arma modeling of time series a method for efficiently generating a rational model of a wide sense stationary time series is presented in this method the autoregressive parameters associated with an arma model consisting of q zeros and p poles are optimally chosen with the selection being based on a finite set of time series observations this selection is made so that a set of yule walker equation approximations are best satisfied the resultant autoregressive parameter estimates have the desired statistical feature of being unbiased and consistent this estimation method has been found to provide a modeling performance which typically equals or exceeds that of contemporary alternatives moreover this method is amenable to a computationally efficient adaptive solution procedure the autoregressive parameters characterizing the resultant arma model estimate can serve the role of decision variables in pattern classification schemes for example these parameters can be utilized in determining whether or not a member s of a given signal class is contained within a noise corrupted measurement signal this approach has been found to be particularly effective in doppler radar and array processing applications in which one is looking for the presence of spectral lines i e sinusoids in the measurement signal

conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

universal configurational structure in two dimensional scalar models monte carlo methods are used to explore the universal configurational structure of two dimensional spin 1 2 spin 1 and border phi 4 models comparison of spin 1 2 and spin 1 data provides evidence that the magnetisation distribution effectively the helmholtz free energy function and its coupling derivative effectively the internal energy function constitute readily accessible signatures of a universality class it is shown that when allowance is made for relatively large corrections to scaling effects the behaviour of the border phi 4 model may be satisfactorily matched to that of the other two models substantiating the view that the border model does indeed belong to the ising universality class

the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

corrections to the kalman yakubovich popov lemma for pritchard salamon systems abstract in this note we correct the result in the paper the kalman yakubovich popov lemma for pritchard salamon systems 3 there was a gap in the proof which can be bridged but only by assuming that the system is exactly controllable

limitations on universality in the continuous spin ising model the authors give by explicit counterexample numerical evidence that critical exponent universality fails for the two dimensional continuous spin ising model this result is contrary to what has previously been assumed

multiplicity of infinite clusters in percolation above six dimensions the author presents monte carlo simulations of site percolation near the percolation threshold in five to seven dimensions in contrast to lower dimensionalities more than one spanning cluster is found in a system of size ld for d 6 these results confirm coniglio s prediction 1985 that the breakdown of hyperscaling for d 6 is caused by a multiplicity of infinite clusters at the percolation threshold

the scaling limit of the incipient infinite cluster in high dimensional percolation ii integrated super brownian excursion for independent nearest neighbor bond percolation on zd with d 6 we prove that the incipient infinite cluster s two point function and three point function converge to those of integrated super brownian excursion ise in the scaling limit the proof is based on an extension of the new expansion for percolation derived in a previous paper and involves treating the magnetic field as a complex variable a special case of our result for the two point function implies that the probability that the cluster of the origin consists of n sites at the critical point is given by a multiple of n 3 2 plus an error term of order n 3 2 e with e 0 this is a strong version of the statement that the critical exponent is given by 2

the value function of the singular quadratic regulator problem with distributed control action we study the regularity properties of the value function of a quadratic regulator problem for a linear distributed parameter system with distributed control action no definiteness assumption on the cost functional is assumed we study the regularity in time of the value function and also the space regularity in the case of a holomorphic semigroup system

monte carlo computation of cluster free energies in the ising model a test for the validity of the capillarity approximation a new monte carlo technique is proposed to compute directly the free energy difference fn 1 fn of two clusters with size n 1 and n the algorithm is applied to the two dimensional square ising model with nearest neighbour interactions results are given for 1 9 but for smaller cluster sizes the obtained energies are larger than predicted by the capillarity model the deviation exhibits no systematic size dependence but a strong temperature dependence the existence of a size independent term in fn is confirmed by the values of the internal energy un obtained as a by product of the calculation

the quadratic regulator problem and the riccati equation for a process governed by a linear volterra integrodifferential equations in this paper we study the quadratic regulator problem for a process governed by a volterra integrodifferential equation in mathbf mathbb r n our main goal is the proof that it is possible to associate a riccati differential equation to this quadratic control problem from which the feedback form of the optimal control can be computed this is in contrast with previous papers on the subject which confine themselves to study the fredholm integral equation which is solved by the optimal control

