quantitative error estimate in modeling the laminar stationary flow of a bingham fluid we present a quantitative a posteriori error estimate when the linear laminar stationary flow of a bingham fluid in a cylindrical pipe is modeled as a newtonian fluid the estimate is proved by using a complementary variational principle for the bingham fluid flow examples show that the estimate is effective

parallel preconditioners for monolithic solution of shear bands shear bands are one of the most fascinating instabilities in metals that occur under high strain rates they describe narrow regions on the order of micron scales where plastic deformations and significant heating are localized which eventually leads to fracture nucleation and failure of the component in this work shear bands are described by a set of four strongly coupled thermo mechanical equations discretized by a mixed finite element formulation a thermo viscoplastic flow rule is used to model the inelastic constitutive law and finite thermal conductivity is prescribed which gives rise to an inherent physical length scale governed by competition of shear heating and thermal diffusion the residual equations are solved monolithically by a newton type method at every time step and have been shown to yield mesh insensitive result the jacobian of the system is sparse and has a nonsymmetric block structure that varies with the different stages of shear bands formation the aim of the current work is to develop robust parallel preconditioners to gmres in order to solve the resulting jacobian systems efficiently the main idea is to design schur complements tailored to the specific block structure of the system and that account for the varying stages of shear bands we develop multipurpose preconditioners that apply to standard irreducible discretizations as well as our recent work on isogeometric discretizations of shear bands the proposed preconditioners are tested on benchmark examples and compared to standard state of practice solvers such as gmres ilu and lu direct solvers nonlinear and linear iterations counts as well as cpu times and computational speedups are reported and it is shown that the proposed preconditioners are robust efficient and outperform traditional state of the art solvers

inexact newton type methods for the solution of steady incompressible viscoplastic flows with the supg pspg finite element formulation in this work we evaluate the performance of inexact newton type schemes to solve the nonlinear equations arising from the supg pspg finite element formulation of steady viscoplastic incompressible fluid flows the flow through an abrupt contraction and the rotational flow in eccentric annulus with power law and bingham rheologies are employed as benchmarks our results have shown that inexact schemes are more efficient than traditional newton type strategies

estimating functions of probability distributions from a finite set of samples this paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution a bayesian analysis of this problem is presented the optimal properties of the bayes estimators are discussed and as an example of the formalism closed form expressions for the bayes estimators for the moments of the shannon entropy function are derived then numerical results are presented that compare the bayes estimator to the frequency counts estimator for the shannon entropy we also present the closed form estimators all derived elsewhere for the mutual information mathrm ensuremath chi 2 covariance and some other statistics c 1995 the american physical society

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

phase field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing this paper describes a novel numerical algorithm for simulating interfacial dynamics of non newtonian fluids the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously the property and evolution of the interfacial layer is governed by a phase field variable that obeys a cahn hilliard type of convection diffusion equation this circumvents the task of directly tracking the interface and produces the correct interfacial tension from the free energy stored in the mixing layer viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase field framework the greatest challenge of this approach is in resolving the sharp gradients at the interface this is achieved by using an efficient adaptive meshing scheme governed by the phase field variable the finite element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large scale two phase systems of complex fluids in two dimensional and axisymmetric three dimensional implementations the numerical toolkit is applied here to drop deformation in shear and elongational flows rise of drops and retraction of drops and torii some of these solutions serve as validation of the method and illustrate its key features while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces

dynamic analyses of information encoding in neural ensembles neural spike train decoding algorithms and techniques to compute shannon mutual information are important methods for analyzing how neural systems represent biological signals decoding algorithms are also one of several strategies being used to design controls for brain machine interfaces developing optimal strategies to desig n decoding algorithms and compute mutual information are therefore important problems in computational neuroscience we present a general recursive filter decoding algorithm based on a point process model of individual neuron spiking activity and a linear stochastic state space model of the biological signal we derive from the algorithm new instantaneous estimates of the entropy entropy rate and the mutual information between the signal and the ensemble spiking activity we assess the accuracy of the algorithm by computing along with the decoding error the true coverage probability of the approximate 0 95 confidence regions for the individual signal estimates we illustrate the new algorithm by reanalyzing the position and ensemble neural spiking activity of ca1 hippocampal neurons from two rats foraging in an open circular environment we compare the performance of this algorithm with a linear filter constructed by the widely used reverse correlation method the median decoding error for animal 1 2 during 10 minutes of open foraging was 5 9 5 5 cm the median entropy was 6 9 7 0 bits the median information was 9 4 9 4 bits and the true coverage probability for 0 95 confidence regions was 0 67 0 75 using 34 32 neurons these findings improve significantly on our previous results and suggest an integrated approach to dynamically reading neural codes measuring their properties and quantifying the accuracy with which encoded information is extracted

