refined iterative algorithms based on arnoldi s process for large unsymmetric eigenproblems abstract arnoldi s method has been popular for computing the small number of selected eigenvalues and the associated eigenvectors of large unsymmetric matrices however the approximate eigenvectors or ritz vectors obtained by arnoldi s method cannot be guaranteed to converge in theory even if the approximate eigenvalues or ritz values do in order to circumvent this potential danger a new strategy is proposed that computes refined approximate eigenvectors by small sized singular value decompositions it is shown that refined approximate eigenvectors converge to eigenvectors if ritz values do moreover the resulting refined algorithms converge more rapidly we report some numerical experiments and compare the refined algorithms with their counterparts the iterative arnoldi and arnoldi chebyshev algorithms the results show that the refined algorithms are considerably more efficient than their counterparts

hierarchical spatial process models for multiple traits in large genetic trials this article expands upon recent interest in bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation the situation is even worse in markov chain monte carlo mcmc contexts where such computations are performed for several thousand iterations here we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling for genetic effects we demonstrate how an initial spectral decomposition of the relationship matrices negates the expensive matrix inversions required in previously proposed mcmc methods for spatial effects we discuss a multivariate predictive process that reduces the computational burden by projecting th

iterated stack automata and complexity classes abstract an iterated pushdown is a pushdown of pushdowns of of pushdowns an iterated exponential function is 2 to the 2 to the to the 2 to some polynomial the main result presented here is that the nondeterministic 2 way and multi head iterated pushdown automata characterize the deterministic iterated exponential time complexity classes this is proved by investigating both nondeterministic and alternating auxiliary iterated pushdown automata for which similar characterization results are given in particular it is shown that alternation corresponds to one more iteration of pushdowns these results are applied to the 1 way iterated pushdown automata 1 they form a proper hierarchy with respect to the number of iterations and 2 their emptiness problem is complete in deterministic iterated exponential time similar results are given for iterated stack checking stack nonerasing stack nested stack checking stack pushdown automata

alternating pushdown and stack automata the classes of languages accepted by alternating pushdown automata alternating stack automata and alternating nonerasing stack automata both with and without an auxiliary space bounded worktape are characterized in terms of complexity classes defined by time bounded deterministic turing machines it is also shown that alternating 2 way finite state machines accept only regular languages

properties of probabilistic pushdown automata properties of probabilistic as well as probabilistic plus nondeterministic pushdown automata and auxiliary pushdown automata are studied these models are analogous to their counterparts with nondeterministic and alternating states complete characterizations in terms of well known complexity classes are given for the classes of languages recognized by polynomial time bounded logarithmic space bounded auxiliary pushdown automata with probabilistic states and with probabilistic plus nondeterministic states also complexity lower bounds are given for the classes of languages recognized by these automata with unlimited running time it follows that by fixing an appropriate mode of computation the difference between classes of languages such as p and pspace nl and sac 1 pl and diff sac 1 is characterized as the difference between the number of stack symbols that is whether the stack alphabet contains one versus two distinct symbols

alternation bounded auxiliary pushdown automata languages accepted by alternating auxiliary pushdown automata using simultaneously a n alternations and s n space are shown to be members of the class of languages accepted by nondeterministic turing machines using a n 2es n space for some c 0 this result is used to show that the hierarchy of classes of languages accepted by pushdown automata based on the number of alternations collapses at the second level of the hierarchy the power of alternation bounded pushdown automata without auxiliary storage is also investigated

a jacobi davidson method for solving complex symmetric eigenvalue problems we discuss variants of the jacobi davidson method for solving the generalized complex symmetric eigenvalue problem the jacobi davidson algorithm can be considered as an accelerated inexact rayleigh quotient iteration we show that it is appropriate to replace the euclidean inner product in mathbb c n with an indefinite inner product the rayleigh quotient based on this indefinite inner product leads to an asymptotically cubically convergent rayleigh quotient iteration advantages of the method are illustrated by numerical examples we deal with problems from electromagnetics that require the computation of interior eigenvalues the main drawback that we experience in these particular examples is the lack of efficient preconditioners

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

on a conjugate gradient type method for solving complex symmetric linear systems abstract we consider large sparse linear systems ax b with complex symmetric coefficient matrices a a t which arise e g from the discretization of partial differential equations with complex coefficients for the solution of such systems we present a new conjugate gradient type iterative method csym which is based on unitary equivalence transformations of a to symmetric tridiagonal form an analysis of csym shows that its convergence depends on the singular values of a and that it has both the minimal residual property and constant costs per iteration step we compare the algorithm with other methods for solving large sparse complex symmetric systems

the geometric measure of multipartite entanglement and the singular values of a hypermatrix it is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation generalizing the singular value equation of the matrix of coefficients of a bipartite state the equation is solved for a class of three qubit states

