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 boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

on stable representations of bell elements abstract the paper is concerned with the space of c 1 continuous polynomial splines of degree 5 on general triangulations such that the restriction to each triangle corresponds to a bell element it is investigated how the standard construction of bell elements which is based on prescribing values and derivatives up to order two at the vertices of the triangulation can be used to define different bases the most straightforward one is the nodal basis which lacks stability but it is shown that this can be improved by scaling the interpolation data however the prime focus of the paper is on the construction of b spline like bases that depend on the choice of special domain triangles associated with the vertices of the triangulation a b spline like basis consists of functions that are locally supported and form a partition of unity if the triangulation satisfies certain geometric constraints e g is acute and the domain triangles are chosen suitably the basis is also non negative the stability analysis of the derived bases is addressed theoretically as well as numerically the latter with the examples of least square fitting and pde solving

m estimation for location and regression parameters in group models a case study using stiefel manifolds we discuss here a general approach to the calculation of the asymptotic covariance of m estimates for location parameters in statistical group models when an invariant objective function is used the calculation reduces to standard tools in group representation theory and the calculation of some constants only the constants depend upon the precise forms of the density or of the objective function if the group is sufficiently large this represents a major simplification in the computation of the asymptotic covariance following the approach of chang and tsai we define a regression model for group models and derive the asymptotic distribution of estimates in the regression model from the corresponding distribution theory for the location model the location model is not in general a subcase of the regression model we illustrate these techniques using stiefel manifolds the stiefel manifold v p m is the collection of p x m matrices x which satisfy the condition x t x i m where m p under the assumption that x has a distribution proportional to exp tr f t x for some p m matrix f downs 1972 gives approximations to maximum likelihood estimation of f in this paper we consider a somewhat different location problem under the assumption that x has a distribution of the form f tr t 0 x for some 0 v p m we calculate the asymptotic distribution of m estimates which minimize an objective function of the form i tr t x i the assumptions on the form of the density and the objective function can be relaxed to a more general invariant form in this case the calculation of the asymptotic distribution of reduces to the calculation of four constants and we present consistent estimators for these constants prentice 1989 introduced a regression model for stiefel manifolds in the prentice model u 1 u 2 u n v p m are fixed v 1 v 2 v n v p m are independent random so that the distribution of v i depends only upon tr v t i a 2 u i a t 1 for unknown a 1 a 2 so m so p we discuss here m estimation of a 1 and a 2 under general invariance conditions for both the density and the objective function using a well studied example on vector cardiograms we discuss the physical interpretation of the invariance assumption as well as of the parameters a 1 a 2 in the prentice regression model in particular a 1 represents a rotation of the u s to the v s in a coordinate system relative to the u s and a 2 represents a rotation of the u s to the v s in a coordinate system fixed to the external world

a stabilized powell sabin finite element method for the 2d euler equations in supersonic regime in this paper a powell sabin finite element ps fem scheme is presented for the solution of the 2d euler equations in supersonic regime the spatial discretization is based on ps splines that are piecewise quadratic polynomials with a global continuity defined on conforming triangulations some geometrical issues related to the practical construction of the ps elements are discussed in particular the generation of the control triangles and the imposition of the boundary conditions a stabilized formulation is considered and a novel shock capturing technique in the context of continuous finite elements is proposed to reduce oscillations around the discontinuity and compared with the classical technique proposed by tezduyar and senga 2006 the code is verified using manufactured solutions and validated using two challenging numerical examples which allows to evaluate the performance of the ps discretization in capturing the shocks

