efficient sequential designs with binary data abstract a class of sequential designs for estimating the percentiles of a quantal response curve is proposed its updating rule is based on an efficient summary of all of the data available via a parametric model the logit mle version of the proposed designs can be viewed as a natural analog of the robbins monro procedure in the case of binary data it is shown to be asymptotically consistent optimal and nonparametric via its connection with the latter procedure for certain choices of initial designs the proposed method performs very well in a simulation study for sample sizes up to 35 a nonparametric sequential design via the spearman karber estimator for estimating the median is also proposed

general framework for dynamic substructuring history review and classification of techniques four decades after the development of the first dynamic substructuring techniques there is a necessity to classify the different methods in a general framework that outlines the relations between them in this paper a certain vision on substructuring methods is proposed by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept thereafter based on the dual and primal assembly of substructures a general framework for the classification of the methods is presented this framework allows us to indicate how the various classes of methods proposed along the years can be derived from a clear mathematical description of substructured problems current bottlenecks in experimental dynamic substructuring as well as solutions found in literature will also be briefly discussed

complex component mode synthesis method using hybrid coordinates for generally damped systems with local nonlinearities abstract in numerous engineering structures with local nonlinearities the nonlinear effects are usually localized and most parts of the structures behave linearly considering this a reduced order modelling technique for generally damped systems with localized nonlinearities is proposed firstly the linear parts with non proportional damping of the system is separated to form one component which can be formulated in state space and transformed into the modal coordinates using its linear vibration complex modes the residual flexibility matrix which can be formulated by using a set of equivalent higher order complex modes has been developed to improve the accuracy by capturing the effects of the neglected higher order complex modes secondly the rest regions of the system form another component behaving nonlinearly which is kept in its original form to adopt the entire set of nonlinear terms next the second order differential synthesis equation can be obtained by using compatibility conditions at the junctions in order to calculate dynamic response of the system the aforementioned synthesis equation needs to transform into the first order differential equation because of the singularity of the equivalent mass matrix finally two numerical examples are given to illustrate the effectiveness and the efficiency of the presented method

design and analysis of phase i clinical trials the phase i clinical trial is a study intended to estimate the so called maximum tolerable dose mtd of a new drug although there exists more or less a standard type of design for such trials its development has been largely ad hoc as usually implemented the trial design has no intrinsic property that provides a generally satisfactory basis for estimation of the mtd in this paper the standard design and several simple alternatives are compared with regard to the conservativeness of the design and with regard to point and interval estimation of an mtd 33rd percentile with small sample sizes using a markov chain representation we found several designs to be nearly as conservative as the standard design in terms of the proportion of patients entered at higher dose levels in monte carlo simulations two two stage designs are found to provide reduced bias in maximum likelihood estimation of the mtd in less than ideal dose response settings of the three methods considered for determining confidence intervals the delta method a method based on fieller s theorem and a likelihood ratio method none was able to provide both usefully narrow intervals and coverage probabilities close to nominal

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

bilinear modal representations for reduced order modeling of localized piecewise linear oscillators abstract a novel reduced order modeling method for vibration problems of elastic structures with localized piecewise linearity is proposed the focus is placed upon solving nonlinear forced response problems of elastic media with contact nonlinearity such as cracked structures and delaminated plates the modeling framework is based on observations of the proper orthogonal modes computed from nonlinear forced responses and their approximation by a truncated set of linear normal modes with special boundary conditions first it is shown that a set of proper orthogonal modes can form a good basis for constructing a reduced order model that can well capture the nonlinear normal modes next it is shown that the subspace spanned by the set of dominant proper orthogonal modes can be well approximated by a slightly larger set of linear normal modes with special boundary conditions these linear modes are referred to as bi linear modes and are selected by an elaborate methodology which utilizes certain similarities between the bi linear modes and approximations for the dominant proper orthogonal modes these approximations are obtained using interpolated proper orthogonal modes of smaller dimensional models the proposed method is compared with traditional reduced order modeling methods such as component mode synthesis and its advantages are discussed forced response analyses of cracked structures and delaminated plates are provided for demonstrating the accuracy and efficiency of the proposed methodology

a calculus for design of two stage adaptive procedures we propose calculus for designing two stage adaptive procedures we describe the design components that specify a two stage adaptive design define their interrelationships and demonstrate how changes in one design component effect changes in the other components our technique allows us to control many aspects of a two stage adaptive clinical trial including the type i and type ii error rates and the maximum total sample size we also conduct an anova type study to understand the effects of different components of the design specification on the performance characteristics of the design stage i components namely sample size type i error rate and type ii error rate are found to be the most influential

iterative order reduction substructuring method for dynamic condensation of finite element models animprovediterativeorder reductionmethodbasedonthestate spacemodelisproposedfornonclassicallydamped systems by fully taking into account the effect of damping on the transformation matrix by combining the original and improved iterative order reduction schemes with the substructuring scheme a new iterative order reduction substructuring method is also proposed to overcome the problem of requiring more computational resources to constructthetransformationmatrixoflarge scale finiteelementmodels theproposedmethodmaybeappliedtothe reduction problems of large scale undamped and damped finite element models with limited computer storage and high computational efficiency two numerical examples are provided to demonstrate the effectiveness of the proposed method

