combined sequence of markov parameters and moments in linear systems the combined sequence of markov parameters and moments in linear systems is discussed this sequence is shown to be generated by a linear feedback shift register application to the minimal degree partial realization from a mixture of any number of markov parameters and moments is considered central in this particular realization problem is the extension of a toeplitz partial behavior matrix this is accomplished on the basis of the algebraic theory of iohvidov indexes for toeplitz matrices

on the methods for solving yule walker equations the three well known fast algorithms for the solution of yule walker equations the levinson euclidean and berlekamp massey algorithms are reviewed and the relationship between each of them and the pade approximation problem is shown the algorithms are classified with reference to three criteria namely 1 the path they follow in the pade table 2 the organization of the computations one pass or two pass and 3 the auxiliary variables used this classification shows that the set of known classical algorithms is not complete and the missing variants are proposed with these variants of the berlekamp massey and euclid algorithms both forward and backward predictors can be obtained without additional cost a unified representation of the two pass algorithms is given in such a way that the application of the divide and conquer strategy becomes straightforward a general doubling algorithm which represents all the associated doubling algorithms in an exhaustive way is provided

structured total least squares and l2 approximation problems abstract it is shown how structured and weighted total least squares and l 2 approximation problems lead to a nonlinear generalized singular value decomposition an inverse iteration scheme to find a local minimum is proposed the emphasis of the paper is not on the convergence analysis of the algorithm rather the purpose is to illustrate its use in numerous applications in systems and control including total least squares with relative errors and or fixed elements inverse singular value problems an errors in variables variant of the kalman filter impulse response realization from noisy data h 2 model reduction h 2 system identification and calculating the largest stability radius of uncertain linear systems several numerical examples are given

series expansion for a stochastic sandpile using operator algebra we extend the series for the activity density in a one dimensional stochastic sandpile with fixed particle density p the first terms of which were obtained via perturbation theory dickman and vidigal 2002 j phys a math gen 35 7269 the expansion is in powers of the time the coefficients are polynomials in p we devise an algorithm for evaluating expectations of operator products and extend the series to constructing pade approximants to a suitably transformed series we obtain predictions for the activity that compare well against simulations in the supercritical regime

a fast algorithm for solving a toeplitz system of equations a fast algorithm for the solution of a toeplitz system of equations is presented the algorithm requires order n log n 2 computations where n is the number of equations for banded toeplitz matrices the order of computations is reduced to only n log n m log m 2 where 2m is the maximum number of nonzero principal subdiagonals of the toeplitz matrix the algorithm is in essence a fast implementation of the trench algorithm in reverse thus the algorithm involves imbedding of the given matrix in a cyclic matrix and a fast hd half divisor algorithm to compute the first row of the inverse matrix the desired solution is then obtained directly from the first row by applying fast fourier transform techniques in order n log n computations finally the extension of the algorithm to block toeplitz matrices is also presented

spectral functions for real symmetric toeplitz matrices we derive separate spectral functions for the even and odd spectra of a real symmetric toeplitz matrix which are given by the roots of those functions these are rational functions also commonly referred to as secular functions two applications are considered spectral evolution as a function of one parameter and the computation of eigenvalues

construction of a hermitian toeplitz matrix from an arbitrary set of eigenvalues a solution to the inverse eigenvalue problem for hermitian toeplitz matrices is presented the approach taken is to first construct a real symmetric negacyclic matrix of order 2n and to then relate the negacyclic matrix to a hermitian toeplitz matrix of order n with the desired eigenspectrum

critical exponents for the restricted sandpile i report large scale monte carlo studies of a one dimensional height restricted stochastic sandpile using the quasistationary simulation method results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems but are consistent with recent predictions derived from a langevin equation for stochastic sandpiles ramasco phys rev e 69 045105 r 2004 this suggests that apparent violations of universality in one dimensional sandpiles are due to strong corrections to scaling and finite size effects

vector adaptive vector quantization with application to speech coding a vector adaptive vector quantization vavq scheme which may be viewed as a generalization of gain adaptive vector quantization is described the proposed scheme adjusts each component of the encoding signal vector according to a statistical estimate of the signal characteristics the vavq scheme can cope with large input dynamic ranges it can be used in either the time domain or the transform domain and exhibits approximately 4 db improvement in segmental signal to noise ratio snr over the fixed vq

on twisted forms and relative algebraic k theory this paper introduces a new approach to the study of certain aspects of galois module theory by combining ideas arising from the study of the galois structure of torsors of finite group schemes with techniques coming from relative algebraic k theory

