universality of amplitude combinations in two dimensional percolation we generated extended low concentration series for the second moment of distances between cluster points a 2 in site and bond percolation on the square lattice and used them to calculate series for the correlation length we analysed these and other series for their critical amplitudes and compared them with results from monte carlo simulations of triangular site square site and square bond percolation the values obtained from the different models for the amplitude combination b 2 0 2 2 0 2 and b are the amplitudes of the second moment of the cluster size distribution m 2 and the strength of the infinite cluster p respectively are all within the range 2 23 0 10 confirming universality

paper approximation of multivariable linear systems with impulse response and autocorrelation sequences this paper considers the construction of approximants of multi input multi output discrete time linear systems from the finite data of the impulse response and autocorrelation sequences in the approximation of a multivariable linear system it is common practice to use a finite portion of its impulse response sequence this is formally equivalent to the pade approximation technique which may produce unstable approximants even though the original system is stable mullis and roberts proposed a new method which yields stable approximants in connection with approximation of digital filters this is however restricted to the single input single output case this paper extends their method to the multi input multi output case and shows a fast recursive algorithm to construct stable approximants of linear systems

three dimensional steady state flow to a well in a randomly heterogeneous bounded aquifer 1 we consider flow in a confined aquifer of uniform thickness due to a well of zero radius that fully penetrates the aquifer and discharges at a constant rate if the lateral extent of the aquifer is infinite a steady state flow regime never develops it is however well known that if the aquifer is additionally uniform a quasi steady state region extends from the well out to a cylindrical surface whose radius expands as the square root of time on the expanding surface head is uniform and time invariant inside this surface head at any time is described by a steady state solution a rigorous analysis of the analogous situation in a randomly heterogeneous aquifer would require the solution of a three dimensional transient stochastic flow problem in an aquifer of infinite lateral extent here we take a different approach by developing a three dimensional steady solution for mean flow to a well in a randomly heterogeneous aquifer with a cylindrical prescribed head boundary in analogy to the uniform case we expect our solution to approximate a quasi steady state region whose radius is initially small in comparison to the horizontal correlation scale of log conductivity but grows with time to become eventually much larger we treat log conductivity as a statistically homogeneous random field characterized by a gaussian spatial covariance function that may have different horizontal and vertical correlation scales our solution consists of analytical expressions for the ensemble mean and variance of head in the aquifer to second order in the standard deviation of log conductivity it is based on recursive approximations of exact nonlocal moment equations that are free of distributional assumptions and so apply to both gaussian and non gaussian log conductivity fields the analytical solution is supported by numerical monte carlo simulations it clarifies the manner in which relationships between the horizontal and vertical scales of the quasi steady state region and those of statistical anisotropy impact the statistical moments of drawdown and the equivalent and apparent hydraulic conductivities of the aquifer both conductivities are shown to exhibit a scale effect by growing with distance from the well within a radius of one to two horizontal integral scales from it

q markov covariance equivalent realizations this paper describes a class of reduced order models which match both the first q markov parameters and the first q output covariances for linear systems subject to white noise inputs the class of reduced models contains the earlier models 2 as a special case

caliper diameter of branched polymers the authors report analyses of exact numerical data for the spanning diameter of two dimensional lattice animals up to size n 17 estimates of the exponent nu are consistent with previous studies the leading correction to scaling has an exponent sigma approximately nu which does not result from irrelevant variable effects interpretation of this correction as a surface term is proposed

weighted q markov covariance equivalent realizations abstract reduced order models which preserve the first q markov parameters and the first q covariances are called q markov covariance equivalent realizations q markov covers this paper extends these notions to the case where the input is coloured instead of white noise we call this the weighted q markov cover

a new formulation of q markov covariance equivalent realization the q markov covariance equivalent realization q markov cover is a state space realization which matches the first q markov parameters and covariance parameters of a system king desai and skelton 5 developed a generalized approach to generate q markov covers desai and skelton 3 presented a recursive computational algorithm for generating q markov covers when q is very large based on the works of the above two papers we developed a new formula for generating q markov covers and also an algorithm to compute them when q is very large the new formula has been applied for model identification of large flexible structures by liu and skelton 6 8 compared with previously developed formulas and algorithms the new formula and algorithm are relatively straightforward and easy to program this formula may simplify the further analytical study of q markov covers and its application to system identification