lower bounds for multiplayer noncooperative games of incomplete information abstract this paper see also 1 extends the alternating turing machine a tm of chandra kozen and stockmeyer 2 the private and the blind alternating machines of reif 3 4 to model multiplayer games of incomplete information we use these machines to provide matching lower bounds for our decision algorithms described in our companion paper 5 we also apply multiple person alternation to other machine types we show that multiplayer games of incomplete information can be undecidable general however one form of incomplete information games that is decidable we term as hierarchical games defined later in this paper in hierarchical multiplayer games each additional clique subset of players with same information increases the complexity of the outcome problem by a further exponential consequently if a multiplayer game of incomplete information with k cliques has a space bound of s n then its outcome can be k repeated exponentials harder than games of complete information with the same space bound s n this paper proves that this exponential blow up must occur in the worst case we define team private peek and team blind peek extending the previous models of peek these new games can be shown to be complete for their respective classes we use these games to establish lower bounds on complexity of multiplayer games of incomplete information and blindfold multiplayer games we analyze the time bounded alternating machines and conclude that time is not a very critical resource for multiplayer alternation we also show dqbf a variant of qbf to be complete in nexptime

properties of the matrix a xy abstract the main topic of this paper is the matrix v a xy where a is a nonsingular complex k k matrix and x and y are k p complex matrices of full column rank because properties of the matrix v can be derived from those of the matrix q i xy we will consider in particular the case where a i for the case that y x i so that q is singular we will derive the moore penrose inverse of q the moore penrose inverse of v in case y a 1 x i then easily follows finally we will focus on the eigenvalues and eigenvectors of the real matrix d xy with d diagonal

tangent bundle maps on the grassmann manifold application to empirical arithmetic averaging the present paper elaborates on tangent bundle maps on the grassmann manifold with application to subspace arithmetic averaging in particular the present contribution elaborates on the work about retraction lifting maps devised for the stiefel manifold in the recently published paper t kaneko s fiori and t tanaka empirical arithmetic averaging over the compact stiefel manifold ieee trans signal process vol 61 no 4 pp 883 894 february 2013 and discusses the extension of such maps to the grassmann manifold tangent bundle maps are devised on the basis of the thin qr matrix decomposition the polar matrix decomposition and the exponential map also tangent bundle pseudo maps based on the matrix cayley transform are devised theoretical and numerical comparisons about the devised tangent bundle maps are performed in order to get an insight into their relative merits and demerits with special emphasis to their computational burden the averaging algorithm based on the thin qr decomposition maps stands out as it exhibits the best trade off between numerical precision and computational burden such algorithm is further compared with two grassmann averaging algorithms drawn from the scientific literature on an handwritten digits recognition data set the thin qr tangent bundle maps based algorithm exhibits again numerical features that make it preferable over such algorithms

a new preconditioner that exploits low rank approximations to factorization error we consider ill conditioned linear systems ax b that are to be solved iteratively and assume that a low accuracy lu factorization a approx widehat l widehat u is available for use in a preconditioner we have observed that for ill conditioned matrices a arising in practice a 1 tends to be numerically low rank that is it has a small number of large singular values importantly the error matrix e widehat u 1 widehat l 1 a i tends to have the same property to understand this phenomenon we give bounds for the distance from e to a low rank matrix in terms of the corresponding distance for a 1 we then design a novel preconditioner that exploits the low rank property of the error to accelerate the convergence of iterative methods we apply this new preconditioner in three different contexts fitting our general framework low floating point precision e g half precision lu factorization incomplete lu factorization and block low rank lu factorization in numerical experiments with gmres based iterative refinement we show that our preconditioner can achieve a significant reduction in the number of iterations required to solve a variety of real life problems

on a matrix identity associated with generalized least squares abstract this note discusses an identity which is useful in the construction of reduced generalized least squares equations in the reml method of estimating variance components and in calculating best linear unbiased predictors the identity is shown to be a singular form of a better known matrix relation some applications of the result are presented

alternating and empty alternating auxiliary stack automata we consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited in this way we get new characterizations of np the polynomial hierarchy pspace and bounded query classes like co dp nl np 1 and 2p pnp o logn in a uniform framework

parallel preconditioners for large scale partial difference equation systems we propose a new preconditioner dasp discrete approximate spectral preconditioner based on the existing well known preconditioners and our computational experience parallel preconditioning strategies for large scale partial difference equation systems arising from partial differential equations are investigated numerical results are given to show the efficiency and effectiveness of the new preconditioners for both model problems and real applications in petroleum reservoir simulation

the effective conductivity of random checkerboards an algorithm is presented for the fast and accurate solution of the electrostatic equation on multi component random checkerboards it relies on a particular choice of integral equation extended as to separate ill conditioning due to singular fields in corners from ill conditioning due to interaction of clusters of well conducting squares at large distances two separate preconditioners take care of the two separate phenomena in a series of numerical examples effective conductivities are computed for random checkerboards containing up to 104 squares with conductivity ratios of up to 106 the achievable relative precision in these examples is on the order of 10 11