a nonlinear weighted least squares finite element method for the oldroyd b viscoelastic flow this paper studies a nonlinear weighted least squares finite element method for the steady oldroyd b viscoelastic flow our least squares functional involves the l 2 norm of the residuals of each equation multiplied by a proper weight the weights include mass conservation constant mesh dependent weight and a nonlinear weighting function we prove that the least squares approximation converges to the solutions of the linearized versions of the viscoelastic fluid model at the best possible rate and then present the planar channel flow problem illustrating our theoretical results results of the least squares approach indicate that with carefully chosen nonlinear weighting functions and linear basis functions the numerical solution exhibits a second order convergence rate for velocity and viscous stress and superlinear convergence rate in polymeric stress and pressure the method is applied to the 4 to 1 planar contraction problem the effects of weissenberg numbers are also presented in the work

implementation of newton s method with an analytical jacobian to solve the 1d sea ice momentum equation new numerical solvers are being considered in response to the rising computational cost of properly solving the sea ice momentum equation at high resolution the jacobian free version of newton s method has allowed models to obtain the converged solution faster than other implicit solvers used previously to further improve on this recent development the analytical jacobian of the 1d sea ice momentum equation is derived and used inside newton s method the results are promising in terms of computational efficiency although robustness remains an issue for some test cases it is improved compared to the jacobian free approach in order to make use of the strong points of both the new and jacobian free methods a hybrid preconditioner using the picard and jacobian matrices to improve global and local convergence respectively is also introduced this preconditioner combines the robustness and computational efficiency of the previously used preconditioning matrices when solving the sea ice momentum equation

efficient preconditioner updates for shifted linear systems we present a technique for building effective and low cost preconditioners for sequences of shifted linear systems a alpha i x alpha b where a is symmetric positive definite and alpha 0 this technique updates a preconditioner for a available in the form of an ldl t factorization by modifying only the nonzero entries of the l factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behavior this approach is supported by a theoretical analysis as well as by numerical experiments showing that it works efficiently for a broad range of values of alpha

on some krylov subspace based methods for large scale nonsymmetric algebraic riccati problems in the present paper we consider large scale nonsymmetric matrix riccati equations with low rank right hand sides these matrix equations appear in many applications such as transport theory wiener hopf factorization of markov chains applied probability and others we show how to apply directly krylov methods such as the extended block arnoldi algorithm to get low rank approximate solutions we also combine the newton method and block krylov subspace methods to get approximations of the desired minimal nonnegative solution we give some theoretical results and report some numerical experiments for the well known transport equation

a second order accurate in time implicit explicit imex integration scheme for sea ice dynamics current sea ice models use numerical schemes based on a splitting in time between the momentum and continuity equations because the ice strength is explicit when solving the momentum equation this can create unrealistic ice stress gradients when using a large time step as a consequence noise develops in the numerical solution and these models can even become numerically unstable at high resolution to resolve this issue we have implemented an iterated implicit explicit imex time integration method this imex method was developed in the framework of an already implemented jacobian free newton krylov solver the basic idea of this imex approach is to move the explicit calculation of the sea ice thickness and concentration inside the newton loop such that these tracers evolve during the implicit integration to obtain second order accuracy in time we have also modified the explicit time integration to a second order runge kutta approach and by introducing a second order backward difference method for the implicit integration of the momentum equation these modifications to the code are minor and straightforward by comparing results with a reference solution obtained with a very small time step it is shown that the approximate solution is second order accurate in time the new method permits to obtain the same accuracy as the splitting in time but by using a time step that is 10 times larger results show that the second order scheme is more than five times more computationally efficient than the splitting in time approach for an equivalent level of error

estimating information rates with confidence intervals in neural spike trains information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus a related work kennel shlens abarbanel chichilnisky 2005 demonstrated how to reliably estimate with a bayesian confidence interval the entropy rate from a discrete observed time series we extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus the average and specific mutual information rates our estimator makes few assumptions about the underlying neural dynamics shows excellent performance in experimentally relevant regimes and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train we validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance finally we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder

classification of algebras arising from the tits process in the preceding paper lo we generalized the second tits construction of simple exceptional jordan algebras 6 to a construction over an arbitrary ring of scalars which we called the tits process and claimed that it plays for jordan rings a role akin to that of the cayley dickson process for alternative rings in this paper we assume that the scalars form a field f and determine the semisimple jordan algebras arising from the tits process we see that except for predictable problems in low characteristics all simple jordan algebras of degree 3 are obtainable by starting from fl and repeating the tits process review let be a unital commutative associative ring a module recall that jv n 1 is a cubic norm structure on f if 1 n f is cubic form 2 f is a quadratic map 1 is an element of 2 2 is an udjoint for n

the incorporation of the semi implicit linear equations into newton s method to solve radiation transfer equations abstract for large time steps the nonlinear equations of radiation transfer may not be solved adequately by the semi implicit linear approximation to yield physical solutions this deficiency is rectified in three steps the equations of the semi implicit linear method are modified the modified equations are incorporated into newton s method to solve nonlinear equations and the transfer equations are solved by the resulting method the new method also uses the photon free method to search for the solution in a lower dimensional space than the space of the underlying transfer equations two algorithms are developed from the new method they solve the modified semi implicit linear equations by different approaches the first is a physics approach it solves the linear equations approximately by the grey transport approximation the second is a mathematical approach it solves the linear equations exactly by the sherman morrison woodbury formula of linear algebra however both algorithms yield the solution to the nonlinear system derived by the photon free method therefore their solutions are equal to within the specified tolerance of the nonlinear solver moreover both methods can take advantage of the unconditional stability which comes with the implicit differencing of the time derivative the time step which both methods can take is much larger than the time step in which time discretization error is discernible we shall relate the mathematical approach to the photon free method numerical results for three test problems are presented

coverage adjusted entropy estimation summary data on neural coding have frequently been analyzed using information theoretic measures these formulations involve the fundamental and generally difficult statistical problem of estimating entropy we review briefly several methods that have been advanced to estimate entropy and highlight a method the coverage adjusted entropy estimator cae due to chao and shen that appeared recently in the environmental statistics literature this method begins with the elementary horvitz thompson estimator developed for sampling from a finite population and adjusts for the potential new species that have not yet been observed in the sample these become the new patterns or words in a spike train that have not yet been observed the adjustment is due to i j good and is called the good turing coverage estimate we provide a new empirical regularization derivation of the coverage adjusted probability estimator which shrinks the maximum likelihood estimate we prove that the cae is consistent and first order optimal with rate op 1 logn in the class of distributions with finite entropy variance and that within the class of distributions with finite qth moment of the log likelihood the good turing coverage estimate and the total probability of unobserved words converge at rate op 1 logn q we then provide a simulation study of the estimator with standard distributions and examples from neuronal data where observations are dependent the results show that with a minor modification the cae performs much better than the mle and is better than the best upper bound estimator due to paninski when the number of possible words m is unknown or infinite copyright q 2007 john wiley sons ltd

an inexact newton type method for inverse singular value problems in this paper an inexact newton type approach is proposed for solving inverse singular value problems we show that the method converges superlinearly this method can reduce significantly the oversolving problem of the newton type method and improve the efficiency numerical experiments is also presented to illustrate our results

bayesian entropy estimation for countable discrete distributions we consider the problem of estimating shannon s entropy h from discrete data in cases where the number of possible symbols is unknown or even countably infinite the pitman yor process a generalization of dirichlet process provides a tractable prior distribution over the space of countably infinite discrete distributions and has found major applications in bayesian non parametric statistics and machine learning here we show that it provides a natural family of priors for bayesian entropy estimation due to the fact that moments of the induced posterior distribution over h can be computed analytically we derive formulas for the posterior mean bayes least squares estimate and variance under dirichlet and pitman yor process priors moreover we show that a fixed dirichlet or pitman yor process prior implies a narrow prior distribution over h meaning the prior strongly determines the entropy estimate in the under sampled regime we derive a family of continuous measures for mixing pitman yor processes to produce an approximately flat prior over h we show that the resulting pitman yor mixture pym entropy estimator is consistent for a large class of distributions finally we explore the theoretical properties of the resulting estimator and show that it performs well both in simulation and in application to real data

size biased sampling of poisson point processes and excursions some general formulae are obtained for size biased sampling from a poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function these formulae explain why in certain cases gamma and stable the size biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking residual allocation scheme defined by independent beta random variables an application is made to length biased sampling of excursions of a markov process away from a recurrent point of its statespace with emphasis on the brownian and bessel cases when the associated inverse local time is a stable subordinator results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by brownian motion