conformal invariance and self avoiding walks in restricted geometries the prediction of conformal invariance for the statistics of self avoiding random walks restricted to both semi infinite and wedge shaped geometries are tested by extrapolating exact enumerations close agreement is found both for the angular distribution of the end to end vector and for the dependence of the critical exponent gamma 2 on the opening angle of the wedge

the fractal dimension and other percolation exponents in four and five dimensions for percolation the fractal dimension df which is identical to the magnetic field scaling power yh has never been calculated for hypercubic lattices of dimension d 5 percolation is studied for systems of high dimensionality using the method of large cell monte carlo position space renormalisation group the estimate df yh 3 69 or 0 02 d 5 and 3 12 or 0 02 d 4 is obtained the thermal scaling power yt 1 nu where nu is the correlation length exponent is calculated yt 1 nu 0 51 or 0 05 d 5 and nu 0 64 or 0 02 d 4 the results are compared with the epsilon expansions of df and nu

the hamiltonian spectrum of directed percolation the authors calculate the spectrum of a quantum hamiltonian which is in the universality class of the reggeon field theory and directed percolation they find that its low lying states follow a self similarity close to the one encountered in the exactly solvable transverse xy model the spectrum can in the finite size scaling limit approximately be described by excitations with a dispersion relation ktheta on the lattice instead of the k2 behaviour of the transverse xy model

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

information theoretic distortion measures for speech recognition a wide variety of speech recognition distortion measures have been proposed and tested including some especially effective ones it is shown that there is a general framework based on the concepts of information theory linking most of these measures the distortion measure between any two speech spectra can be defined in terms of the distortions between the associated probability distributions this general framework defines three broad families of distortion measures for speech recognition and provides a consistent way of combining the energy and the spectral information of a phonetic event in addition the cepstral domain representation for several distortion measures is derived allowing comparison of these measures in a domain that also yields convenient equations for their practical implementation

non perturbative renormalization using dimensional regularization applications to the epsilon expansion the authors give a prescription for the one loop renormalisation of the imaginary parts of vertex functions in g phi 4 which are generated when g 0 within the dimensional regularisation scheme this involves another non perturbative renormalisation over and above the usual one loop perturbative renormalisation the authors use an extended minimal subtraction scheme so that the resulting renormalisation group functions have a simple dependence on epsilon 4 d in contrast to the usual case however both the beta function and the renormalised coupling gr are in general complex for real g and the fixed point for epsilon gr 0 is non perturbative in epsilon this fixed point determines the imaginary parts of the critical exponents which are generated when epsilon 0 and allows the determination of the high order behaviour of the perturbation series in epsilon for these exponents the generalisation of these ideas to the o n symmetric g phi 2 2 model is also given

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

critical percolation clusters in seven dimensions and on a complete graph we study critical bond percolation on a seven dimensional hypercubic lattice with periodic boundary conditions 7d and on the complete graph cg of finite volume number of vertices v we numerically confirm that for both cases the critical number density n s v of clusters of size s obeys a scaling form n s v s n over s v d f with identical volume fractal dimension d f 2 3 and exponent 1 1 d f 5 2 we then classify occupied bonds into bridge bonds which includes branch and junction bonds and nonbridge bonds a bridge bond is a branch bond if and only if its deletion produces at least one tree deleting branch bonds from percolation configurations produces leaf free configurations whereas deleting all bridge bonds leads to bridge free configurations composed of blobs it is shown that the fraction of nonbridge biconnected bonds vanishes n cg 0 for large cgs but converges to a finite value n 7d 0 0061931 7 for the 7d hypercube further we observe that while the bridge free dimension d bf 1 3 holds for both the cg and 7d cases the volume fractal dimensions of the leaf free clusters are different d lf 7d 0 669 9 2 3 and d lf cg 0 3337 17 1 3 on the cg and in 7d the whole leaf free and bridge free clusters all have the shortest path volume fractal dimension d min 1 3 characterizing their graph diameters we also study the behavior of the number and the size distribution of leaf free and bridge free clusters for the number of clusters we numerically find the number of leaf free and bridge free clusters on the cg scale as lnv while for 7d they scale as v for the size distribution we find the behavior on the cg is governed by a modified fisher exponent 1 while for leaf free clusters in 7d it is governed by fisher exponent 5 2 the size distribution of bridge free clusters in 7d displays two scaling behavior with exponents 4 and 1 the probability distribution p c 1 v dc 1 of the largest cluster of size c 1 for whole percolation configurations is observed to follow a single variable function p over x dx with x c 1 v d f for both cg and 7d up to a rescaling factor for the variable x the probability functions for cg and 7d collapse on top of each other within the entire range of x the analytical expressions in the x 0 and x limits are further confirmed our work demonstrates that the geometric structure of high dimensional percolation clusters cannot be fully accounted for by their complete graph counterparts

