maximum likelihood estimation of the autoregressive model by relaxation on the reflection coefficients a method for autoregressive parameter estimation which successively maximizes the likelihood with respect to each reflection coefficient while keeping the others fixed is presented the algorithm generalizes the recursive maximum likelihood technique of s m kay 1983 which corresponds to performing only one iteration cycle an interesting application is the estimation of a toeplitz covariance matrix simulations show that the algorithm converges quite fast and provides much better estimates than current procedures for short record length

on periodic autoregressive processes estimation we consider the autoregressive estimation for periodically correlated processes using the parametrization given by the partial autocorrelation function we propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation a comparison with other methods is made relationships with the stationary multivariate case are discussed

the time dependent quartic oscillator a feynman path integral approach the schrodinger equation with a time dependent quadratic plus quartic hamiltonian is considered a rigorous feynman path integral representation for its solution is given in terms of a well defined infinitedimensional oscillatory integral

coexistence of symmetric periodic points in the standard map the problem of the coexistence of symmetric periodic points of the standard map has been investigated first it is shown that there is another reversibility in addition to the one already known the dominant axis of this reversibility is the remaining coordinate axis using these reversibilities simple recursion formulas that determine the positions of symmetric periodic points have been derived second bifurcation structures of symmetric periodic points from the fixed point at the origin have been investigated it is shown that periodic points bifurcate along both the dominant axes of two reversibilities every time the rotation number of the fixed point passes through a rational number third the problem of the coexistence of symmetric periodic points has been numerically investigated with the aid of the recursion formulas a devil s staircase form of the evolution of the outermost kolmogorov arnold moser kam curve of the fixed point with the change of the perturbation parameter is observed this indicates that bifurcated periodic points do not disappear by inverse bifurcation as long as they are in the invariant region of the fixed point

source separation using a criterion based on second order statistics it is often assumed that blind separation of dynamically mixed sources cannot be done with second order statistics it is shown that separation of dynamically mixed sources indeed can be performed using second order statistics only a criterion based on second order statistics for the purpose of separating crosswise mixtures is stated the criterion is used in order to derive a gradient based separation algorithm as well as a newton type separation algorithm the uniqueness of the solution representing the separation is also investigated this reveals that 1 the channel system is parameter identifiable under weak conditions and 2 if the sources have the same color there exists at most two solutions the local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence furthermore the estimates of the channel system are shown to be consistent or to locally minimize the criterion

separation of an instantaneous mixture of gaussian autoregressive sources by the exact maximum likelihood approach this paper deals with the problem of blind separation of an instantaneous mixture of gaussian autoregressive sources without additive noise by the exact maximum likelihood approach the maximization of the likelihood function is divided using relaxation into two suboptimization problems solved by relaxation methods as well the first one consists of the estimation of the separating matrix when the autoregressive structure of the sources is fixed the second one aims at estimating this structure when the separating matrix is fixed we show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints we prove the existence and the consistency of the maximum likelihood estimator we also give the expression of fisher s information matrix then we study by computer simulations the performance of our estimator and show the improvement of its achievements w r t both quasimaximum likelihood and second order blind identification sobi estimators

periodic orbits in k symmetric dynamical systems abstract a map l is called k symmetric if itskth iterate lk possesses more symmetry than l for some value of k in k symmetric systems there exists a notion of k symmetric orbits this paper deels with k symmetric periodic orbits we derive a relation between orbits that are k symmetric with respect to reversing k symmetries and symmetric orbits of lk with this relation we set out an efficient method for finding systematically all periodic orbits that are k symmetric with respect to reversing k symmetries this k symmetric fixed set iteration fsi method generalizes a celebrated method due to devogelaere that applies to symmetric periodic orbits in reversible dynamical systems we use the fsi method to study k symmetric periodic orbits of a map of the planer2 possessing a crystallographic reversing k symmetry group the explicit findings illustrate a typically k symmetric phenomenon consisting of a nontrivial relation between the symmetry properties of periodic orbits and their periods

