full analytical sensitivities in nurbs based isogeometric shape optimization abstract non uniform rational b spline nurbs has been widely used as an effective shape parameterization technique for structural optimization due to its compact and powerful shape representation capability and its popularity among cad systems the advent of nurbs based isogeometric analysis has made it even more advantageous to use nurbs in shape optimization since it can potentially avoid the inaccuracy and labor tediousness in geometric model conversion from the design model to the analysis model although both positions and weights of nurbs control points affect the shape until very recently usually only control point positions are used as design variables in shape optimization thus restricting the design space and limiting the shape representation flexibility this paper presents an approach for analytically computing the full sensitivities of both the positions and weights of nurbs control points in structural shape optimization such analytical formulation allows accurate calculation of sensitivity and has been successfully used in gradient based shape optimization the analytical sensitivity for both positions and weights of nurbs control points is especially beneficial for recovering optimal shapes that are conical e g ellipses and circles in 2d cylinders ellipsoids and spheres in 3d that are otherwise not possible without the weights as design variables

isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

isogeometric shape design sensitivity analysis using transformed basis functions for kronecker delta property abstract the isogeometric shape design sensitivity analysis dsa includes the desirable features easy design parameterization and accurate shape sensitivity embedding the higher order geometric information of curvature and normal vector due to the non interpolatory property of nurbs basis however the imposition of essential boundary condition is not so straightforward in the isogeometric method taking advantages of geometrically exact property an isogeometric dsa method is developed applying a mixed transformation to handle the boundary condition a set of control point and nurbs basis function is added using the h refinement and newton iterations to precisely locate the control point to impose the boundary condition in spite of additional transformation its computation cost is comparable to the original one with penalty approach since the obtained kronecker delta property enables to reduce the size of system matrix through demonstrative numerical examples the effectiveness accuracy and computing cost of the developed dsa method are discussed

test of marginal compatibility and smoothing methods for exchangeable binary data with unequal cluster sizes exchangeable binary data are often collected in developmental toxicity and other studies and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature while these distributions can be matched to have the same marginal probability and intra cluster correlation they can be quite different in terms of shape and higher order quantities of interest such as the litter level risk of having at least one malformed fetus a sensible alternative is to fit a saturated model bowman and george 1995 journal of the american statistical association 90 871 879 using the expectation maximization em algorithm proposed by stefanescu and turnbull 2003 biometrics 59 18 24 the assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data stefanescu and turnbull proposed a modified trend test to test this assumption their test however fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p values this drawback is rectified in this article when the data are sparse the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed we extend the penalized likelihood method simonoff 1983 annals of statistics 11 208 218 to the present case of unequal cluster sizes and implement the method using an em type algorithm in the presence of covariate we propose a penalized kernel method that performs smoothing in both the covariate and response space the proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations

a random effects model for binary data summary this paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects with the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects the marginal likelihood can be computed without numerical integrations the method uses local independence models as well as those that incorporate additional dependence among the responses two examples a panel study with binary responses and an analysis of item response data will be used to illustrate the method

remark on closedness of perturbation set and regularity of associated extremal solution abstract we investigate here the effect of dimension on closedness of k the set of perturbation term for some semi linear elliptic equation u f u g x posed on a bounded smooth domain in r n with dirichlet boundary condition some closedness of k and continuous of the map g u g are established moreover we show a counter example for power case f u e u when n 9