q markov cover identification using pseudo random binary signals the original q markov covariance equivalent realization q markov cover method for identification required white noise test signals which cannot be generated exactly this paper replaces the unrealizable white noise signal with a realizable signal the pseudo random binary signal prbs and proves that when the period of the prbs approaches infinity the q markov cover algorithm operating with prbs matches the first q markov and covariance parameters as in the original theory with white noise test signals the existing q markov cover algorithm will fail to match covariance and markov parameters exactly due to non white test signals the new algorithm will fail to match covariance and markov parameters exactly due to the finite period of prbss we demonstrate however that the results with prbss are far superior to results with white noise signals apparently the non whiteness of the test signal degrades the identification performance worse than the non infinite period of the prbs

two dimensional characterization of hydraulic heterogeneity by multiple pumping tests 1 the conventional analysis of pumping tests by type curve methods is based on the assumption of a homogeneous aquifer applying these techniques to pumping test data from real heterogeneous aquifers leads to estimates of the hydraulic parameters that depend on the choice of the pumping and observation well positions in this paper we test whether these values may be viewed as pseudo local values of transmissivity and storativity which can be interpolated by kriging we compare such estimates to those obtained by geostatistical inverse modeling where heterogeneity is assumed in all stages of estimation we use drawdown data from multiple pumping tests conducted at the test site in krauthausen germany the geometric mean values of transmissivity and storativity determined by type curve analysis are very close to those obtained by geostatistical inversion but the conventional approach failed to resolve the spatial variability of transmissivity in contrast the estimate from geostatistical inversion reveals more structure this indicates that the estimates of the type curve approaches can not be treated as pseudo local values concerning storativity both analysis methods show strong fluctuations because the variability of all terms making up the storativity is small we believe that the estimated variability of storativity is biased we examine the influence of measurement error on estimating structural parameters of covariance functions in the inversion we obtain larger correlation lengths and smaller prior variances if we trust the measured data less

on the number of lattice animals embeddable in the square lattice enumeration of lattice animals embeddable in a square lattice has been extended to 24 cell animals by redelmeier 1981 it is shown that the number of animals per site an approximately 0 317 4 0626 nn 1 exp 0 465 n 0 87 to a high degree of accuracy

size of rings in two dimensions the authors report enumeration results for the radius of gyration and caliper size distribution of self avoiding unrooted polygons of up to 28 steps on the square lattice the second moment radius of gyration series is sufficiently smooth to allow verification of the theoretical prediction v rings v walks to 0 2 accuracy

cluster renormalisation study of site lattice animals in two and three dimensions the author studies site lattice animals using the cluster renormalisation cr approach previously applied to bond animals the exponent v characterising the asymptotic behaviour of the mean square radius of gyration of site animals and the fractal dimension df 1 v are determined in two and three dimensions he finds v 0 649 or 0 009 and v approximately 0 51 in two and three dimensions respectively in addition he studies restricted valence site animals on a triangular lattice using a single parameter cr approach

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

inverse stochastic moment analysis of steady state flow in randomly heterogeneous media 1 nonlocal stochastic moment equations have been used successfully to analyze steady state and transient flow in randomly heterogeneous media conditional on measured values of medium properties we present a nonlinear geostatistical inverse algorithm for steady state flow that makes it possible to further condition such analyses on measured values of state variables our approach accounts for all scales of spatial variability resolvable by the computational grid it is based on recursive finite element approximations of exact nonlocal first and second conditional moment equations hydraulic conductivity is parameterized geostatistically on the basis of measured values at discrete locations and unknown values at discrete pilot points prior estimates of pilot point values are obtained optionally by generalized kriging posterior estimates at pilot points and optionally at measurement points are obtained by calibrating mean flow against measured values of head the parameters are projected onto a computational grid via kriging maximum likelihood calibration allows estimating not only hydraulic but also optionally unknown variogram parameters with or without prior information about the former the approach yields covariance matrices for parameter estimation as well as head and flux prediction errors the latter being obtained a posteriori we implement our inverse approach on highly and mildly heterogeneous media under superimposed mean uniform and convergent flows in a bounded two dimensional domain our examples illustrate how conductivity and head data act separately and jointly to reduce parameter estimation errors and to model predictive uncertainty we also evaluate the functional form of the log conductivity variogram and its parameters using likelihood based model discrimination criteria

