order and stepsize control in extrapolation methods the paper presents a new theory for joint order and stepsize control in extrapolation methods this theory defines a locally optimal order that can be determined along any trajectory to be computed in addition shannon s information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non stiff integration by the new device moreover a significant increase in reliability robustness and portability of the extrapolation codes is achieved

adaptivity in space and time for reaction diffusion systems in electrocardiology the paper introduces and studies numerical methods that are fully adaptive in both three dimensional 3d space and time to challenging multiscale cardiac reaction diffusion models in these methods temporal adaptivity comes via stepsize control in function space oriented linearly implicit time integration while spatial adaptivity is realized within multilevel finite element methods controlled by a posteriori local error estimators in contrast to other recent adaptivity approaches to cardiac modeling that discretize first in space and then in time so called method of lines our method discretizes first in time and then in space so called rothe method an approach that has already proven to be highly efficient in a number of challenging multiscale problems in science and technology kardos code library with this method the evolution of a complete heartbeat from the excitation to the recovery phase is simulated both in the frame of the anisotropic monodomain models and in the more realistic anisotropic bidomain models coupled with either a variant of the simple fitzhugh nagumo model or the more complex phase i luo rudy ionic model the numerical results exhibit a rather satisfactory performance of our adaptive method for complex cardiac reaction diffusion models on 3d domains up to moderate sizes in particular the method accurately resolves the evolution of the intra and extracellular potentials gating variables and ion concentrations during the excitation plateau and recovery phases

multi time step domain decomposition and coupling methods for nonlinear parabolic problems abstract in this paper we propose and examine a multi time step algorithm using a feti based domain decomposition method for nonlinear parabolic problems the computational domain is divided into a set of smaller subdomains that may be integrated concurrently with their own time steps the continuity condition at the interface is ensured employing local lagrange multipliers the equation of continuity of primary unknowns at the interface is written only at the so called system time step the subdomain problems are coupled together by requiring the lagrange multipliers on the interface at the intermediate time steps to match a suitable interpolation of the values at the system time steps this allows each subdomain to be solved with its own time step the rigorous nonlinear stability is performed via the energy method several numerical examples will be solved to illustrate the overall performance of the proposed coupling method

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

thermal modelling of selective beam melting processes using heterogeneous time step sizes abstract in the context of powder bed based additive manufacturing complex part geometries are realised in a layer by layer fashion and by the fusion of powdered material in locally defined regions by means of e g a laser or electron beam simulating these manufacturing processes from a macroscopic point of view may lead to computationally expensive models due to different scales in space and time highly non linear material behaviour and methods to account for the layer wise build i e dynamic growth of the computational domain aiming towards a reduction of the computational cost multiple numerical methods are therefore combined one approach in the context of finite element simulations is given by adaptive mesh refinement and coarsening this allows to locally refine the mesh where it is needed e g in the region currently exposed to the beam while keeping it relatively coarse in other regions yet the time step size of the model is constrained by the resolution of the beam path which clearly limits the size of the problem under investigation within the present contribution we employ heterogeneous time step sizes for the arising thermal problem in different parts of the computational domain in order to account for the distinct scales in time in addition a line heat input model is utilised to further lower the computational cost

a distribution free procedure for comparing receiver operating characteristic curves from a paired experiment summary a distribution free permutation test procedure is proposed for comparing receiver operating characteristic curves based on continuous data from a paired design the method tests the hypothesis that the two curves are identical for all operating points unlike previously proposed methods which test the equivalence of the areas under the curves the new test is shown by simulation to have very similar operating characteristics to the standard method based on comparisons of the areas when the curves are parallel but markedly superior power when the curves cross that is when the curves are different but have similar areas the prospects of generalising the approach to unpaired experiments and to comparisons of ordinal rating data are discussed

anisotropic grid adaptation for navier stokes equations navier stokes equations are discretized in space by a finite volume method error equations are derived which are approximately satisfied by the errors in the solution the dependence of the solution errors on the discretization errors is analyzed in certain flow cases the grid is adapted based on the estimated discretization errors the refinement and coarsening of the grid are anisotropic in the sense that it is different in different directions in the computational domain the adaptation algorithm is applied to laminar viscous flow over a flat plate in a channel with a bump and around a cylinder and an airfoil

sensitivity and specificity of a monitoring test summary the usefulness of a diagnostic test is generally assessed by calculating the sensitivity and specificity or the predictive value positive and predictive value negative of the test when subjects are monitored periodically for evidence of disease these calculations must incorporate the varying amounts of information per individual if in addition the test results lie on a continuous scale these quantities vary with the cutoff value cutpoint used to define a positive test they are usually calculated for a spectrum of potential cutpoints in order to produce receiver operator characteristic curves in this paper we use a partial likelihood solution to the discrete logistic model in order to obtain estimates of the diagnostic test indices and to provide a significance test when the diagnostic test is administered repeatedly to individuals

block monotone iterative method for semilinear parabolic equations with nonlinear boundary conditions two block monotone iterative schemes called jacobi and gauss seidel monotone iterations are presented for numerical solutions of a class of semilinear parabolic equations under nonlinear boundary conditions by the finite difference method these iteration schemes extend the method for semilinear elliptic boundary value problems to parabolic equations including a comparison result between them it is shown that by using an upper solution and a lower solution as initial iterations each of the iterative schemes yields two sequences which converge monotonically from above and below respectively to a unique solution of the finite difference system some error estimates and a convergence theorem are given and various sufficient conditions for the construction of upper and lower solutions are obtained numerical results are presented for some physical model problems including some problems with known continuous solutions and two problems with l shaped and trapezoidal domains

a family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data summary in this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers one can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class as special cases one can compare the entire area under the receiver operator curve hanley mcneil 1982 or one can compare the sensitivities at a fixed common specificity usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities test procedures and confidence intervals are based on asymptotic normality these procedures are applicable for paired data in which both diagnostic markers are performed on each subject and for unpaired data the procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers

multi time step domain decomposition method with non matching grids for parabolic problems evolution of time dependent physical quantities such as current heat etc in composite materials are modeled by initial boundary value problems for parabolic pdes these physical quantities follow different evolution patterns in different parts of the computational domain depending on the material properties size of constituent material subdomains coupling scheme etc therefore the stability and accuracy requirements of a numerical integration scheme may necessitate domain dependent time discretization parabolic problems are usually solved by discretizing spatially using finite elements and then integrating over time using discrete solvers we propose an asynchronous multi domain time integration scheme for parabolic problems for efficient parallel computing of large problems we present the dual decomposition method with local lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains the proposed method enables us to use domain dependent rothe method on different parts of a computational domain and thus provide an efficient and robust approach to solving large scale composite material problems

adaptive local overlapping grid methods for parabolic systems in two space dimensions abstract adaptive mesh refinement techniques are described for two dimensional systems of parabolic partial differential equations solutions are calculated using galerkin s method with a piecewise bilinear basis in space and backward euler integration in time a posteriori estimates of the local discretization error of piecewise bilinear finite element solutions are obtained by a p refinement technique these error estimates are used to control a local h refinement strategy where finer grids are recursively introduced in regions where a prescribed tolerance is exceeded fine grids at a given level of refinement may overlap each other and independent solutions are generated on each of them a version of the schwarz alternating principle is used to coordinate solutions between overlapping fine grids computational results demonstrating the performance of the adaptive procedure on linear and nonlinear problems and apparent convergence of the error estimate for linear heat conduction problem and uniform global refinement is presented

sample size determination for diagnostic accuracy studies involving binormal roc curve indices receiver operating characteristic roc curves and their associated indices are valuable tools for the assessment of the accuracy of diagnostic tests the area under the roc curve is a popular summary measure of the accuracy of a test the full area under the roc curve however has been criticized because it gives equal weight to all false positive error rates alternative indices include the area under the roc curve in a particular range of false positive rates partial area and the sensitivity of the test for a single fixed false positive rate fpr we present a unified approach for computing sample size for binormal roc curves and their indices our method uses taylor series expansions to derive approximate large sample estimates of the variance and covariance of binormal roc curve parameters several examples from diagnostic radiology illustrate the proposed method

enabling local time stepping in the parallel implicit solution of reaction diffusion equations via space time finite elements on shallow tree meshes for many applications local time stepping offers an interesting and worthwhile alternative to the by now well established global time step control in fact local time stepping can allow for a highly detailed resolution of localized features of the solution with strongly reduced computational cost when compared to global time step control however local time stepping is not applicable in a straight forward manner in the context of fully implicit time discretizations here we present a method for the efficient parallel adaptive solution of non linear partial differential equations in particular reaction diffusion equations using spatially adapted time step sizes in the context of a fully implicit solution strategy our proposed method uses a discontinuous galerkin method in time approach within a full space time approach moreover it is designed from scratch for efficient parallel computation we employ shallow tree based mesh data structures in order to ensure a low memory footprint of the adaptive meshes by solving the time dependent partial differential equation on a d 1 dimensional non conforming mesh space time adaptivity is naturally achieved in combination with a discontinuous galerkin method in time the size of the arising systems can be precisely controlled we additionally introduce and discuss a stabilization scheme for space time mortar element methods that also has a highly positive impact on the efficiency of preconditioning techniques for the arising systems of equations we present results from extensive numerical experiments that address the question of convergence and efficiency linear and non linear solver performance parallel scalability up to 2048 cores as well as accuracy for the linear heat equation and a real world non linear reaction diffusion equation from the field of computational electrocardiology

robust detector for narrow band signals in non gaussian noise for the detection of a bandpass signal with rayleigh amplitude and uniform phase we first show the degradation in performance of the square law detector when the in phase and quadrature noise components have small degrees of non gaussian contamination a robust detector using limiter squarers instead of square law characteristics to limit the influence of occasional large observations is proposed specific numerical results illustrate the considerable advantage of the robust structure when small degrees of deviation occur from the nominal gaussian assumption

an adaptive method of lines with error control for parabolic equations of the reaction diffusion type abstract a piecewise linear finite element based method of lines is presented for the numerical solution of coupled parabolic partial differential equations which model biological and physicochemical reaction diffusion processes in one space dimension the vertial lines emanating from the space nodes in this method change at automatically selected times when in order to control a norm of the space discretization error adaptive spatial regridding occurs the regridding algorithm is an extension of one described previously by the authors 7 and is implemented in the program femol 1 which uses the lsodi package 14 15 of hindmarsh and painter to integrate the ordinary differential equations in time along the vertical lines computational results show that the method is efficient that a posteriori estimates of the space discretization error are accurate and that the adaptive procedure reliably controls the space discretization error

detection of narrow band signals in spherically invariant noise this paper deals with noncoherent discrete time detection of a narrow band signal subject to slow and nonselective fading and embedded in correlated non gaussian noise modeled as a spherically invariant random process whose modulating random variable is continuous at first an asymptotic sufficient statistic for an arbitrary fading law is derived then the asymptotically optimum detector for rayleigh distributed amplitude fluctuations is synthesized the detection structure implementation requires the knowledge but for a scale factor of the correlation function of the noise but is independent of the distribution function of the modulating random variable the performance of the asymptotically optimum detector synthesized for rayleigh fading is assessed via computer simulations the results show that the performance degradation with respect to the fully optimum performance is scarcely significant even for low values of the sample size moreover in highly non gaussian noise the proposed detector largely outperforms the fully optimum detector synthesized under the correlated gaussian noise assumption

three class roc analysis the equal error utility assumption and the optimality of three class roc surface using the ideal observer previously we have developed a decision model for three class receiver operating characteristic roc analysis based on decision theory the proposed decision model maximizes the expected decision utility under the assumption that incorrect decisions have equal utilities under the same hypothesis equal error utility assumption this assumption reduced the dimensionality of the general three class roc analysis and provided a practical figure of merit to evaluate the three class task performance however it also limits the generality of the resulting model because the equal error utility assumption will not apply for all clinical three class decision tasks the goal of this study was to investigate the optimality of the proposed three class decision model with respect to several other decision criteria in particular besides the maximum expected utility meu criterion used in the previous study we investigated the maximum correctness mc or minimum error maximum likelihood ml and nyman pearson n p criteria we found that by making assumptions for both meu and n p criteria all decision criteria lead to the previously proposed three class decision model as a result this model maximizes the expected utility under the equal error utility assumption maximizes the probability of making correct decisions satisfies the n p criterion in the sense that it maximizes the sensitivity of one class given the sensitivities of the other two classes and the resulting roc surface contains the maximum likelihood decision operating point while the proposed three class roc analysis model is not optimal in the general sense due to the use of the equal error utility assumption the range of criteria for which it is optimal increases its applicability for evaluating and comparing a range of diagnostic systems

linear combinations of biomarkers to improve diagnostic accuracy with three ordinal diagnostic categories many researchers have addressed the problem of finding the optimal linear combination of biomarkers to maximize the area under receiver operating characteristic roc curves for scenarios with binary disease status in practice many disease processes such as alzheimer can be naturally classified into three diagnostic categories such as normal mild cognitive impairment and alzheimer s disease ad and for such diseases the volume under the roc surface vus is the most commonly used index of diagnostic accuracy in this article we propose a few parametric and nonparametric approaches to address the problem of finding the optimal linear combination to maximize the vus we carried out simulation studies to investigate the performance of the proposed methods we apply all of the investigated approaches to a real data set from a cohort study in early stage ad copyright 2012 john wiley sons ltd

a local space time adaptive scheme in solving two dimensional parabolic problems based on domain decomposition methods we describe a local space time adaptive refinement and derefinement method for solving systems of parabolic partial differential equations solutions are calculated on local space time meshes using a domain decomposition finite element algorithm in space and an extrapolation algorithm in time an a posteriori spatial error estimate controls a local spatial refinement strategy and an a posteriori temporal error estimate monitors temporal refinement and order of the integration a multiplicative schwarz algorithm is used to coordinate solutions between overlapping grids we use nearly minimal fine meshes which follow the dynamics of the problems in an efficient manner

measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups this article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups we use a receiver operating characteristic roc surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed under the assumption of normal distributions of the diagnostic test from three diagnostic groups we present the maximum likelihood estimate to the volume under the roc surface and give the asymptotic variance to the estimate we further propose several asymptotic confidence interval estimates to the volume under the roc surface the performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study in addition we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate finally we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage alzheimer s disease based on the neuropsychological database of the washington university alzheimer s disease research center

asymptotically optimum diversity detection in correlated non gaussian noise the letter deals with noncoherent diversity detection of bandpass signals subject to slow and nonselective fading and embedded in correlated non gaussian noise modeled as a spherically invariant random process at first an asymptotic sufficient statistic for arbitrary fading laws on the diversity branches is derived then the asymptotically optimum detector for rayleigh distributed amplitude fluctuations is synthesized and its performance is assessed

three class roc analysis toward a general decision theoretic solution multiclass receiver operating characteristic roc analysis has remained an open theoretical problem since the introduction of binary roc analysis in the 1950s previously we have developed a paradigm for three class roc analysis that extends and unifies decision theoretic linear discriminant analysis and probabilistic foundations of binary roc analysis in a three class paradigm one critical element in this paradigm is the equal error utility eeu assumption this assumption allows us to reduce the intrinsic space of the three class roc analysis 5 d hypersurface in 6 d hyperspace to a 2 d surface in the 3 d space of true positive fractions sensitivity space in this work we show that this 2 d roc surface fully and uniquely provides a complete descriptor for the optimal performance of a system for a three class classification task i e the triplet of likelihood ratio distributions assuming such a triplet exists to be specific we consider two classifiers that utilize likelihood ratios and we assumed each classifier has a continuous and differentiable 2 d sensitivity space roc surface under these conditions we proved that the classifiers have the same triplet of likelihood ratio distributions if and only if they have the same 2 d sensitivity space roc surfaces as a result the 2 d sensitivity surface contains complete information on the optimal three class task performance for the corresponding likelihood ratio classifier