use of the gibbs sampler to invert large possibly sparse positive definite matrices abstract a problem that is frequently encountered in statistics is that of computing some of the elements e g the diagonal elements of the inverse of a large possibly sparse positive definite matrix let w w ij represent an m m positive definite matrix let v v ij w 1 and let x x i represent an m 1 random vecor whose distribution is multivariate normal with null mean vector and variance covariance matrix v the gibbs sampler can be used to generate a sequence of m 1 vectors x 1 x 2 such that for sufficiently large values of k x k can be regarded as a sample value of x letting x 1 k x m k represent the elements of x k x i k is a draw from a univariate normal distribution with mean and variance w ii 1 the sample values of x can be used to obtain a monte carlo estimate of expectation e x i x i and hence since v ij e x i x j of v ij a possibly more efficient alternatives is to use the sample values to evaluate the outer expectation in the expression e e x i x j x t where x t is a subvector of x that excludes x i and or x j sparsity or various other kinds of structure in w can be used to computational advantage in generating the draws x 1 x 2 numerical results indicate that if w is well conditioned then the statistical dependence between the draws is relatively small reasonably accurate monte carlo estimates can be obtained from a relatively small number of draws and the conditioning of x i x j on x t leads to significant improvements in accuracy

boundary element solution for stochastic groundwater flow random boundary condition and recharge this paper presents an integral equation technique for solving stochastic boundary value problems in groundwater flow the aquifer considered has deterministic hydraulic conductivity but is subject to random boundary condition and domain recharge using the distribution of fictitious sources and dipoles stochastic integral equations for the mean and covariance of head and flux are derived an iterative boundary element technique is applied for numerical solution two one dimensional examples are examined and compared with exact solution a two dimensional problem is then presented

pushdown module checking with imperfect information the model checking problem for finite state open systems module checking has been extensively studied in the literature both in the context of environments with perfect and imperfect information about the system recently the perfect information case has been extended to infinite state systems pushdown module checking in this paper we extend pushdown module checking to the imperfect information setting i e to the case where the environment has only a partial view of the email protected s control states and pushdown store content we study the complexity of this problem with respect to the branching time temporal logics ctl ctl and the propositional m calculus we show that pushdown module checking which is by itself harder than pushdown model checking becomes undecidable when the environment has imperfect information we also show that undecidability relies on hiding information about the pushdown store indeed we prove that with imperfect information about the control states but a visible pushdown store the problem is decidable and its complexity is 2exptime complete for ctl and the propositional m calculus and 3exptime complete for ctl

a survey of space complexity abstract the main properties of deterministic and nondeterministic space complexity classes are given with emphasis on closure under complementation various limitations and generalizations of these classes are studied weakly space bounded classes classes defined by one way alternating or probabilistic machines and nonuniform classes in each case intrinsic properties of these classes and relationship between these classes are given then three ways of relativizing complexity classes are examined finally the space complexity of rams is defined and its relation to usual classes is given

on the solution of generalized non linear complex symmetric eigenvalue problems this paper brings an attempt toward the systematic solution of the generalized non linear complex symmetric eigenproblem k o i c 1 2 m 1 i 3 c 2 4 m 2 0 with real symmetric matrices ko c j m j r nxn which are associated with the dynamic governing equations of a structure submitted to viscous damping as laid out in the frame of an advanced mode superposition technique the problem can be restated as k m where k o k t and m m t are complex symmetric matrices given as power series of the complex eigenfrequencies such that if is a solution eigenpair t m 1 and t k the traditional rayleigh quotient iteration and the more recent jacobi davidson method are outlined for complex symmetric linear problems and shown to be mathematically equivalent both with asymptotically cubic convergence the jacobi davidson method is more robust and adequate for the solution of a set of eigenpairs the non linear eigenproblem subject of this paper can be dealt with in the exact frame of the linear analysis thus also presenting cubic convergence two examples help us to visualize some of the basic concepts developed three more examples illustrate the applicability of the proposed algorithm to solve non linear problems in the general case of underdamping but also for overdamping combined with multiple and close eigenvalues

proxies versus omitted variables in regression analysis when some variables to be used in a regression analysis contain measurement error the ols estimator will be inconsistent when these variables are left out ols will also be inconsistent in an appropriate metric the first type of inconsistency is smaller than the second type

a perturbation boundary element code for steady state groundwater flow in heterogeneous aquifers a boundary element code is developed for the steady state darcy s flow in heterogeneous porous media the solution is based on the expansion of the piezometric head into perturbation series the governing equation is decomposed into a laplace equation and a sequence of poisson equations with known right hand sides regular boundary element procedure is applied for their solutions three numerical examples with moderate hydraulic conductivity variations are provided to demonstrate the applicability of the code the convergence of the perturbation solution is discussed using a one dimensional problem

schur complements and statistics abstract in this paper we discuss various properties of matrices of the type s h ge 1 f which we call the schur complement of e in a e f g h the matrix e is assumed to be nonsingular when e is singular or rectangular we consider the generalized schur complements s h ge f where e is a generalized inverse of e a comprehensive account of results pertaining to the determinant the rank the inverse and generalized inverses of partitioned matrices and the inertia of a matrix is given both for schur complements and for generalized schur complements we survey the known results in a historical perspective and obtain several extensions numerous applications in numerical analysis and statistics are included the paper ends with an exhaustive bibliography of books and articles related to schur complements