geometrically invariant interactions in capillary wave surface models the authors examine the role of geometrically invariant interactions such as curvature in modulating the long distance behaviour of surface tension models in the context of a perturbative epsilon expansion approach first discussed by wallace and zia 1979 a suggestive semiclassical calculation shows how some of these interactions arise the renormalisation and hence scaling properties of the simplest of these interactions the contraction of the second fundamental form with the metric tensor g b are considered

droplet structure in ising and potts models the structure of a recently introduced droplet in the q state potts model is analysed the authors derive exact relations from which it follows that the incipient infinite droplet at the critical temperature is a self similar fractal made of links and blobs just as recently found in random percolation the number of links nlinks between two points separated by a distance of the order b is given by nlinks varies as b1 nu b q where nu b q is the connectedness length exponent when t tc q and pb is used as an independent variable this result and the available calculations of nu b q indicate that the number of links decreases as q increases an analysis of the structure of the usual clusters made of nearest neighbour sites in a given potts site configuration is also made in particular it shows that for d 2 the incipient infinite cluster is made only of blobs and no links

tests of a method for estimating corrections to scaling from series the author studies a recently developed pade type method of series analysis which allows for the leading confluent singularity a number of properties are described and by applying the method to various test series some pitfalls of the technique are revealed

a weighted cepstral distance measure for speech recognition a weighted cepstral distance measure is proposed and is tested in a speaker independent isolated word recognition system using standard dtw dynamic time warping techniques the measure is a statistically weighted distance measure with weights equal to the inverse variance of the cepstral coefficients the experimental results show that the weighted cepstral distance measure works substantially better than both the euclidean cepstral distance and the log likelihood ratio distance measures across two different databases the recognition error rate obtained using the weighted cepstral distance measure was about 1 percent for digit recognition this result was less than one fourth of that obtained using the simple euclidean cepstral distance measure and about one third of the results using the log likelihood ratio distance measure the most significant performance characteristic of the weighted cepstral distance was that it tended to equalize the performance of the recognizer across different talkers

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

droplet theory of correlations in ordered phases the explicit droplet theory of low dimensional phase transitions developed recently is extended to yield a description of the pair correlation function for the universality class of q state potts models in the ordered phase and in zero external field it is shown that in d 1 epsilon dimensions the short distance behaviour of the correlation function and in particular the exponent eta are controlled by nested nearly spherical droplets in contrast it is argued that the spatial dependence of the large distance behaviour in d 2 or above is controlled by highly anisotropic droplets thus illuminating the widom relation sigma xi d 1 approximately constant linking the dimensionless surface tension sigma and the bulk correlation length xi in the particular case of d 2 the statistical weight of the relevant droplets is determined as that of two appropriately interacting strings in the spirit of recent independent arguments by abraham and by fisher a non ornstein zernike correlation function prefactor and the result of sigma xi 1 2 follow in accord with exact results for the q 2 ising case and with implications for the q to 1 percolation problem

time coarse graining near critical points the authors investigate the statistical properties of local variables coarse grained in time in systems undergoing continuous phase transitions a general theory is developed which suggests universal scaling behaviour in the limit of large coarse graining times the predictions are substantiated with monte carlo studies of two dimensional scalar models a simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale invariant character the theory is used to study the critical behaviour of local resonance lineshapes in the two dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow motion lineshape