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

maximum entropy spectral estimation for regular time series of degenerate rank this paper deals with multichannel time series of degenerate rank and extends the maximum entropy method over the degenerate rank case in order to define the entropy of a multichannel time series of degenerate rank we must first clarify all the deterministic relationships in the time series this will be done for any regular time series matching given finite data r 0 r 1 r n of the autocorrelation sequence r k min infin infin a necessary and sufficient condition of the existence of a regular time series matching the data will be presented next the entropy h m p of a time series with its power spectrum p of rank less than equal to m is defined by h m p int min pi max pi logs m p omega d omega where s m p denotes the sum of all the principal minors of order m of the matrix p the main purpose of this paper is to show that the maximum entropy power spectrum i e the power spectrum which maximizes the entropy is identical with the autoregressive power spectrum i e the power spectrum obtained by the autoregressive fitting even in the degenerate rank case

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

how to simulate the quasistationary state for a large class of processes with an absorbing state statistical properties of the surviving sample attain time independent values in the quasistationary qs regime we propose a practical simulation method for studying quasistationary properties based on the equation of motion governing the qs distribution in applications to the contact process the method is shown to reproduce exact results for the process on a complete graph and known scaling behavior to high precision at the critical point our method is about an order of magnitude more efficient than conventional simulation

formally biorthogonal polynomials and a look ahead levinson algorithm for general teoplitz systems abstract systems of linear equations with toeplitz coefficient matrices arise in many important applications the classical levinson algorithm computes solutions of toeplitz systems with only o n 2 arithmetic operations as compared to o n 3 operations that are needed for solving general linear systems however the levinson algorithm in its original form requires that all leading principal submatrices be nonsingular in this paper an extension of the levinson algorithm to general toeplitz systems is presented the algorithm uses look ahead to skip over exactly singular as well as ill conditioned leading submatrices and at the same time it still fully exploits the toeplitz structure in our derivation of this algorithm we make use of the intimate connection of toeplitz matrices with formally biorthogonal polynomials in particular the occurence of singular or ill conditioned submatrices corresponds to a breakdown or near breakdown in the standard recurrence relations for biorthogonal polynomials we present new general recurrence relations that connect successive pairs in any given subsequence of all existing formally biorthogonal polynomials these recurrences then immediately lead to the proposed look ahead levinson algorithm for solving toeplitz systems implementation details for this algorithm and operation counts are given numerical experiments for toeplitz systems with ill conditioned submatrices are reported

oslo model hyperuniformity and the quenched edwards wilkinson model we present simulations of the one dimensional oslo rice pile model in which the critical height at each site is randomly reset after each toppling we use the fact that the stationary state of this sand pile model is hyperuniform to reach system of sizes 10 7 most previous simulations were seriously flawed by important finite size corrections we find that all critical exponents have values consistent with simple rationals 4 3 for the correlation length exponent d 9 4 for the fractal dimension of avalanche clusters and z 10 7 for the dynamical exponent in addition we relate the hyperuniformity exponent to the correlation length exponent finally we discuss the relationship with the quenched edwards wilkinson model where we find in particular that the local roughness exponent is loc 1

conserved lattice gas model with infinitely many absorbing states in one dimension the conserved lattice gas model with infinitely many absorbing states is studied on a chain and on a ladder in both one dimensional lattices it exhibits a phase transition from an absorbing phase to an active state the model defined on a chain is solved exactly and shows a critical behavior with classical critical exponents however the model defined on a ladder shows a critical behavior obtained from numerical simulation that places the model in the same universality class as the manna model