from frequency dependent mass and stiffness matrices to the dynamic response of elastic systems abstract more than three decades ago przemieniecki introduced a formulation for the free vibration analysis of bar and beam elements based on a power series of frequencies in the present paper the authors generalize this formulation for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements based on the mode superposition method a set of coupled higher order differential equations of motion is transformed into a set of uncoupled second order differential equations which may be integrated by means of standard procedures motivation for this theoretical achievement is the hybrid boundary element method which has been developed by the authors for time dependent as well as frequency dependent problems this formulation as a generalization of pian s previous achievements for finite elements yields a stiffness matrix for which only boundary integrals are required for arbitrary domain shapes and any number of degrees of freedom the use of higher order frequency terms drastically improves numerical accuracy the introduced modal assessment of the dynamic problem is applicable to any kind of finite element for which a generalized stiffness matrix is available some academic examples illustrate the theory

alternation in two way finite automata abstract the study of alternation in two way finite automata 2 fa s has been quite non systematic since the 1970 s various authors with a variety of motivations have studied 2 fa s with various types of alternation and a variety of names creating a fairly long list of sporadic contributions with little internal consistency this article attempts to organize the subject into a single unifying framework we start with a detailed account of all contributions to date that reveals the large variety of approaches and the lack of consistency between them we then identify and name four types of automata that these contributions have really studied over the years general two way boolean finite automata 2 b fa s monotone 2 b fa s basic 2 b fa s and monotone basic or alternating 2 b fa s 2 a fa s next we identify four different ways by which authors have described how such automata compute each offering a distinct view onto their operation the circuit view where computation is modelled by a circuit of boolean gates the formula view where computation is modelled by a boolean formula over configuration variables the run view where decisions are determined by the existence of appropriate trees of configuration goal pairs called runs and the most classic tree view where computation is modelled by a tree of configurations after carefully defining each 2 b fa type and each view we prove the following first that within each type every two of the four views are equivalent to each other in the strong sense that each of them closely mimics the other at every step of the computation second that not all types of 2 b fa s are equivalent although general 2 b fa s are as powerful as monotone 2 b fa s and basic 2 b fa s are as powerful as 2 a fa s up to polynomial differences in the number of states general 2 b fa s may need exponentially fewer states than 2 a fa s

a multi resolution approximation for massive spatial datasets abstractautomated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high resolution observations of spatial fields over large spatial regions if these datasets can be efficiently exploited they can provide new insights on a wide variety of issues however traditional spatial statistical techniques such as kriging are not computationally feasible for big datasets we propose a multi resolution approximation m ra of gaussian processes observed at irregular locations in space the m ra process is specified as a linear combination of basis functions at multiple levels of spatial resolution which can capture spatial structure from very fine to very large scales the basis functions are automatically chosen to approximate a given covariance function which can be nonstationary all computations involving the m ra including parameter inference and prediction are highly scalable for massive datasets crucially the inference algorithms can also be parallelize

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

a krylov subspace projection method for simultaneous solution of helmholtz problems at multiple frequencies abstract a krylov subspace projection method which provides simultaneous solutions of the helmholtz equation at multiple frequencies in one solution step is presented the projector is obtained with an unsymmetric block lanczos algorithm applied to a transfer function derived from a finite element discretization this approach is equivalent to a matrix valued pade approximation of the transfer function the proposed method is an extension of the formulation presented in j comput acoust 8 2000 223 to unsymmetric systems and allows the treatment of a much wider range of practical problems including near field and fluid structure interaction computations

an advanced direct time domain bem for 3 d wave propagation in acoustic media this paper presents a new boundary element method bem in the direct time domain for the solution of the wave propagation problem in 3d homogenous inviscid acoustic media the methodology is based on impulse response techniques to this end the fundamental solutions associated with the boundary integral equation are derived for concentrated sources of higher order b spline time modulation high order spatial discretization is adopted the solution is obtained in two major steps first the b spline impulse response functions birf for a system of a specific geometry are calculated birf functions are independent of the actual external excitation and need to be calculated only once for a given geometry the second step calculates the response of the system to arbitrary excitations through a mere superposition of the birf functions this paper discusses the development of the proposed bem methodology and its validation the method is shown to be stable regardless of the selection of the analysis time step as opposed to the retarded potential techniques reported in the literature the high level of accuracy and the efficiency of the method are demonstrated

constructive entanglement test from triangle inequality we derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system the main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices the obtained bound leads to entanglement criteria with a straightforward interpretation the proposed criteria provide an experimentally accessible powerful entanglement test

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

the sum of nonsingular matrices is often nonsingular abstract if m is a set of nonsingular k k matrices then for many pairs of matrices a b m the sum is nonsingular det a b 0 we prove a more general statement on nonsingular sums with a geometric application

numerical treatment of acoustic problems with the hybrid boundary element method abstract the symmetric hybrid boundary element method in the frequency and time domain is introduced for the computation of acoustic radiation and scattering in closed and infinite domains the hybrid stress boundary element method in a frequency domain formulation is based on the dynamical hellinger reissner potential and leads to a hermitian frequency dependent stiffness equation as compared to previous results published by the authors new considerations concerning the interpretation of singular contributions in the stiffness matrix are communicated on the other hand the hybrid displacement boundary element method for time domain starts out from hamilton s principle formulated with the velocity potential the field variables in both formulations are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of singular fundamental solutions generated by dirac distributions and generalized loads that are time dependent in the transient case the domain is modified such that small spheres centered at the nodes are subtracted then the property of the dirac distribution now acting outside the domain cancels the remaining domain integral in the hybrid principle and leads to a boundary integral formulation incorporating singular integrals in the time domain formulation an analytical transformation is employed to transform the remaining domain integral into a boundary one this approach results in a linear system of equations with a symmetric stiffness and mass matrix earlier 2d results are generalized in the present paper by a 3d implementation numerical results of transient pressure wave propagation in a closed domain are presented