finite mixture models for proportions summary six data sets recording fetal control mortality in mouse litters are presented the data are clearly overdispersed and a standard approach would be to describe the data by means of a beta binomial model or to use quasi likelihood methods for five of the examples we show that the beta binomial model provides a reasonable description but that the fit can be significantly improved by using a mixture of a beta binomial model with a binomial distribution this mixture provides two alternative solutions in one of which the binomial component indicates a high probability of death but is selected infrequently this accounts for outlying litters with high mortality the influence of the outliers on the beta binomial fits is also demonstrated the location and nature of the two main maxima to the likelihood are investigated through profile log likelihoods comparisons are made with the performance of finite mixtures of binomial distributions data describing fetal deaths in litters are frequently overdispersed relative to the binomial distribution due to differential litter effects in some cases sample sizes may be too small for a significant effect of overdispersion to be detected in others however data sets are certainly large enough and six illustrations of such data sets are given in tables 1 6 the data of tables 3 6 have been published before while those of tables 1 and 2 have been formed by pooling smaller sets of data that have previously been analyzed by james and smith 1982 we shall refer to the data sets in order as el e2 hs1 hs2 hs3 avss different data sets highlight different aspects of the work of this paper statisticians analyzing such data might adopt a parametric approach for example by fitting a beta binomial or a correlated binomial distribution the more robust approach provided by quasilikelihood is an alternative see liang and hanfelt 1994 the various options are described in morgan 1992 chapter 6 and model details are given in section 2 also shiown in tables 1 6 are the expected values from fitting the beta binomial distribution the fits appear to be reasonably good except for the small numbers of litters with high mortality because of small cell frequencies we use simulation to test goodness of fit taking the el data set as an example we can simulate from the fitted beta binomial model a data set that matches el with regard to numbers of litters of the various different sizes observed and that uses as parameter values the maximum likelihood estimates resulting from fitting the model to the real data the model can then be fitted to the simulated data and the maximum log likelihood recorded this process may then be repeated many times to provide a goodness of fit reference for the maximum

on maximal eigenfrequency separation in two material structures the 1d and 2d scalar cases abstract we present a method to maximize the separation of two adjacent eigenfrequencies in structures with two material components the method is based on finite element analysis and topology optimization in which an iterative algorithm is used to find the optimal distribution of the materials results are presented for eigenvalue problems based on the 1d and 2d scalar wave equations two different objectives are used in the optimization the difference between two adjacent eigenfrequencies and the ratio between the squared eigenfrequencies in the 1d case we use simple interpolation of material parameters but in the 2d case the use of a more involved interpolation is needed and results obtained with a new interpolation function are shown in the 2d case the objective is reformulated into a double bound formulation due to the complication from multiple eigenfrequencies it is shown that some general conclusions can be drawn that relate the material parameters to the obtainable objective values and the optimized designs

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies abstract a new optimization strategy for eigenfrequency optimization of functionally graded fg structures within the framework of isogeometric analysis iga approach is introduced the proposed methodology which utilizes a concurrent procedure by combining the shape and material composition optimization of these structures employs an extended form of the standard iga method by allowing for gradation of material properties through patches the distributions of the graded material properties are considered as imaginary surfaces over the computational domain and captured in a fully isogeometric formulation using the same nurbs based parameterization which is employed for the geometry modeling as well as the solution approximation considering the in plane coordinates of the control points defining the design boundary surfaces as well as the applicates of all the control points describing the variations of material properties as design variables we subsequently adopt a mathematical programming algorithm to simultaneously find the optimum shape and material composition of fg structures a couple of illustrative numerical examples in 2d elasticity with eigenfrequencies as their either constraints or objective functions are presented to demonstrate the high performance of the proposed methodology it will be seen that the obtained results by this concurrent optimization procedure have much better dynamic performance compared to the optimal results of the simple shape or material composition design

doubly robust estimation optimally truncated inverse intensity weighting and increment based methods for the analysis of irregularly observed longitudinal data longitudinal data arising from routine follow up of patients will often have irregular measurement times existing methods for analysis include joint modelling of the outcome and measurement processes and inverse intensity weighting iiw this work extends previously proposed analysis of increments to the case of irregular follow up yielding a model for the increments that can be used as a stand alone method furthermore we propose two ways of combining the increments and iiw estimators first we use the increment model to select the truncation point for the inverse intensity weights that minimises the mean squared error of the iiw estimator second we use the increment model to augment the usual iiw estimating equations to form a doubly robust estimator we evaluate the methods through simulation and apply these to a recent study of juvenile dermatomyositis

remark on a convex nonlinear problem where 1 a f denotes the first eigenvalue of a f g with zero dirichlet condition if u u is another solution of 1 relative to the same g then m a f u 5 0 or c 0 if f u is strictly convex 3 assumej u is strictly convex the solution of 1 is unique for g e k int k we are interested in the properties of the map g y g g cp c q on int k this map is continuous indeed let g g e int k since a f g 0 we may apply the inverse function theorem and say that there exists uk solution of