an interpolation based parametric reduced order model combined with component mode synthesis abstract this paper presents an efficient interpolation based parametric reduced order model with component mode synthesis the off line sampling of a large scale structural dynamic system containing many parameters requires many computations to investigate the parameter dependency of a dynamical system therefore we introduce a dynamic substructuring scheme to execute off line sampling in the subdomain level in addition we suggest discriminating the interpolation of the subsystem depending on the characteristics of each substructural mode we synthesize the substructures and we then construct a two level semi parametrized rom by reducing the degrees of freedom of the interface in the on line stage we then demonstrate the efficiency and accuracy of the present method by computing the relative eigenvalue errors and the transient responses of the system with random values for the parameters and we conduct the design optimization of large scale systems under dynamic loading conditions a comparison of the present method with the full order model and a conventional reduced order model indicates that the present method is useful in carrying out an efficient analysis and design optimization for various large scale structural dynamic systems

a general model reduction with primal assembly in structural dynamics abstract a new formulation of general model reduction in structural dynamics is presented the proposed method consists of four attributes a hybrid method combining dynamic condensation and component mode synthesis that are arguably the most popular model reduction techniques a precise model reduction taking the inertia effect into consideration primal assembly at the boundary interface of substructures and general formulations of model reduction with primal assembly comparisons of the proposed model reduction method with the conventional methods are provided as well as an efficient model reduction procedure of the proposed method in particular its advantages and performance of the proposed method are thoroughly investigated with various numerical examples

semiparametric dose finding methods summary we describe a new class of dose finding methods to be used in early phase clinical trials under some added parametric conditions the class reduces to the family of continual reassessment method crm designs under some relaxation of the underlying structure the method is equivalent to the cumulative cohort design the modified toxicity probability interval method or bayesian optimal interval design classes of methods which are non parametric in nature whereas the crm class can be viewed as being strongly parametric the class proposed is characterized as being semiparametric since it corresponds to the crm with a nuisance parameter performance is good matching that of the crm class and improving on it in some cases the structure allows theoretical questions to be more easily investigated and to understand better how different classes of methods relate to one another

an automated multilevel substructuring method for eigenspace computation in linear elastodynamics we present an automated multilevel substructuring amls method for eigenvalue computations in linear elastodynamics in a variational and algebraic setting amls first recursively partitions the domain of the pde into a hierarchy of subdomains then amls recursively generates a subspace for approximating the eigenvectors associated with the smallest eigenvalues by computing partial eigensolutions associated with the subdomains and the interfaces between them we remark that although we present amls for linear elastodynamics our formulation is abstract and applies to generic h1 elliptic bilinear forms in the variational formulation we define an interface mass operator that is consistent with the treatment of elastic properties by the familiar steklov poincare operator with this interface mass operator all of the subdomain and interface eigenvalue problems in amls become orthogonal projections of the global eigenvalue problem onto a hierarchy of subspaces convergence of amls is determined in the continuous setting by the truncation of these eigenspaces independent of other discretization schemes the goal of amls in the algebraic setting is to achieve a high level of dimensional reduction locally and inexpensively while balancing the errors associated with truncation and the finite element discretization this is accomplished by matching the mesh independent amls truncation error with the finite element discretization error our report ends with numerical experiments that demonstrate the effectiveness of amls on a model problem and an industrial problem

a comparison of model reduction techniques from structural dynamics numerical mathematics and systems and control in this paper popular model reduction techniques from the fields of structural dynamics numerical mathematics and systems and control are reviewed and compared the motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently in addition the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique on the basis of the desired objectives and properties of the model reduction problem in particular a detailed review is given on mode displacement techniques moment matching methods and balanced truncation whereas important extensions are outlined briefly in addition a qualitative comparison of these methods is presented hereby focusing both on theoretical and computational aspects finally the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example

periodic steady state response of large scale mechanical models with local nonlinearities abstract long term dynamics of a class of mechanical systems is investigated in a computationally efficient way due to geometric complexity each structural component is first discretized by applying the finite element method frequently this leads to models with a quite large number of degrees of freedom in addition the composite system may also possess nonlinear properties the method applied overcomes these difficulties by imposing a multi level substructuring procedure based on the sparsity pattern of the stiffness matrix this is necessary since the number of the resulting equations of motion can be so high that the classical coordinate reduction methods become inefficient to apply as a result the original dimension of the complete system is substantially reduced subsequently this allows the application of numerical methods which are efficient for predicting response of small scale systems in particular a systematic method is applied next leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation an appropriate continuation scheme is also applied leading to evaluation of complete branches of periodic solutions in addition the stability properties of the located motions are also determined finally respresentative sets of numerical results are presented for an internal combustion car engine and a complete city bus model where possible the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models moreover emphasis is placed in comparing results obtained by employing the nonlinear or the corresponding linearized models

using singular value decomposition of component eigenmodes for interface reduction the aim of this paper is to describe the development of a reduced order model for modal analysis in a design context the design process of most industrial systems is based on the re utilization of certain components here we propose a reduction method involving component eigenmodes to recover the modal behaviour of an assembled structure the contribution of this work is that it uses component eigenmodes to build an interface reduction basis lastly the reduction methodology proposed is compared to the craig and bampton method by applying it to two case studies of which one is an industrial model of an open rotor blade

automated multi level substructuring amls for electromagnetics abstract we present an algebraic setting of an automated multi level substructuring amls method for electromagnetic maxwell eigenproblem solution to our knowledge it is novel and it involves a non trivial generalisation of the corresponding method for elastodynamics and acoustics in comparison to the amls method for elliptic problems the electromagnetic stiffness matrix is singular it has a large kernel of gradients of h 1 conforming shape functions this difficulty was overcome by confining the method to solenoidal fields only the goal of amls is to achieve a high level of dimensional reduction inexpensively using multi level modal substructuring enabling reliable solution of huge response problems without compromising the accuracy of the quantity of interest as proof of concept we present simple numerical experiments on rectangular domains verifying a correct implementation of a truly multi level version of the generalised algorithm for real life applications the algorithm need to be equipped with automated nested mesh dissection and an algorithm for automatic subdomain eigenspace truncation finally the algorithm needs to be tuned and parallelised