asymptotic behavior of the order parameter in a stochastic sandpile we derive the first four terms in a series for the order paramater the stationary activity density in the supercritical regime of a one dimensional stochastic sandpile in the two dimensional case the first three terms are reported this is done by reorganizing the pertubation theory derived using a path integral formalism dickman and vidigal j phys a 35 7269 2002 to obtain an expansion for stationary properties since the process has a strictly conserved particle density p the fourier mode n 1 k 0 p when n and so is not a random variable isolating this mode we obtain a new effective action leading to an expansion for in the parameter 1 1 4p this requires enumeration and numerical evaluation of more than 200 000 diagrams for which task we develop a computational algorithm predictions derived from this series are in good accord with simulation results we also discuss the nature of correlation functions and one site reduced distributions in the small high density limit

recursive partial realization from the combined sequence of markov parameters and moments abstract in this paper we develop the recursive structure of partial realization from a two sided sequence of markov parameters and moments the specific feature of this recursive structure is that it accommodates sequences growing in two directions like in the two point pade approximation we present a recursive algorithm for the minimal partial realization from a sequence of markov parameters and moments that amounts to recursive lu factorization of a toeplitz behavior matrix leaping over nongeneric sections it turns out that this algorithm reveals a new continued fraction expansion which extends the classical cauer third form as a corollary various results related to toeplitz matrices two point pade approximations continued fractions etc are unified within this partial realization setting

boundary element solution for periodic acoustic problems abstract this work shows when using the boundary element method to solve 3d acoustic scattering problems from periodic structures the coefficient matrix can be represented as a block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct the coefficient matrix are significantly reduced to solve the linear system of equations the original matrix is embedded into a larger and more structured matrix called the block circulant matrix discrete fourier transform is then employed in an iterative algorithm to solve the block toeplitz system to demonstrate the effectiveness of the formulation for periodic acoustic problems two exterior acoustic case studies are considered the first case study examines a continuous structure to predict the noise generated by a sharp edged flat plate under quadrupole excitation directivity plots obtained using the periodic boundary element method technique are compared with numerical results obtained using a conventional boundary element model the second case study examines a discrete periodic structure to predict the acoustic performance of a sonic crystal noise barrier results for the barrier insertion loss are compared with both finite element results and available data in the literature

adaptive tracking of multiple sinusoids whose power levels are widely separated the behavior of the gradient transversal filter lms the gradient lattice gl and the least squares lattice lsl when used to track multiple sinusoidal or narrow band components whose power levels are widely separated is investigated these approaches to the realization of the pth order one step linear predictor of the time series are recursive in time the lags of the instantaneous frequency estimates from their actual underlying values are of particular interest the frequency tracking characteristics of the lms gl and lsl algorithms are illustrated in several situations included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech

an eigenvalue recursion for toeplitz matrices in this correspondence a recursive algorithm for finding eigenvalues of a real symmetric toeplitz matrix from the eigenvalues of nested toeplitz submatrices is presented given the eigenvalues of two nested toeplitz submatrices the eigenvalues of the next larger toeplitz matrix can be found simply by solving a vandermonde set of equations and rooting two polynomials

optimized compact support interpolation kernels in this paper we investigate the problem of designing compact support interpolation kernels for a given class of signals by using calculus of variations we simplify the optimization problem from an nonlinear infinite dimensional problem to a linear finite dimensional case and then find the optimum compact support function that best approximates a given filter in the least square sense l2 norm the benefit of compact support interpolants is the low computational complexity in the interpolation process while the optimum compact support interpolant guarantees the highest achievable signal to noise ratio snr our simulation results confirm the superior performance of the proposed kernel compared to other conventional compact support interpolants such as cubic spline

an extended berlekamp massey algorithm for the inversion of toeplitz matrices the berlekamp massey algorithm bma which solves special toeplitz systems of linear equations is extended to an algorithm for inverting toeplitz matrices the original bma itself leads to one row of the inverse of the corresponding toeplitz matrix the other rows are derived using the same operations that are central to the original bma two alternatives for the extended bma are presented the first includes the usual bma without any changes and the second simplifies the structure by some modifications also in the original bma part both versions follow a tree like structure if the branches of the tree are implemented in parallel the time demand would be nearly the same as for the usual bma in contrast to other toeplitz algorithms only slight modifications must be incorporated to handle singular submatrices