linear interference alignment in full duplex mimo networks with imperfect csi in this paper we consider a system where full duplex fd base stations bss communicate with half duplex hd downlink dl and uplink ul users in a multi user multi cell network where all nodes are equipped with multiple antennas the introduction of fd bss offers potential to increase spectral efficiency however it also causes a surge in the number of interference links compared with the hd network counterpart here we apply linear interference alignment ia to manage interference in this network under imperfect channel state information csi first we characterize the performance losses incurred with respect to the achievable sum rate and degrees of freedom dofs results show that the general trend in performance loss is mainly determined by how the error scales with the signal to noise ratio snr in particular full ul and dl dof can be achieved even under imperfect csi when the channel error is at least inversely proportional to snr moreover in such cases the sum rate loss is always finite and either goes to zero or is upper bounded by a derived value second we design two linear ia algorithms applicable to the system under consideration these are based on minimizing the mean square error mmse and maximizing the signal to interference plus noise ratio and consider statistical knowledge of the csi error for added robustness the proposed algorithms follow specific design principles that distribute the different interference components amongst the various beamformers and result in unitary receivers and precoders in addition we show that under certain conditions both designs result in identical beamforming solutions even though the mmse algorithm has lower computational complexity finally we also derive the proper condition for ia feasibility in the multi cell system under consideration

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

fixed rank kriging for very large spatial data sets summary spatial statistics for very large spatial data sets is challenging the size of the data set n causes problems in computing optimal spatial predictors such as kriging since its computa tional cost is of order a73 in addition a large data set is often defined on a large spatial domain so the spatial process of interest typically exhibits non stationary behaviour over that domain a flexible family of non stationary covariance functions is defined by using a set of basis functions that is fixed in number which leads to a spatial prediction method that we call fixed rank kriging specifically fixed rank kriging is kriging within this class of non stationary covariance functions it relies on computational simplifications when n is very large for obtaining the spatial best linear unbiased predictor and its mean squared prediction error for a hidden spatial process a method based on minimizing a weighted frobenius norm yields best estimators of the covari ance function parameters which are then substituted into the fixed rank kriging equations the new methodology is applied to a very large data set of total column ozone data observed over the entire globe where n is of the order of hundreds of thousands

nonlinear entanglement witnesses entanglement detection typically relies on linear inequalities for mean values of certain observables entanglement witnesses where violation indicates entanglement we provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions the nonlinearities are of different orders and can be directly measured in experiments often without any extra effort

toward an understanding of entanglement for generalized n qubit w states we solve stationarity equations of the geometric measure of entanglement for multi qubit w type states in this way we compute analytically the maximal overlap of one parameter n qubit and two parameter four qubit w type states and their nearest product states possible extensions to arbitrary w type states and geometrical interpretations of these results are discussed in detail

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

complex variable boundary element method for potential flow with thin objects a complex variable boundary element method cvbem is developed for potential flow in the presence of thin objects singularities caused by such objects are expressed analytically through the conformal mapping technique and the resultant singular solution is coupled with the cvbem by the principle of superposition this can be done by virtue of the semi analytic nature of the cvbem the numerical results for example problems including flow barriers and high conductivity fractures confirm that the proposed model yields accurate solutions of the velocity potential and the stream function within the flow domain

alternating space is closed under complement and other simulations for sublogarithmic space abstract we present some new simulations for aspace s n the class of languages accepted by alternating turing machines with o s n space with absolutely no assumptions on s n these simulations provide the following inclusions a aspace s n dtime n 2 o s n this extends to sublogarithmic space bounds the classic result stating that aspace s n dtime 2 o s n proved under the assumption s n log n b aspace s n ntimespace n 2 o s n 2 o s n a simulation by nondeterministic machines with simultaneous bounds on time and space this improves the known inclusion stating that aspace s n nspace 2 o s n proved under the assumption s n log log n c aspace s n co aspace s n i e the alternating space is closed under complement independently of whether s n is above log n and of whether the original machine can get into an infinite loop this solves a long standing open problem quite surprisingly this complementary simulation does not eliminate infinite loops the new machine itself goes to infinite loops along some computation paths

a characterization of exponential time languages by alternating context free grammars we show that the class of exponential time languages or equivalently the class of languages accepted by alternating pushdown automata apdas is exactly the class of languages generated by linear erasing alternating context free grammars acfgs an acfg is generalization of an ordinary context free grammar in which we allow the use of universal nonterminals in much the same way as universal states are used in apdas it was recently claimed in 9 that apdas are equivalent to acfgs however the proofs in both directions have major flaws which do not seem to be correctable as it turns out the proof of the claim does not follow from a simple extension of the well known constructions for the nonalternating case our proof is in fact for a modified claim apdas are equivalent to linear erasing acfgs where linear erasing means that there is a constant c such that every string of length n in the language generated by the acfg has a derivation in which all intermediate sentential forms are at most cn long