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

on the analysis of count data of birth and death process type with application to molecularly targeted cancer therapy for molecularly targeted cancer therapy potency of a novel monoclonal antibody is typically studied in vitro in order to observe directly the effect of the antibody on a malignant tumour cell population numbers of viable cells of the population are counted over time to evaluate how the antibody may change the population growth pattern usually such count data is analysed by a log linear model to estimate the average antibody effects but it is based on a poisson like process and is not appropriate for modelling the growth pattern of the tumour cells in this paper we propose to analyse the count data from the point of view of a birth and death process which is a more natural description of the biological process in these experiments assuming a simple birth and death process and a naive regression model for the birth rate and death rate we show that the log linear relationship still holds for the average count and the covariates although the linear predictor needs to satisfy a specific functional form the estimation can be based on the quasi likelihood method the variance is not a simple function of the mean but can be adequately approximated by a function of mean of either quadratic form or linear form available in most standard statistical packages we perform a simulation study to show that the proposed method provides consistent and robust estimations the utility of the method is demonstrated by the analysis of a data set for experiment for anti lymphoma monoclonal antibodies

shape changes in the plane for landmark data this paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane we provide inference procedures on the complex projective plane for a basic measure of shape change in the plane on observing that shapes of configurations of k 1 landmarks in the plane may be represented as points on cp k 1 and that complex rotations are the only maps on cs k 1 which preserve the usual hermitian inner product specifically if u 1 u n are fixed points on cp k 1 represented as cs k 1 u 1 and v 1 v n are random points on cp k 1 such that the distribution of v j depends only on v j au j 2 for some unknown complex rotation matrix a then this paper provides asymptotic inference procedures for a it is demonstrated that shape changes of a kind not detectable as location shifts by standard euclidean analysis can be found by this frequency domain method a numerical example is given

generator estimation of markov jump processes estimating the generator of a continuous time markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics several methods have been devised for this purpose a quadratic programming approach cf d t crommelin e vanden eijnden fitting timeseries by continuous time markov chains a quadratic programming approach j comp phys 217 2006 782 805 a resolvent method cf t muller modellierung von proteinevolution phd thesis heidelberg 2001 and various implementations of an expectation maximization algorithm s asmussen o nerman m olsson fitting phase type distributions via the em algorithm scand j stat 23 1996 419 441 i holmes g m rubin an expectation maximization algorithm for training hidden substitution models j mol biol 317 2002 753 764 u nodelman c r shelton d koller expectation maximization and complex duration distributions for continuous time bayesian networks in proceedings of the twenty first conference on uncertainty in ai uai 2005 pp 421 430 m bladt m sorensen statistical inference for discretely observed markov jump processes j r statist soc b 67 2005 395 410 some of these methods however seem to be known only in a particular research community and have later been reinvented in a different context the purpose of this paper is to compile a catalogue of existing approaches to compare the strengths and weaknesses and to test their performance in a series of numerical examples these examples include carefully chosen model problems and an application to a time series from molecular dynamics

surface fitting using convex powell sabin splines abstract convexity conditions for powell sabin splines are derived and an algorithm is presented for fitting a convex powell sabin spline to a set of scattered data part of this algorithm deals with the elimination of as many redundant conditions as possible the powell sabin splines are defined in terms of basis functions b splines with local support making use of their bernstein bezier representation leads to an easy handling of and an efficient calculating with these b splines numerical examples are supplied to illustrate the usefulness of surface fitting by means of convex powell sabin splines

triangulation based isogeometric analysis of the cahn hilliard phase field model abstract this paper presents triangulation based isogeometric analysis of the cahn hilliard phase field model the cahn hilliard phase field model is governed by a time dependent fourth order partial differential equation the corresponding primal variational form involves second order operators making it difficult to be directly analyzed with traditional c 0 finite element analysis in this paper we construct c 1 bernstein bezier simplicial elements through macro element techniques including various triangle split based macro elements in both 2d and 3d space we extend triangulation based isogeometric analysis to solving the primal variational form of the cahn hilliard equation we validate our method by convergence analysis showing the nodal and degree of freedom advantages over c 0 finite element analysis we then demonstrate detailed system evolution from randomly perturbed initial conditions in periodic two dimensional squares and three dimensional cubes we incorporate an adaptive time stepping scheme in these numerical experiments our numerical study demonstrates that triangulation based isogeometric analysis offers optimal convergence and time step stability is applicable to complex geometry and allows local refinement