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

quantitative risk assessment for teratological effects abstract this article presents a quantitative procedure for using a benchmark dose to obtain low dose risk estimates for reproductive and developmental toxic effects this procedure combines the best features of the previously proposed methods for handling litter effects for teratology data and the currently used methods for quantitative risk assessment the beta binomial distribution is used to account for litter effects and the weibull dose response model is used for modeling teratogenic effects a benchmark dose defined to be the lowest dose at which the excess risk does not exceed 1 with 95 confidence is proposed to replace the no observed effect level noel the noel is generally the highest experimental dose that is not statistically different from the control the noel approach does not use experimental data effectively for quantitative risk estimation in this article a lower limit on the safe dose is estimated by linearly extrapolating downward from the benchmark dose this procedure is

isogeometric shape optimization of photonic crystals via coons patches abstract in this paper we present an approach that extends isogeometric shape optimization from optimization of rectangular like nurbs patches to the optimization of topologically complex geometries we have successfully applied this approach in designing photonic crystals where complex geometries have been optimized to maximize the band gaps salient features of this approach include the following 1 multi patch coons representation of design geometry the design geometry is represented as a collection of coons patches where the four boundaries of each patch are represented as nurbs curves the use of multiple patches is motivated by the need for representing topologically complex geometries the coons patches are used as a design representation so that designers do not need to specify interior control points and they provide a mechanism to compute analytical sensitivities for internal nodes in shape optimization 2 exact boundary conversion to the analysis geometry with guaranteed mesh injectivity the analysis geometry is a collection of nurbs patches that are converted from the multi patch coons representation with geometric exactness in patch boundaries the internal nurbs control points are embedded in the parametric domain of the coons patches with a built in mesh rectifier to ensure the injectivity of the resulting b spline geometry i e every point in the physical domain is mapped to one point in the parametric domain 3 analytical sensitivities sensitivities of objective functions and constraints with respect to design variables are derived through nodal sensitivities the nodal sensitivities for the boundary control points are directly determined by the design parameters and those for internal nodes are obtained via the corresponding coons patches

a shared response model for clustered binary data in developmental toxicity studies summary existing distributions for modeling fetal response data in developmental toxicology such as the beta binomial distribution have a tendency of inflating the probability of no malformed fetuses and hence understating the risk of having at least one malformed fetus within a litter as opposed to a shared probability extra binomial model we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response an explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses the em algorithm can be used to estimate the model parameters results of a simulation study show that the em estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form but not so for the estimates of intralitter correlation and the litter level probability of having at least one malformed fetus the proposed model is fitted to a set of data from the u s national toxicology program for the same dose response relationship the fit based on the shared response distribution is superior to that based on the beta binomial and comparable to that based on the recently proposed q power distribution kuk 2004 applied statistics53 369 386 an advantage of the shared response model over the q power distribution is that it is more interpretable and can be extended more easily to the multivariate case to illustrate this a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation

bounding the influence of domain parameterization and knot spacing on numerical stability in isogeometric analysis abstract isogeometric analysis iga was introduced by hughes et al 2005 1 as a new method to bridge the gap between the geometry description and numerical analysis similar to the finite element approach the iga concept to solve a partial differential equation leads to a linear system of equations the condition number of the coefficient matrix is a crucial factor for the stability of the system it depends strongly on the domain parameterization which provides the isogeometric discretization in this paper we derive a bound for the condition number of the stiffness matrix of the poisson equation in particular we investigate the influence of the domain parameterization and the knot spacing on the stability of the numerical system the factors appearing in our bound reflect the stability properties of a given domain parameterization

shape optimization directly from cad an isogeometric boundary element approach using t splines abstract we develop a t spline isogeometric boundary element method igabem simpson et al 2012 scott et al 2013 simpson et al 2014 to shape sensitivity analysis and gradient based shape optimization in three dimensional linear elasticity contrary to finite element based isogeometric analysis iga approaches no parametrization of the volume is required hence the iterative optimization algorithm can be implemented directly from cad without any mesh generation or postprocessing step for returning the resulting structure to cad designers t splines also guarantee a water tight geometry without the manual geometrical repair work as with non uniform rational b splines nurbs we demonstrate the worth of the method by analysing problems with and without analytical solutions including engineering examples involving complex shapes additionally we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking to provide helpful reference problems for 3d shape optimization