blind separation of instantaneous mixture of sources via an independent component analysis in this paper we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the kullback leibner distance by replacing the unknown density with a kernel estimate we derive useful forms of this criterion when only a sample from that distribution is available we also compute the gradient and hessian of our criteria for use in an iterative minimization setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem except that here these functions are adapted to the observed data finally some simulations are given illustrating the good performance of the method

quick solution of least square equations and inversion of block matrices of low displacement rank a general algorithm for the inversion of block matrices of low displacement rank is proposed it is particularly adapted to the solution of the least squares linear prediction problem some explicit formulas for the inverses of such matrices and a characterization of them are also provided the method is based on the representation of the shift difference of the considered matrix as the difference between two low rank positive matrices

non algebraic integrability of the chew low reversible dynamical system of the cremona type and the relation with the 7th hilbert problem non resonant case abstract a smooth reversible dynamical system srds and a system of nonlinear functional equations defined by a certain rational quadratic cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions the chew low equations for p wave n scattering are considered this srds is splitted into 1 and 2 dimensional ones an explicit cremona transformation that completely determines the exact solution of the two dimensional system is found this solution depends on an odd function satisfying a nonlinear autonomous 3 point functional equation non algebraic integrability of srds under consideration is proved using the method of poincare normal forms and the siegel theorem on biholomorphic linearization of a mapping at a non resonant fixed point the proof is based on the classical feldman baker theorem on linear forms of logarithms of algebraic numbers which in turn relies upon solving the 7th hilbert problem by a i gel fond and t schneider and new powerful methods of a baker in the theory of transcendental numbers the general theorem following from the feldman baker theorem on applicability of the siegel theorem to the set of the eigenvalues c n of a mapping at a non resonant fixed point which belong to the algebraic number field a is formulated and proved the main results are presented in theorems 1 3 5 7 8 and remarks 3 7

a note on borel summability in this article nevanlinna s theorem about borel summability is improved moreover the borel summability of the asymptotic expansion in the method of stationary phase in infinitely many dimensions is discussed

recursive maximum likelihood estimation of autoregressive processes a new method of autoregressive parameter estimation is presented the technique is a closer approximation to the true maximum likelihood estimator than that obtained using linear prediction techniques the advantage of the new algorithm is mainly for short data records and or sharply peaked spectra simulation results indicate that the parameter bias as well as the variance is reduced over the yule walker and the forward backward approaches of linear prediction also spectral estimates exhibit more resolution and less spurious peaks a stable all pole filter estimate is guaranteed the algorithm operates in a recursive model order fashion which allows one to successively fit higher order models to the data

separation of independent sources from correlated inputs the characterization of independent stationary stochastic components sources is generally achieved by using the spectral matrix of partially correlated measurements which are linearly related to the components of interest in the general case where no assumptions are made concerning the way the sources are mixed on the measurements the spectral matrix is not able to extract the true sources while spectral analysis only uses second order properties of independent stochastic sources a procedure based on higher order analysis fourth order cross cumulants is developed this approach leads to a complete identification of the sources

signal separation by symmetric adaptive decorrelation stability convergence and uniqueness the performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference in the lms algorithm signal leakage into the noise reference leads to signal distortion and poor noise cancellation the origin of the problem lies in the fact that lms decorrelates the signal estimate with the noise reference which in the case of signal leakage makes little sense an algorithm is proposed that decorrelates the signal estimate with a signal free noise estimate obtained by adding a symmetric filter to the classical structure the symmetric adaptive decorrelation sad algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied apart from limitations on the adaptation constants stability around the desired solution can only be guaranteed for a subclass of signal mixtures furthermore the decorrelation criterion does not yield a unique solution and expressions for the phantom solutions are derived simulations with short fir filters confirm the predicted behavior