bivariate splines of various degrees for numerical solution of partial differential equations bivariate splines with various degrees are considered in this paper a matrix form of the extended smoothness conditions for these splines is presented upon this form the multivariate spline method for numerical solution of partial differential equations pdes proposed by awanou lai and wenston in the multivariate spline method for scattered data fitting and numerical solutions of partial differential equations in wavelets and splines g chen and m j lai eds nashboro press brentwood tn 2006 pp 24 76 is generalized to obtain a new spline method it is observed that combined with prelocal refinement of triangulation and automatic degree raising over triangles of interest the new spline method of bivariate splines of various degrees is able to solve linear pdes very effectively and efficiently

orientation statistics without parametric assumptions summary maximum likelihood estimation using the matrix von mises fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations essentially because of the inconvenient form of the normalizing constant in the probability distribution for the case of 3 x 2 or 3 x 3 orientations the main cases of practical importance an alternative approach is developed here by transforming the data into unsigned four dimensional directions and using known results on the sampling properties of the spectral decomposition of the resulting sample moment of inertia matrix it is demonstrated that the necessary computations are relatively simple by applying some of the techniques to a set of vectorcardiogram data

deconvolution density estimation on so n this paper develops nonparametric deconvolution density estimation over so n the group of n x n orthogonal matrices of determinant 1 the methodology is to use the group and manifold structures to adapt the euclidean deconvolution techniques to this lie group environment this is achieved by employing the theory of group representations explicit to so n general consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions application to empirical bayes prior estimation and inference is also discussed

a distribution free method of interval estimation for unsigned directional data summary a method of moments is suggested for large samples of unsigned directional data the point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a bingham distribution however the calculations necessary for interval and regional estimation are considerably simpler the statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations davis 1977 tyler 1981 a numerical example first treated by bingham 1974 is examined and found to yield very similar regional estimates the hypothesis of rotational symmetry is discounted by using a test statistic suggested by watson 1965

spherical regression on matched pairs of orientation statistics the matched pairs section of the analysis of 3 x 3 orientation statistics in prentice 1986 may be improved on by constructing a rotational regression model an analogue of spherical regression the results obtained are relatively simple consequences of the work of chang and are therefore presented here for general orientation statistics rigid orthogonal m frames in p dimensions before application to the matched pairs of vectorcardiogram orientations m p 3 which provided the original motivation for this paper

scalable extrinsic calibration of omni directional image networks we describe a linear time algorithm that recovers absolute camera orientations and positions along with uncertainty estimates for networks of terrestrial image nodes spanning hundreds of meters in outdoor urban scenes the algorithm produces pose estimates globally consistent to roughly 0 1 2 milliradians and 5 centimeters on average or about four pixels of epipolar alignment we assume that adjacent nodes observe overlapping portions of the scene and that at least two distinct vanishing points are observed by each node the algorithm decouples registration into pure rotation and translation stages the rotation stage aligns nodes to commonly observed scene line directionss the translation stage assigns node positions consistent with locally estimated motion directions then registers the resulting network to absolute earth coordinates the paper s principal contributions include extension of classic registration methods to large scale and dimensional extents a consistent probabilistic framework for modeling projective uncertaintys and a new hybrid of hough transform and expectation maximization algorithms we assess the algorithm s performance on synthetic and real data and draw several conclusions first by fusing thousands of observations the algorithm achieves accurate registration even in the face of significant lighting variations low level feature noise and error in initial pose estimates second the algorithm s robustness and accuracy increase with image field of view third the algorithm surmounts the usual tradeoff between speed and accuracys it is both faster and more accurate than manual bundle adjustment