the method of fundamental solutions applied to some inverse eigenproblems in this work we address the application of the method of fundamental solution mfs as a forward solver in some shape optimization problems in two and three dimensional domains it is well known kac s problem that a set of eigenvalues does not determine uniquely the shape of the domain moreover even the existence problem is not well defined due to the ashbaugh benguria inequality although these results constitute counterexamples in the general problem of shape determination from the eigenfrequencies we can address simpler questions in shape determination using the mfs for instance we apply the mfs to build domains that include a specific finite set of eigenvalues or that have an eigenmode that verifies some prescribed conditions as a particular case an eigenmode that defines a certain nodal line

planar domain parameterization for isogeometric analysis based on teichmuller mapping abstract given the boundary curve of a planar domain finding a parametric spline representation for the domain is called domain parameterization a good parameterization of the computational domain plays a key role in isogeometric analysis since it influences the accuracy of the subsequent analysis in this paper we propose a new approach for planar domain parameterization based on teichmuller map a special map in the class of quasi conformal map under given correspondence of four boundary curves a unique teichmuller map between a unit square and a computational domain can be obtained which guarantees a bijection map and minimizes the maximal conformality distortion we propose an efficient iterative algorithm to compute the teichmuller map based on alternating direction method of multipliers admm experimental results show that our method can produce more uniform parameterization and increase the accuracy as well as decrease the condition numbers of the stiffness matrices in isogeometric analysis than other state of the art approaches

beta binomial model for meta analysis of odds ratios in meta analysis of odds ratios ors heterogeneity between the studies is usually modelled via the additive random effects model rem an alternative multiplicative rem for ors uses overdispersion the multiplicative factor in this overdispersion model odm can be interpreted as an intra class correlation icc parameter this model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta distributed resulting in beta binomial distributions we propose two new estimators of the icc for meta analysis in this setting one is based on the inverted breslow day test and the other on the improved gamma approximation by kulinskaya and dollinger 2015 p 26 to the distribution of cochran s q the performance of these and several other estimators of icc on bias and coverage is studied by simulation additionally the mantel haenszel approach to estimation of ors is extended to the beta binomial model and we study performance of various icc estimators when used in the mantel haenszel or the inverse variance method to combine ors in meta analysis the results of the simulations show that the improved gamma based estimator of icc is superior for small sample sizes and the breslow day based estimator is the best for n 100 the mantel haenszel based estimator of or is very biased and is not recommended the inverse variance approach is also somewhat biased for ors 1 but this bias is not very large in practical settings developed methods and r programs provided in the web appendix make the beta binomial model a feasible alternative to the standard rem for meta analysis of ors 2017 the authors statistics in medicine published by john wiley sons ltd

optimizing domain parameterization in isogeometric analysis based on powell sabin splines we address the problem of constructing a high quality parameterization of a given planar physical domain defined by means of a finite set of boundary curves we look for a geometry map represented in terms of powell sabin b splines powell sabin splines are c 1 quadratic splines defined on a triangulation and thus the parameter domain can be any polygon the geometry map is generated by the following three step procedure first the shape of the parameter domain and a corresponding triangulation are determined in such a way that its number of corners matches the number of corners of the physical domain second the boundary control points related to the powell sabin b spline representation are chosen so that they parameterize the boundary curve of the physical domain third the remaining inner control points are obtained by solving a nimble optimization problem based on the winslow functional the proposed domain parameterization procedure is illustrated numerically in the context of isogeometric galerkin discretizations based on powell sabin splines it turns out that the flexibility rising from the generality of the parameter domain has a beneficial effect on the quality of the parameterization and also on the accuracy of the computed approximate solution

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

isogeometric shape optimization of shells using semi analytical sensitivity analysis and sensitivity weighting abstract we present isogeometric shape optimization for shell structures applying sensitivity weighting and semi analytical analysis we use a rotation free shell formulation and all involved geometry models i e initial design analysis model optimization model and final design use the same geometric basis in particular nurbs a sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update a multilevel design approach is applied such that the design space can be chosen independently from the analysis space the use of semi analytical sensitivities allows having different polynomial degrees for design and analysis model different numerical examples are performed which confirm the applicability of the proposed method furthermore a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods

isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization an important feature that drives the auxetic behaviour of the star shaped auxetic structures is the hinge functional connection at the vertex connections this feature poses a great challenge for manufacturing and may lead to significant stress concentrations to overcome these problems we introduced smoothed petal shaped auxetic structures where the hinges are replaced by smoothed connections to accommodate the curved features of the petal shaped auxetics a parametrisation modelling scheme using multiple nurbs patches is proposed next an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance to ensure a minimum thickness for each member a geometry sizing constraint is imposed via piece wise bounding polynomials this geometry sizing constraint in the context of isogeometric shape optimization is particularly interesting due to the non interpolatory nature of nurbs basis the effective poisson ratio is used directly as the objective function and an adjoint sensitivity analysis is carried out the optimized designs smoothed petal auxetic structures are shown to achieve low negative poisson s ratios while the difficulties of manufacturing the hinges are avoided for the case with six petals an in plane isotropy is achieved

a mesh regularization scheme to update internal control points for isogeometric shape design optimization abstract this paper presents a variational method to update internal control points in isogeometric shape optimization the important properties of domain parameterization such as bijective mapping between parametric and physical domains uniform mesh and orthogonal mesh are enforced simultaneously the bijective mapping is achieved by minimizing a dirichlet energy functional to prevent the divergent behavior of the minimizing process due to the severely distorted initial mesh a constraint is introduced to enforce the positive jacobian of mapping from parametric to physical domains in spite of adding the constraint that might increase computational costs the proposed method is more efficient due to the convexity of dirichlet energy functional compared with the other unconstrained methods also it turns out that the proposed method is more effective to achieve the bijective mapping especially near a concave boundary the uniform parameterization of the domain is achieved by minimizing the dirichlet energy functional and the orthogonality of mesh is performed by minimizing a dimensionless functional the required design sensitivity of the employed functional and constraint is derived with respect to the position of internal control points the developed scheme of mesh regularization is effective to maintain the high quality of domain parameterization during the shape optimization process

a note on generating correlated binary variables summary it is important to be able to generate correlated binary data in an efficient easily programmed manner for among other things the generation of large bootstrap samples in this note nothing more than the basic ingredient of the uniform random number generator is required for simulating binary data from the most commonly occurring correlation structures

initial solution estimation for one step inverse isogeometric analysis in sheet metal stamping abstract recently isogeometric analysis iga based on incremental methods for simulating the stamping process has been researched to the best of our knowledge however few studies have combined iga and one step inverse approach which is based on total deformation theory of plasticity a key step for one step inverse iga is to estimate a good initial solution traditional mesh based initial solution algorithms for one step inverse approach are not suitable for one step inverse nurbs based iga in this paper we presented a method which can rapidly unfold the undevelopable nurbs surface onto a planar domain and obtain a good initial solution estimation for one step inverse iga the key idea of the presented method is unfolding the control net of a nurbs surface for isogeometric analysis by energy based initial solution estimation algorithm in addition we developed a cutting stitching algorithm which can separate a complex control net into several parts with simple shapes numerical examples illustrate the initial solutions using the presented method are approaching the final results by one step inverse finite element method this implies that the iterative steps and computational time of one step inverse iga will be reduced significantly compared with that of one step inverse finite element method

spline parameterization method for 2d and 3d geometries based on t mesh optimization abstract we present a method to obtain high quality spline parameterization of 2d and 3d geometries for their use in isogeometric analysis as input data the proposed method demands a boundary representation of the domain and it constructs automatically a spline transformation between the physical and parametric domains parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric t mesh onto the physical domain by applying a t mesh untangling and smoothing procedure which is the key of the method mesh optimization is based on the mean ratio shape quality measure the spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one to one correspondence between the meshes of the parametric and physical domains we give a detailed description of the proposed technique and show some examples also we present some examples of the application of isogeometric analysis in geometries parameterized with our method

isogeometric analysis in electromagnetics b splines approximation abstract we introduce a new discretization scheme for maxwell equations in two space dimension inspired by the new paradigm of isogeometric analysis introduced in hughes et al 2005 16 we propose an algorithm based on the use of bivariate b splines spaces suitably adapted to electromagnetics we construct b splines spaces of variable interelement regularity on the parametric domain these spaces and their push forwards on the physical domain form a de rham diagram and we use them to solve the maxwell source and eigen problem our scheme has the following features i is adapted to treat complex geometries ii is spectral correct iii provides regular e g globally c 0 discrete solutions of maxwell equations