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

a note on entropy estimation we compare an entropy estimator recently discussed by zhang 2012 with two estimators and introduced by grassberger 2003 and schurmann 2004 we prove the identity which has not been taken into account by zhang 2012 then we prove that the systematic error bias of is less than or equal to the bias of the ordinary likelihood or plug in estimator of entropy finally by numerical simulation we verify that for the most interesting regime of small sample estimation and large event spaces the estimator has a significantly smaller statistical error than

an adaptively refined least squares finite element method for generalized newtonian fluid flows using the carreau model we implemented an adaptively refined least squares finite element approach for the navier stokes equations that govern generalized newtonian fluid flows using the carreau model to capture the flow region we developed an adaptive mesh refinement approach based on the least squares method the generated refined grids agree well with the physical attributes of the flows we also proved that the least squares approximation converges to the linearized versions solutions of the carreau model at the best possible rate model problems considered in the study are the flow past a planar channel and 4 to 1 contraction problems we presented the numerical results of the model problems revealing the efficiency of the proposed scheme and investigated the physical parameter effects

interrelation between laplace constants and the gradient distortion effect in laplace domain waveform inversion abstractlaplace domain waveform inversion wi is generally used to generate smooth initial velocity models for frequency or time domain full waveform inversion however in the inversion results of laplace domain wi anomalies such as salt domes are sometimes shifted we evaluate the gradient distortion effect that causes undesirable changes in parameter updates and found that this is caused by the relationship between the partial derivatives of laplace wavefields with respect to two different parameters by analyzing the gradient of the laplace domain misfit function we found that the gradient distortion effect increases as the laplace constants used in the laplace domain wi decrease the velocity model inverted in the laplace domain is generally blurred from shallower parameters to deeper parameters because the partial derivatives of the laplace wavefields with respect to shallower parameters tend to be larger than those of deeper parameters we found two solutions for suppressing the gradient dist

cohomological invariants of jordan algebras with frames abstract in a previous paper the author determined all possible cohomological invariants of aut j torsors in galois cohomology with mod 2 coefficients where j is a split central simple jordan algebra of odd degree n 3 in the present paper we extend these results to a larger class of groups g n 1 n d r indexed by r 0 1 2 or 3 and n i positive integers that add to n 3 such that n 1 is odd we also give precise values for the essential dimension of these groups

on projected newton krylov solvers for instationary laminar reacting gas flows numerical aspects of computational modeling of chemical vapor deposition are discussed large sparse strongly nonlinear algebraic systems are to be solved per time step for this inexact newton methods and preconditioned krylov subspace methods are suitable to ensure positivity of concentrations we propose a novel approach namely a projected inexact newton method unlike the commonly used method of clipping this conserves mass efficiency of several preconditionings is compared our numerical tests culminate in an unusually large computation namely a three dimensional case with 17 species and 26 reactions

estimating the shannon entropy recurrence plots versus symbolic dynamics recurrence plots were first introduced to quantify the recurrence properties of chaotic dynamics a few years later the recurrence quantification analysis was introduced to transform graphical representations into statistical analysis among the different measures introduced a shannon entropy was found to be correlated with the inverse of the largest lyapunov exponent the discrepancy between this and the usual interpretation of a shannon entropy is solved here by using a new definition still based on the recurrence plots and it is verified that this new definition is correlated with the largest lyapunov exponent as expected from the pesin conjecture a comparison with a shannon entropy computed from symbolic dynamics is also provided

a geometric newton method for oja s vector field newton s method for solving the matrix equation runs up against the fact that its zeros are not isolated this is due to a symmetry of f by the action of the orthogonal group we show how differential geometric techniques can be exploited to remove this symmetry and obtain a geometric newton algorithm that finds the zeros of f the geometric newton method does not suffer from the degeneracy issue that stands in the way of the original newton method