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

extending the state space model to accommodate missing values in responses and covariates this article proposes an extended state space model for accommodating multivariate panel data the novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses missing covariate data are handled by a second state space model nested inside the first to represent unobserved exogenous information relevant kalman filter equations are derived and explicit expressions are provided for both the e and m steps of an expectation maximization em algorithm to obtain maximum gaussian likelihood estimates of all model parameters in the presence of missing data the resulting em algorithm becomes computationally intractable but a simplification of the m step leads to a new procedure that is shown to be an expectation conditional maximization ecm algorithm under exogeneity of the covariates simulation studies reveal that the approach appears to be relatively robust to moderate percentages of missing dat

information matrix computation from conditional information via normal approximation summary this paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters philosophically the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference technically the method makes use of two facts the information for a one dimensional parameter can be well computed when the loglikelihood is approximately quadratic over the range corresponding to a small positive confidence interval and the covariance matrix of a normal distribution can be obtained from its one dimensional conditional distributions whose sample spaces span the sample space of the joint distribution we illustrate the method with its application to a linear mixed effects model

the dynamic expectation conditional maximization either algorithm summary the expectation conditional maximization either ecme algorithm has proven to be an effective way of accelerating the expectation maximization algorithm for many problems recognizing the limitation of using prefixed acceleration subspaces in the ecme algorithm we propose a dynamic ecme decme algorithm which allows the acceleration subspaces to be chosen dynamically the simplest decme implementation is what we call decme 1 which uses the line that is determined by the two most recent estimates as the acceleration subspace the investigation of decme 1 leads to an efficient simple stable and widely applicable decme implementation which uses two dimensional acceleration subspaces and is referred to as decme 2 the fast convergence of decme 2 is established by the theoretical result that in a small neighbourhood of the maximum likelihood estimate it is equivalent to a conjugate direction method the remarkable accelerating effect of decme 2 and its variant is also demonstrated with several numerical examples

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

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

isogeometric triangular bernstein bezier discretizations automatic mesh generation and geometrically exact finite element analysis isogeometric analysis iga was introduced as a way to bypass the design to analysis bottleneck inherent in the traditional computer aided design cad through finite element analysis fea paradigm however an outstanding problem in the field of iga is that of surface to volume parameterization in cad packages solid objects are represented by a collection of nurbs or t spline bounding surfaces but to perform engineering analysis on real world problems we must find a way to parameterize the volumes of these objects as well this has proven to be difficult using traditional iga as the tensor product nature of trivariate nurbs and t splines limit their ability to create analysis suitable parameterizations of arbitrarily complex volumes to overcome the limitations of trivariate nurbs and t splines we propose the use of rational bernstein bezier tetrahedra to create analysis suitable volumetric parameterizations for isogeometric analysis in this paper which is part one of a two part series we present the methodology for discretizing two dimensional geometries using rational bernstein bezier triangles in addition to presenting finite element analysis methodologies based on rational bernstein bezier triangles we also introduce two new mesh generation strategies for automatically creating high quality geometrically exact curvilinear meshes we assess the quality of our mesh generation schemes using a suite of challenging two dimensional geometries and we verify the accuracy of our proposed numerical discretization approach using the method of manufactured solutions

an improved nurbs based isogeometric analysis with enhanced treatment of essential boundary conditions the nurbs based isogeometric analysis offers a seamless integration between the cad and subsequent finite element analysis and has been shown to be very effective for wide classes of problems due to its accurate geometric description however similar to the moving least square or reproducing kernel meshfree shape functions the nurbs basis functions generally are not interpolatory functions in this work it is shown that the direct imposition of the inhomogeneous essential boundary conditions to the nurbs control points may lead to significant errors with deteriorated rates of convergence consequently an improved formulation for nurbs based isogeometric analysis is proposed this is fulfilled by employing a transformation method that relates the control variables to the collocated nodal values at the essential boundary by using open knot vectors the resulting nurbs basis functions associated with the interior control points vanish at the boundary thus unlike the meshfree approximation the nurbs control points can be clearly partitioned into boundary and interior groups therefore the transformation method can be only applied to the boundary control points via invoking collocation of physical values at a set of boundary points the nurbs approximation enhanced with transformed physical boundary variables is kinematically admissible and the essential boundary conditions can be enforced straightforwardly like the finite element method several potential and elasticity problems evince that much higher solution accuracy with optimal convergence rates can be achieved by the present improved formulation compared with the method with direct imposition of essential boundary conditions to control variables