range of correlation matrices for dependent bernoulli random variables summary we say that a pair p r is compatible if there exists a multivariate binary distribution with mean vector p and correlation matrix r in this paper we study necessary and sufficient conditions for compatibility for structured and unstructured correlation matrices we give examples of correlation matrices that are incompatible with any p using our results we show that the parametric binary models of emrich piedmonte 1991 and qaqish 2003 allow a good range of correlations between the binary variables we also obtain necessary and sufficient conditions for a matrix of odds ratios to be compatible with a given p our findings support the popular belief that the odds ratios are less constrained and more flexible than the correlations

a computational formulation for constrained solid and liquid membranes considering isogeometric finite elements abstract a geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements and is suitable for both solid and liquid membranes the curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane in the latter case this avoids the use of local cartesian coordinates at the element level consequently no transformation of derivatives is required the formulation considers a split of the in plane and out of plane membrane contributions which allows the construction of a stable formulation for liquid membranes with constant surface tension the proposed membrane formulation is general and accounts for dead and live loading as well as enclosed volume area and contact constraints the new formulation is illustrated by several challenging examples considering linear and quadratic lagrange elements as well as isogeometric elements based on quadratic nurbs and cubic t splines it is seen that the isogeometric elements are much more accurate than standard lagrange elements the gain is especially large for the liquid membrane formulation since it depends explicitly on the surface curvature

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

isogeometric sizing and shape optimisation of beam structures based on the recently proposed framework of isogeometric analysis a study of structural sizing and shape optimisation of curved beam structures is presented the idea of the isogeometric approach is to analyse the structure using its intrinsic and hence exact geometric definition the structural response is approximated using the same basis functions describing the geometry the presented isogeometric framework employs non uniform rational b splines shape changes can be represented by altering both spatial location of control points and the corresponding weights towards the optimal design adaptation of identical geometric representations for both design and analysis resolves the problem of repetitive conversion between the computer aided and facet based geometries used in conventional finite element analysis sizing variables defined at the control points are interpolated using the same basis functions due to the fact that both analysis sizing and shape design share the same underlying description direct sensitivities can be easily evaluated analytically which improves the performance of the optimisation process while sizing should reflect local stress states shape design is preferably performed on a global level thus a multilevel design approach is proposed where shape design is carried on a coarser level projecting the shape design sensitivities bridges the gap between the different levels the proposed design formulation is applied to compliance minimisation problems numerical results indicate the applicability of the method

implementation of regularized isogeometric boundary element methods for gradient based shape optimization in two dimensional linear elasticity the present work addresses shape sensitivity analysis and optimization in two dimensional elasticity with a regularized isogeometric boundary element method igabem non uniform rational b splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations with the advantage of tight integration of design and analysis the application of igabem in shape optimization reduces the mesh generation regeneration burden greatly the work is distinct from the previous literatures in igabem shape optimization mainly in two aspects 1 the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives which were the main implementation difficulty in igabem and 2 although based on the same computer aided design cad model the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh thus achieving a balance between less design variables for efficiency and refined mesh for accuracy this technique was initially used in isogeometric finite element method and was incorporated into the present igabem implementation

superconvergent isogeometric free vibration analysis of euler bernoulli beams and kirchhoff plates with new higher order mass matrices abstract a superconvergent isogeometric free vibration analysis is presented for euler bernoulli beams and kirchhoff plates this method is featured by new higher order mass matrices for the 1d euler bernoulli beam problem it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix the reduced bandwidth mass matrix is designed based upon the consistent mass matrix and it contains adjustable parameters to be determined via maximizing the order of accuracy of the vibration frequency as a result 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices while their corresponding consistent mass matrices are 2nd and 4th order accurate respectively thus the higher order beam mass matrices have more superior frequency accuracy simultaneously with smaller bandwidth compared with their corresponding consistent mass matrices while for the 2d kirchhoff plate problem in order to compute arbitrary frequency in a superconvergent fashion a mixed mass matrix is formulated through a linear combination of the consistent mass matrix and the reduced bandwidth mass matrix then by introducing the wave propagation angle the higher order plate mass matrix can be rationally derived from the mixed mass matrix it is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency it is shown that the quadratic and cubic higher order mass matrices possess 4th and 6th orders of accuracy which are two orders higher than those of the consistent plate mass matrices the construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples

modelling and generating correlated binary variables summary many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters the usual approach to use correlation models appropriate for normally distributed responses suffers from two drawbacks when the marginal probabilities within the clusters differ first as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses it may fail to model realistically the range of correlations present in the data secondly computer simulation of observations from these models is very difficult we present an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation some key wor ds binary variable computer simulation correlation structure generalised estimating equation