the ising model below tc calculation of nonuniversal amplitudes using a primitive droplet model using recent exact results for the surface free energies of ising droplets on a square lattice and applying a primitive droplet theory due to langer 1967 the author obtains an expression for the principal nonuniversal amplitude appearing in the imaginary part of the analytic continuation of the free energy across the coexistence line for the square lattice ising model below tc the significance of this calculation is the known dependence on this amplitude of the large order terms in the expansion of the physical free energy in powers of h thus allowing a direct numerical comparison with existing series data to be made after carrying out a simple renormalisation of the droplet volume term the author finds excellent numerical agreement

universal local dynamics the authors suggest that near a critical point the statistical behaviour of local variables averaged over times long on microscopic scales is universal reflecting large scale partial structure the contention is supported with monte carlo studies of two dimensional scalar models

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

cluster size distribution above the percolation threshold discusses how the cluster size distribution above the percolation threshold is related to the existence of metastable states of the potts model the authors thus find that the average number of clusters per site containing n sites is given by c n approximately n theta exp constant n1 1 d where d is the dimensionality of the lattice the exponent theta is given for a range of values of d

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

distortion performance of vector quantization for lpc voice coding the distortion performance of the vector quantization approach for lpc voice coding is examined both analytically and experimentally analytically interpretations of the interparameter coupling effects of a distortion measure and the clustering nature of the algorithm for lpc vector quantization are obtained to show its relationship with the residual minimization process in lpc analysis experimentally a large database of speech is used to compare its performance and properties to scalar quantization the results lend further insight into the superior performance of vector quantization

finite size effect in seven dimensional site percolation on a hypercubic lattice with l7 sites and l up to 21 the site percolation threshold for the spanning of a cluster from top to bottom is found to approach its asymptotic value with a 1 l law in contrast to the ising curie temperature in five dimensions

numerical tests of nucleation theories for the ising models the classical nucleation theory cnt is tested systematically by computer simulations of the two dimensional 2d and three dimensional 3d ising models with a glauber type spin flip dynamics while previous studies suggested potential problems with cnt our numerical results show that the fundamental assumption of cnt is correct in particular the becker doring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input this validates the coarse graining of the system into a one dimensional markov chain with the largest droplet size as the reaction coordinate furthermore in the 2d ising model the droplet free energy predicted by cnt matches numerical results very well after a logarithmic correction term from langer s field theory and a constant correction term are added but significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3d ising model our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories

finite size scaling study of the equilibrium cluster distribution of the two dimensional ising model the authors use a very fast and efficient algorithm to study by monte carlo methods the equilibrium cluster distribution cl l and the mean number of clusters per lattice site containing l particles in a square lattice of l2 sites of the two dimensional ising model at the critical point finite size scaling theory is then used to analyse the scaling ansatz cl l l tau f ls l tau and s being critical exponents the second moment of the cluster distribution p2 l sigma l2cl is shown to behave as p2 l approximately ltheta with theta 1 895 or 0 010 the effect of corrections to scaling is also discussed

scaling at the percolation threshold above six dimensions the fractal dimensionality of the infinite cluster at the percolation threshold for dimensionalities d 6 is shown to be d 4 rather than the naive finite size scaling prediction d d 2 similarly the conductivity of a sample of size l scales as l d rather than l 6 this anomalous behaviour is related to a dangerous irrelevant variable associated with the probability to have vertices of three bonds the crossover to the homogeneous behaviour occurs at length scales which are short compared with the correlation length the links and blobs picture is confirmed for d 6 and the size of the latter is estimated

estimation of all pole model parameters from noise corrupted sequences least squares estimates of the parameters of all pole signal models are biased when applied to noise corrupted all pole sequences this bias has been shown to be proportional to the inverse of the signal to noise ratio an autocorrelation like procedure is shown to increase under some circumstances the signal to noise ratio while retaining the pole locations when the noise is white the signal to noise ratio improvement varies for each mode in the all pole sequence with modes corresponding to pole locations close to the unit circle showing the most improvement a signal to noise ratio cutoff exists for each mode below which no improvement can be obtained this cutoff depends on the proximity of the pole location to the unit circle approaching zero as the pole nears the origin this cutoff corresponds to the point at which a mode s spectral value just equals the level of the noise floor this procedure can be applied recursively until an acceptable signal to noise ratio is obtained the all pole parameters can then be estimated from the processed sequence using least squares estimation

