estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

percolation in half spaces equality of critical densities and continuity of the percolation probability renormalization arguments are developed and applied to independent nearest neighbor percolation on various subsets of d d 2 yielding equality of the critical densities p c for a half space quarter space etc and ford 2 equality with the limit of slab critical densities continuity of the phase transition for the half space quarter space etc i e vanishing of the percolation probability p atp p c

ising models on hyperbolic graphs we consider ising models with ferromagnetic interactions and zero external magnetic field on the hyperbolic graph v f where v is the number of neighbors of each vertex and f is the number of sides of each face let tc be the critical temperature and t c sup t tc f 2 where f is the free boundary condition b c gibbs state is the plus b c gibbs state and is the minus b c gibbs state we prove that if the hyperbolic graph is self dual i e v f or if v is sufficiently large how large depends on f e g v 35 suffices for any f 3 and v 17 suffices for any f 17 then 0 t c tc in contrast with that t c tc for ising models on the hypercubic lattice zd with d 2 a result due to lebowitz 22 while whenever t t c f 2 the last result is an improvement in comparison with the analogous statement in refs 28 and 33 in which it was only proved that f 2 when t t c and it remains to show in both papers that f 2 whenever t t c therefore t c and tc divide 0 into three intervals 0 t c t c tc and tc in which but f 2 and f 2 and respectively

nonparametric estimation of instantaneous frequency the local polynomial approximation of time varying phase is used in order to estimate the instantaneous frequency and its derivatives for a complex valued harmonic signal given by discrete time observations with a noise the considered estimators are high order nonparametric generalizations of the short time fourier transform and the wigner ville distribution the asymptotic variance and bias of the estimates are obtained

the gamma filter a new class of adaptive iir filters with restricted feedback generalized feedforward filters a class of adaptive filters that combines attractive properties of finite impulse response fir filters with some of the power of infinite impulse response iir filters are described a particular case the gamma filter generalizes widrow s adaptive transversal filter adaline to an infinite impulse response filter yet the stability condition for the gamma filter is trivial and lms adaptation is of the same computational complexity as the conventional transversal filter structure preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter the authors extend the wiener kopf equation to the gamma filter and develop some analysis tools

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

the contact process on trees the contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter is varied for small values of a single infection eventually dies out for larger the infection lives forever with positive probability but eventually leaves any finite set the survival probability is a continuous function of and the proof of this is much easier than it is for the contact process on d dimensional integer lattices for still larger the infection converges in distribution to a nontrivial invariant measure for an n ary tree with n large the first of these transitions occurs when 1 n and the second occurs when 1 2 n e n nonhomogeneous trees whose vertices have degrees varying between 1 and n behave essentially as homogeneous n ary trees provided that vertices of degree n are not too rare in particular letting n go to galton watson trees whose vertices have degree n with probability that does not decrease exponentially with n may have both phase transitions occur together at 0 the nature of the second phase transition is not yet clear and several problems are mentioned in this regard

identifiability and aliasing in polynomial phase signals polynomial phase signals have numerous applications including radar sonar geophysics and radio communication many techniques for estimating the parameters of polynomial phase signals have been described in the literature despite the significant interest aliasing of polynomial phase parameters has not been fully clarified we address the problem of identifiability and aliasing in polynomial phase signals we fully describe the region in which aliasing does not occur for polynomial phase signals of any order we call this the identifiable region we find that this region is the voronoi region of a lattice generated by the coefficients of a set of polynomials known as the integer valued polynomials we show how aliasing can be resolved by solving the nearest lattice point problem we discuss some of the consequences of these results on a popular estimator for polynomial phase signals that is based on the discrete polynomial phase transform dppt it is shown that the range of parameters suitable for the dppt estimator is very small compared to the identifiable region