a dose finding approach based on shrunken predictive probability for combinations of two agents in phase i trials we develop a novel dose finding method for two agent combination phase i trials on the basis of the shrunken predictive probability of toxicity in this method a shrinkage logistic regression model that allows distinct shrinkage multipliers for the coefficients of the main effects of two agents and their interaction on the probability of toxicity constructs the toxicity outcome we also propose dose escalation de escalation decision rules on the basis of the shrunken predictive probability of toxicity simulation studies under various patterns of monotonic dose response relationships for combinations of two agents demonstrated that the proposed method performed no worse than the existing two dose finding methods we selected copyright 2013 john wiley sons ltd

the min max algorithm and isotonic regression there is growing interest in statistical inference under order restrictions a major demand in this subject is to have a fast direct method to solve the least squares problem of partially ordered isotonic regression the min max algorithm is such a method in which the user searches for the global minimum and the local maximum successively a comparison of algorithms for partially ordered isotonic regression is included as an application using this efficient algorithm it is feasible to approximate critical values of isotonic tests by simulation

beyond automated multilevel substructuring domain decomposition with rational filtering this paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems the proposed technique is purely algebraic an

an extension of the continual reassessment method using decision theory the primary goal of a phase i trial is to find the maximally tolerated dose mtd of a treatment the mtd is usually defined in terms of a tolerable probability q of toxicity our objective is to find the highest dose with toxicity risk that does not exceed q a criterion that is often desired in designing phase i trials this criterion differs from that of finding the dose with toxicity risk closest to q that is used in methods such as the continual reassessment method we use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q among the doses under consideration the proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial it includes as an important special case the continual reassessment method numerical study indicates the strategy compares favourably with other phase i designs

multi level substructuring combined with model order reduction methods abstract in many fields of engineering problems linear time invariant dynamical systems lti systems play an outstanding role they result for instance from discretizations of the unsteady heat equation and they are also used in optimal control problems often the order of lti systems is a limiting factor since it becomes easily very large as a consequence these systems cannot be treated efficiently without model reduction algorithms in this paper a new approach for the combination of model order reduction methods and recent multi level substructuring mls techniques is presented similar multi level substructuring methods have already been applied successfully to huge eigenvalue problems up to several millions of degrees of freedom however the presented approach does not make use of a modal analysis like former algorithms instead the original system is decomposed in smaller lti systems which are treated with recent model reduction methods furthermore the error which is induced by this substructuring approach is analysed and numerical examples based on the oberwolfach benchmark collection are given in this paper

adaptive component mode synthesis in linear elasticity component mode synthesis cms is a classical method for the reduction of large scale finite element models in linear elasticity in this paper we develop a methodology for adaptive refinement of c

dose finding using the biased coin up and down design and isotonic regression we are interested in finding a dose that has a prespecified toxicity rate in the target population in this article we investigate five estimators of the target dose to be used with the up and down biased coin design bcd introduced by durham and flournoy 1994 statistical decision theory and related topics these estimators are derived using maximum likelihood weighted least squares sample averages and isotonic regression a linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied

incorporating toxicity considerations into the design of two stage phase ii clinical trials phase ii study designs are proposed that evaluate both clinical response and toxicity and that are similar in structure to simon s two stage designs sample sizes and decision criteria are chosen to minimize the maximum expected accrual given that the treatment is unacceptable either in terms of clinical response or toxicity this is achieved subject to control of error rates either uniformly over all possible correlation structures linking response and toxicity or alternatively under an assumption of independence between response and toxicity in the latter case bounds on the error rates show that effective control is still uniformly achieved even if the independence assumption is relaxed

mathcal h h matrix approximability of the inverses of fem matrices we study the question of approximability for the inverse of the fem stiffness matrix for scalar second order elliptic boundary value problems by blockwise low rank matrices such as those given by the mathcal h h matrix format introduced by hackbusch computing 62 2 89 108 1999 we show that exponential convergence in the local block rank r r can be achieved we also show that exponentially accurate lu lu decompositions in the mathcal h h matrix format are possible for the stiffness matrices arising in the fem our analysis avoids any coupling of the block rank r r to the mesh width h h we also cover fairly general boundary conditions of mixed dirichlet neumann robin boundary conditions

considering the higher order effect of residual modes in the craig bampton method in this paper the accuracy of the craig bampton method one of the most widely used component mode synthesis methods is improved considering the higher order effect of residual modes that are si

a dynamic condensation method using algebraic substructuring summary in this paper we develop a robust reduced order modeling method named algebraic dynamic condensation which is based on the improved reduced system irs method using algebraic substructuring the global mass and stiffness matrices are divided into many small submatrices without considering the physical domain and substructures and interface boundary are defined in the algebraic perspective the reduced model is then constructed using three additional procedures substructural stiffness condensation interface boundary reduction and substructural inertial effect condensation the formulation of the reduced model is simply expressed at a submatrix level without using a transformation matrix that induces huge computational cost through various numerical examples the performance of the proposed method is demonstrated in terms of accuracy and computational cost

novel modal methods for transient analysis with a reduced order model based on enhanced craig bampton formulation abstract for transient analysis of structural dynamics with reduced order model rom data recovery procedures that use modal methods such as the classical mode acceleration ma and modal displacement md methods are an important step in order to increase the convergence and accuracy of the solution in this work we propose novel ma and md methods for highly accurate transient analysis with a reduced order model based on enhanced craig bampton ecb formulation which is an extension of the classical craig bampton cb method that is a way to reduce the size of a finite element fe model the performance of the proposed data recovery approach is demonstrated with two numerical examples we also investigate the relation between the proposed and classical ma and md methods