reduced models of albert algebras we prove existence and uniqueness of reduced models for arbitrary albert algebras and relate them to the tits process this relationship yields explicit noncohomological realizations of the invariants mod 2 due to serre and rost we also construct nontrivial examples of albert division algebras with nonvanishing invariants mod 2

a meshless rbf method for computing a numerical solution of unsteady burgers type equations in this paper we discuss a meshless method for the computation of a numerical solution of unsteady coupled burgers type equations which are in the most general case nonlinear partial differential equations our approach is based on the interpolation of the solution by radial basis functions rbfs and is independent of the geometry of the domain the existence and unicity of such of an interpolant will be established by the mean of linear algebra arguments this spatial discretization transforms the initial problem into a system of ordinary differential equations odes we give a simple formulation of implicit runge kutta irk schemes that can be used to numerically solve this system of odes the main difficulty in the implementation of an irk method lies in the fact that it leads to a potentially large linear or nonlinear system that has to be solved at each time step a matrix gmres approach coupled with a newton based linearization technique in the nonlinear case will be used to numerically solve these systems some numerical examples will be provided to illustrate the performance of our approach

a parallel two level domain decomposition based one shot method for shape optimization problems summary a two level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible navier stokes equations the optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one shot lagrange newton krylov schwarz algorithms in this approach the shape of the domain its corresponding finite element mesh the flow fields and their corresponding lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations highly scalable parallel algorithms are absolutely necessary to solve such an expensive system the one level domain decomposition method works reasonably well when the number of processors is not large aiming for machines with a large number of processors and robust nonlinear convergence we introduce a two level inexact newton method with a hybrid two level overlapping schwarz preconditioner as applications we consider the shape optimization of a cannula problem and an artery bypass problem in 2d numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns copyright 2014 john wiley sons ltd

parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed sphere high resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate in this paper we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second order well balanced finite volume method on the cubed sphere with the fully implicit approach the time step size is no longer limited by the stability condition and with the multilevel preconditioners good scalabilities are obtained on computers with a large number of processors the investigation focuses on the use of semismooth inexact newton method for the case with nonsmooth topography and the use of two and three level overlapping schwarz methods with different order of discretizations for the preconditioning of the jacobian systems we test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors

nonlinear krylov acceleration applied to a discrete ordinates formulation of the k eigenvalue problem we compare a variant of anderson mixing with the jacobian free newton krylov and broyden methods applied to an instance of the k eigenvalue formulation of the linear boltzmann transport equation we present evidence that one variant of anderson mixing finds solutions in the fewest number of iterations we examine and strengthen theoretical results of anderson mixing applied to linear problems

bayesian non parametric inference for species variety with a two parameter poisson dirichlet process prior summary a bayesian non parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems such problems concern the evaluation conditional on a sample of size n of the species variety featured by an additional sample of size m genomic applications pose the additional challenge of having to deal with large values of both n and m in such a case the computation of the bayesian non parametric estimators is cumbersome and prevents their implementation we focus on the two parameter poisson dirichlet model and provide completely explicit expressions for the corresponding estimators which can be easily evaluated for any sizes of n and m we also study the asymptotic behaviour of the number of new species conditionally on the observed sample such an asymptotic result combined with a suitable simulation scheme allows us to derive asymptotic highest posterior density intervals for the estimates of interest finally we illustrate the implementation of the proposed methodology by the analysis of five expressed sequence tags data sets

inexact block newton methods for solving nonlinear equations in the paper two parallelizable inexact block newton methods are presented for solving large and sparse nonlinear equations the basic idea is simple and direct combining the simplified newton method with the component averaging cav method parallel comput 27 2001 777 results in an inexact newton method called simplified newton cav method parallel tests of the algorithm are implemented on a message passing distributed memory multiprocessor architecture such as a cluster of workstations the results show that the new algorithm can achieve good performance moreover as a development of the simplified newton cav method the overlapped block newton cav method is further proposed and discussed

least squares p r finite element methods for incompressible non newtonian flows a least squares mixed p type finite element method is developed for numerical solution of incompressible non newtonian flows hierarchical piecewise polynomials are introduced as element basis functions while singularities and boundary layers are treated by a combination of mesh redistribution and polynomial refinement scaling of the original differential equations is found to be important for the least squares minimization process we discuss both nonlinear algebraic and differential constitutive models and present numerical examples to illustrate benefits and shortcomings of the present approach