parallel and superfast algorithms for hankel systems of equations utilizing kernel structure properties a unified construction of hankel matrix inversion algorithms is presented three types of algorithms are obtained 1 o n 2 complexity levinson type 2 o n parallel complexity schur type and 3 o n log2 n complexity asymptotically fast ones all algorithms work without additional assumption like strong nonsingularity

sampling methods for the quasistationary regime of epidemic processes on regular and complex networks a major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing disease free state at sufficiently long times due to the finite size of the networks where epidemics evolves in the present work we compare different quasistationary qs simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved we analyze the standard qs sqs method where the sampling is constrained to active configurations the reflecting boundary condition rbc where the dynamics returns to the pre absorbing configuration and hub reactivation hr where the most connected vertex of the network is reactivated after a visit to an absorbing state we apply the methods to the contact process cp and susceptible infected susceptible sis models on regular and scale free networks the investigated methods yield the same epidemic threshold for both models for cp that undergoes a standard collective phase transition the methods are equivalent for sis whose phase transition is ruled by the hub mutual reactivation the sqs and hr methods are able to capture localized epidemic phases while rbc is not we also apply the autocorrelation time as a tool to characterize the phase transition and observe that this analysis provides the same finite size scaling exponents for the critical relaxation time for the investigated methods finally we verify the equivalence between rbc method and a weak external field for epidemics on networks

effects of pair correlation on mean field theory of btw sand pile model we extend the mean field calculation of btw sand pile model to one that includes the correlation between pairs of nearest neighbors specifically we derive dynamical equations of both one site and two site densities and solve the equations order by order starting with the mean field solution the investigation provides analytical results for both stationary and dynamic states of the sand pile near the critical point which are valid in the regime where h e2 1h e2 1 h incoming rate of sand grains e bulk dissipation rate of sand grainse bulk dissipation rate of sand grains in the stationary case we evaluate the pair correlation and the correction to the mean field single site densities due to the correlation the correction is found to be of the same order as the mean field solution in the dynamic case the initial state deviates from the stationary state by a small fluctuation which subsequently decays exponentially with the time constant being reduced from the corresponding mean field value again the correction to the time constant in this case is found comparable to the mean field value itself

n site approximations and coherent anomaly method analysis for a stochastic sandpile n site cluster approximations for a stochastic sandpile in one dimension are developed a height restriction is imposed to limit the number of states each site can harbor at most two particles height z i l 2 this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded on the basis of results for nl 11 sites the critical particle density as ensuremath zeta c 0 930 1 is estimated in good agreement with simulations a coherent anomaly analysis yields estimates for the order parameter exponent ensuremath beta 0 41 1 and the relaxation time exponent ensuremath nu ensuremath simeq 2 5

a schur based algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite toeplitz matrix abstract recent progress in signal processing and estimation has generated c onsiderable interest in the problem of computing the smallest eigenvalue of symmetric positive definite toeplitz matrices several algorithms have been proposed in the literature they compute the smallest eigenvalue in an iterative fashion many of them relying on the levinson durbin solution of sequences of yule walker systems exploiting the properties of two algorithms recently developed for estimating a lower and an upper bound of the smallest singular value of upper triangular matrices respectively an algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite toeplitz matrix is derived the algorithm relies on the computation of the r factor of the qr factorization of the toeplitz matrix and the inverse of r the simultaneous computation of r and r 1 is efficiently accomplished by the generalized schur algorithm