a real decoupled method and free interface component mode synthesis methods for generally damped systems this paper reports on the development of a new transformation method in contrast to most existing mode transformation methods in which the first order state space equation of the damped vibration system is transformed into a decoupled form with complex coefficient matrices using the decoupled method presented in this paper the equation of the damped system can be decomposed into a decoupled equation with real coefficient matrices two new free interface component mode synthesis methods are also presented the equivalent full mode matrix of the damped structure is used to capture the effects of the higher order modes additionally this work modifies the compatibility conditions at the junctions that are employed in most of the previous component mode synthesis methods for generally damped systems the first component mode synthesis method is performed in complex space whereas the second method can be applied in real space because the coefficient matrices of the coupled equation constructed by the second component mode synthesis method are all real valued the solution of the eigenproblem for this coupled equation can be performed in real space as well additionally numerical examples demonstrate the accuracy and validity of these two component mode synthesis methods

stochastic reduction of loss in estimating normal means by isotonic regression cf barlow bartholomew bremner and brunk 1972 page 19 the estimator fi has been compared to the unrestricted estimator y and several results point to the superiority of the isotonic regression estimator when the order restriction holds it has been shown cf robertson wright and dykstra 1988 that the total error of the estimator is reduced through isotonic regression on any order restriction in the sense that

a component mode selection method based on a consistent perturbation expansion of interface displacement abstract a mode selection method is presented for the reduced order modeling rom of structural systems in conjunction with the craig bampton component mode synthesis technique the proposed method is derived by using a consistent expansion of the interface displacement in terms of a frequency dependent small parameter as applied to a craig bampton like rom formulation it is found that this procedure yields a coupling mechanism of the modes of the full model to those of substructures the present mode selection method employs this coupling mechanism as an indicator labeled as the cms method for the substructural modal contributions to the full model the performance of the proposed method is demonstrated by various numerical examples and compared favorably with existing method such as the cms method

a design for phase i trials in completely or partially ordered groups we propose a design for dose finding for cytotoxic agents in completely or partially ordered groups of patients by completely ordered groups we mean that prior to the study there is clinical information that would indicate that for a given dose the groups can be ordered with respect to the probability of toxicity at that dose with partially ordered groups at a given dose only some of the groups can be ordered with respect to the probability of toxicity at that dose the method we propose includes elements of the parametric model used in the continual reassessment method combined with the hwang peddada order restricted estimation procedure we evaluate the operating characteristics of these designs in a family of dose toxicity curves representing complete and partial orders copyright 2017 john wiley sons ltd

a family of craig bampton methods considering residual mode compensation abstract in this paper we investigate the formulation of a family of craig bampton cb methods considering residual modes by o callahan s approximation and adding generalized coordinate vectors containing unknown eigenvalues in addition we propose an nth order higher order cb hcbn method for compensating the n 1 th residual flexibility in the nth order hcb hcbn method by o callahan s approach therefore various cb methods with improved performance such as the enhanced craig bampton ecb method which uses o callahan s approximation and the higher order craig bampton hcb method which adds generalized coordinate vectors and hcb are employed for the comparison of performance with the aid of multiprecision computing through three benchmark examples it is revealed that the hcb1 method a modified version of the first order hcb method hcb1 with the aid of o callahan s approximation proposed shows better performance than hcb1 with the same number of retained modes however hcb2 and hcb3 modified versions of the second and third order hcb method respectively cannot be improved further from the results we concluded that this was due to the limitation of o callahan s approach which many researchers have fundamentally questioned

small sample confidence sets for the mtd in a phase i clinical trial properties of procedures for interval estimation of the maximum tolerable dose mtd in a phase i clinical trial are examined using a two stage stochastic sampling scheme storer 1989 as a paradigm for development although the likelihood function for the data arising from such a scheme is identical to one arising under a conditional binomial sampling assumption intervals based on the exact distribution of the usual large sample statistics under this assumption do not offer improvement over unadjusted intervals however consideration of the distribution of these statistics based on the true stochastic sampling scheme can lead to the construction of intervals with correct coverage probabilities that do not depend on the true values of the model parameters membership in the confidence set can be evaluated by monte carlo simulation at a restricted maximum likelihood estimate of the nuisance slope parameter despite upward bias in its estimation from the up and down sampling scheme the lack of information in the small sample setting is reflected in a large proportion of confidence intervals that include infinite values for the mtd especially when the dose response curve is shallow intervals based on a likelihood ratio criterion perform best in this regard

billiards with pesin region of measure one we give a description of a large class of plane billiards with pesin region of measure one open conditions including properly those founded by wojtkowski w1 forc4 focusing boundaries are obtained lyapunov s forms introduced by lewowicz are used

analysis and comparison of several component mode synthesis methods on one dimensional domains component mode synthesis methods enable to compute the eigenpairs of a differential operator on a domain that can be subdivided in different subdomains on each of which the eigenpairs of the same operator are assumed to be partially known error estimates are given for several of these methods applied to second order elliptic operators on one dimensional domains they are partly tied to an argument which is called here asymptotic hidden regularity of eigenfunctions of an elliptic operator

bayesian model averaging continual reassessment method in phase i clinical trials the continual reassessment method crm is a popular dose finding design for phase i clinical trials this method requires that practitioners prespecify the toxicity probability at each dose such prespecification can be arbitrary and different specifications of toxicity probabilities may lead to very different design properties to overcome the arbitrariness and further enhance the robustness of the design we propose using multiple parallel crm models each with a different set of prespecified toxicity probabilities in the bayesian paradigm we assign a discrete probability mass to each crm model as the prior model probability the posterior probabilities of toxicity can be estimated by the bayesian model averaging bma approach dose escalation or deescalation is determined by comparing the target toxicity rate and the bma estimates of the dose toxicity probabilities we examine the properties of the bma crm approach through extensive simulation studies and also compare this new method and its vari