comparison of multifrequency selection strategies for simultaneous source full waveform inversion abstractthe computational cost of full waveform inversion fwi is a major obstacle to estimating the velocity model for large scale problems one way to reduce the overall cost of waveform inversion is by adopting a simultaneous source strategy in other words multiple sources are simultaneously fired to simulate supershot gathers and thereby reduce the number of seismic modeling simulations that are performed during the inversion however the use of simultaneous sources introduces crosstalk artifacts that arise from the interference among the sources that constitute a supershot we analyzed the influence of different simultaneous multifrequency selection strategies on crosstalk artifacts our analysis focused on a frequency domain fwi algorithm that is implemented with simultaneous sources that are randomly encoded with random time shifts in the multiscale conventional fwi strategies a finite set of discrete frequencies was selected and the inversion was carried out sequentially from low to high fr

a nonlinear weighted least squares finite element method for the carreau yasuda non newtonian model abstract we study a nonlinear weighted least squares finite element method for the navier stokes equations governing non newtonian fluid flows by using the carreau yasuda model the carreau yasuda model is used to describe the shear thinning behavior of blood we prove that the least squares approximation converges to linearized solutions of the non newtonian model at the optimal rate by using continuous piecewise linear finite element spaces for all variables and by appropriately adjusting the nonlinear weighting function we obtain optimal l 2 norm error convergence rates in all variables numerical results are given for a carreau fluid in the 4 to 1 contraction problem revealing the shear thinning behavior the physical parameter effects are also investigated

nonlinear feti dp and bddc methods a unified framework and parallel results parallel newton krylov feti dp finite element tearing and interconnecting dual primal domain decomposition methods are fast and robust solvers e g for nonlinear implicit problems in structural mechanics in these methods the nonlinear problem is first linearized and then decomposed into loosely coupled linear problems which can be solved in parallel by changing the order of the operations new parallel communication can be constructed where the loosely coupled local problems are nonlinear we discuss different nonlinear feti dp methods which are equivalent when applied to linear problems but which show a different performance for nonlinear problems moreover a new unified framework is introduced which casts all nonlinear feti dp domain decomposition approaches discussed in the literature into a single algorithm furthermore the equivalence of nonlinear feti dp methods to specific nonlinearly right preconditioned newton krylov methods is shown for the methods using nested newton iteration

on the invariants mod 2 of albert algebras the existence of a new invariant for central simple exceptional jordan algebras nowadays called albert algebras over an arbitrary base field k of characteristic not 2 or 3 following a suggestion of serre se has recently been established by rost ro1 in fact serre loc cit has raised the question as to whether this new invariant called the invariant mod 3 together with the ordinary trace form already employed in the work of springer sp classifies albert algebras over k

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

real non unital division algebras with su 3 as derivation algebra abstract we obtain a family of non unital eight dimensional division algebras over a field f out of a separable quadratic field extension s of f a three dimensional anisotropic hermitian form over s of determinant one and three invertible elements c d e s these algebras contain a four dimensional subalgebra which can be viewed as a generalization of a nonassociative quaternion algebra the four dimensional algebras are studied independently over r this construction can be used to generate division algebras with derivation algebra isomorphic to su 3 which are the direct sum of two one dimensional modules and a six dimensional irreducible su 3 module albert isotopes with derivation algebra isomorphic to su 3 are considered briefly as well

entropy estimation in turing s perspective a new nonparametric estimator of shannon s entropy on a countable alphabet is proposed and analyzed against the well known plug in estimator the proposed estimator is developed based on turing s formula which recovers distributional characteristics on the subset of the alphabet not covered by a size n sample the fundamental switch in perspective brings about substantial gain in estimation accuracy for every distribution with finite entropy in general a uniform variance upper bound is established for the entire class of distributions with finite entropy that decays at a rate of o ln n n compared to o ln n 2 n for the plug in in a wide range of subclasses the variance of the proposed estimator converges at a rate of o 1 n and this rate of convergence carries over to the convergence rates in mean squared errors in many subclasses specifically for any finite alphabet the proposed estimator has a bias decaying exponentially in n several new bias adjusted estimators are also discussed