monte carlo and series study of corrections to scaling in two dimensional percolation corrections to scaling for percolation cluster numbers in two dimensions are studied by monte carlo simulations of very large systems up to 17 109 lattice sites and by series analysis both series and monte carlo work suggests that the value of the correction to scaling exponent is slightly lower at the percolation threshold than away from it moreover the corrections to scaling observed at pc omega equivalent to 0 64 might be due to the mixing of scaling fields rather than to the irrelevant scaling fields the monte carlo results are compatible with finite size scaling and finite size scaling corrections are estimated technical problems associated with monte carlo simulation of very large systems are discussed in an appendix

reduction of linear continuous time multivariable systems by matching first and second order information this paper considers the approximation of stable continuous time multivariable linear systems from a finite number of markov parameters and second order information indexes it is shown that by properly choosing these indexes it is possible to uniquely identify an input output model of given order from an equal number of first and second order data

universal amplitude in the sizes of rings in two dimensions for self avoiding rings of n steps in two dimensions the limiting value as n to infinity of the combination npn r2 nxcn where pn is the number of distinct rings r2 n is their mean square radius of gyration and xc is the critical fugacity is equal to a calculable lattice dependent number times a universal amplitude this latter quantity is calculated exactly using methods of conformal invariance the value is in good agreement with the results of enumeration studies

some asymptotic properties of multivariable models identified by equation error techniques some interesting properties are derived for simple equation error identification techniques least squares and basic instrumental variable methods applied to a class of linear time invariant time discrete multivariable models the system at hand is not supposed to be contained in the chosen model set assuming that the input is unit variance white noise it is shown that the markov parameters of the system are estimated asymptotically unbiased over a certain interval around t 0

a generalized approach to q markov covariance equivalent realizations for discrete systems abstract a new algorithm is developed which constructs q markov covariance equivalent realizations q markov covers of multivariable linear discrete time systems a q markov cover is a state realization which matches exactly a finite portion of the impulse response sequence markov parameters and output autocorrelation sequence covariance parameters of a linear system the algorithm generates the q markov covers starting with only the basic data namely the q markov parameters and the q covariance parameters the algorithm leads to a parameterization of all minimal stable q markov covers which can be constructed since the data are easily computed from a given state space model the algorithm presented will be useful for both realization and model reduction of multivariable linear discrete time systems an example is presented to demonstrate the algorithm

model sets and parametrizations for identification of multivariable equation error models abstract equation error or linear regression models are known to inherently require the a priori choice for specific signal variables to be considered as regressand and or regressor this implies that a model set should be a priori restricted in some way in order to define an acceptable identification problem in the case of approximate identification i e the system to be modelled is not contained in the model set this restriction acts as a design variable with the identified models being dependent on its specific choice in this paper the necessity of this restriction is quantified by the property of discriminability i e the ability of an identification criterion to distinguish between all the different models in a model set employing a deterministic signal oriented framework several sets of sufficient conditions are derived for model sets to be discriminable by a least squares identification criterion to this end use is made of polynomial model representations in two shift operators although it is of a different nature the problem discussed is shown to be closely related to the problem of constructing identifiable parametrizations for sets of rational transfer functions it is shown that the pseudo canonical or overlapping parametrization of all transfer functions with fixed mcmillan degree constitutes a nonoverlapping set of equation error models that is discriminable by a least squares identification criterion

geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown 1 pumping tests belong to the most common techniques of hydrogeological site assessment while the steady state drawdown is determined by the distribution of transmissivity alone the transient behavior is also influenced by the storativity field in geostatistical inverse modeling the spatial distributions of both transmissivity and storativity are inferred from the drawdown curves and prior information on the spatial correlation of the parameter fields so far however transient data have hardly been analyzed by geostatistical inverse methods because the computational effort is rather high in the present study we characterize the drawdown by its temporal moments we present moment generating equations and corresponding equations to compute the sensitivity of the temporal moments of drawdown with respect to the distributions of transmissivity and storativity we utilize these equations to infer the transmissivity and storativity fields from transient pumping tests using the quasi linear geostatistical approach of inverse modeling considering temporal moments rather than full drawdown curves drastically reduces the computational effort of the estimation procedure in test cases we show that the first two temporal moments are sufficient to characterize the drawdown curves we investigate how erroneous assumptions regarding the spatial variability of storativity affect the estimate of the transmissivity field and we analyze the effect of truncating the measured drawdown curves