schrodinger invariance and strongly anisotropic critical systems the extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated for the special case of an anisotropy or dynamical exponent z 2 the group of local scale transformation considered is the schrodinger group which can be obtained as the nonrelativistic limit of the conformal group the requirement of schrodinger invariance determines the two point function in the bulk and reduces the three point function to a scaling form of a single variable scaling forms are also derived for the two point function close to a free surface which can be either spacelike or timelike these results are reproduced in several exactly solvable statistical systems namely the kinetic ising model with glauber dynamics lattice diffusion lifshitz points in the spherical model and critical dynamics of the spherical model with a nonconserved order parameter for generic values of evidence from higher order lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two point function

percolation fractals and the finite size scaling of existence probability abstract based on the connection between phase transitions of thermodynamic systems and percolation transitions we obtain the geometrical meaning of critical exponents using finite size scaling of the percolation probability p and the existence probability e p for percolating clusters and percolating subgraphs respectively where e p is the ratio of the total probability weight for percolating subgraphs to the total probability weight for all subgraphs we use a histogram monte carlo simulation method to calculate e p for a q state bond correlated percolation model qbcpm which is corresponding to the q state potts model on the square lattice with various linear dimensions we find that for a given q e p has very good scaling behavior but e p for different q has different scaling functions

percolation in high dimensions is not understood abstract the number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation

collapse transition and asymptotic scaling behavior of lattice animals low temperature expansion a low temperature expansion for the free energy density of lattice animals is derived analysis of the series yields a collapse transition temperature oftc 0 54 in close agreement with previous estimates it is demonstrated that p k the number ofp particle p bond animals obeys the asymptotic scaling law log p k pg k p o p the low temperature series and numerical data are used to estimate the scaling function

equivalent conditions for the solvability of the nonstandard lq problem for pritchard salamon systems equivalent conditions are presented for the solvability of the infinite horizon lq problem with stability for a class of infinite dimensional systems with unbounded input and output operators in particular these equivalent conditions are given in terms of a riccati equation and a frequency domain inequality just as in the finite dimensional case

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

droplet theory in low dimensions ising systems in zero field the authors develop a theory of the universal configurational physics underlying critical point phenomena in the ising universality class the theory is formally justifiable in d 1 epsilon dimensions and may be regarded as the natural continuation of the kink based theory of one dimension which it incorporates as a limiting case in d 1 epsilon the configurational building block is the droplet the typical droplet is not spherical and the many droplet assembly is not dilute the implied problems are handled with renormalisation group methods it is found that droplet shape fluctuation effects control the correlation length exponent nu while the nesting of droplets within droplets control the order parameter exponent beta the exponents nu and beta thus effectively define respectively the fractal dimensions of the droplet surface and the droplet volume the theory is used to determine and illuminate the critical behaviour of further quantities including the free energy the susceptibility the droplet number distribution and the distribution of the intra droplet order

random directed polymers and their bosonic and fermionic field theories derives a bosonic and fermionic field theory for randomly directed polymers the bosonic field theory needs replicas and it is shown that the problem can be mapped in an o n symmetric lagrangian with an attractive phi 4 term the fermionic field theory introduces alternatively anticommutating fields and a supersymmetric lagrangian is derived for the randomly directed polymer

the incipient infinite cluster for high dimensional unoriented percolation we consider bond percolation on mathbb z d at the critical occupation density p c for d 6 in two different models the first is the nearest neighbor model in dimension d 6 the second model is a spread out model having long range parameterized by l in dimension d 6 in the spread out case we show that the cluster of the origin conditioned to contain the site x weakly converges to an infinite cluster as x when d 6 and l is sufficiently large we also give a general criterion for this convergence to hold which is satisfied in the case d 6 in the nearest neighbor model by work of hara 12 we further give a second construction by taking p 6 the probability for invasion percolation to reach a site x is asymptotic to c x d 4 as x