a fast multi level boundary element method for the helmholtz equation abstract most recently we have developed a novel multi level boundary element method mlbem for the solution of the steady heat diffusion equation involving asymptotically decaying non oscillatory log singular and strongly singular kernels this hierarchical approach generalizes the pioneering work of brandt and lubrecht on multi level multi integration mlmi and c cycle multi grid to the broader class of mixed boundary value problems the result is a fast accurate and efficient boundary element method the present paper extends this new computational methodology to the solution of the helmholtz equation involving oscillatory log singular and strongly singular kernels for two dimensional problems we consider a direct boundary element formulation and due to the nature of the fundamental solutions split the corresponding boundary integral equation into real and imaginary parts then we introduce double noded corners to facilitate a patch by patch application of the mlmi algorithm for fast matrix vector and matrix transpose vector multiplications within bi conjugate gradient methods the performance of the proposed fast mlbem is investigated using a numerical example that possesses an exact solution for wave numbers 20 and below we demonstrate that the fast mlbem algorithm for the helmholtz equation is robust accurate and exceptionally efficient

sequential optimal design of neurophysiology experiments adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical models of neural systems however application of adaptive methods to neurophysiology has been limited by severe computational challenges since most neurons are high dimensional systems optimizing neurophysiology experiments requires computing high dimensional integrations and optimizations in real time here we present a fast algorithm for choosing the most informative stimulus by maximizing the mutual information between the data and the unknown parameters of a generalized linear model glm that we want to fit to the neuron s activity we rely on important log concavity and asymptotic normality properties of the posterior to facilitate the required computations our algorithm requires only low rank matrix manipulations and a two dimensional search to choose the optimal stimulus the average running time of these operations scales quadratically with the dimensionality of the glm making real time adaptive experimental design feasible even for high dimensional stimulus and parameter spaces for example we require roughly 10 milliseconds on a desktop computer to optimize a 100 dimensional stimulus despite using some approximations to make the algorithm efficient our algorithm asymptotically decreases the uncertainty about the model parameters at a rate equal to the maximum rate predicted by an asymptotic analysis simulation results show that picking stimuli by maximizing the mutual information can speed up convergence to the optimal values of the parameters by an order of magnitude compared to using random nonadaptive stimuli finally applying our design procedure to real neurophysiology experiments requires addressing the nonstationarities that we would expect to see in neural responses our algorithm can efficiently handle both fast adaptation due to spike history effects and slow nonsystematic drifts in a neuron s activity

a fast eigenvalue algorithm for hankel matrices abstract we present an algorithm that can find all the eigenvalues of an n n complex hankel matrix in o n 2 log n operations our scheme consists of an o n 2 log n lanczos type tridiagonalization procedure and an o n qr type diagonalization method

assessing influence in multiple linear regression with incomplete data the problem of assessing influence and detecting influential cases in multiple linear regression with incomplete data is considered a case is said to be influential if appreciable changes in fitted regression coefficients occur when it is removed from the data a one step influence measure is derived based on the em algorithm for detecting cases that are influential in the maximum likelihood estimation of the regression coefficients results are compared with the complete data cook s distance measure techniques are demonstrated by examples

miscellanea updating the average efficiency factor in α designs this paper presents a method for updating the average efficiency factor of an design after an exchange or interchange in the array this allows the average efficiency factor to be used directly as the objective function in an design computer search algorithm

boundary integral equation solutions to moving interface between two fluids in porous media the boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media the mixing between two fluids is assumed to be insignificant a sharp interface exists between them numerical and experimental results are presented for the tilting of a vertical interface in a hele shaw cell during the initial stage of the interfacial movement nonlinear effects are clearly demonstrated the biem results are also compared to experimental results for a transient salt water intrusion problem

hybrid methods for radiation transport using diagonally implicit runge kutta and space time discontinuous galerkin time integration abstract in this work we describe extensions of a hybrid method for time dependent linear kinetic radiation transport problems to high order time integration schemes of the diagonally implicit runge kutta dirk and space time discontinuous galerkin stdg types the hybrid methods are constructed by splitting the radiation flux into collided and uncollided components to which low and high resolution discrete ordinates approximations are applied the efficiency of hybrid methods constructed using dirk stdg integral deferred correction idc and implicit euler schemes is compared using a test problem in one dimensional slab geometry containing material discontinuities it is observed that i higher order methods are more efficient than the implicit euler method often by an order of magnitude or more ii third order methods yield solutions of a given error in roughly half the time of the second order method of the same type and iii for a given order of accuracy it is found that the most efficient class of time integration scheme is stdg followed by dirk with idc the least efficient for the test problem considered two test problems in two dimensional xy geometry are used to compare the computational efficiency of hybrid and standard discrete ordinates methods constructed with dirk and stdg integrators we observe that replacing a standard discrete ordinates method using an angular quadrature of order n with a hybrid discrete ordinates method using angular quadratures of order 2n and n 2 for the uncollided and collided fluxes respectively usually reduces overall solution time by a factor of 2 or more while simultaneously reducing the resulting solution error by a factor of 2 or more for the test problems considered