past input reconstruction in fast least squares algorithms this paper solves the following problem given the computed variables in a fast least squares prediction algorithm determine all past input sequences that would have given rise to the variables in question this problem is motivated by the backward consistency approach to numerical stability in this algorithm class the set of reachable variables in exact arithmetic is known to furnish a stability domain our problem is equivalent to a first and second order interpolation problem introduced by mullis and roberts 1976 and studied by others our solution differs in two respects first relations to classical interpolation theory are brought out which allows us to parametrize all solutions by products of our formulation are correct necessary and sufficient conditions for the problem to be solvable in contrast to previous works whose claimed sufficient conditions are shown to fall short second our solution obtains any valid past input as the impulse response of an appropriately constrained orthogonal filter whose rotation parameters derive in a direct manner from the computed variables in a fast least squares prediction algorithm formulas showing explicitly the form of all valid past inputs should facilitate the study of what past input perturbation is necessary to account for accumulated arithmetic errors in this algorithm class this in turn is expected to have an impact in studying accuracy aspects in fast least squares algorithms

generation of a time series having a specified power spectrum with minimum roundoff noise the problem of determining a shaping filter which minimized the output roundoff noise variance is discussed it is shown that in the family of shaping filters of an identical mcmillan degree having an identical power spectrum the shaping filter of minimum phase attains a minimum output roundoff noise variance in either the case of optimal word lengths or the case of equal word lengths it is shown out by examples that this is not valid in the family of shaping filters having an identical power spectrum and different mcmillan degrees

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

bayesian identification of the local transmissivity using time drawdown data from pumping tests 1 conventional pumping test analysis techniques focus mostly on estimating the effective transmissivity of the perturbed subsurface volume surrounding the extraction and observation wells ignoring the existing local scale heterogeneity the purpose of this paper is to explore whether transient drawdown data derived from pumping tests can also be used to identify the statistical spatial structure of the local transmissivity field the log transmissivity is modeled as a multivariate random spatial function with stationary mean and exponential semivariogram monte carlo simulations are used to compute the transient drawdown for different values of the log transmissivity variance and integral scale on the basis of these simulations a bayesian procedure is developed to estimate the probability density functions of these two statistical parameters the main benefit of using a bayesian approach is that it readily accounts for the uncertainty of the estimated parameters application of the proposed procedure to simulated drawdown data shows that it is possible to characterize the local transmissivity from pumping test data and that the reliability of the estimates increases with an increase in the number of available tests

multichannel stable systems that extend the partial impulse response matrices this paper addresses the problem of identifying the class of all multichannel stable system transfer functions that extend the given partial impulse response matrix sequence this is achieved by making use of the left and right schur recursion algorithms for bounded matrix functions and in this context the classical pade approximations that are also stable are shown to be a special case of this general formulation further the theory developed here is utilized to generate multichannel non minimum phase optimal rational approximations to multichannel nonrational systems from their partial impulse response matrix sequence

model reduction by matching markov parameters time moments and impulse response energies this paper presents a simple procedure for constructing reduced order models that match some markov parameters and time moments of an original system as well as the energies of its impulse response and of other combinations of the system modes in this way the stability of the reduced model of a stable system is ensured

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha

size and shape of directed lattice animals uses position space renormalisation and exact enumeration methods to study configurational properties of directed lattice animals clusters of directed bonds in which the tail of a new bond must be added to the head of existing bonds exponents are found for the divergence of correlation lengths parallel and perpendicular to the preferred axis in addition an exponent is found that characterises the singularity of the directed animal generating function and critical points are located

finite time and asymptotic behaviour of the maximal excursion of a random walk we evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self similar supports under the assumption of spherical symmetry this distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods we then focus on the early time behaviour of this quantity the instantaneous diffusion exponent n exhibits a systematic overshooting of the long time exponent exact results are obtained in one dimension up to third order in n 1 2 in two dimensions on a regular lattice and on the sierpinski gasket we find numerically that the analytic scaling n an holds