a posteriori error analysis of component mode synthesis for the elliptic eigenvalue problem we develop a posteriori error estimates for the error associated with model reduction of elliptic eigenvalue problems using component mode synthesis cms the estimates reflect to what degree each cms subspace influence the overall error in the reduced solution this allows for automatic error control through adaptive algorithms that determine suitable dimensions of each cms subspace

characterization of the likelihood continual reassessment method this paper deals with the design of the likelihood continual reassessment method which is an increasingly widely used model based method for dose finding studies it is common to implement the method in a two stage approach whereby the model based stage is activated after an initial sequence of patients has been treated while this two stage approach is practically appealing it lacks a theoretical framework and it is often unclear how the design components should be specified this paper develops a general framework based on the coherence principle from which we derive a design calibration process a real clinical trial example is used to demonstrate that the proposed process can be implemented in a timely and reproducible manner while offering competitive operating characteristics we explore the operating characteristics of different models within this framework and show the performance to be insensitive to the choice of dose toxicity model

principles for the design of billiards with nonvanishing lyapunov exponents we introduce a large class of billiards with convex pieces of the boundary which have nonvanishing lyapunov exponents

an algebraic substructuring method for large scale eigenvalue calculation this paper is concerned with solving large scale eigenvalue problems by algebraic substructuring algebraic substructuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem through an algebraic analysis we identify critical conditions under which a simple version of algebraic substructuring works well this particular version of substructuring is identical to the component mode synthesis cms method see r r craig and m c c bampton em coupling of substructures for dynamic analysis aiaa j 6 1968 pp 1313 1319 and w c hurty em vibrations of structure systems by component mode synthesis j engrg mech 86 1960 pp 51 69 when the matrix reordering is based on a geometric partitioning of the computational domain we observe an interesting connection between the accuracy of an approximate eigenpair obtained through substructuring and the distribution of the components of eigenvectors of a canonical matrix pencil congruent to the original problem a priori error bounds for the smallest eigenpair approximation are developed this development leads to a simple heuristic for choosing spectral components modes from each substructure the effectiveness of such a heuristic is demonstrated with numerical examples we show that algebraic substructuring can be effectively used to solve a generalized eigenvalue problem arising from the finite element analysis of an accelerator structure

interval estimation of the median lethal dose summary assuming a logistic dose response curve one can construct a confidence interval for the ld50 from the asymptotic likelihood ratio test reasons are given for preferring this likelihood ratio interval to the established interval calculated by applying fieller s theorem to the maximum likelihood estimates

on the use of modal derivatives for nonlinear model order reduction summary modal derivative is an approach to compute a reduced basis for model order reduction of large scale nonlinear systems that typically stem from the discretization of partial differential equations in this way a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller based on the resulting small scale state space model we investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction which has been missing so far concentrating on the application field of structural mechanics and structural dynamics we show that the concept of modal derivatives can also be applied as nonlinear extension of the craig bampton family of methods for substructuring we furthermore generalize the approach from a pure projection scheme to a novel reduced order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables this complexity reduction leads to a frequency preserving nonlinear quadratic state space model numerical examples with carefully chosen nonlinear model problems and three dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods along with the current limitations copyright 2016 john wiley sons ltd

sequential implementation of stepwise procedures for identifying the maximum tolerated dose this article considers the problem of finding the maximum tolerated dose mtd of a drug in human trials the mtd is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate we adopt the multiple test framework with step down tests used in an escalation stage and step up tests used in a deescalation stage to allow sequential dose assignments for ethical purposes by formulating the estimation problem as a testing problem the proposed procedures formally control the error probability of selecting an unsafe dose in addition we can control the probability of correctly selecting the mtd under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate the so called indifference zone this frequentist property which is currently lacking in the conduct of dose finding trials in humans is appealing from a regulatory standpoint we give the general expressions of the se

bayesian dose finding in phase i ii clinical trials using toxicity and efficacy odds ratios a bayesian adaptive design is proposed for dose finding in phase i ii clinical trials to incorporate the bivariate outcomes toxicity and efficacy of a new treatment without specifying any parametric functional form for the drug dose response curve we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy after observing all the responses of each cohort of patients the dosage for the next cohort is escalated deescalated or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities a novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes we conduct simulation studies to evaluate the operating characteristics of the proposed method under various scenarios the new bayesian design based on the toxicity efficacy odds ratio trade offs exhibits good properties and treats most patients at the desirable dose levels the method is illustrated with a real trial design for a breast medical oncology study

markov chain modelling of bioassay toxicity procedures many bioassay procedures to test a new substance for toxicity like some phase i clinical trials can be modelled as first order markov chains with absorbing states we provide a general framework for such procedures we show how one may calculate under any dose response curve assumption final absorption probabilities and a number of total average costs such as time required until trial completion number of subjects treated number of subjects exhibiting unaceptable levels of toxicity and amount of medication administered one may use the above information associated with the trial for an a priori comparison between competing designs under consideration we provide an example of such a comparison

