factor according to a prespecified parametric model the fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose response model multiple comparison procedures regard the dose as a qualitative factor and make very few if any assumptions about the underlying dose response model the primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect one approach is to evaluate the significance of contrasts between different dose levels while preserving the family wise error rate such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation we describe a unified strategy to the analysis of data from dose response studies which combines multiple comparison and modeling techniques we assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose response curve while preserving the family wise error rate the selected model is then used to provide inference on adequate doses

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

stable imposition of stiff constraints in explicit dynamics for embedded finite element methods summary we investigate various strategies to enforce the kinematics at an embedded interface for transient problems within the extended finite element method in particular we focus on explicit time integration of the semi discrete equations of motion and extend both dual and primal variational frameworks for constraint enforcement to a transient regime we reiterate the incompatibility of the dual formulation with purely explicit time integration and the severe restrictions placed by the courant friedrichs levy condition on primal formulations we propose an alternate consistent formulation for the primal method and derive an estimate for the stabilization parameter which is more amenable in an explicit dynamics framework importantly the use of the new estimate circumvents the need for any tolerances as an interface approaches an element boundary we also show that with interfacial constraints existing mass lumping schemes can lead to prohibitively small critical time steps accordingly we propose a mass lumping procedure which provides a more favorable estimate these techniques are then demonstrated on several benchmark numerical examples where we compare and contrast the accuracy of the primal methods against the dual methods in enforcing the constraints copyright 2012 john wiley sons ltd

hotelling s theorem on the volume of tubes some illustrations in simultaneous inference and data analysis we illustrate with contemporary examples hotelling s geometric approach to simultaneous probability calculations hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere and shows that this volume is often exactly given by length times cross sectional area we review hotelling s result together with some recent complements and then use the approach to set simultaneous prediction regions for some data from gait analysis to study andrews plots in multivariate data analysis and to construct significance tests for projection pursuit regression a by product is a numerical criterion for tube self overlap relevant for example to uniqueness of certain nonlinear least squares estimates

admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative this paper establishes the asymptotic admissibility of the likelihood ratio lr test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis the paper also establishes the finite sample admissibility of the lr test for testing problems of this sort that arise in gaussian linear regression models with known variance

on generation of lumped mass matrices in partition of unity based methods summary the partition of unity based methods such as the extended finite element method and the numerical manifold method are able to construct global functions that accurately reflect local behaviors through introducing locally defined basis functions beyond polynomials in the dynamic analysis of cracked bodies using an explicit time integration algorithm as a result huge difficulties arise in deriving lumped mass matrices because of the presence of those physically meaningless degrees of freedom associated with those locally defined functions observing no spatial derivatives of trial or test functions exist in the virtual work of inertia force we approximate the virtual work of inertia force in a coarser manner than the virtual work of stresses where we inversely utilize the from local to global skill the proposed lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix but has more excellent dynamic property than the latter meanwhile the critical time step of the numerical manifold method equipped with an explicit time integration scheme and the proposed mass lumping scheme does not decrease even if the crack in study approaches the mesh nodes a very excellent dynamic property copyright 2017 john wiley sons ltd

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

asymptotics for likelihood ratio tests under loss of identifiability this paper describes the large sample properties of the likelihood ratio test statistic lrts when the parameters characterizing the true null distribution are not unique it is well known that the classical asymptotic theory for the likelihood ratio test does not apply to such problems and the lrts may not have the typical chi squared type limiting distribution this paper establishes a general quadratic approximation of the log likelihood ratio function in a hellinger neighborhood of the true density which is valid with or without loss of identifiability of the true distribution under suitable conditions the asymptotic null distribution of the lrts under loss of identifiability can be obtained by maximizing the quadratic form these results extend the work of chernoff and le cam in particular applications to testing the number of mixture components in finite mixture models are discussed

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

a comment on the article a finite element method for simulation of strong and weak discontinuities in solid mechanics by a hansbo and p hansbo comput methods appl mech engrg 193 2004 3523 3540

stability of multi time step partitioned integrators for first order finite element systems abstract mixed time integration procedures are those in which different time steps and different integrators are used in different parts of the mesh a rigorous stability analysis is provided for the first time for this type of time integration for first order semidiscretizations such as arise in diffusion problems the stability analysis is verified by some numerical examples