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

computing the smallest eigenpair of a symmetric positive definite toeplitz matrix an algorithm for computing the smallest eigenvalue of a symmetric positive definite toeplitz matrix is presented the eigenvalue is approximated from below by newton s method applied to the characteristic polynomial of the matrix the newton s step is calculated by a levinson durbin type recursion simultaneously this recursion produces a realistic error bound of the actual approximation without additional computing effort as well as a simple and efficient way to compute the associated eigenvector

fast algorithms for generalized displacement structures and lossless systems abstract we derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure that includes as special cases a variety of previously studied classes such as toeplitz like and hankel like matrices the derivation is based on combining a simple gaussian elimination procedure with displacement structure and leads to a transmission like interpretation in terms of two cascades of first order sections we further derive state space realizations for each section and for the entire cascades and show that these realizations satisfy a generalized embedding result and a generalized notion of j losslessness the cascades turn out to have intrinsic blocking properties which can be shown to be equivalent to interpolation constrains

on arithmetic class invariants let f be a number field with ring of integers of and let s be a finite set of places of f assume that s contains the set s of archimedean places of f and write sf for the set of finite places contained in s let os or o when there is no danger of confusion denote the ring of sf integers of f write f for an algebraic closure of f let y be any scheme over spec o suppose thatg is a finite flat commutative group scheme over y of exponent n and let g denote the cartier dual of g let x y be ag torsor and write 0 g y for the trivialg torsor thenox is anog comodule and so it is also anogd module see 12 as an ogd module ox is locally free of rank one and it therefore gives a line bundle m over g set l m m 1 0 then the map h y g pic g l

modeling of multichannel time series and extrapolation of matrix valued autocorrelation sequences this paper deals with multichannel time series and extends the autocorrelation method for fitting the time series from the nondegenerate case to the general case we shall show that the ar model obtained by solving the normal equations is always stable even in the degenerate case the multichannel levinson algorithm for solving the normal equations is extended from the nondegenerate case to the general case in the nondegenerate case the first n 1 values of the auto correlation sequence of the obtained ar model of order n are identical with those of the original data the next considered is the extrapolation problem of an autocorrelation sequence that is given data r 0 r 1 r n it is to construct a model whose first n 1 values of the autocorrelation sequence are identical with these data we shall show that even in the degenerate case when the given data r 0 r 1 r n are taken from the autocorrelation sequence of a purely nondeterministic time series they are identical with the first n 1 values of the autocorrelation sequence of the ar model of order n

schur algorithms for hermitian toeplitz and hankel matrices with singular leading principal submatrices it is shown how a simple matrix algebra procedure can be used to induce schur type algorithms for the solution of certain toeplitz and hankel linear systems of equations when given levinson durbin algorithms for such problems the algorithm of p delsarte et al 1985 for hermitian toeplitz matrices in the singular case is used to induce a schur algorithm for such matrices an algorithm due to g heinig and k rost 1984 for hankel matrices in the singular case is used to induce a schur algorithm for such matrices the berlekamp massey algorithm is viewed as a kind of levinson durbin algorithm and so is used to induce a schur algorithm for the minimal partial realization problem the schur algorithm for hermitian toeplitz matrices in the singular case is shown to be amenable to implementation on a linearly connected parallel processor array of the sort considered by kung and hu 1983 and in fact generalizes their result to the singular case

an algorithm for solving discrete time wiener hopf equations based upon euclid s algorithm an algorithm for solving a discrete time wiener hopf equation is presented based upon euclid s algorithm the discrete time wiener hopf equation is a system of linear inhomogeneous equations with a given toeplitz matrix m a given vector b and an unknown vector lambda such that m lambda b the algorithm is able to find a solution of the discrete time wiener hopf equation for any type of toeplitz matrices except for the all zero matrix while the levinson algorithm and the trench algorithm are not available when at least one of the principal submatrices of the toeplitz matrix m is singular the algorithm gives a solution if one exists even when the toeplitz matrix m is singular while the brent gustavson yun algorithm only states that the toeplitz matrix m is singular the algorithm requires o t 2 arithmetic operations for t unknowns in the sense that the number of multiplications or divisions is directly proportional to t 2 like the levinson and trench algorithms furthermore a faster algorithm is also presented based upon the half greatest common divisor algorithm and hence it requires o t log 2 t arithmetic operations like the brent gustavson yun algorithm