iterative method for dynamic condensation combined with substructuring scheme an iterated improved reduced system iirs procedure combined with substructuring scheme for both undamped and nonclassically damped structures is presented iterated iirs method is an efficient reduction technique because the highly accurate eigenproperties from the repeatedly updated condensed matrices can be obtained without consuming expensive computational cost however single domain direct approach of this method to large structures requires much computational resources and even makes analysis intractable in the case only limited computer storage is available these problems can be overcome by combining the substructuring scheme with iirs procedure the newly developed iirs method combined with a substructuring scheme can provide an efficient methodology for large scale eigenvalue problems the validation of the present method and the evaluation of computational efficiency are demonstrated through the numerical examples

on correction equations and domain decomposition for computing invariant subspaces by considering the eigenvalue problem as a system of nonlinear equations it is possible to develop a number of solution schemes which are related to the newton iteration for example to compute eigenvalues and eigenvectors of an n n matrix a the davidson and the jacobi davidson techniques construct good basis vectors by approximately solving a correction equation which provides a correction to be added to the current approximation of the sought eigenvector that equation is a linear system with the residual r of the approximated eigenvector as right hand side one of the goals of this paper is to extend this general technique to the block situation i e the case where a set of p approximate eigenpairs is available in which case the residual r becomes an n p matrix as will be seen solving the correction equation in block form requires solving a sylvester system of equations the paper will define two algorithms based on this approach for symmetric real matrices the first algorithm converges quadratically and the second cubically a second goal of the paper is to consider the class of substructuring methods such as the component mode synthesis cms and the automatic multi level substructuring amls methods and to view them from the angle of the block correction equation in particular this viewpoint allows us to define an iterative version of well known one level substructuring algorithms cms or one level amls experiments are reported to illustrate the convergence behavior of these methods 2006 published by elsevier b v

the estimation of extreme quantiles in logit bioassay summary suppose that we administer a low dose of a drug and if no response is observed increase this dose by a fixed amount which is administered to a second experimental subject this procedure continues until at some dose level a response is finally observed this whole sequence may be repeated we investigate the features of an experimental design of this kind for estimating the dose at which the expected response is small this design is highly efficient when the number of responses e g deaths is considered the major portion of the cost of the study and various alternatives having some advantage over maximum likelihood estimation are suggested

computation of smallest eigenvalues using spectral schur complements the automated multilevel substructuring method amls was recently presented as an alternative to well established methods for computing eigenvalues of large matrices in the context of structural engineering this technique is based on exploiting a high level of dimensional reduction via domain decomposition and projection methods this paper takes a purely algebraic look at the method and explains that it can be viewed as a combination of three ingredients a a first order expansion to a nonlinear eigenvalue problem that approximates the restriction of the original eigenproblem on the interface between the subdomains b judicious projections on partial eigenbases that correspond to the interior of the subdomains c recursivity this viewpoint leads us to explore variants of the method which use krylov subspaces instead of eigenbases to construct subspaces of approximants the nonlinear eigenvalue problem viewpoint yields a second order approximation as an enhancement to the first order technique inherent to amls numerical experiments are reported to validate the approaches presented

assessment of reduced models for the detection of modal interaction through rotor stator contacts interactions through direct contact between blade tips and outer casings in modern turbomachines require complex formulations and subsequent expensive computational efforts when the classical finite element method is considered the construction of reduced order models through component mode synthesis techniques usually improves the computational efficiency and may be used for fast parameter studies yielding a better knowledge of the phenomena of interest in this highly nonlinear framework the present study is dedicated to the investigation of the capabilities of fixed and free interface reduction strategies to handle accurately such problems through a realistic 2d model and complements former results involving a direct modal projection with respective strong kinematic restrictions the equations of motion are solved using an explicit time integration scheme together with the lagrange multiplier method where friction is accounted for the presented work discusses the notions of both displacement and motion convergences and the possibility to conduct fast parameter studies with the use of relevant reduction bases it also shows that kinematic restrictions artificially enhance the detection of modal interactions

designs for single or multiple agent phase i trials phase i trials of cytotoxic agents in oncology are usually dose finding studies that involve a single cytotoxic agent many statistical methods have been proposed for these trials all of which are based on the assumption of a monotonic dose toxicity curve for single agent trials this is a valid assumption in many trials however investigators are interested in finding the maximally tolerated dose based on escalating multiple cytotoxic agents when there are multiple agents monotonicity of the dose toxicity curve is not clearly defined in this article we present a design for phase i trials in which the toxicity probabilities follow a partial order meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial we compare the new design to existing methods for simple orders and investigate the properties of the design for two partial orders

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

a dual craig bampton method for dynamic substructuring a novel component mode synthesis method for dynamic analysis of structures is presented it is based on free interface vibration modes and residual flexibility components although the ingredients are the same as in previously published procedures e g macneal or rubin our method is fundamentally different in that it assembles the substructures using interface forces dual assembly and enforces only weak interface compatibility the new formulation is based on a fully consistent reduction approach and the reduced matrices so obtained are exactly dual to the craig bampton reduced matrices the new free interface substructuring method proposed here is thus more natural then classical free interface synthesis procedures and leads to simpler reduced matrices we illustrate the efficiency of the dual craig bampton approach for reducing the dynamical representation on a three dimensional frame

a nodeless dual superelement formulation for structural and multibody dynamics application to reduction of contact problems summary a nodeless superelement formulation based on dual component mode synthesis is proposed in which the superelement dynamic behavior is described in terms of modal intensities playing the role of intrinsic variables a computational scheme is proposed to build an orthogonal set of static modes so that the system matrices can have a diagonal or nearly diagonal form providing thus high computational efficiency for application in the context of structural dynamics as well as flexible multibody dynamics connection to adjacent components is expressed through kinematic relationships between intrinsic variables and local displacements the efficiency of the method is demonstrated on a simple example involving multiple unilateral contact copyright 2015 john wiley sons ltd