development of a continuity preserving segregated method for incompressible navier stokes equations the present study aims to develop a new method for obtaining the non oscillatory incompressible navier stokes solutions on the non staggered grids within the segregated grid framework the divergence free equation is chosen to replace one of the momentum equations so as to preserve the fluid incompressibility for the sake of numerical accuracy the five point stencil convection diffusion reaction scheme is developed to obtain the nodally exact solution for this chosen momentum equation the validity of the proposed mass preserving navier stokes method is justified by solving the three problems which are amenable to analytical solutions the simulated solution quality is shown to outperform that of the conventional segregated approach besides gaining a very high spatial rate of convergence

goal oriented model constrained optimization for reduction of large scale systems optimization oriented reduced order models should target a particular output functional span an applicable range of dynamic and parametric inputs and respect the underlying governing equations of the system to achieve this goal we present an approach for determining a projection basis that uses a goal oriented model constrained optimization framework the mathematical framework permits consideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems results for a simple linear model problem of the two dimensional heat equation demonstrate the ability of the goal oriented approach to target a particular output functional of interest application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

the upward bias in measures of information derived from limited data samples extracting information measures from limited experimental samples such as those normally available when using data recorded in vivo from mammalian cortical neurons is known to be plagued by a systematic error which tends to bias the estimate upward we calculate here the average of the bias under certain conditions as an asymptotic expansion in the inverse of the size of the data sample the result agrees with numerical simulations and is applicable as an additive correction term to measurements obtained under such conditions moreover we discuss the implications for measurements obtained through other usual procedures

adaptive eigenspace for multi parameter inverse scattering problems abstract a nonlinear optimization method is proposed for inverse scattering problems in the frequency domain when the unknown medium is characterized by one or several spatially varying parameters the time harmonic inverse medium problem is formulated as a pde constrained optimization problem and solved by an inexact truncated newton type method combined with frequency stepping instead of a grid based discrete representation each parameter is projected to a separate finite dimensional subspace which is iteratively adapted during the optimization each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori the small and slowly increasing finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard tikhonov type regularization numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi parameter problems including the well known marmousi model from geosciences

implicit boundary equations for conservative navier stokes equations abstract co existence of the physical and numerical boundary conditions makes implicit boundary treatment a particularly difficult problem in modern cfd simulations previous studies adopted space time extrapolation or specially designed partial differential equations on the boundaries that are different from those of interior points they are often formulated in terms of primitive variables and are very challenging for complicated boundary types to be converted to and implemented in the conservative variables that are preferred in numerical simulations more importantly different boundary equations or different extrapolation techniques may compromise the stability accuracy or convergence rate of the a stable schemes that are developed for interior points a new methodology for implicit boundary treatment is proposed in this study by introducing a simple correction matrix t a set of generalized equations q t i t r are developed in terms of conservative variables it is applicable for both the interior domain t 0 and the boundaries t 0 it is in a partial differential equation form satisfies the boundary conditions accurately independent of the time and spatial discretizations any one sided schemes can be used on the boundaries but still maintain the upwind property implicit solution techniques are made significantly easy to implement using for example the data parallel lower upper relation method and the newton method combined with the gmres method for subsidiary iterations numerical experiments show that the proposed methodology produces stable simulations for very large cfl numbers and preserve the imposed boundary values accurately

inexact overlapped block broyden methods for solving nonlinear equations in this paper a parallelizable overlapped block broyden method is presented for solving large systems of nonlinear equations the basic idea is to perform the block broyden iteration described in siam j sci comput 18 1997 1367 for the overlapped blocks and then assemble the overlapping solutions in a weighted average manner at each iteration a family of nonlinear overlapped solvers could be generated combining it with some iterative or direct linear solvers the conditions under which the algorithm is locally convergent are studied and many useful techniques regarding the implementation are also considered

inexact newton methods for inverse eigenvalue problems in this paper we survey some of the latest development in using inexact newton methods for solving inverse eigenvalue problems these methods require the solutions of nonsymmetric and large linear systems i e the large jacobian equations one can solve these systems by iterative methods inner iterations however iterative methods usually oversolve the problem in the sense that they require far more inner iterations than is required for the convergence of the newton outer iterations the inexact methods can avoid the oversolving problem and hence improve the efficiency the convergence rate of the inexact methods are superlinear and a good tradeoff between the required inner and outer iterations can be obtained