split algorithms for hermitian toeplitz matrices with arbitrary rank profile abstract split algorithms for toeplitz matrices exploit besides the toeplitz structure additional symmetry properties to reduce the number of operations in this paper split levinson and schur algorithms for hermitian toeplitz matrices are presented that work in contrast to previous algorithms without additional conditions like strong nonsingularity the main contribution is the generalization of the split levinson type algorithms of b krishna h krishna and h krishna s morgera to general nonsingular hermitian toeplitz matrices furthermore a schur type counterpart of this algorithm is presented that is also new in the strongly nonsingular case some auxiliary considerations concerning the kernel structure of hermitian toeplitz matrices might be of independent interest

on stability and root location of linear prediction models simple algebraic proofs are given for some results pertaining to the location of the roots of linear prediction models also called all pole or autoregressive models

vector predictive coding of speech at 16 kbits s vector quantization in its simplest form may be regarded as a generalization of pcm independent quantization of each sample of a waveform to what might be called vector pcm where a block of consecutive samples a vector is simultaneously quantized as one unit in theory a performance arbitrarily close to the ultimate rate distortion limit is achievable with waveform vector quantization if the dimension of the vector k is large enough the main obstacle in effectively using vector quantization is complexity a vector quantizer of dimension k operating at a rate of r bits sample requires a number of computations on the order of k2 kr and a memory of the same order however a low dimensional vector quantizer dimensions 4 8 achieves a remarkable improvement over scalar quantization pcm consequently using the vector quantizer as a building block and imbedding it with other waveform data compression techniques may lead to the development of a new and powerful class of waveform coding systems this paper proposes and analyzes a waveform coding system adaptive vector predictive coding avpc in which a low dimensionality vector quantizer is used in an adaptive predictive coding scheme in the encoding process a locally generated prediction of the current input vector is subtracted from the current vector and the resulting error vector is coded by a vector quantizer each frame consisting of many vectors is classified into one of m statistical types this classification determines which one of m fixed predictors and of m vector quantizers will be used for encoding the current frame

a look ahead bareiss algorithm for general toeplitz matrices the bareiss algorithm is one of the classical fast solvers for systems of linear equations with toeplitz coefficient matrices the method takes advantage of the special structure and it computes the solution of a toeplitz system of order n with only o n 2 arithmetic operations instead of o n 3 operations however the original bareiss algorithm requires that all leading principal submatrices be nonsingular and the algorithm is numerically unstable if singular or ill conditioned submatrices occur in this paper an extension of the bareiss algorithm to general toeplitz systems is presented using look ahead techniques the proposed algorithm can skip over arbitrary blocks of singular or ill conditioned submatrices and at the same time it still fully exploits the toeplitz structure implementation details and operations counts are given and numerical experiments are reported we also discuss special versions of the proposed look ahead bareiss algorithm for hermitian indefinite toeplitz systems and banded toeplitz systems

sticky grains do not change the universality class of isotropic sandpiles we revisit the sandpile model with sticky grains introduced by mohanty and dhar phys rev lett 89 104303 2002 whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models while for directed models this conclusion is unquestionable for isotropic models we present strong evidence that the asymptotic scaling in the self organized regime in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate is like other stochastic sandpiles generically in the manna universality class this conclusion is drawn from extensive monte carlo simulations and is strengthened by the analysis of the langevin equations proposed by the same authors to account for this problem argued to converge upon coarse graining to the well established set of langevin equations for the manna class

critical density of the abelian manna model via a multitype branching process a multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the abelian manna model this branching process incorporates partially the spatiotemporal correlations of the activity which are essential for the dynamics in particular in low dimensions an analytical expression for the critical density in arbitrary dimensions is derived which significantly improves the results over mean field theories as confirmed by comparison to the literature on numerical estimates from simulations the method can easily be extended to lattices and dynamics other than those studied in the present work