a fast convergent numerical method for matrix sign function with application in sdes in this article a new matrix iterative method for computing the sign of a matrix is offered convergence along with asymptotical stability of the presented method is studied an accelerated form of the iteration will further be constructed finally the application of the given approach in numerical solution of stochastic differential equations and in solving algebraic riccati equations is pointed out

further results on entanglement detection and quantification from the correlation matrix criterion the correlation matrix cm criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions it has been shown that it can be stronger than the positive partial transpose ppt criterion as well as the computable cross norm or realignment ccnr criterion in different situations however it remained as an open question whether there existed sets of states for which the cm criterion could be stronger than both criteria simultaneously here we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the ppt and ccnr criteria whose entanglement is revealed by the cm condition we also show that the cm can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general mixed states

the convergence behavior of ritz values in the presence of close eigenvalues abstract a number of results for ritz values are presented these are used to study the local effects in the convergence behavior of ritz values corresponding to a pair of close eigenvalues in the spectrum the local effects that are typical for such a situation are illustrated by numerical examples

a time domain discontinuous galerkin method for mechanical resonator quality factor computations numerical simulations are becoming increasingly important in the design of micromechanical resonators in particular for the prediction of complex frequency response in high quality devices where damping is controlled by anchor losses frequency based approaches have been shown to predict these accurately however they require the solution of eigenvalue problems or the inversion of helmholtz type operators which are known to be very difficult for large scale iterative solvers we propose using a time domain approach instead where a broadband input signal is propagated through the system with a local explicit time stepper this is achieved using a new high order discontinuous galerkin dg discretization for the linear elasticity equations in particular a second order formulation with compact dg fluxes and a runge kutta time integrator where the block diagonal mass matrices allow for efficient stable and accurate time stepping our solver scales well on distributed parallel computers even in three spatial dimension and for large problem sizes the resulting output signal is analyzed using a well known filter diagonalization method which is capable of finding accurate frequencies and quality factors for as little as a hundred periods of data we validate the properties of our scheme on model problems and demonstrate the feasibility of our proposed analysis process on two high quality factor disk resonators using an axisymmetric formulation as well as full three dimensional simulations which is shown to scale well

construction of stable and globally convergent schemes for the matrix sign function abstract in this paper we propose a dynamics based approach to develop efficient matrix iterations for computing the matrix sign function considering an iterative method with unknown weight functions our approach constructs a double sequence of weight functions so that for a quadratic polynomial with distinct roots the julia set of the method associated with each term of the sequence is the perpendicular bisector of the line segment from one root to another based on the sequence generated methods we introduce a double sequence of matrix iterations for computing the matrix sign function and perform precise convergence and stability analyses of these iterations we show that our matrix iterations contain the well known globally convergent principal pade family and its reciprocal as special cases based on the result of the numerical experiments we found several of our methods that do not belong to the principal pade family and its reciprocal which are more efficient in computing the matrix sign function

exact confidence sets for variance components in unbalanced mixed linear models we present a general procedure for obtaining an exact confidence set for the variance components in a mixed linear model the procedure can be viewed as a generalization of the anova method used with balanced models our procedure uses as pivotal quantities quadratic forms that are distributed independently as chi squared variables these quadratic forms are constructed with reference to spaces that are orthogonal with respect to the covariance matrix of the observation vector which is a function of the variance components for balanced models these pivotal quantities simplify to multiples of the sums of squares used in the anova method an exact confidence set for the vector of ratios of the effect variances to the error variance is also presented based on the same collection of quadratic forms computing formulas for calculating approximations to these confidence sets are presented and the results of their application to several two way data sets are given

estimating entanglement measures in experiments we present a method to estimate entanglement measures in experiments we show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses hence witness measurements are given a quantitative meaning without the need of further experimental data we apply our results to a recent multiphoton experiment m bourennane et al phys rev lett 92 087902 2004 giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment

improving resolution for autoregressive spectral estimation by decimation in this paper we present a method for efficiently improving the resolution of autoregressive spectral estimation algorithms we derive the exact autoregressive spectrum for k complex sinusoids in additive white noise from this equation resolution boundaries are constructed which give the resolution in terms of the model order and the signal to noise ratio simulation results are used to compare the resolution boundaries for decimated and undecimated spectra our results demonstrate that decimation by d with a model order m yields the same resolution as a model order md used with the undecimated signal and that decimation reduces the computation

the invariance of some score tests in the linear model with classical measurement error the linear model with classical measurement error is an alternative to the standard regression model in which it is assumed that the independent variables are subject to error this assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model however in some cases inferences remain unchanged even though the independent variables are assumed to be subject to error this article investigates the invariance property of score tests for assessing heteroscedasticity first order autoregressive disturbance and the need for a box cox power transformation under specific constraints we show that the score tests for measurement error models are identical to the corresponding well established tests derived from standard regression models hence practitioners can assess assumptions of constant variance and independent errors as well as the need for a box cox transformation irrespective of whether or not the variables are measu