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

isogeometric shape optimization of vibrating membranes we consider a model problem of isogeometric shape optimization of vibrating membranes whose shapes are allowed to vary freely the main obstacle we face is the need for robust and inexpensive extension of a b spline parametrization from the boundary of a domain onto its interior a task which has to be performed in every optimization iteration we experiment with two numerical methods one is based on the idea of constructing a quasi conformal mapping whereas the other is based on a spring based mesh model for carrying out this task which turn out to work sufficiently well in the present situation we perform a number of numerical experiments with our isogeometric shape optimization algorithm and present smooth optimized membrane shapes our conclusion is that isogeometric analysis fits well with shape optimization

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

range of the first two eigenvalues of the laplacian for each planar domain d of unit area the first two dirichlet eigenvalues of on d determine a point 1 d 2 d in the 1 2 plane as d varies over all such domains this point varies over a set r which we determine its boundary consists of two semi infinite straight lines and a curve connecting their endpoints this curve is found numerially we also show how to minimize the n th eigenvalue when the minimizing domain is diconnected for n 3 we show that the minimizing domain is connected and that 3 is a local minimum for d a circular disc

isogeometric shape optimization for quasi static processes summary a framework to solve shape optimization problems for quasi static processes is developed and implemented numerically within the context of isogeometric analysis iga recent contributions in shape optimization within iga have been limited to static or steady state loading conditions in the present contribution the formulation of shape optimization is extended to include time dependent loads and responses a general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems an adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of iga the methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi axial tension and pure shear under quasi static loading conditions the method is validated using a passive control approach with an a priori known solution several applications of time dependent mechanical problems are shown to illustrate the capabilities of this approach in particular a problem is considered where an external load is allowed to move along the surface of a structure the shape of the structure is modified in order to control the time dependent displacement of the point where the load is applied according to a pre specified target copyright 2015 john wiley sons ltd

b splines with applications to isogeometric analysis abstract a novel spline named b splines boundary plus plus splines is developed to address the expression of a trimmed nurbs patch in an analytic form which is a central idea of surface representation the presented method converts each trimmed nurbs patch into a b spline patch that incorporates of specific boundary points as the boundary presentation emphasis is placed on the construction of a new analytic formula of a trimmed nurbs patch defined by the boundary points at the trimming curves and a group of enriched control points b spline basis functions are linearly independent build a partition of unity and satisfy the kronecker delta property each b spline basis function is a linear combination of the basis functions of the trimmed nurbs patch these properties allow imposing the dirichlet boundary conditions strongly at the boundary of the trimmed patch without the necessity of modifying the basis functions of the trimmed patch isogeometric analysis using b splines for two dimensional elastic solids is also proposed several numerical examples are used to demonstrate the reliability of the presented method the numerical example for the patch test illustrates that the b spline patch passes the standard patch test

isogeometric shape design sensitivity analysis of stress intensity factors for curved crack problems abstract an isogeometric shape design sensitivity analysis method is developed for the stress intensity factors sifs in curved crack problems in order to obtain an enhanced shape sensitivity of sifs exact higher order geometric information of curvature and normal vector is embedded in the isogeometric shape sensitivity expressions a direct differentiation method is employed for the design sensitivity analysis and the size and orientation of the crack are selected as design variables in the isogeometric approach the nurbs basis functions in cad system are directly utilized in the response analysis which enables a seamless incorporation of exact geometry and higher continuity into the computational framework the precise evaluation of the crack face integral as well as the interaction integral is essential for the computation of the stress intensity factors for the curved crack problems in a mixed mode the cad based exact representation of tangential and normal vectors enables us to exactly define a local coordinate system at the crack tip whose shape dependency naturally leads to configuration design variations that include the change of crack orientation compared with the conventional finite element approach a higher continuity of stress and strain fields are expected in the interaction integral domain the design dependencies of auxiliary field and q function are considered in the design sensitivity formulation reflecting the convection effects due to the non constant design velocity in the interaction integral domain various numerical examples of curved crack problems are presented to verify the developed isogeometric sensitivity analysis method through the comparison with exact and finite element solutions