reversing symmetry group of and matrices with connections to cat maps and trace maps dynamical systems can have both symmetries and time reversing symmetries together these two types of symmetries form a group called the reversing symmetry group with the symmetries forming a normal subgroup of we give a complete characterization of and hence in the dynamical systems associated with the groups of integral matrices and to do this we use well known methods of number theory such as dirichlet s unit theorem for quadratic fields and gaus results on the equivalence of integer quadratic forms and employ the algebraic structure of the modular group as a free product we show how some recently discussed generalizations of the reversing symmetry group are also nicely illustrated when we consider affine extensions of these matrix groups our results are applicable to hyperbolic toral automorphisms anosov or cat maps pseudo anosov maps and the group of three dimensional 3d trace maps that preserve the fricke vogt invariant

time reversible and equivariant pitchfork bifurcation abstract in this note we describe a new phenomenon in steady state bifurcations of time reversible and equivariant vector fields when the eigenspace associated with a pair of imaginary eigenvalues that passes through zero onto the real line is separable from the nullspace associated with the fixed zeros of the spectrum we prove that a pitchfork bifurcation occurs

underdetermined blind source separation based on subspace representation this paper considers the problem of blindly separating sub and super gaussian sources from underdetermined mixtures the underlying sources are assumed to be composed of two orthogonal components one lying in the rowspace and the other in the nullspace of a mixing matrix the mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo inverse of the mixing matrix the mapping from the nullspace component to zero by the mixing matrix is noninvertible and there are infinitely many solutions to the nullspace component the latent nullspace component which is of lower complexity than the underlying sources is estimated based on a mean square error mse criterion this leads to a source estimator that is optimal in the mse sense in order to characterize and model sub and super gaussian source distributions the parametric generalized gaussian distribution is used the distribution parameters are estimated based on the expectation maximization em algorithm when the mixing matrix is unavailable it must be estimated and a novel algorithm based on a single source detection algorithm which detects time frequency regions of single source occupancy is proposed in our simulations the proposed algorithm compared to other conventional algorithms estimated the mixing matrix with higher accuracy and separated various sources with higher signal to interference ratio

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

tupling in three dimensional reversible mappings feigenbaum s parameter scaling exponents s are calculated for l 3m l 5m l 7m l 9m sequences of periodic orbits in a class of three dimensional non measure preserving reversible mappings some preliminary results on orbit scaling exponents for l 3m sequences are also included scaling exponents found so far are the same as those found for two dimensional reversible mappings

an iterated implicit complex map abstract iterated complex maps defined by a root of a biquadratic equation g z z 0 are studied numerical studies suggest conjugacy functions with differentiable natural boundaries and maps having island chains occupying much of the riemann sphere an analogy with hamiltonian systems is discussed

exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori abstract an approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in hamiltonian systems of one and a half degrees of freedom similar to that of escande and doveil it is a free semi group with two generators this scheme is solved exactly for its orbits stable manifolds unstable manifolds and critical set various results are found including a cantor set of universal fractal diagrams the robustness of noble tori and a scaling law for areas near critical circles

sample partial autocorrelation function a new estimation procedure for a partial autocorrelation coefficient of a stationary time series based on a natural geometrical analysis of the sample data is proposed a method for autoregressive parameter estimation which is midway between the constrained least squares procedure of burg and the unconstrained one given by the for ward backward least squares method is then obtained the method provides a stable filter and operates in a recursive model order fash ion simulation results indicate that the method eliminates some short comings of classical least squares procedures and stays close to the ex act maximum likelihood estimation method

analysis and online realization of the cca approach for blind source separation a critical analysis of the canonical correlation analysis cca approach in blind source separation bss is provided it is proved that by maximizing the autocorrelation functions of the recovered signals we can separate the source signals successfully it is further shown that the cca approach represents the same class of generalized eigenvalue decomposition gevd problems as the matrix pencil method finally online realizations of the cca approach are discussed with a linear predictor based algorithm studied as an example