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

a system identification algorithm using orthogonal functions an adaptive filter adf structure is proposed for applications in which large order adfs are required it is based on modeling the impulse response of the system to be identified as a linear combination of a set of discrete legendre orthogonal functions the proposed adaptive filter structure has desirable stability features and a unimodal mean square error surface as well as a modular structure that permits an easy increase of the filter order without changing the previous stages computer simulations in which the proposed structure is used to identify actual acoustic echo path impulse responses show that the legendre adf has better convergence performance than the transversal adf when identifying systems with long impulse response

adaptive time varying cancellation of wideband interferences in spread spectrum communications based on time frequency distributions the paper proposes an adaptive method for suppressing wideband interferences in spread spectrum ss communications the proposed method is based on the time frequency representation of the received signal from which the parameters of an adaptive time varying interference excision filter are estimated the approach is based on the generalized wigner hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise the performance of the proposed approach is evaluated in the presence of linear and sinusoidal fm interferences plus white gaussian noise in terms of the snr improvement factor and bit error rate ber

frequency domain analysis of tracking and noise performance of adaptive algorithms in this paper an analysis of the tracking and noise performance of several adaptive algorithms is carried out for the case of model structures with fixed pole positions such structures have previously been proposed as an efficient generalization of the common fir model structure the focus of this work is to analyze the associated tradeoff between noise sensitivity and tracking ability in the frequency domain by illustrating how it is influenced by such things as input and noise spectral densities step size and in particular the choice of the fixed pole locations the latter influence is not described by preexisting analysis but is shown here to be amenable to attack by a particular class of orthonormal bases

crossing on hyperbolic lattices we divide the circular boundary of a hyperbolic lattice into four equal intervals and study the probability of a percolation crossing between an opposite pair as a function of the bond occupation probability p we consider the 7 3 heptagonal enhanced or extended binary tree ebt the ebt dual and the 5 5 pentagonal lattices we find that the crossing probability increases gradually from 0 to 1 as p increases from the lower p l to the upper p u critical values we find bounds and estimates for the values of p l and p u for these lattices and identify the self duality point p corresponding to where the crossing probability equals 1 2 comparison is made with recent numerical and theoretical results

phase transitions on nonamenable graphs we survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph most attention is devoted to transitive graphs and trees

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

an efficient numerical scheme for the euler equations a finite difference scheme based on flux difference splitting is presented for the solution of the euler equations for the compressible flow of an ideal gas a linearised riemann problem is defined and a scheme based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem an average of the flow variables across the interface between cells is required and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging this is in contrast to the usual square root averages found in this type of riemann solver where the computational expense can be prohibitive the method of upwind differencing is used for the resulting scalar problems together with a flux limiter for obtaining a second order scheme which avoids nonphysical spurious oscillations the scheme is applied to a shock tube problem and a blast wave problem each approximate solution compares well with those given by other schemes and for the shock tube problem is in agreement with the exact solution

the cramer rao lower bound for signals with constant amplitude and polynomial phase the authors derive the cramer rao lower bound crlb for complex signals with constant amplitude and polynomial phase measured in additive gaussian white noise the exact bound requires numerical inversion of an ill conditioned matrix while its o n sup 1 approximation is free of matrix inversion the approximation is tested for several typical parameter values and is found to be excellent in most cases the formulas derived are of practical value in several radar applications such as electronic intelligence systems elint for special pulse compression radars and motion estimation from doppler measurements consequently it is of interest to analyze the best possible performance of potential estimators of the phase coefficients as a function of signal parameters the signal to noise ratio the sampling rate and the number of measurements this analysis is carried out

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

an approximate riemann solver for the h system in generalized coordinates abstract an approximate riemann solver is presented for the solution of the pseudo unsteady equations representing steady inviscid flow of an ideal gas commonly known as the h system a simple modification enables nonideal gases to be treated the scheme applies to the system in generalized coordinates enabling the use of body fitted meshes the scheme is applied to a standard test problem of flow down a channel containing a circular arc bump

an efficient shock capturing scheme for the pseudo unsteady equations representing steady inviscid flow an efficient algorithm is presented for the solution of the steady euler equations of gas dynamics the scheme is based on solving linearised riemann problems approximately and in more than one dimension incorporates operator splitting the scheme is applied to a standard test problem of flow down a channel containing a circular arc bump for three different mesh sizes

online optimization of the time scale in adaptive laguerre based filters a new online method to optimize the free parameter in adaptive laguerre based filters is presented it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error the proposed technique presents a fast convergence and a good robustness

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

continuity of percolation probability on hyperbolic graphs let t be a ibrwarding tree of degree k where each vertex other than the origin has k children and one parent and the origin has k children but no parent k 2 define g to be the graph obtained by adding to t nearest neighbor bonds connecting the vertices which are in the same generation g is regarded as a discretization of the hyperbolic plane h in the same sense that z a is a discretization of r a independent percolation on g has been proved to have multiple phase transitions we prove that the percolation probability l p is continuous on 0 1 as a function ofp