choosing the forcing terms in an inexact newton method an inexact newton method is a generalization of newton s method for solving f x 0 f mathbb r n to mathbb r n in which at the kth iteration the step s k from the current approximate solution x k is required to satisfy a condition f x k f x k s k leqslant eta k f x k for a forcing term eta k in 0 1 in typical applications the choice of the forcing terms is critical to the efficiency of the method and can affect robustness as well promising choices of the forcing terms are given their local convergence properties are analyzed and their practical performance is shown on a representative set of test problems

a nonlinear weighted least squares finite element method for stokes equations the paper concerns a nonlinear weighted least squares finite element method for the solutions of the incompressible stokes equations based on the application of the least squares minimization principle to an equivalent first order velocity pressure stress system model problem considered is the flow in a planar channel the least squares functional involves the l 2 norms of the residuals of each equation multiplied by a nonlinear weighting function and mesh dependent weights using linear approximations for all variables by properly adjusting the importance of the mass conservation equation and a carefully chosen nonlinear weighting function the least squares solutions exhibit optimal l 2 norm error convergence in all unknowns numerical solutions of the flow pass through a 4 to 1 contraction channel will also be considered

estimation of entropy and mutual information we present some new results on the nonparametric estimation of entropy and mutual information first we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators the setup is related to grenander s method of sieves and places no assumptions on the underlying probability measure generating the data second we prove a converse to these consistency theorems demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information even given unlimited data this inconsistency theorem leads to an analytical approximation of the bias valid in surprisingly small sample regimes and more accurate than the usual 1 n formula of miller and madow over a large region of parameter space the two most practical implications of these results are negative 1 information estimates in a certain data regime are likely contaminated by bias even if bias corrected estimators are used and 2 confidence intervals calculated by standard techniques drastically underestimate the error of the most common estimation methods finally we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem by casting bias calculation problems in this approximation theory framework we obtain the best possible generalization of known asymptotic bias results more interesting this framework leads to an estimator with some nice properties the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions and this maximum error turns out to be surprisingly small we demonstrate the application of this new estimator on both real and simulated data

on a one dimensional optimization problem derived from the efficiency analysis of newton pcg like algorithms the newton pcg preconditioned conjugate gradient like algorithms are usually very efficient however their efficiency is mainly supported by the numerical experiments recently a new kind of newton pcg like algorithms is derived in j optim theory appl 105 2000 97 superiority analysis on truncated newton method with preconditioned conjugate gradient technique for optimization in preparation by the efficiency analysis it is proved from the theoretical point of view that their efficiency is superior to that of newton s method for the special cases where newton s method converges with precise q order 2 and 2 respectively in the process of extending such kind of algorithms to the more general case where newton s method has no fixed convergence order the first is to get the solutions to the one dimensional optimization problems with many different parameter values of if these problems were solved by numerical method one by one the computation cost would reduce the efficiency of the newton pcg algorithm and therefore is unacceptable in this paper we overcome the difficulty by deriving an analytic expression of the solution to the one dimensional optimization problem with respect to the parameter

invariants mod 2 and subgroups of g2 and f4 abstract let k be a field of characteristic different from 2 and 3 let g be a simple group of type f 4 or g 2 defined over k in this paper we discuss embeddings of connected simple algebraic groups of type a 1 and a 2 in g in terms of the mod 2 galois cohomological invariants attached to these groups we prove that k groups of type f 4 resp g 2 arising from division algebras are generated by k subgroups of type a 2 resp a 1 see theorem 3 11 theorem 4 1 we derive a necessary and sufficient condition for an albert algebra to have zero f 5 invariant theorem 3 4 further for a k group g of type f 4 we derive a condition necessary for a k group h of type a 1 or a 2 to embed in g over k we prove that in order to embed h in g over k the mod 2 invariant of h must divide f 5 g see section 2 and remark 2 8 remark 2 3 for definition of invariants along similar lines we derive a condition for a k group h of type a 2 to embed in a k group g of type g 2 we prove that h embeds in g over k if and only if f 3 h f 3 g theorem 4 4 next we derive a necessary and sufficient condition for a k group h of type a 1 to embed in a k group g of type g 2 if g aut c is a group of type g 2 over k for an octonion algebra c over k then this condition provides a natural bijection between k conjugacy classes of involutions in g k and isometry classes of 2 fold pfister divisors of the pfister form n c the norm form of the octonion algebra c section 4 proposition 4 2

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100