explicit representation of finite predictor coefficients and its applications we consider the finite past predictor coefficients of stationary time series and establish an explicit representation for them in terms of the ma and ar coefficients the proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future applying the result to long memory processes we give the rate of convergence of the finite predictor coefficients and prove an inequality of baxter type

self rotation number using the turning angle abstract the self rotation number as defined by peckham is the rotation rate of the image of a point about itself here we use the notion of turning angle to give a simplified algorithm to compute the self rotation number for maps that avoid an angle we show that the orientation preserving henon map does avoid an angle moreover the self rotation number for orbits of the henon map can be computed once and for all at the anti integrable limit by a simple algorithm depending upon the symbol sequence for the orbit

trace maps as 3d reversible dynamical systems with an invariant one link between the theory of quasicrystals and the theory of nonlinear dynamics is provided by the study of so called trace maps a subclass of them are mappings on a one parameter family of 2d surfaces that foliate 3 and also 3 they are derived from transfer matrix approaches to properties of 1d quasicrystals in this article we consider various dynamical properties of trace maps we first discuss the fibonacci trace map and give new results concerning boundedness of orbits on certain subfamilies of its invariant 2d surfaces we highlight a particular surface where the motion is integrable and semiconjugate to an anosov system i e the mapping acts as a pseudo anosov map we identify properties of symmetry and reversibility time reversal symmetry in the fibonacci trace map dynamics and discuss the consequences for the structure of periodic orbits we show that a conservative period boubling sequence can be identified when moving through the one parameter family of 2d surfaces by using generator trace maps in terms of which all trace maps obtained from invertible two letter substitution rules can be expressed we show that many features of the fibonacci trace map hold in general the role of the fricke character hat i x y z x 2 y 2 z 2 2xyz 1 its symmetry group and reversibility for the nielsen trace maps are described algebraically finally we outline possible higher dimensional generalizations

reversible systems with first integrals abstract a reversible system of ordinary differential equations ode possessing some first integrals is considered a simple description of the first integral space is given it is shown that under the auxiliary assumption that the integrals are symmetric i e they do not change sign under the action of the reversing involution the presence of the integrals allows one to bring the problem of dynamical stability for a symmetric equilibrium to the similar problem but for the reduced system the reduced system is merely the restriction of the initial system to the intersection of the surfaces of level of the integrals passing through the equilibrium

the method of stationary phase for oscillatory integrals on hilbert spaces we develop the method of stationary phase for the normalized oscillatory integral on hilbert space giving borel summable expansions the developments that we obtain hold for more general situations than the ones of previous papers on the same subject

verblunsky coefficients and nehari sequences we are concerned with a rather unfamiliar condition in the theory of the orthogonal polynomials on the unit circle in general the szego function is determined by its modulus while the condition in question is that it is also determined by its argument or in terms of the function theory that the square of the szego function is rigid in prediction theory this is known as a spectral characterization of complete nondeterminacy for stationary processes studied by bloomfield jewel and hayashi 1983 going back to a small but important result in the work of levinson and mckean 1964 it is also related with the cerebrated result of adamyan arov and krein 1968 for the nehari problem and there is a one one correspondence between the verblunsky coefficients and the negatively indexed fourier coefficients of the phase factor of the szego function which we call a nehari sequence we presents some fundamental results on the correspondence including extensions of the strong szego and baxter s theorems

the finite dimensional reversible kam theory abstract the main results of the theory of quasi periodic motions in finite dimensional reversible dynamical systems are surveyed lower dimensional invariant tori and excitation of elliptic normal modes are discussed in detail the case where the reversing involution is perturbed is considered several fundamental differences between the reversible and hamiltonian theories are listed

generating functions for dynamical systems with symmetries integrals and differential invariants abstract we give a survey and some new examples of generating functions for systems with symplectic structure systems with a first integral systems that preserve volume and systems with symmetries and or time reversing symmetries both odes and maps are treated and we discuss how generating functions may be used in the structure preserving numerical integration of odes with the above properties

invariant circles for the piecewise linear standard map we investigate invariant circles for a one parameter family of piecewise linear twist homeomorphisms of the annulus we show that invariant circles of all types and rotation numbers occur and we classify them into families we compute parameter ranges in which there are no invariant circles

stability of discrete solitons in nonlinear schrodinger lattices we consider the discrete solitons bifurcating from the anti continuum limit of the discrete nonlinear schrodinger nls lattice the discrete soliton in the anti continuum limit represents an arbitrary finite superposition of in phase or anti phase excited nodes separated by an arbitrary sequence of empty nodes by using stability analysis we prove that the discrete solitons are all unstable near the anti continuum limit except for the solitons which consist of alternating anti phase excited nodes we classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons

period doubling in two parameter families abstract we study two aspects of the cross over from dissipative to area preserving behaviour for period doubling cascades first we consider the smoothness of the limiting bifurcation curve at the crossover point we make a conjecture and give supporting numerical evidence second we study the spectrum of the linearised doubling operator acting on arbitrary mappings and show that it can be expressed in terms of the spectrum of its restriction to area preserving mappings

second order blind separation of sources based on canonical partial innovations this paper is devoted to the study of the second order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise we introduce the notion of symmetric recursive canonical partial innovation then their components for the observation process meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct this property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods two other separation methods related to partial autocorrelation are also discussed

time reversibility and particle sedimentation this paper studies an ordinary differential equation ode model called the stokeslet model and describes sedimentation of small clusters of particles in a highly viscous fluid this model has a trivial solution in which the n particles arrange themselves at the vertices of a regular n sided polygon when n 3 hocking j fluid mech 20 1964 pp 129 139 and caflisch et al phys fluids 31 1988 pp 3175 3179 prove the existence of periodic motion in the frame moving with the center of gravity in the cluster in which the particles form an isosceles triangle the study of periodic and quasiperiodic solutions of the stokeslet model is continued with emphasis on the spatial and time reversal symmetry of the model time reversibility is due to infinite viscosity and spatial dihedral symmetry is due to the assumption of identical particles and the symmetry of the trivial solution for three particles the existence of a second family of periodic solutions and a family of quasiperiodic solu

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

mating quadratic maps with the modular group in 1994 s bullett and c penrose introduced the one complex parameter family of 2 2 holomorphic correspondences mathcal f a begin aligned left frac aw 1 w 1 right 2 left frac aw 1 w 1 right left frac az 1 z 1 right left frac az 1 z 1 right 2 3 end aligned and proved that for every value of a in 4 7 subset mathbb r the correspondence mathcal f a is a mating between a quadratic polynomial q c z z 2 c c in mathbb r and the modular group vargamma psl 2 mathbb z they conjectured that this is the case for every member of the family mathcal f a which has a in the connectedness locus we show here that matings between the modular group and rational maps in the parabolic quadratic family per 1 1 provide a better model we prove that every member of the family mathcal f a which has a in the connectedness locus is such a mating

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

feynman path integrals and the trace formula for the schrodinger operators we study schrodinger operators of the form h frac h 2 2 delta frac 1 2 x cdot a 2 x v x on d wherea2 is a strictly positive symmetricd d matrix andv x is a continuous real function which is the fourier transform of a bounded measure if n are the eigenvalues ofh we show that the theta function theta t sum limits n exp left frac i h t lambda n right is explicitly expressible in terms of infinite dimensional oscillatory integrals feynman path integrals over the hilbert space of closed trajectories we use these explicit expressions to give the asymptotic behaviour of t for smallh in terms of classical periodic orbits thus obtaining a trace formula for the schrodinger operators this then yields an asymptotic expansion of the spectrum ofh in terms of the periodic orbits of the corresponding classical mechanical system these results extend to the physical case the recent work on poisson and trace formulae for compact manifolds