the short time modified coherence representation and noisy speech recognition a technique for robust spectral representation of all pole sequences is proposed it is shown that the autocorrelation of an all pole sequence obtained by passing white noise through an all pole filter 1 a z is an all pole sequence of the form 1 a sup 2 z a short time modified coherence smc representation is proposed that is an all pole modeling of the autocorrelation sequence with a spectral shaper the spectral shaper essentially a square root operator in the frequency domain compensates for the inherent spectral distortion introduced by the autocorrelation operation on the autocorrelation sequence of the signal the properties of the smc representation especially its robustness to additive white noise are analyzed initial implementation of the smc in a speaker dependent isolated word recognizer shows an improvement in recognition accuracy equivalent to an increase in input snr of approximately 13 db as compared to the lpc recognizer

the kalman yakubovich popov lemma for pritchard salamon systems in this paper we generalize the kalman yakubovich popov lemma to the pritchard salamon class of infinite dimensional systems i e systems determined by semigroups of operators on a hilbert space with unbounded input and output operators at the same time we prove a comparison theorem for riccati equations of the same class

the two dimensional spin 1 ising system and related models although the two dimensional spin 1 2 ising model was solved in zero field in 1944 no exact results are yet available for the spin 1 model this model should have the same dominant critical exponents as the spin 1 2 model but appears to exhibit non analytic corrections to scaling as expected for a phi 4 model and unlike the spin 1 2 model in this paper new 45 term low temperature series for the magnetisation specific heat and susceptibility of the spin 1 model on the square lattice are presented and analysed a new 24 term staggered susceptibility series for the hard square model is presented and the extant order parameter series for this model which is also in the phi 4 universality class are also considered for both models a non analytic confluent correction with exponent 1 0 delta 1 1 3 is found the validity of this result is enhanced by a comparison with the s 1 2 case

universality in the two dimensional continuous spin model monte carlo methods have been used to analyse the critical behaviour of the d 2 border phi 4 model which according to a recent series expansion study violates expectations based upon universality the results suggest that the model does in fact fall into the ising universality class at least as regards those parameters which characterise the critical point configurations of the ordering variable

transfer matrix calculation of the relative noise exponent in a two dimensional percolating network a new method is given for calculating the relative noise exponent describing the size dependence of macroscopic fluctuations due to microscopic resistance noise of a random resistor network at the percolation threshold pc the macroscopic fluctuation is calculated exactly using the transfer matrix idea in a given network the asymptotic exponent b is found by finite size scaling

directed lattice animals and the lee yang edge singularity the exponents nu perpendicular to gamma of directed animals in d dimensions are shown to equal those for the lee yang problem in d 1 dimensions for d 2 the author obtains the exact results nu perpendicular to theta 1 2 and for d or 7 the scaling relation theta d 1 nu perpendicular to

the regulator problem with indefinite quadratic cost for boundary control systems the finite horizon case in this paper we study the finite horizon non standard lq problem for an abstract dynamics which models a large class of hyperbolic like partial differential equations we provide necessary sufficient conditions for finiteness of the value function corresponding to the control problem sharpness of sufficient conditions is shown by means of counterexamples the specific features of the finite in contrast to infinite horizon case are illustrated

droplet theory in low dimensions potts models and percolation a recently developed droplet theory of low dimensional ising systems is generalised to describe the q state potts universality class and thence the percolation problem realised in the q to 1 limit an integral equation for the potts model free energy is derived and used to obtain the generating function for the cluster size probability distribution in the percolation problem above the percolation threshold a closed equation for the distribution is obtained and shown to yield scaling behaviour the form of the distribution is determined analytically in the regimes of small and large cluster sizes yielding respectively power law decay and kunz souillard exponential decay the form of the distribution in the regime of intermediate cluster sizes is determined numerically in space dimension d 2

effective hamiltonians for strings and their spatial symmetry the effective hamiltonian governing the fluctuations of a d n dimensional string into the remaining n dimensions in a d bulk dimensional system is derived using semiclassical methods in the long distance limit and found to represent the hypersurface area of the string the author also derives the effective hamiltonian for strings with an associated o 2 goldstone mode and obtains a field theory defined on a curved surface given by the interface s position the role of spatial symmetries in determining the form of the effective hamiltonian is illustrated