bezier projection a unified approach for local projection and quadrature free refinement and coarsening of nurbs and t splines with particular application to isogeometric design and analysis abstract we introduce bezier projection as an element based local projection methodology for b splines nurbs and t splines this new approach relies on the concept of bezier extraction and an associated operation introduced here spline reconstruction enabling the use of bezier projection in standard finite element codes bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global l 2 projection bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging degree elevation and reduction basis roughening and smoothing and spline reparameterization in fact bezier projection provides a quadrature free approach to refinement and coarsening of splines in this sense bezier projection provides the fundamental building block for h p k r adaptivity in isogeometric analysis

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

the ecme algorithm a simple extension of em and ecm with faster monotone convergence a generalisation of the ecm algorithm meng rubin 1993 which is itselfan extension of the em algorithm dempster laird rubin 1977 can be obtained by replacing some cm steps of ecm which maximise the constrained expected complete data loglikelihood function with steps that maximise the correspondingly constrained actual likelihood function this algorithm which we call ecme algorithm for expectation conditional maximisation either shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods moreover ecme can have a substantially faster convergence rate than either em or ecm measured using either the number of iterations or actual computer time

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

two new triangular g1 conforming finite elements with cubic edge rotation for the analysis of kirchhoff plates abstract two triangular g 1 conforming elements based on the triangular gregory patch suitable for the analysis of the kirchhoff plate model are presented both have cubic normal derivative along the sides so that they can be effectively used in combination with generalized hermitian elements the gregory patch consists in a rational enhancement of the base polynomial spaces useful to design g 1 conforming elements on general c 0 conforming unstructured meshes because of the presence of the rational functions the second derivatives at the corners of the element present finite discontinuities that prevent the elements from passing the bending patch test the discontinuities are removed using a constrained version of the gregory patch with lagrange multipliers in this way the rational conforming space collapses into a conforming rearrangement of the original polynomial interpolant spaces the proposed formulation design elements that pass the bending patch test and present optimal rate of convergence on general unstructured meshes

continued fractions with applications i introductory examples ii more basics iii convergence criteria iv continued fractions and three term recurrence relations v correspondence of continued fractions vi hypergeometric functions vii moments and orthogonality viii pade approximants ix some applications in number theory x zero free regions xi digital filters and continued fractions xii applications to some differential equations appendix some continued fraction expansions references index

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

conjugate gradient acceleration of the em algorithm the em algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates although its implementation is generally simple the em algorithm often exhibits slow convergence and is costly in some areas of application past attempts to accelerate the em algorithm have most commonly been based on some form of aitken acceleration here we propose an alternative method based on conjugate gradients the key as we show is that the em step can be viewed approximately at least as a generalized gradient making it natural to apply generalized conjugate gradient methods in an attempt to accelerate the em algorithm the proposed method is relatively simple to implement and can handle problems with a large number of parameters an important feature of most em algorithms to demonstrate the effectiveness of the proposed acceleration method we consider its application to several problems in each of the following areas estimation of a covariance matrix from incomplete mu

from nurbs to nurps geometries abstract quadratic powell sabin splines and their rational extension the so called nurps surfaces are an interesting alternative for classical tensor product nurbs in the context of isogeometric analysis because they allow the use of local refinements while retaining a b spline like representation and exact description of conic sections in this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic nurbs representation into a nurps representation suitable for the analysis

bivariate spline spaces and minimal determining sets abstract the paper describes bivariate spline spaces and minimal determining sets shows applications of these concepts presents two new triangular finite elements describes public domain software for the analysis of spline spaces and concludes with a concise history of these subjects the software described in this paper is available on http www math utah edu alfeld mds that page also contains links to colored versions of the figures in this paper