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

ar and ma representation of partial autocorrelation functions with applications we prove a representation of the partial autocorrelation function pacf or the verblunsky coefficients of a stationary process in terms of the ar and ma coefficients we apply it to show the asymptotic behaviour of the pacf we also propose a new definition of short and long memory in terms of the pacf

euler poisson equations and existence of quasi periodic motions of heavy tops abstract we study the existence of quasi periodic motions of an asymmetric heavy top by using two different approaches the standard moser weinstein theorem and an extended liapounov center theorem we take advantage of the multiple reversibility of the euler poisson equations and are able to show that the extended liapounov center theorem yields more normal modes than does the moser weinstein theorem

on the numerical evaluation of fredholm determinants some significant quantities in mathematics and physics are most naturally expressed as the fredholm determinant of an integral operator most notably many of the distribution functions in random matrix theory though their numerical values are of interest there is no systematic numerical treatment of fredholm determinants to be found in the literature instead the few numerical evaluations that are available rely on eigenfunction expansions of the operator if expressible in terms of special functions or on alternative numerically more straightforwardly accessible analytic expressions e g in terms of painleve transcendents that have masterfully been derived in some cases in this paper we close the gap in the literature by studying projection methods and above all a simple easily implementable general method for the numerical evaluation of fredholm determinants that is derived from the classical nystrom method for the solution of fredholm equations of the second kind using gauss legendre or clenshaw curtis as the underlying quadrature rule we prove that the approximation error essentially behaves like the quadrature error for the sections of the kernel in particular we get exponential convergence for analytic kernels which are typical in random matrix theory the application of the method to the distribution functions of the gaussian unitary ensemble gue in the bulk scaling limit and the edge scaling limit is discussed in detail after extending the method to systems of integral operators we evaluate the two point correlation functions of the more recently studied airy and airy 1 processes

on classification of intrinsic localized modes for the discrete nonlinear schrodinger equation abstract we consider localized modes discrete breathers of the discrete nonlinear schrodinger equation i d n dt n 1 n 1 2 n n 2 n 1 n z we study the diversity of the steady state solutions of the form n t ei tvn and the intervals of the frequency of their existence the base for the analysis is provided by the anticontinuous limit negative and large enough where all the solutions can be coded by the sequences of three symbols 0 and using dynamical systems approach we show that this coding is valid for 3 4533 and the point is a point of accumulation of saddle node bifurcations also we study other bifurcations of intrinsic localized modes which take place for and give the complete table of them for the solutions with codes consisting of less than four symbols

markovian source separation a maximum likelihood ml approach is used to separate the instantaneous mixtures of temporally correlated independent sources with neither preliminary transformation nor a priori assumption about the probability distribution of the sources a markov model is used to represent the joint probability density of successive samples of each source the joint probability density functions are estimated from the observations using a kernel method for the special case of autoregressive models the theoretical performance of the algorithm is computed and compared with the performance of second order algorithms and i i d based separation algorithms

simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circle abstract in this note by using a discrete analog of a projection formula introduced by a seghier in 1978 we calculate the orthogonal polynomials on the unit circle for a rational spectral density having no zeros there and derive simple matrix representations of themselves their squared norms and the verblunsky coefficients

on the numerical integration of ordinary differential equations by symmetric composition methods differential equations of the form dot x x a b are considered where the vector fields a and b can be integrated exactly enabling numerical integration of x by composition of the flows of a and b various symmetric compositions are investigated for order complexity and reversibility free lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order a new more accurate way of applying the methods thus obtained to compositions of an arbitrary first order integrator is described and tested the determining equations are explored and new methods up to 100 times more accurate at constant work than those previously known are given

symmetries and reversing symmetries of area preserving polynomial mappings in generalised standard form abstract we determine the symmetries and reversing symmetries within g the group of real planar polynomial automorphisms of area preserving nonlinear polynomial maps l in generalised standard form l x x p 1 y y y p 2 x where p 1 and p 2 are polynomials we do this by using the amalgamated free product structure of g our results lead to normal forms for polynomial maps in generalised standard form and to a classification of the group structures of the reversing symmetry groups for such maps

feynman integrals and fredholm determinants in this article simple properties of feynman integrals such as the translation invariance fubini theorem and cameron martin formula are used in order to derive a product formula for fredholm determinants this formula enables us to compute explicitly some of such determinants as well as the index of the related fredholm operators some examples are done which have applications in the semiclassical approximation 0