analysis of coppersmith s block wiedemann algorithm for the parallel solution of sparse linear systems by using projections by a block of vectors in place of a single vector it is possible to parallelize the outer loop of iterative methods for solving sparse linear systems we analyze such a scheme proposed by coppersmith for wiedemann s coordinate recurrence algorithm which is based in part on the krylov subspace approach we prove that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors our analysis is valid for fields of entries that have sufficiently large cardinality our analysis also deals with an arising subproblem of solving a singular block toeplitz system by use of the theory of toeplitz like matrices

human ankle joint stiffness over the full range of muscle activation levels abstract system identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels subjects lay supine on an experimental table with their left foot encased in a rigid low inertia cast which was fixed to an electro hydraulic actuator operating as a position servo subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions mvc during repeated presentations of a stochastic ankle angular position perturbation compliance impulse response functions irf were determined from every 2 5 s perturbation sequence the gain g natural freqency n and damping parameters of the second order model providing the best fit to each irf were determined and used to compute the corresponding inertial i viscous b and elastic k stiffness parameters the behaviour of these parameters with mean torque was found to follow two simple rules first the elastic parameter k increased in proportion to mean ankle torque as it was varied from rest to mvc these changes were considerable involving increases of more than an order of magnitude second the damping parameter remained almost invariant over the entire range of contractions despite the dramatic changes in k

on the eigenvectors of symmetric toeplitz matrices this paper presents a number of results concerning the eigenvectors of a symmetric toeplitz matrix and the location of the zeros of the filters eigenfilters whose coefficients are the elements of the eigenvectors one of the results is that the eigenfilters corresponding to the maximum and minimum eigenvalues if distinct have their zeros on the unit circle while the zeros of the other eigenfilters may or may not have their zeros on the unit circle even if the zeros of the eigenfilters of a matrix are all on the unit circle the matrix need not be toeplitz examples are given to illustrate the different properties

superfast tikhonov regularization of toeplitz systems toeplitz structured linear systems arise often in practical engineering problems correspondingly a number of algorithms have been developed that exploit toeplitz structure to gain computational efficiency when solving these systems the earliest fast algorithms for toeplitz systems required o n 2 operations while more recent superfast algorithms reduce the cost to o n log n 2 or below in this work we present a superfast algorithm for tikhonov regularization of toeplitz systems using an extension and transformation technique our algorithm translates a tikhonov regularized toeplitz system into a type of specialized polynomial problem known as tangential interpolation under this formulation we can compute the solution in only o n log n 2 operations we use numerical simulations to demonstrate our algorithm s complexity and verify that it returns stable solutions

on the galois structure of equivariant line bundles on curves let it be a finite field and let x be a smooth protective curve over k with structure sheaf o let g be a finite group and write cl 0 g for the reduced grothendieck group of the category of g vector bundles in this paper we describe explicitly the subgroup of cl 0 g which is generated by the classes arising from g stable invertible sheaves on tame galois covers of x which have galois group g introduction let k be a finite field of characteristic p9 and let g be a finite abelian group suppose that y x is a tamely ramified galois covering of smooth projective curves over k with galois group g we shall refer to such coverings as tame g covers of x in this paper we study the structure of g stable line bundles on such curves y in order to be more precise we let cl ox g 9 respectively cl k g 9 denote the reduced grothendieck group of x g vector bundles respectively of finitely generated fc g modules which are cohomologically trivial for g suppose that a is a g stable line bundle on y then 4 is an ox g vector bundle and it gives rise to a class f a g c ox g we shall say that an element of c1 0x g is realizable if it may be obtained in this manner for some choice of y and a we shall combine techniques of c m and bu to obtain an explicit description of the subgroup 9 x g of cl ox g which is generated by the subset of realizable classes in conjunction with a riemann roch theorem these results are sufficient to describe explicitly those elements of c k g which arise as the image of the vector bundles a under the refined euler poincare characteristic

on the eigenstructure of toeplitz matrices in spite of the fact that toeplitz eigenvalue problems have important applications in signal processing relatively little is known about the eigenstructure of finite real symmetric toeplitz matrices in this paper we exhibit two facts about the toeplitz eigenstructure problem first we show that any reciprocal or anti reciprocal n vector is an eigenvector for at least an n 1 2 dimensional linear space of real symmetric n n toeplitz matrices the second result is the fact that every n n toeplitz matrix can be imbedded into an n 1 n 1 toeplitz matrix which has a repeated smallest eigenvalue