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

x fem explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries this paper deals with the use of the extended finite element method x fem for rapid dynamic problems to solve the equations of motion a common technique is the explicit direct integration with a newmark scheme since this temporal scheme is only conditionally stable the critical time step must be determined it is generally induced by mesh constraints the idea of the paper is to weaken constraints on mesh generation algorithms so that the critical time step is as large as possible using the x fem one allows a non conformity between mesh and discontinuities such as cracks holes or interfaces in a first part we present a summary about direct integration schemes and about the extended finite element method then we focus on the theoretical description of a 1d x fem finite element and its generalization to 2d and 3d finite elements then dynamic numerical simulations are shown they concern structures under impact with holes or external boundaries not exactly matched by the mesh comparisons are made with numerical results coming from the abaqus software it shows that developments are satisfactory we conclude with some outlooks concerning this work

generalized multiple contrast tests in dose response studies in the process of developing drugs proof of concept studies can be helpful in determining whether there is any evidence of a dose response relationship a global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques mcp mod which involves the specification of a candidate set of several plausible dose response models for each model a test is performed for significance of an optimally chosen contrast among the sample means an overall p value is obtained from the distribution of the maximum of the contrast statistics this is equivalent to basing the test on the minimum of the p values arising from these contrast statistics and hence can be viewed as a method for combining dependent p values we generalize this idea to the use of different statistics for combining the dependent p values such as fisher s combination method or the inverse normal combination method simulation studies show that the generalized multiple contrast tests gmcts based on the fisher and inverse normal methods are generally more powerful than the mcp mod procedure based on the minimum of the p values except for cases where the true dose response model is in a sense near the extremes of the candidate set of dose response models the proposed gmcts can also be used for model selection and dosage selection by employing a closed testing procedure

pattern recognition based on scale invariant discriminant functions some probability models for classifying individuals as belonging to one of two or more populations using scale invariant discriminant functions are considered the investigation is motivated by practical situations where the observed data on an individual are in the form of ratios of some basic measurements or measurements scaled by an unknown nonnegative number the probability models are obtained by considering a p vector random variable x with a known distribution and deriving the distribution of the random vector y g x 1 x where g x is a nonnegative measure of size such that g x g x for 0 explicit expressions are obtained for the densities of what are called angular gaussian compositional gaussian type 1 and compositional gaussian type 2 distributions

likelihood ratio tests for a dose response effect using multiple nonlinear regression models we consider the problem of testing for a dose related effect based on a candidate set of typically nonlinear dose response models using likelihood ratio tests for the considered models this reduces to assessing whether the slope parameter in these nonlinear regression models is zero or not a technical problem is that the null distribution when the slope is zero depends on non identifiable parameters so that standard asymptotic results on the distribution of the likelihood ratio test no longer apply asymptotic solutions for this problem have been extensively discussed in the literature the resulting approximations however are not of simple form and require simulation to calculate the asymptotic distribution in addition their appropriateness might be doubtful for the case of a small sample size direct simulation to approximate the null distribution is numerically unstable due to the non identifiability of some parameters in this article we derive a numerical algorithm to approximate the exact distribution of the likelihood ratio test under multiple models for normally distributed data the algorithm uses methods from differential geometry and can be used to evaluate the distribution under the null hypothesis but also allows for power and sample size calculations we compare the proposed testing approach to the mcp mod methodology and alternative methods for testing for a dose related trend in a dose finding example data set and simulations

an explicit dynamics extended finite element method part 1 mass lumping for arbitrary enrichment functions this paper presents a general mass lumping technique for explicit dynamics simulations using the extended finite element method with arbitrary enrichment functions the proposed mass lumping technique is a generalization of previously published results for cracks and holes time step estimates are studied for crack singular enrichment functions and for hole enrichment in both cases we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element the performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published x fem results

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

element local level set method for three dimensional dynamic crack growth summary an approximate level set method for three dimensional crack propagation is presented in this method the discontinuity surface in each cracked element is defined by element local level sets ellss the local level sets are generated by a fitting procedure that meets the fracture directionality and its continuity with the adjacent element crack surfaces in a least square sense a simple iterative procedure is introduced to improve the consistency of the generated element crack surface with those of the adjacent cracked elements the discrete discontinuity is treated by the phantom node method which is a simplified version of the extended finite element method xfem the ells method and the phantom node technology are combined for the solution of dynamic fracture problems numerical examples for three dimensional dynamic crack propagation are provided to demonstrate the effectiveness and robustness of the proposed method copyright q 2009 john wiley sons ltd