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

statistical inference for discretely observed markov jump processes summary likelihood inference for discretely observed markov jump processes with finite state space is investigated the existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated this topic is closely related to the imbedding problem for markov chains it is demonstrated that the maximum likelihood estimator can be found either by the em algorithm or by a markov chain monte carlo procedure when the maximum likelihood estimator does not exist an estimator can be obtained by using a penalized likelihood function or by the markov chain monte carlo procedure with a suitable prior the methodology and its implementation are illustrated by examples and simulation studies

a bayesian robust chi squared test for testing simple hypotheses abstract in this paper we introduce a new bayesian chi squared test based on an adjusted quadratic loss function for testing a simple null hypothesis we show that the asymptotic null distribution of our suggested test is a central chi squared distribution under some assumptions required for the bayesian large sample theory we refer to our test as the bayesian robust chi squared test since it is robust to parametric misspecification in the alternative model that is the limiting null distribution of our test is a central chi squared distribution irrespective of parametric misspecification in the alternative model in addition to being robust to parametric misspecification our test also shares properties of the test suggested by li et al 2015 based on a quadratic loss function we provide four examples to illustrate the implementation of our suggested bayesian test statistic

numerical solution of partial differential equations with powell sabin splines powell sabin splines are piecewise quadratic polynomials with global c 1 continuity they are defined on conforming triangulations of two dimensional domains and admit a compact representation in a normalized b spline basis recently these splines have been used successfully in the area of computer aided geometric design for the modelling and fitting of surfaces in this paper we discuss the applicability of powell sabin splines for the numerical solution of partial differential equations defined on domains with polygonal boundary a galerkin type pde discretization is derived for the variable coefficient diffusion equation special emphasis goes to the treatment of dirichlet and neumann boundary conditions finally an error estimator is developed and an adaptive mesh refinement strategy is proposed we illustrate the effectiveness of the approach by means of some numerical experiments

estimation for general birth death processes birth death processes bdps are continuous time markov chains that track the number of particles in a system over time while widely used in population biology genetics and ecology statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear bdps in which per particle birth and death rates are constant researchers often observe the number of particles at discrete times necessitating data augmentation procedures such as expectation maximization em to find maximum likelihood estimates mles for bdps on finite state spaces there are powerful matrix methods for computing the conditional expectations needed for the e step of the em algorithm for bdps on infinite state spaces closed form solutions for the e step are available for some linear models but most previous work has resorted to time consuming simulation remarkably we show that the e step conditional expectations can be expressed as convolutions of computable transition probabi

direct calculation of the information matrix via the em algorithm summary a simple explicit formula is provided for the matrix of second derivatives of the observed data log likelihood in terms of derivatives of the criterion function the conditional expectation of the complete data log likelihood given the observed data invoked by the em algorithm

a gradient algorithm locally equivalent to the em algorithm in many problems of maximum likelihood estimation it is impossible to carry out either the e step or the m step of the em algorithm the present paper introduces a gradient algorithm that is closely related to the em algorithm this em gradient algorithm approximately solves the m step of the em algorithm by one iteration of newton s method since newton s method converges quickly the local properties of the em gradient algorithm are almost identical with those of the em algorithm any strict local maximum point of the observed likelihood locally attracts the em and em gradient algorithm at the same rate of convergence and near the maximum point the em gradient algorithm always produces an increase in the likelihood with proper modification the em gradient algorithm also exhibits global convergence properties that are similar to those of the em algorithm our proof of global convergence applies and improves existing theory for the em algorithm these theoretical points are reinforced by a discussion of three realistic examples illustrating how the em gradient algorithm can succeed where the em algorithm is intractable