design of consensus and adaptive consensus filters for distributed parameter systems this work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network it is assumed that the sensor network consists of groups of sensors each of which provides a number of state measurements from sensing devices that are not necessarily identical and which only transmit their information to their own sensor group a modification to the local spatially distributed filters provides the non adaptive case of spatially distributed consensus filters which penalize the disagreement amongst themselves in a dynamic manner a subsequent modification to this scheme incorporates the adaptation of the consensus gains in the disagreement terms of all local filters both the well posedness of these two consensus spatially distributed filters and the convergence of the associated observation errors to zero in appropriate norms are presented their performance is demonstrated on three different examples of a diffusion partial differential equation with point measurements

equilibrium cluster distributions of the three dimensional ising model in the one phase region abstract we analyse equilibrium cluster distributions obtained numerically from a ferromagnetic ising model simple cubic lattice 125000 sites and periodic boundary conditions along the coexistence line and in the one phase region below t c we find evidences that the distribution of sizes and energies scales with temperature and external magnetic field giving binder s droplet exponent y 4 9 the mean number of incident interior and exterior bonds on a cluster of size l s l seems to behave as l x with x 9 10 when not far away from t c we conclude that while the classical nucleation theory may provide an approximate description around 0 59 t c it has to be modified at higher and lower temperatures the fisher droplet model and the approach by penrose et al based on a renormalized fugacity are also discussed we thus obtain simple semiphenomenological expressions for the cluster equilibrium distributions and partition functions

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

dynamic critical behaviour of semi infinite systems conformal invariance and mirror theory the critical dynamics of the d dimensional semi infinite systems is studied at bulk critical temperature as a result of the conformal invariance the dynamic response and correlation functions depend only on the real distance r the image distance r and the time t mirror theory assuming the non conserved order parameter with o n symmetry the authors evaluate the response and correlation functions exactly in the large n limit and also to first order in epsilon 4 d the authors results satisfy the mirror theory for the various types of the phase transitions including the ordinary special anisotropic special and extraordinary transitions

stability of the isotropic fixed point near one dimension within the context of the l epsilon expansion and the near planar interface hamiltonian the isotropic fixed point is found to be stable to a wide class of perturbations in particular the universality class includes all non singular forms of anisotropic surface tension

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

order propagation near the percolation threshold a new monte carlo method for studying bond percolation clusters is developed and used to identify new critical quantities associated with the percolation threshold the bonds in each cluster are partitioned into three distinct connectivity classes red singly connected backbone bonds blue multiply connected backbone bonds and yellow non backbone bonds often called dangling ends among the new cluster properties studied are the mean number of red bonds a critical quantity diverging at p c with exponent y r approximately 1 and the length of the shortest connected path through the cluster which is critical with exponent y min 1 35 0 02 for all cluster properties studies the authors also compute averages over only the largest clusters the corresponding critical exponents are found to be significantly different from those obtained by averaging over clusters of all sizes

droplet theory of low dimensional potts models formulates a generalisation of the droplet theory of ising systems to droplet systems containing more than two phases valid near one dimension and based on the configurational energy of surface tension thermal and magnetic exponents for these multi phase systems are compared with the results for a q state potts model in the external field the potts exponents are obtained using a migdal recursion formula and are shown to be of very similar structure

asymptotic behaviour of the perturbation expansion in n 0 field theories the author develops a method for studying the high order behaviour of the perturbation expansion in theories in which the number of field components n is taken to zero this procedure is illustrated on the field theory formulation of the percolation problem which can be considered as the n 0 limit of the n 1 state potts model the saddle points controlling the asymptotic behaviour are labelled by an integer r 1 2 n for positive integer n but after continuation to n 0 the dominant contribution effectively comes from the saddle point with r infinity the perturbation expansion is found to be oscillatory at large orders and its behaviour is calculated