tame realisable classes over hopf orders abstract letobe the ring of algebraic integers in a number fieldkand letgbe a finite abelian group mcculloh has characterised the classes in the locally free classgroup cl og which are realisable by rings of integers of tame normal extensions ofkwith galois groupg we extend this to certain extensions which in general need be neither tame nor normal by replacingogwith a hopf order a and introducing the strongly a tame orders as an analogue of tame rings of integers we also describe the classes realised by principal homogeneous spaces over the dual of a

stable row recurrences for the pade table and generically superfast lookahead solvers for non hermitian toeplitz systems abstract we present general recurrences for the pade table that allow us to skip ill conditioned pade approximants while we proceed along a row of the table in conjunction with a certain inversion formula for toeplitz matrices these recurrences form the basis for fast algorithms for solving non hermitian toeplitz systems under the assumption that the lookahead step size i e the number of successive skipped approximants remains bounded we give both o n 2 and o n log 2 n algorithms which are presumably weakly stable with little additional work still in o n 2 operations we can also obtain a decomposition of the toeplitz matrix t according to tr ld where r is upper triangular l is unit lower triangular and d is block diagonal the relation to continued fractions is also discussed

is every matrix similar to a toeplitz matrix abstract we show that every n n complex nonderogatory matrix is similar to a unique unit upper hessenberg toeplitz matrix the proof is constructive and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n we also prove that every n n complex matrix with n 4 is similar to a toeplitz matrix

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

equivariant epsilon constants discriminants and etale cohomology let l k be a finite galois extension of number fields we formulate and study a conjectural equality between an element of the relative algebraic k group k 0 mathbb z mathrm gal l k mathbb r which is constructed from the equivariant artin epsilon constant of l k and a sum of structural invariants associated to l k the precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the tamagawa number conjecture of bloch and kato as formulated by flach and the second named author should be compatible with the functional equation of the associated l function we show that more concretely our conjecture also suggests a completely systematic refinement of the central approach and results of classical galois module theory in particular the evidence for our conjecture that we present here already strongly refines many of the main results of galois module theory

on the splitting of classical algorithms in linear prediction theory the levinson algorithm has been shown recently to be redundant in complexity it can be broken down into two simpler algorithms either of these split levinson algorithms needs only to be processed in the present paper it is shown that the schur algorithm the lattice algorithm and the normalized lattice algorithm for computing reflection coefficients can be broken down in a similar manner the number of multiplications in each of the resulting split algorithms is reduced with respect to the classical version by a factor lying between 1 5 and 2

levinson type algorithms for polynomial fitting and for cholesky and q factors of hankel and vandermonde matrices this paper presents levinson 1947 type algorithms for i polynomial fitting ii obtaining a q decomposition of vandermonde matrices and a cholesky factorization of hankel matrices iii obtaining the inverse of hankel matrices the algorithm for the least squares solution of hankel systems of equations requires 3n sup 2 9n 3 multiply and divide operation mdo the algorithm for obtaining an orthogonal representation of an m spl times n vandermonde matrix x and computing the cholesky factors f of hankel matrices requires 5mn n sup 2 2n 3m mdo and the algorithm for generating the inverse of hankel matrices requires 3 n sup 2 n 2 2 mdo our algorithms have been tested by means of fitting of polynomials of various orders and fortran versions of all subroutines are provided in the appendix

sandpiles with height restrictions we study stochastic sandpile models with a height restriction in one and two dimensions a site can topple if it has a height of two as in manna s model but in contrast to previously studied sandpiles here the height or number of particles per site cannot exceed two this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded two toppling rules are considered in one the particles are redistributed independently while the other involves some cooperativity we study the fixedenergy system no input or loss of particles using cluster approximations and extensive simulations and find that it exhibits a continuous phase transition to an absorbing state at a critical value z c of the particle density the critical exponents agree with those of the unrestricted manna sandpile