unification and extension of monolithic state space and iterative cochlear models time domain cochlear models have primarily followed a method introduced by allen and sondhi j acoust soc am 66 123 132 1979 recently the state space formalism proposed by elliott et al j acoust soc am 122 2759 2771 2007 has been used to simulate a wide range of nonlinear cochlear models it used a one dimensional approach that is extended to two dimensions in this paper using the finite element method the recently developed state space formalism in fact shares a close relationship to the earlier approach working from diependaal et al j acoust soc am 82 1655 1666 1987 the two approaches are compared and the relationship formalized understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths a second method to derive the state space matrices required for the state space formalism is also presented this method offers improved numerical properties because it uses the information available about the mod

two sided and alternating jacobi davidson we discuss two variants of a two sided jacobi davidson jd method which have asymptotically cubic convergence for nonnormal matrices and aim to find both right and left eigenvectors these methods can be seen as jacobi davidson analogs of ostrowski s two sided rayleigh quotient iteration rqi some relations between exact and inexact two sided jacobi davidson and exact and inexact two sided rayleigh quotient iteration are given together with convergence rates furthermore we introduce an alternating jacobi davidson process that can be seen as the jacobi davidson analog of parlett s alternating rayleigh quotient iteration the methods are extended to the generalized and polynomial eigenproblem advantages of the methods are illustrated by numerical examples

tree automata and attribute grammars the translational mechanism of attribute grammars using tree automata are investigated the pushdown tree to string transducer with a certain synchronization facility as a model to realize transformations by attribute grammars is proposed and its basic properties using tree walking finite state automata are studied to demonstrate the utility of this model it is shown that noncircular attribute grammars are equally powerful as arbitrary attribute grammars and a method is provided to show that a certain type of transformations is impossible by attribute grammars

a complex variable boundary element method for solving a steady state advection diffusion reaction equation abstract an accurate complex variable boundary element method is proposed for the numerical solution of two dimensional boundary value problems governed by a steady state advection diffusion reaction equation with the aid of the cauchy integral formulae the task of constructing a complex function which gives the solution of the boundary value problem under consideration is reduced to solving a system of linear algebraic equations the method is applied to solve several specific problems which have exact solutions in closed form and a problem of practical interest in engineering

darcy s flow with variable permeability a boundary integral solution a boundary integral equation method biem for darcy s flow with spatially varied permeability is developed the formulation requires that green s function be found for each given permeability variation for a few permeability functions in one and two dimensions which can be used to fit field permeability data closed form green s functions are obtained numerical examples are solved and verified

factorizing complex symmetric matrices with positive definite real and imaginary parts complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for lu factorization this result adds to the classes of matrix for which it is known to be safe not to pivot in lu factorization block mathrm ldl t factorization with the pivoting strategy of bunch and kaufman is also considered and it is shown that for such matrices only 1 times 1 pivots are used and the same growth factor bound of 2 holds but that interchanges that destroy band structure may be made the latter results hold whether the pivoting strategy uses the usual absolute value or the modification employed in linpack and lapack

a note on the optimality of decomposable entanglement witnesses and completely entangled subspaces entanglement witnesses ews constitute one of the most important entanglement detectors in quantum systems nevertheless their complete characterization in particular with respect to the notion of optimality is still missing even in the decomposable case here we show that for any qubit qunit decomposable ew dew w the three statements are equivalent i the set of product vectors obeying e f w e f 0 spans the corresponding hilbert space ii w is optimal and iii w q with q denoting a positive operator supported on a completely entangled subspace ces and standing for the partial transposition while implications i ii and ii iii are known here we prove that iii implies i this is a consequence of a more general fact saying that product vectors orthogonal to any ces in span after partial conjugation the whole space on the other hand already in the case of the hilbert space there exist dews for which iii does not imply i consequently either i does not imply ii or ii does not imply iii and the above transparent characterization obeyed by qubit qunit dews does not hold in general

on the inverse of generalized λ matrices with singular leading term an algorithm is introduced for the inverse of a matrix given as the truncated series a0 i a1 2a2 i 3a3 4a4 o n 1 with square coefficient matrices and singular leading term a0 moreover a1 may be conditionally singular and no restrictions are made for the remaining terms the result is a matrix given as a unique truncated series of the same error order motivation for this problem is the evaluation of the frequency dependent stiffness matrix of general boundary or macro finite elements in the frame of a hybrid variational formulation that is based on a flexibility matrix f expressed as a truncated power series of the circular frequency copyright 2005 john wiley sons ltd

on the sign patterns of the smallest signless laplacian eigenvector abstract let h be a connected bipartite graph whose signless laplacian matrix is q h suppose that the bipartition of h is s t and that x is the eigenvector of the smallest eigenvalue of q h it is well known that x is positive and constant on s and negative and constant on t the resilience of the sign pattern of x under addition of edges into the subgraph induced by either s or t is investigated and a number of cases in which the sign pattern of x persists are described

hankel singular values and lqg characteristic values of discrete time linear systems in cascade with inner systems recent results have shown that for continuous time systems obtained by cascading an asymptotically stable system with an inner system the first n hankel singular values are greater than or equal to those of the original system similarly cascading a system in minimal form with an inner system the same property holds for the linear quadratic gaussian lqg characteristic values in this article we consider the discrete time case and demonstrate that the property also holds for these systems a very important consequence stemming from these results is that the hankel singular values and the lqg characteristic values of input delayed discrete systems are greater than or equal to those of their zero delay counterpart