droplet theory in low dimensions ising systems in an ordering field the authors extend the microscopic droplet theory of ising systems developed recently to incorporate the effects of an ordering field the theory yields a free energy which is the solution of a renormalisation group equation describing droplet nesting and which has a full scaling form the behaviour near the coexistence curve is investigated and found to display the essential singularity suggested by primitive droplet models but with parameters renormalised in a physically intelligible way the droplet population function implied by the theory is parametrised in a simple way in space dimension d 2 to yield predictions for various thermodynamic properties including the equation of state which are found to be in fair accord with series based results the structure of the field dependent droplet number distributions is investigated and contrasted with the forms assumed in phenomenological droplet theories the domain of validity of the theory is assessed it is concluded that the theory fails to describe sufficiently large droplets in the presence of a finite field and is thus in principle trustworthy only in a region close to the coexistence curve

validity of classical nucleation theory for ising models while the classical nucleation theory cnt is widely used to predict the rate of first order phase transitions its validity has been questioned due to discrepancies with experiments we systematically test the individual components of cnt by computer simulations of the ising models and confirm its fundamental assumptions under a wide range of conditions h 0 01 text char21 0 13j t 0 44 text char21 0 84 t c in two dimensions and h 0 30 text char21 0 60j t 0 48 text char21 0 62 t c in three dimensions first cnt accurately predicts the nucleation rate if the correct droplet free energy is provided furthermore theoretical prediction of droplet free energy matches numerical results very well in the two dimensional 2d ising model if appropriate correction terms are added this establishes the 2d ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters

diffusion on random clusters and the parasite problem in the parasite problem a particle ant diffuses randomly on a random percolation cluster in the limit of concentration to 0 lattice animal monte carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t 1 za with time t the authors find za approximately 3 4 on the simple cubic lattice and za approximately 2 6 on the square lattice this anomalous diffusion is in rough agreement with a generalisation of a suggestion by alexander and orbach 1982 heuristic arguments in favour of this suggestion are given also they look at corrections to scaling for concentrations equal to the percolation threshold

the mean size of ising clusters a confluent singularity analysis the authors re examine using a confluent singularity analysis existing low temperature series for the mean size of finite clusters for the pure spin 1 2 nearest neighbour ising model in two dimensions although the triangular lattice is problematical results for the honeycomb and square lattices may be interpreted as indicating a dominant exponent theta 1 87 or 0 04 consistent with the theoretical prediction theta gamma beta together with competing analytic and non analytic delta 1 1 35 or 0 25 correction to scaling terms

a family of distortion measures based upon projection operation for robust speech recognition consideration is given to the formulation of speech similarity measures a fundamental component in recognizer designs that are robust to the change of ambient conditions the authors focus on the speech cepstrum derived from linear prediction coefficients the lpc cepstrum by using some common models for noisy speech they show analytically that additive white noise reduces the norm length of the lpc cepstral vectors empirical observations on the parameter histograms not only confirm the analytical results through the use of noise models but further reveal that at a given global signal to noise ratio snr the norm reduction on cepstral vectors with larger norms is generally less than on vectors with smaller norms and that lower order coefficients are more affected than higher order terms in addition it is found that the orientation or direction of the cepstral vector is less susceptible to noise perturbation than the vector norm as a consequence of the above results a family of distortion measures based on the projection between two cepstral vectors is proposed the new measures have the same computational efficiency as the band pass cepstral distortion measure

clusters and droplets in the q state potts model a potts correlated polychromatic percolation is studied the clusters are made of sites corresponding to a given value of the q state potts variables connected by bonds being active with probability pb to treat this problem an s state potts hamiltonian diluted with q state potts variables instead of lattice gas variables is introduced to which the the migdal kadanoff renormalisation group is applied it is found for a particular choice of pb 1 e k where k is the potts coupling constant divided by the boltzmann factor that these clusters called droplets diverge at the potts critical point with potts exponents

surface tension in potts models and percolation the kasteleyn fortuin relation 1969 is used to give a simple proof for the s state potts model of the relation beta sigma xi 1 between the correlation length in a particular direction on a planar lattice and the surface tension of an interface with corresponding orientation on the dual thus generalising a well known result for the ising model the relation is also used to give an interpretation of the surface tension in the percolation problem in general dimensions