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

half line schrodinger operators with no bound states acting in l2 0 c with the boundary condition r for convenience we require that the potential v be uniformly locally square integrable we write l l 2 for the banach space of such functions the free operators that is when v 0 can be diagonalized by the fourier transform this shows that they have spectra 2 2 and 0 co respectively and that in both cases the spectrum is purely absolutely continuous for a general discrete operator the mere fact that the spectrum is contained in 2 2 forces it to be purely absolutely continuous this is our first main result

efficient computation of autoregressive estimates through a sufficient statistic it is shown that various time reversible methods in particular burg s algorithm for autoregressive model estimation may be performed through the use of a simple sufficient statistic this provides more efficient computation of the estimators

generalized henon maps the cubic diffeomorphisms of the plane abstract in general a polynomial diffeomorphism of the plane can be transformed into a composition of generalized henon maps these maps exhibit some of the familiar properties of the quadratic henon map including a bounded set of bounded orbits and an anti integrable limit we investigate in particular the cubic area preserving case which reduces to two two parameter families of maps the bifurcations of low period orbits of these maps are discussed in detail

on universality for area preserving maps of the plane abstract we present detailed evidence that one parameter families of area preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter we relate this behaviour to a fixed point equation of the form 1 and det d 1 r 2 r 2 in particular we argue that the scaling transformation r 2 r 2 is conjugate to the transformation 0 x y x y with 2 and in fact 2 we present some numerical evidence that 8 721 1 4 018 1 16 36 where is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2k described above

statistical inference for independent component analysis application to structural var models abstract the well known problem of non identifiability of structural var models disappears if the structural shocks are independent and if at most one of them is gaussian in that case the relevant estimation technique is the independent component analysis ica since the introduction of ica by comon 1994 various semi parametric estimation methods have been proposed for orthogonalizing the error terms these methods include pseudo maximum likelihood pml approaches and recursive pml the aim of our paper is to derive the asymptotic properties of the pml approaches in particular to study their consistency we conduct monte carlo studies exploring the relative performances of these methods finally an application based on real data shows that structural var models can be estimated without additional identification restrictions in the non gaussian case and that the usual restrictions can be tested

circular lattice filtering using pagano s method recently pagano has found a one to one relationship between multivariate autoregression and scalar periodic autoregressions and derived a set of fundamental yule walker yw type equations for estimating the parameters of the periodic autoregressions in this paper we first obtain a levinson type recursive algorithm for solving the above mentioned yw equations then using this recursion we show a circular lattice structure of the process this enables us to obtain a burg type algorithm which guarantees the filter stability lastly we modify it to an adaptive form for on line computation this circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples the most salient feature of the algorithm is that it consists of calculations of scalar quantities thus completely avoiding matrix manipulations accompanying usual multivariate processing methods

anti integrability in dynamic and variational problems abstract we show using a series of examples that the existence of a singular limit called anti integrable can be useful for proving the existence of chaotic solutions and elucidating some of their properties leading to some new and unexpected results in particular the existence proof of chaotic trajectories in large classes of dynamical systems with discrete time becomes straightforward the method applies even for maps in infinite dimension symplectic or not similar ideas can be used for proving the existence of breathers or self localised modes and of chaotic distributions of breathers in any array of weakly coupled non linear oscillators with continuous time the existence of insulating bipolaronic structures in electron phonon systems electronic self localisation at large electron phonon coupling can also be proven on the same basis