domain decomposition preconditioners for p and hp finite element approximation of stokes equations abstract domain decomposition preconditioning techniques are developed in the context of hp finite element approximation of the stokes problem two basic types of preconditioner are considered a block diagonal scheme based on decoupling the velocity and pressure components and a scheme based on an indefinite system similar to the original stokes system for each type of scheme theoretical estimates are obtained for the location of the eigenvalues of the preconditioned operators in terms of the polynomial degree the mesh sizes on the coarse and fine grids and the inf sup constant for the method theoretical estimates show that the growth of the bounds is modest as the mesh is refined and the polynomial order is increased the preconditioners are shown to be applicable to various iterative schemes for the stokes systems the theoretical bounds are compared with actual quantities obtained in practical computations for several representative problems

mass lumping strategies for x fem explicit dynamics application to crack propagation this paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method more precisely we are interested in explicit algorithms we prove that by using a specific lumping technique the critical time step is exactly the same as if no crack were present this somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack the new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids to be precise the results obtained are valid only when the crack is modelled by the heaviside enrichment note also that the resulting lumped matrix is block diagonal blocks of size 2 2 for constant strain elements linear simplex elements the critical time step is not modified when the element is cut thanks to the lumped mass matrix the critical time step never tends to zero moreover the lumping techniques conserve kinetic energy for rigid motions in addition tensile stress waves do not propagate through the discontinuity hence the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack both these techniques will be used in a numerical experiment copyright 2007 john wiley sons ltd

testing effect of a drug using multiple nested models for the dose response summary during development of a drug typically the choice of dose is based on a phase ii dose finding trial where selected doses are included with placebo two common statistical dose finding methods to analyze such trials are separate comparisons of each dose to placebo using a multiple comparison procedure or a model based strategy where a dose response model is fitted to all data the first approach works best when patients are concentrated on few doses but cannot conclude on doses not tested model based methods allow for interpolation between doses but the validity depends on the correctness of the assumed dose response model bretz et al 2005 biometrics 61 738 748 suggested a combined approach which selects one or more suitable models from a set of candidate models using a multiple comparison procedure the method initially requires a priori estimates of any non linear parameters of the candidate models such that there is still a degree of model misspecification possible and one can only evaluate one or a few special cases of a general model we propose an alternative multiple testing procedure which evaluates a candidate set of plausible dose response models against each other to select one final model the method does not require any a priori parameter estimates and controls the type i error rate of selecting a too complex model

a fully smoothed xfem for analysis of axisymmetric problems with weak discontinuities in this paper we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities the salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique this is accomplished by combining the gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique which is used to transform the domain integral into boundary integral the proposed technique completely eliminates the need for isoparametric mapping and the computing of jacobian matrix even for the mass matrix when employed over the enriched elements the proposed technique does not require sub triangulation for the purpose of numerical integration the accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities it can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion

a nonoverlapping domain decomposition method for stabilized finite element approximations of the oseen equations abstract a nonoverlapping domain decomposition algorithm of robin robin type is applied to the discretized oseen equations using stabilized finite element approximations of velocity and pressure thus allowing in particular equal order interpolation as a crucial result we have to inspect the proof of a modified inf sup condition in particular the dependence of the stability constant with respect to the reynolds number cf appendix after proving coercivity and strong convergence of the method we derive an a posteriori estimate which controls convergence of the discrete subdomain solutions to the global discrete solution provided that jumps of the discrete solution converge at the interface furthermore we obtain information on the design of some free parameters within the robin type interface condition which essentially influence the convergence speed some numerical results confirm the theoretical ones

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

understanding mcp mod dose finding as a method based on linear regression mcp mod is a testing and model selection approach for clinical dose finding studies during testing contrasts of dose group means are derived from candidate dose response models a multiple comparison procedure is applied that controls the alpha level for the family of null hypotheses associated with the contrasts provided at least one contrast is significant a corresponding set of good candidate models is identified the model generating the most significant contrast is typically selected there have been numerous publications on the method it was endorsed by the european medicines agency the mcp mod procedure can be alternatively represented as a method based on simple linear regression where simple refers to the inclusion of an intercept and a single predictor variable which is a transformation of dose it is shown that the contrasts are equal to least squares linear regression slope estimates after a rescaling of the predictor variables the test for each contrast is the usual t statistic for a null slope parameter except that a variance estimate with fewer degrees of freedom is used in the standard error selecting the model corresponding to the most significant contrast p value is equivalent to selecting the predictor variable yielding the smallest residual sum of squares this criteria orders the models like a common goodness of fit test but it does not assure a good fit common inferential methods applied to the selected model are subject to distortions that are often present following data based model selection