consistency of continual reassessment method under model misspecification summary this paper studies large sample behaviour of the continual reassessment method used to determine the target dose levels in phase i clinical trials a sequential maximum likelihood procedure is investigated for local estimation of a given targeted toxicity level consistency and asymptotic normality for the maximum likelihood estimates are established under model misspecification and it is shown that in general the recommended dose level will converge to the target level there are however situations in which the recommended dose may converge to a level close to the target level but not necessarily the closest this contrasts with the conclusions of o quigley pepe fisher 1990 and we describe this situation as well as providing the conditions under which convergence is assured

using integrability to produce chaos billiards with positive entropy a new open class of convex 2 dimensional planar billiards with positive lyapunov exponent almost everywhere is constructed we introduce the notion of a focusing arc and show that such arcs can be used to build billiard systems with positive lyapunov exponents we prove that under smallc6 perturbations focusing arcs remain focusing and thereby show that perturbations of the bunimovich stadium billiard have positive lyapunov exponents

confidence interval estimation subject to order restrictions this article deals with the construction of confidence intervals when the components of the location parameter mu of the random variable mathbf x which is elliptically symmetrically distributed are subject to order restrictions several domination results are proved by studying the derivative of the coverage probability of the confidence intervals centered at the improved point estimators consequently we strengthen the previously known results regarding the simple ordering and obtain several new results for other general forms of order restrictions including the simple tree ordering the umbrella ordering the simple and the double loop ordering and some combination of these these domination results are obtained under the assumption that sigma is a diagonal matrix when sigma is nondiagonal some new intervals are introduced which dominate the standard intervals centered at the unrestricted maximum likelihood estimator for various types of order restrictions similar results are obtained for scale parameters as well contrary to the location problems in case of the scale parameters satisfying the simple ordering we find that the restricted maximum likelihood estimator of the largest parameter fails to universally dominate the unrestricted maximum likelihood estimator a similar negative result is noted for simple tree order restriction

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

on the bernoulli property of planar hyperbolic billiards we consider billiards in non polygonal domains of the plane with boundary consisting of curves of three different types straight segments strictly convex inward curves and strictly convex outward curves of a special kind the billiard map for these domains is known to have non vanishing lyapunov exponents a e provided that the distance between the curved components of the boundary is sufficiently large and the set of orbits having collisions only with the flat part of the boundary has zero measure under a few additional conditions we prove that there exists a full measure set of the billiard phase space such that each of its points has a neighborhood contained up to a zero measure set in one bernoulli component of the billiard map using this result we show that there exists a large class of planar hyperbolic billiards that have the bernoulli property this class includes the billiards in convex domains bounded by straight segments and strictly convex inward arcs constructed by donnay

a two stage hybrid procedure for estimating an inverse regression function we consider a two stage procedure tsp for estimating an inverse regression function at a given point where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two we establish that the convergence rate of the second stage estimate can attain the parametric n 1 2 rate furthermore a bootstrapped variant of tsp btsp is introduced and its consistency properties studied this variant manages to overcome the slow speed of the convergence in distribution and the estimation of the derivative of the regression function at the unknown target quantity finally the finite sample performance of btsp is studied through simulations and the method is illustrated on a data set

subcomponent modelling of input parameters for statistical energy analysis by using a wave based boundary condition this paper presents a new and efficient method to calculate point mobilities from subcomponents of a full structure subcomponent modelling is a commonly used method to gain information on the dynamic behaviour of complex assembly structures using smaller and more efficient models for instance point mobility calculations on subcomponent level are used to obtain more accurate input parameters for statistical energy analysis sea models a full system analysis is often too computationally expensive so normally only individual subcomponents of the structure are extracted and analysed this procedure yields a large reduction in computational effort but also often results in a substantial loss of accuracy this is due to the use of an approximation of boundary conditions to represent the eliminated remainder part of the structure i e the full structure except the subcomponent at hand commonly these boundary conditions are simplified by assuming clamped free or simply supported edges however this is a huge simplification and may introduce large errors especially in the low and mid frequency ranges earlier work has shown that a more accurate description of the boundary conditions can be achieved by describing the interface dynamics by a combination of so called dynamic waves in this paper the method is developed further and a more robust and efficient wave extraction procedure is presented an industrial body in white biw is used as a test case and results are presented for three different cases the results show that the wave based boundary condition for point impedance calculations from a subcomponent model gives more accurate results than the results obtained with free or clamped boundary conditions

the important modes of subsystems a moment matching approach substructure coupling methods such as the component mode synthesis cms method have been studied in structural dynamics analysis since 1960s the modes of subsystems associated with the lowest frequencies are typically retained in these methods in this paper we present a coupling matrix based mode selection scheme for the cms method referred to as the cms method this new scheme is derived using a moment matching principle defined on the interface between substructures it is compatible to the one in recently proposed optimal modal reduction omr method due to givoli et al the improvements of the cms method to the cms and omr methods are demonstrated by numerical examples from structural dynamics in both frequency and time domains copyright 2006 john wiley sons ltd

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

heterogeneity in phase i clinical trials prior elicitation and computation using the continual reassessment method heterogeneity in a phase i clinical trial patient population may lead to distinctly different dose response relationships along covariate values for a given target probability of toxicity this implies different maximum tolerated doses mtds for each distinct subpopulation within the framework of o quigley pepe and fisher s 1990 continual reassessment method we propose the notion of average and patient specific mtds by augmenting the dose response model with other covariates to account for such differences a method to elicit prior distributions on the dose and other covariate parameters are proposed based on the predictive approach of ibrahim and laud 1994 laud and ibrahim 1995 and ibrahim ryan and chen 1998 this approach relies on prior predictions for the response vector y 0 and a quantity a 0 specifying uncertainty in y 0 then y 0 and a 0 are used to specify a prior for the regression coefficients in a semi automatic fashion the elicitation scheme for y 0 uses results from previous phase i cancer clinical trials the average and patient specific mtds and an elicitation method are demonstrated in logistic regression examples

hyperbolic billiards with nearly flat focusing boundaries i abstract the standard wojtkowski markarian donnay bunimovich technique for the hyperbolicity of focusing or mixed billiards in the plane requires the diameter of a billiard table to be of the same order as the largest ray of curvature along the focusing boundary this is due to the physical principle that is used in the proofs the so called defocusing mechanism of geometrical optics in this paper we construct examples of hyperbolic billiards with a focusing boundary component of arbitrarily small curvature whose diameter is bounded by a constant independent of that curvature our proof employs a nonstandard cone bundle that does not solely use the familiar dispersing and defocusing mechanisms

a random walk rule for phase i clinical trials we describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose response study or phase i clinical trial patients are sequentially assigned the next higher same or next lower dose level according to some probability distribution which may be determined by ethical considerations as well as the patient s response it is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest estimation of the quantile is discussed the maximum likelihood estimator and its variance are derived under a two parameter logistic distribution and the maximum likelihood estimator is compared with other nonparametric estimators random walk rules have clear advantages they are simple to implement and finite and asymptotic distribution theory is completely worked out for a specific random walk rule we compute finite and asymptotic properties and give examples of its use in planning studies having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design the small sample properties of our rule as determined by exact theory compare favorably to those of the continual reassessment method determined by simulation

high fidelity flexibility based component mode synthesis method with interface degrees of freedom reduction the partitioned structural equations of motion via the method of localized lagrange multipliers palm consist of internal and interface variables the model reduction achieved based on palm is called flexibility based component mode synthesis f cms and it thus far has concentrated on reducing the internal degrees of freedom dofs or reducing the internal and interface dofs at once in this work well defined three level reduction formulations of the f cms method are proposed for better precision internal dofs the localized lagrange multipliers and the interface boundary displacement the proposed formulations include three different reduction techniques for the interface boundary displacement for better computational efficiency numerical experiments indicate that the proposed formulations can substantially reduce the overall reduced order models further without compromising the accuracy thus achieving a substantial additional reduction of computational cost compared with the previous works in a

focusing components in typical chaotic billiards should be absolutely focusing we demonstrate that the defocusing mechanism fails to work if not all focusing components of the boundary are absolutely focusing more precisely we construct billiard tables with arbitrary long free path away from a non absolutely focusing component such that a nonlinearly stable periodic orbit exists therefore the only known standard procedure of constructing chaotic ergodic billiards works in general only if all focusing boundary components are absolutely focusing

an iterative substructuring approach to the calculation of eigensolution and eigensensitivity the eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level which is time consuming or even prohibitive for large scale structures several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure however these approaches are not usually accurate as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded in this paper a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures with this new approach the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results the eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration upon convergence the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly the computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super tall structure

many dimensional nowhere dispersing billiards with chaotic behavior abstract we consider some examples of domains in the d dimensional euclidean space d 3 that generate billiards with chaotic behavior time correlations in these billiards tend to zero in the limit t the rate of decay of the correlations is a power law for billiards in discrete time and could be a power law or quasiexponential for billiards with continuous time

stochastic non convex envelopment of data applying isotonic regression to frontier estimation abstract isotonic nonparametric least squares inls is a regression method for estimating a monotonic function by fitting a step function to data in the literature of frontier estimation the free disposal hull fdh method is similarly based on the minimal assumption of monotonicity in this paper we link these two separately developed nonparametric methods by showing that fdh is a sign constrained variant of inls we also discuss the connections to related methods such as data envelopment analysis dea and convex nonparametric least squares cnls further we examine alternative ways of applying isotonic regression to frontier estimation analogous to corrected and modified ordinary least squares cols mols methods known in the parametric stream of frontier literature we find that inls is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings in the absence of noise the corrected inls cinls has a higher discriminating power than fdh in the case of noisy data we propose to apply the method of non convex stochastic envelopment of data non convex stoned which disentangles inefficiency from noise based on the skewness of the inls residuals the proposed methods are illustrated by means of simulated examples

generalized methodology for assembly and reduction of component models for dynamic substructuring a classic issue in component mode synthesis methods is the choice for fixed or free boundary conditions at the interface degrees of freedom and the associated vibration modes in the component s reduction basis closely related is the aspect of substructure assembly in this paper a general approach to mixed boundary component mode synthesis problems is proposed by considering component reduction and assembly separately first a general framework for substructure assembly is presented enabling assembly of all types of reduced component models regardless of their interface conditions thereafter a general mixed boundary component mode synthesis method called the mixed craig bampton method is introduced the method is derived by dividing the substructure degrees of freedom into a set of internal degrees of freedom free interface degrees of freedom and fixed interface degrees of freedom using a simple but effective selection scheme based on this selection a reduction basis is computed consisting of vibration modes constraint modes and residual flexibility modes which leads to relatively sparse reduced matrices as such the mixed craig bampton method forms a natural generalization of the classic craig bampton and more recent dual craig bampton methods finally the method is applied to a test problem revealing that the proposed method has comparable or better accuracy and superior versatility with respect to existing methods

bivariate isotonic design for dose finding with ordered groups we consider the problem of dose finding where subjects can be stratified into two populations with possibly different susceptibility to toxicity the goal is to find the maximally tolerated dose for each population we propose a non parametric design for this problem toxicity is estimated using the bivariate isotonic regression estimator the new design is compared with the two sample continual reassessment method