a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

symplectic methods for the nonlinear schrodinger equation abstract in this paper we show that the spatial discretization of the nonlinear schrodinger equation leads to a hamiltonian system which can be simulated with symplectic numerical schemes in particular we apply two symplectic integrators to the nonlinear schrodinger equation and we demonstrate that they are able to produce accurate results and to preserve very well the invariants of the original system such as the energy and charge

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

large scale topology optimization using preconditioned krylov subspace methods with recycling summary the computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis we propose fast iterative solvers for large threedimensional topology optimization problems to address this problem since the linear systems in the sequence of optimization steps change slowly from one step to the next we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems in addition we introduce a minres minimum residual method version with recycling and a short term recurrence to make recycling more efficient for symmetric problems furthermore we discuss preconditioning to ensure fast convergence we show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density we demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast pc

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

finite difference solutions of a non linear schrodinger equation abstract this paper describes a finite difference method to approximate a schrodinger equation with a power non linearity a special case of this equation is currently used to model the propagation of a laser beam in a plasma the main feature of the method we present is that it satisfies a discrete analogue of some important conservation laws of the equations we present numerical results which show in particular the propagation and the formation of solitions in the one dimensional case

numerical simulation of nonlinear schro dinger systems a new conservative scheme we present a new numerical scheme for nonlinear schrodinger type equations the scheme conserves the energy and charge of the systems and it is linearly implicit numerical experiments for several physical problems show that our scheme is stable accurate and efficient

an enhanced genetic algorithm for structural topology optimization genetic algorithms gas have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures in this paper a versatile robust and enhanced ga is proposed for structural topology optimization by using problem specific knowledge the original discrete black and white 0 1 problem is directly solved by using a bit array representation method to address the related pronounced connectivity issue effectively the four neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns a simpler version of the perimeter control approach is developed to obtain a well posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge free design to handle the problem of representation degeneracy effectively a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner an efficient fem based function evaluation method is developed to reduce the computational cost a dynamic penalty method is presented for the ga to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy with all these enhancements and appropriate choice of the ga operators the present ga can achieve significant improvements in evolving into near optimum solutions and viable topologies with checkerboard free mesh independent and hinge free characteristics numerical results show that the present ga can be more efficient and robust than the conventional gas in solving the structural topology optimization problems of minimum compliance design minimum weight design and optimal compliant mechanisms design it is suggested that the present enhanced ga using problem specific knowledge can be a powerful global search tool for structural topology optimization copyright 2005 john wiley sons ltd

a general class of bayesian survival models with zero and nonzero cure fractions we propose a new class of survival models which naturally links a family of proper and improper population survival functions the models resulting in improper survival functions are often referred to as cure rate models this class of regression models is formulated through the box cox transformation on the population hazard function and a proper density function by adding an extra transformation parameter into the cure rate model we are able to generate models with a zero cure rate thus leading to a proper population survival function a graphical illustration of the behavior and the influence of the transformation parameter on the regression model is provided we consider a bayesian approach which is motivated by the complexity of the model prior specification needs to accommodate parameter constraints due to the non negativity of the survival function moreover the likelihood function involves a complicated integral on the survival function which may not have an analytical closed form and thus makes the implementation of gibbs sampling more difficult we propose an efficient markov chain monte carlo computational scheme based on gaussian quadrature the proposed method is illustrated with an example involving a melanoma clinical trial

pseudo spectral solution of nonlinear schro dinger equations abstract we compare four pseudo spectral split step methods for solving a class of nonlinear schrodinger nls equations the importance of observing the l 2 invariance of the continuous problem is demonstrated through numerical experiments the best performance is obtained by transforming the given equation to an nls equation where two of the coefficients satisfy a simple algebraic relationship the problem can be solved efficiently in terms of the new variables and the l 2 norm of the computed solution is time invariant

finite element approximation for 2nd order elliptic eigenvalue problems with nonlocal boundary or transition conditions in this paper we use two symplectic schemes to simulate the ablowitz ladik model associated to the cubic nonlinear schrodinger equation and we compare them with nonsymplectic methods

a quadratic b spline finite element method for solving nonlinear schrodinger equation a numerical solution of the nonlinear schrodinger nls equation is obtained by using the quadratic b spline finite element method test problems concerning motion birth and bound states of solitons of the nlg equation are studied to evaluate the method results are compared with various numerical methods

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

a flexible family of transformation cure rate models in this paper we introduce a flexible family of cure rate models mainly motivated by the biological derivation of the classical promotion time cure rate model and assuming that a metastasis competent tumor cell produces a detectable tumor mass only when a specific number of distinct biological factors affect the cell special cases of the new model are among others the promotion time proportional hazards the geometric proportional odds and the negative binomial cure rate model in addition our model generalizes specific families of transformation cure rate models and some well studied destructive cure rate models exact likelihood inference is carried out by the aid of the expectation maximization algorithm a profile likelihood approach is exploited for estimating the parameters of the model while model discrimination problem is analyzed by the aid of the likelihood ratio test a simulation study demonstrates the accuracy of the proposed inferential method finally as an illustration we fit the proposed model to a cutaneous melanoma data set copyright 2017 john wiley sons ltd

design space optimization using a numerical design continuation method summary a generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed in conventional optimization only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted a design space is speci9ed by the number of design variables and the layout or con9guration to solve this type of design space problems a simple initial design space is selected and gradually improved while the usual design variables are being optimized to make the design space evolve into a better one one may increase the number of design variables but in this transition there are discontinuities in the objective and constraint functions accordingly the sensitivity analysis methods based on continuity will not apply to this discontinuous stage to overcome the di culties a numerical continuation scheme is proposed based on a new concept of a pivot phase design space two new categories of structural optimization problems are formulated and concrete examples shown copyright 2001 john wiley sons ltd

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

numerical methods for the simulation of trapped nonlinear schrodinger systems we propose analyze and compare the efficiency and accuracy of different numerical schemes for the solution of the nonlinear schrodinger equation with a trapping potential in particular we study schemes of finite difference pseudospectral and spectral types for the space discretization together with explicit symplectic multistep split step and standard variable step integrators to solve the time evolution all of these schemes are evaluated comparatively and some recommendations based on their accuracy and computational efficiency are made

a linear rank test for use when the main interest is in differences in cure rates for diseases with a positive probability of being cured a family of alternatives to the null hypothesis of equality of survival distributions is introduced which is designed to focus power against alternatives with differences in cure rates the optimal linear rank test for this alternative is derived and found to be substantially more efficient than the log rank test for this alternative when cure rates are less than 50 while there is little difference between the tests if the cure rates are 50 or greater the simple test based on the difference of kaplan meier estimates of the proportion cured is also examined and found to be fully efficient for this alternative with no censoring while its efficiency rapidly drops as censoring is increased the new test is not a pure test of equality of cure rates when the data are censored but rather is a test of equality of survival distributions that focuses power against late differences in the survival curves

a proportional hazards model taking account of long term survivors a proportional hazards ph model is modified to take account of long term survivors by assuming the cumulative hazard to be bounded but otherwise unspecified to yield an improper survival function a marginal likelihood is derived under the restriction for type i censoring patterns for a ph model with cure the marginal and the partial likelihood are not the same in the absence of covariate information the estimate of the cure rate based on the marginal likelihood reduces to the value of the kaplan meier estimate at the end of the study an example of low asymptotic efficiency of the partial likelihood as compared to the marginal profile and parametric likelihoods is given an algorithm is suggested to fit the full ph model with cure

numerical experience with the nonlinear schrodinger equation abstract increasing the magnitude of the parameter multiplying the nonlinear term of the nonlinear schrodinger equation without changing the initial condition u x 0 sech x leads to bound states of an increasing number of solitons this results in very steep gradients in space and time and so provides a more severe test of numerical methods than before in particular we find that methods which satisfy various conservation laws theoretically may now fail to do so in practice various analytical and numerical results relevant to this situation are discussed and illustrated by numerical examples

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

a class of bayesian shared gamma frailty models with multivariate failure time data nous proposons ici dans le cadre des donnees de survie une nouvelle classe de modeles a fragilite gamma partagee en appliquant la transformation de box cox a la fonction de hasard ainsi qu au produit du risque de base et de la fragilite cette nouvelle classe de modeles offre un large eventail de formes et relations entre la fonction de hasard et le risque de base et inclut en tant que cas particuliers le modele de cox usuel a fragilite gamma ainsi qu un nouveau modele additif a fragilite gamma de par la contrainte que le risque soit non negatif ce modele a fragilite gamma partagee presente un defi calculatoire dans le paradigme bayesien les distributions conjointes a priori sont definies par une distribution conditionnelle marginale ou la distribution conditionnelle est univariee cela permet d integrer les contraintes non lineaires sur les parametres la partie marginale de la distribution a priori quant a elle est libre de toute contrainte les distributions a priori permettent de programmer facilement l integralite des distributions conditionnelles requises pour l echantillonnage de gibbs tout en integrant les contraintes un jeu reel de donnees permet d illustrer cette classe de modeles a fragilite gamma partagee

bayesian semiparametric models for survival data with a cure fraction we propose methods for bayesian inference for a new class of semiparametric survival models with a cure fraction specifically we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution we show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates several novel properties of the proposed model are derived in addition we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior also a class of informative priors based on historical data is proposed and its theoretical properties are investigated a case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology

compact finite difference schemes with high accuracy for one dimensional nonlinear schrodinger equation abstract in this paper two compact finite difference schemes are presented for the numerical solution of the one dimensional nonlinear schrodinger equation the discrete l 2 norm error estimates show that convergence rates of the present schemes are of order o h 4 2 numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy

an investigation into the effect of product approximation in the numerical solution of the cubic nonlinear schro dinger equation abstract we study the effect of product approximation on the galerkin solutions of the one dimensional cubic schrodinger equation a crank nicolson scheme is used to discretize in time the paper describes two numerical experiments in the first we examine the approximation obtained by the standard galerkin method and discuss the possibility of enforcing discrete analogs of the conservation laws satisfied by the exact solution in the second experiment numerical results obtained by the product approximation version of the galerkin method are compared and the effectiveness of the method for different combinations of test and trial functions is also investigated

reducing dimensionality in topology optimization using adaptive design variable fields topology optimization methodologies typically use the same discretization for the design variable and analysis meshes analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense this paper proposes leveraging properties of the heaviside projection method hpm to separate the design variable field from the analysis mesh in continuum topology optimization hpm projects independent design variables onto element space over a prescribed length scale a single design variable therefore influences several elements creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space the algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses the technique is demonstrated on minimum compliance maximum stiffness problems solved using continuous optimization and genetic algorithms for the former the proposed algorithm typically identifies solutions having objective functions within 1 of those found using full design variable fields computational savings are minor to moderate for the minimum compliance formulation with a single constraint and are substantial for formulations having many local constraints when using genetic algorithms solutions are consistently obtained on mesh resolutions that were previously considered intractable copyright 2009 john wiley sons ltd

a numerical scheme for the simulation of blow up in the nonlinear schrodinger equation we present a self adaptive multigrid version of a conservative finite difference scheme useful for the study of collapse processes in nonlinear schrodinger equations nlses as an example we study the character of the focusing singularity of the two dimensional critical nlse

on fully discrete galerkin methods of second order temporal accuracy for the nonlinear schrodinger equation we approximate the solutions of an initial and boundary value problem for nonlinear schrodinger equations with emphasis on the cubic nonlinearity by two fully discrete finite element schemes based on the standard galerkin method in space and two implicit crank nicolson type second order accurate temporal discretizations for both schemes we study the existence and uniqueness of their solutions and provel 2 error bounds of optimal order of accuracy for one of the schemes we also analyze one step of newton s method for solving the nonlinear systems that arise at every time step we then implement this scheme using an iterative modification of newton s method that at each time stept n requires solving a number of sparse complex linear systems with a matrix that does not change withn the effect of this inner iteration is studied theoretically and numerically

the numerical study of blowup with application to a nonlinear schrodinger equation abstract we discuss the use of numerical methods in the study of the solutions of evolution problems which exhibit finite time unbounded growth we first examine a naive approach in which the growth rate of the numerical solution is accepted as an approximation of the true growth rate as we shall demonstrate for a radial nonlinear schrodinger equation this approach is inadequate since different discretizations exhibit different growth rates the spurious behaviour of discretizations in the neighbourhood of the singularity is discussed a reliable procedure for the estimation of the blowup parameters is considered which eliminates the discrepancies between different numerical methods

orthogonal spline collocation methods for schr o dinger type equations in one space variable we examine the use of orthogonal spline collocation for the semi discreti za tion of the cubic schr o dinger equation and the two dimensional parabolic equation of tappert in each case an optimal order l 2 estimate of the error in the semidiscrete approximation is derived for the cubic schr o dinger equation we present the results of numerical experiments in which the integration in time is performed using a routine from a software library