large eddy simulation of turbulent taylor couette flow using isogeometric analysis and the residual based variational multiscale method we present an application of the residual based variational multiscale turbulence modeling rbvms methodology to the computation of turbulent taylor couette flow at high reynolds number we show that the rbvms formulation globally conserves angular momentum a feature that is felt to be important for flows dominated by rotation and that is not shared by standard stabilized formulations of fluid flow weak imposition of dirichlet boundary conditions is employed to enhance the accuracy of the rbvms framework in the presence of thin turbulent boundary layers near solid walls calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions nurbs based isogeometric analysis is employed for the spatial discretization and mesh refinement is performed to assess the convergence characteristics of the proposed methodology numerical tests show that very accurate results are obtained on relatively coarse grids to the best of the authors knowledge this paper is the first to report large eddy simulation computations of this challenging test case

direct calculation of the information matrix via the em a simple explicit formula is provided for the matrix of second derivatives of the observed data log likelihood in terms of derivatives of the criterion function conditional expectation of the complete data log likelihood given the observed data invoked by the em algorithm

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

rotation free bernstein bezier elements for thin plates and shells development and validation abstract a new finite element procedure for thin plates and shells is presented it combines a geometrically non linear rotation free kirchhoff love formulation with triangular and quadrilateral bernstein bezier elements and c 1 and g 1 inter element continuity conditions as well as boundary conditions for clamping and for symmetry the formulation is free from transverse shear locking and relies on a high polynomial degree to mitigate membrane locking bernstein bezier elements are as opposed to nurbs suitable for arbitrary triangulations unlike with hermite elements no stress concentrations occur if the boundary is partially clamped and the formulation can be potentially extended to stiffened plates and shells and to step wise changes of thickness and material properties the convergence behaviour is demonstrated and the computational efficiency is compared with that of c reissner mindlin elements on several numerical examples

continuity and convergence in rational triangular bezier spline based isogeometric analysis abstract this paper presents a method for isogeometric analysis using rational triangular bezier splines rtbs where optimal convergence rates are achieved in this method both the geometry and the physical field are represented by bivariate splines in bernstein bezier form over the triangulation of a domain from a given physical domain bounded by nurbs curves a parametric domain and its triangulation are constructed by imposing continuity constraints on bezier ordinates we obtain a set of global c r smooth basis functions convergence analysis shows that isogeometric analysis with such c r rtbs basis can deliver the optimal rate of convergence provided that the c r geometric map remains unchanged during the refinement process this condition can be satisfied by constructing a pre refinement geometric map that is sufficiently smooth numerical experiments verify that optimal rates of convergence are achieved for poisson and linear elasticity problems

isogeometric analysis with bezier tetrahedra abstract this paper presents an approach for isogeometric analysis of 3d objects using rational bezier tetrahedral elements in this approach both the geometry and the physical field are represented by trivariate splines in bernstein bezier form over the tetrahedrangulation of a 3d geometry given a nurbs represented geometry either untrimmed or trimmed we first convert it to a watertight geometry represented by rational triangular bezier splines rtbs for trimmed geometries a compatible subdivision scheme is developed to guarantee the watertightness the rtbs geometry preserves exactly the original nurbs surfaces except for an interface layer between trimmed surfaces where controlled approximation occurs from the watertight rtbs geometry a bezier tetrahedral partition is generated automatically by imposing continuity constraints on bezier ordinates of the elements we obtain a set of global c r smooth basis functions and use it as the basis for analysis numerical examples demonstrate that our method achieves optimal convergence in c r spaces and can handle complicated geometries

isogeometric analysis using t splines on two patch geometries we develop optimal approximation estimates for t splines in the case of geometries obtained by gluing two standard tensor product patches we derive results both for the t spline space in the parametric domain and the mapped t nurbs in the physical one a set of numerical tests in complete accordance with the theoretical developments is also presented

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

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures