cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

a finite volume solution to the geophysical electromagnetic forward problem using unstructured grids abstractthe application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces we investigated the generalization of the standard yee s staggered scheme to unstructured tetrahedral voronoi grids using a finite volume approach we discretized the helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements to compute the electric and magnetic fields at the observation points an interpolation technique was employed which uses the edge vector interpolation functions of the tetrahedral elements to verify the presented scheme two examples were evaluated which revealed the computation of the total and secondary fields due to ele

a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

3d finite element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids abstractwe present a finite element solution to the 3d electromagnetic forward modeling problem in the frequency domain the method is based on decomposing the electric field into vector and scalar potentials in the helmholtz equation and in the equation of conservation of charge edge element and nodal element basis functions were used respectively for the vector and scalar potentials this decomposition was performed with the intention of satisfying the continuity of the tangential component of the electric field and the normal component of the current density across the interelement boundaries therefore finding an efficient solution to the problem the computational domain was subdivided into unstructured tetrahedral elements the system of equations was discretized using the galerkin variant of the weighted residuals method with the approximated vector and scalar potentials as the unknowns of a sparse linear system a generalized minimum residual solver with an incomplete lu preconditioner was use

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

on multivalued fuzzy entropies abstract we analyze an axiomatic system that justifies the introduction of the concept of multivalued fuzzy entropy this is a natural extension of the concept of fuzzy entropy given by de luca and termini we also extend the results of trillas riera and knopfmacher to the class of finite measure spaces

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

the generalized finite element method for helmholtz equation part ii effect of choice of handbook functions error due to absorbing boundary conditions and its assessment abstract in part i t strouboulis i babuska r hidajat the generalized finite element method for helmholtz equation theory computation and open problems comput methods appl mech engrg 195 2006 4711 4731 we introduced the q version of the generalized finite element method gfem for the helmholtz equation and we addressed its a pollution error due to the wave number b exponential q convergence c robustness to perturbations of the mesh the roundoff and numerical quadrature errors and d a posteriori error estimation here we continue the development of the gfem for helmholtz and we address the effects of a alternative handbook functions and mesh types b the error due to the artificial truncation boundary conditions and its assessment the conclusions are 1 the employment of plane wave wave band and vekua handbook functions lead to equivalent results and 2 for high q the most significant component of error may be the one due to the artificial truncation boundary conditions a rather straightforward approach for assessing this error is proposed

measuring fuzzy uncertainty first this paper reviews several well known measures of fuzziness for discrete fuzzy sets then new multiplicative and additive classes are defined we show that each class satisfies five well known axioms for fuzziness measures and demonstrate that several existing measures are relatives of these classes the multiplicative class is based on nonnegative monotone increasing concave functions the additive class requires only nonnegative concave functions some relationships between several existing and the new measures are established and some new properties are derived the relative merits and drawbacks of different measures for applications are discussed a weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced finally we comment on the construction of measures that may assess all of the uncertainties associated with a physical system

local asymptotic normality and mixed normality for markov statistical models we prove local asymptotic normality resp local asymptotic mixed normality of a statistical experiment when the observation is a positive recurrent resp null recurrent with an additional technical assumption markov chain or markov step process under rather mild regularity assumptions on the transition kernel for markov chains on the infinitesimal generator for markov processes the proof makes intensive use of hellinger processes thus avoiding almost completely to study the more complicated structure of the likelihoods themselves

fisher informations and local asymptotic normality for continuous time quantum markov processes we consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input output formalism for irreducible markov processes we show that in the limit of large times the system output state can be approximated by a quantum gaussian state whose mean is proportional to the unknown parameter this approximation holds locally in a neighbourhood of size in the parameter space and provides an explicit expression of the asymptotic quantum fisher information in terms of the markov generator furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical fisher informations the general theory is illustrated with the examples of a two level system and the atom maser our results contribute towards a better understanding of the statistical and probabilistic properties of the output process with relevance for quantum control engineering and the theory of non equilibrium quantum open systems

fast finite volume simulation of 3d electromagnetic problems with highly discontinuous coefficients we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies and the permeability permittivity and conductivity may vary significantly the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain the present article extends methods we proposed earlier for constant permeability e haber u ascher d aruliah and d oldenburg j comput phys 163 2000 pp 150 171 d aruliah u ascher e haber and d oldenburg math models methods appl sci to appear to handle also problems in which the permeability is variable and may contain significant jump discontinuities in order to address the problem of slow convergence we reformulate maxwell s equations in terms of potentials applying a helmholtz decomposition to either the electric field or the magnetic field the null space of the curl operators can then be annihilated by adding a stabilizing term using a gauge condition and thus obtaining a strongly elliptic differential operator a staggered grid finite volume discretization is subsequently applied to the reformulated pde system this scheme works well for sources of various types even in the presence of strong material discontinuities in both conductivity and permeability the resulting discrete system is amenable to fast convergence of ilu preconditioned krylov methods we test our method using several numerical examples and demonstrate its robust efficiency we also compare it to the classical yee method using similar iterative techniques for the resulting algebraic system and we show that our method is significantly faster especially for electric sources

a finite difference time domain solution for three dimensional electromagnetic modeling we have developed a finite difference solution for three dimensional 3 d transient electromagnetic problems the solution steps maxwell s equations in time using a staggered grid technique the time stepping uses a modified version of the du fort frankel method which is explicit and always stable both conductivity and magnetic permeability can be functions of space and the model geometry can be arbitrarily complicated the solution provides both electric and magnetic field responses throughout the earth because it solves the coupled first order maxwell s equations the solution avoids approximating spatial derivatives of physical properties and thus overcomes many related numerical difficulties moreover since the divergence free condition for the magnetic field is incorporated explicitly the solution provides accurate results for the magnetic field at late times an inhomogeneous dirichlet boundary condition is imposed at the surface of the earth while a homogeneous dirichlet condition is employed along the subsurface boundaries numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth order difference method at early times and a second order method at other times numerical checks against analytical integral equation and spectral differential difference solutions show that the solution provides accurate results execution time for a typical model is about 3 5 hours on an ibm 3090 600s computer for computing the field to 10 ms that model contains 100 x 100 x 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry with the smallest grid spacing at 10 m and the highest resistivity at 100 omega m the execution time indicates that the solution is computer intensive but it is valuable in providing much needed insight about tem responses in complicated 3 d situations

fast simulation of 3d electromagnetic problems using potentials we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies the permeability is constant the conductivity may vary significantly and the range of frequencies is moderate the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain we use a potential current formulation a with a coulomb gauge the potentials a and decompose the electric field e into components in the active and null spaces of the operator we develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces after discretization we eliminate the current and the resulting large sparse linear system of equations has a block structure that is diagonally dominant allowing an efficient solution with preconditioned krylov space methods a particularly efficient algorithm results from the combination of bicgstab and an incomplete lu decomposition we demonstrate the efficacy of our method in several numerical experiments

3d time domain simulation of electromagnetic diffusion phenomena a finite element electric field approach we present a finite element time domain fetd approach for the simulation of 3d electromagnetic em diffusion phenomena the finite element algorithm efficiently simulates transient electric fields and the time derivatives of magneticfields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms to compute transient electromagnetic fields theelectricfielddiffusionequationistransformedinto asystemofdifferentialequationsviagalerkin smethodwith homogeneous dirichlet boundary conditions to ensure numerical stability and an efficient time step the system of the differential equations is discretized in time using an implicit backward euler scheme the resultant fetd matrix vector equation is solved using a sparse direct solver along with a fill inreducedorderingtechnique whenadvancingthesolution in time the fetd algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution to simulate a step off source waveform the 3d fetd algorithm also incorporates a 3d finite element direct current fedcalgorithmthatsolvespoisson sequationusingasecondarypotentialmethodforageneralanisotropicearthmodel examples of controlled source fetd simulations are compared with analytic and or 3d finite difference time domain solutions and are used to confirm the accuracy and efficiencyofthe3dfetdalgorithm

nonprobabilistic entropies and indetermination measures in the setting of fuzzy sets theory abstract our purpose in this paper is first of all to build an axiomatic generalization for the nonprobabilistic entropy of de luca and termini in the setting of fuzzy sets theory we then build from this entropy an indetermination measure which can be used like discriminant function in pattern recognition when patterns are described by means of fuzzy sets

asymptotic inference for continuous time markov chains this paper deals with asymptotic optimal inference in a time continuous ergodic markov chain with countable state space based on observation of the process up to timet let the infinitesimal generator depend on an unknown parameter under weak assumptions on the parametrization we show local asymptotic normality for the statistical model ast as a consequence limit distributions of sequences of competing estimators for the unknown parameter are more spread out than a specified normal distribution

3d finite difference frequency domain modeling of controlled source electromagnetic data direct solution and optimization for high accuracy three dimensional modeling of marine controlled source electromagnetic csem data is vital to improve the understanding of electromagnetic em responses collected in increasingly complex geologic settings a modeling tool for simulating 3d marine csem surveys based on a finite difference discretization of the helmholtz equation for the electric fields has been developed optimizations for csem simulations include the use of a frequency domain technique a staggering scheme that reduces inaccuracies especially for horizontal electric dipole sources located near the seafloor and a new interpolation technique that provides highly accurate em field values for receivers located in the immediate vicinity of the seafloor source singularities are eliminated through a secondary field approach in which the primary fields are computed analytically for a homogeneous or a 1d layered background the secondary fields are computed using the finite difference technique exploiting recent advances in computer technology and algorithmic developments the system of finite difference equations is solved using the mumps direct matrix solver in combination with the other optimizations this allows accurate em field computations for moderately sized models on small computer clusters the explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme comparisons of simulated data for 1 1d models to data generated using a 1d reflectivity technique and 2 3d models to published 3d data demonstrate the accuracy and benefits of the approach

the variational theory of complex rays a predictive tool for medium frequency vibrations abstract today the main numerical modeling techniques for the analysis of medium frequency vibrations are all based on finite element or boundary element approaches in order to represent small wavelength phenomena in complex structures such as car chassis satellites or ships these techniques require a huge number of degrees of freedom at least seven elements per wavelength are required to represent oscillating solutions in addition the solution obtained is highly sensitive to material properties and boundary conditions the use of high frequency approaches such as the statistical energy analysis sea or any of its improvements does not appear to be suitable for medium frequency vibrations the vibrational behavior becomes too smooth and in general the coupling loss factor cannot be calculated in a predictive way in this paper a new and multiscale approach to the calculation of the vibrations of elastic structures in the medium frequency range called the variational theory of complex rays is presented the feasibility and effectiveness of the method are demonstrated for structures made of plate assemblies several 3d examples are analyzed and compared to the results from a classical finite element approach and from a sea code this comparison shows that our method is able to predict the effective quantities at a very low numerical cost

transient electromagnetic response of a three dimensional body in a layered earth the three dimensional 3 d electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation three dimensional responses are then fourier transformed with sine and cosine digital filters or with the decay spectrum the digital filter technique is applied to a sparsely sampled frequency sounding which is replaced by a cubic spline interpolating function prior to convolution with the digital filters typically 20 to 40 frequencies at five to eight points per decade are required for an accurate solution a calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time the decay spectrum usually requires ten frequencies for a satisfactory solution however the solution using the decay spectrum appears to be less accurate than the solution using the digital filters particularly after early times checks on the 3 d solution include reciprocity and convergence checks in the frequenc

on two dimensional infinite elements utilizing basis functions with compact support in this paper improvements are made in the numerical conditioning of infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving two dimensional exterior problems for the helmholtz equation

three effective inverse laplace transform algorithms for computing time domain electromagnetic responses abstractthe inverse laplace transform is one of the methods used to obtain time domain electromagnetic em responses in geophysics the gaver stehfest algorithm has so far been the most popular technique to compute the laplace transform in the context of transient electromagnetics however the accuracy of the gaver stehfest algorithm even when using double precision arithmetic is relatively low at late times due to round off errors to overcome this issue we have applied variable precision arithmetic in the matlab computing environment to an implementation of the gaver stehfest algorithm this approach has proved to be effective in terms of improving accuracy but it is computationally expensive in addition the gaver stehfest algorithm is significantly problem dependent therefore we have turned our attention to two other algorithms for computing inverse laplace transforms namely the euler and talbot algorithms using as examples the responses for central loop fixed loop and horizontal electri

three dimensional induction logging problems part 2 a finite difference solution a 3 d finite difference solution is implemented for simulating induction log responses in the quasi static limit that include the wellbore and bedding that exhibits transverse anisotropy the finite difference code uses a staggered grid to approximate a vector equation for the electric field the resulting linear system of equations is solved to a predetermined error level using iterative krylov subspace methods to accelerate the solution at low induction numbers lins a new preconditioner is developed this new preconditioner splits the electric field into curl free and divergence free projections which allows for the construction of an approximate inverse operator test examples show up to an order of magnitude increase in speed compared to a simple jacobi preconditioner comparisons with analytical and mode matching solutions demonstrate the accuracy of the algorithm

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

three dimensional infinite elements utilizing basis functions with compact support abstract in this paper improvements are made in the numerical conditioning of three dimensional infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving three dimensional exterior problems for the helmholtz equation

3d vector finite element electromagnetic forward modeling for large loop sources using a total field algorithm and unstructured tetrahedral grids abstractunstructured tetrahedral grids with local refinement facilitate the use of total field solution approaches to geophysical electromagnetic em forward problems these approaches when combined with the vector finite element fe method and with refinement near transmitters and receivers can give accurate solutions and can easily handle realistic models with complex geometry and topography we have applied this approach to 3d forward modeling for fixed and moving loop configurations mumps a direct solver was used to solve the linear system of equations generated by fe analysis a direct solver is particularly suited to the moving loop configuration for which the right side is different for every transmitter loop but for which the coefficient matrix is unchanged therefore the coefficient matrix need only be factorized once and then the system can be solved efficiently for all different right sides we compared our results with several typical scenarios from the literature a conductive bric

a parallel finite difference approach for 3d transient electromagnetic modeling with galvanic sources a parallel finite difference algorithm for the solution of diffusive three dimensional 3d transient electromagnetic field simulations is presented the purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources grounded wires over arbitrarily complicated distributions of conductivity and magnetic permeability using a staggered grid and a modified dufort frankel method the scheme steps maxwell s equations in time electric field initialization is done by a conjugate gradient solution of a 3d poisson problem as is common in 3d resistivity modeling instead of calculating the initial magnetic field directly its time derivative and curl are employed in order to advance the electric field in time a divergence free condition is enforced for both the magnetic field time derivative and the total conduction current density providing accurate results at late times in order to simulate large realistic earth models the algorithm has been designed to run on parallel computer platforms the upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two dimensional parallel fast fourier transform example simulations are compared with analytical integral equation and spectral lanczos decomposition solutions and demonstrate the accuracy of the scheme

extension of the variational theory of complex rays to shells for medium frequency vibrations a new approach to the calculation of vibrations of weakly damped elastic structures in the medium frequency range called the variational theory of complex rays vtcr is being developed here the extension of this theory to shells of relatively small curvature is considered numerical examples of structures made of plates and shells demonstrate the capabilities of the vtcr

fuzzy measures and measures of fuzziness abstract in this paper the fuzzy integral defined by z x wang fuzzy math wuhan china in press which is different from that defined by m sugeno theory of fuzzy integrals and its applications ph d tokyo inst of technology 1974 is further considered and it is shown that the fuzzy measures of ordinary sets and fuzzy sets can be determined by each other summing up the results on the measure of fuzziness by a deluca and s a termini inform and control 20 1972 301 312 z x wang op cit and r r yager internat j gen systems 5 1979 221 229 inform and control 44 1980 236 260 the axioms for measures of fuzziness are given furthermore as an application of the furry integrals a measure of fuzziness is defined inversely it is proven that a measure of fuzziness satisfying some conditions can surely be expressed as a fuzzy integral with respect to some fuzzy measure

on the use of fuzzy constraints in semisupervised clustering this paper introduces fuzzy hss a semisupervised hierarchical clustering approach that uses fuzzy instance level constraints these constraints are external information on the shape of fuzzy must link and fuzzy cannot link restrictions they allow uncertainty when indicating whether two instances of a dataset belong to the same group fuzzy must link constraints give a degree of belief of two instances belonging to the same group analogously fuzzy cannot link constraints indicate the degree of belief of two instances not belonging to the same group these constraints have been introduced in a hierarchical clustering process allowing us to obtain the optimal number of groups in a dendrogram when the number of clusters is not known the optimal amount of constraints needed in the process is determined by means of fuzzy entropy an extensive experimental study is provided by comparing this fuzzy semisupervised approach with classic unsupervised methods as well as a crisp semisupervised alternative

a parallel finite element tearing and interconnecting algorithm for solution of the vector wave equation with pml absorbing medium a domain decomposition method based on the finite element tearing and interconnecting feti algorithm is presented for the solution of the large sparse matrices associated with the finite element method fem solution of the vector wave equation the feti algorithm is based on the method of lagrange multipliers and leads to a reduced order system which is solved using the biconjugate gradient method bicgm it is shown that this method is highly scalable and is more efficient on parallel platforms when solving large matrices than traditional iterative methods such as a preconditioned conjugate gradient algorithm this is especially true when a perfectly matched layer pml absorbing medium is used to terminate the problem domain