critical behavior of a kam surface i empirical results kolmogorov arnol d moser kam surfaces are studied in the context of a perturbed two dimensional twist map in particular we ask how a kam surface can disappear as the perturbation parameter is increased following greene we use cycles to numerically construct the kam curve and discover that at the critical coupling it shows structure at all length scales aspects of this structure are fitted by a scaling analysis critical indices and scaling functions are determined numerically some evidence is presented which suggests that the results are universal

hierarchical labeler in a speech recognition system a speech coding apparatus and method uses a hierarchy of prototype sets to code an utterance while consuming fewer computing resources the value of at least one feature of an utterance is measured during each of a series of successive time intervals to produce a series of feature vector signals representing the feature values a plurality of level subsets of prototype vector signals is computed wherein each prototype vector signal in a higher level subset is associated with at least one prototype vector signal in a lower level subset each level subset contains a plurality of prototype vector signals with lower level subsets containing more prototypes than higher level subsets the closeness of the feature value of the first feature vector signal is compared to the parameter values of prototype vector signals in the first level subset of prototype vector signals to obtain a ranked list of prototype match scores for the first feature vector signal and each prototype vector signal in the first level subset the closeness of the feature value of the first feature vector signal is compared to the parameter values of each prototype vector signal in a second lower level subset that is associated with the highest ranking prototype vectors in the first level subset to obtain a second ranked list of prototype match scores the identification value of the prototype vector signal in the second ranked list having the best prototype match score is output as a coded utterance representation signal of the first feature vector signal

solution of the boundary value problem for optimal escape in continuous stochastic systems and maps topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps a topological method is introduced that simplifies the solution of boundary value problems the activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path the method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps

presentation functions fixed points and a theory of scaling function dynamics presentation functions provide the time ordered points of the forward dynamics of a system as successive inverse images they generally determine objects constructed on trees regular or otherwise and immediately determine a functional form of the transfer matrix of these systems presentation functions for regular binary trees determine the associated forward dynamics to be that of a period doubling fixed point they are generally parametrized by the trajectory scaling function of the dynamics in a natural way the requirement that the forward dynamics be smooth with a critical point determines a complete set of equations whose solution is the scaling function these equations are compatible with a dynamics in the space of scalings which is conjectured with numerical and intuitive support to possess its solution as a unique globally attracting fixed point it is argued that such dynamics is to be sought as a program for the solution of chaotic dynamics in the course of the exposition new information pertaining to universal mode locking is presented

singular hamiltonian system with several spectral parameters ii odd order case abstract in this paper we deal with a singular hamiltonian system of odd order with several spectral parameters and we investigate the behavior of the solution of this system at singular point with the aid of the characteristic function theory moreover some results have been introduced for the weyl titchmarsh function for some special hamiltonian systems of odd order with several spectral parameters

average trajectories and fluctuations from noisy nonlinear maps the average trajectories and fluctuations around them resulting from an ensemble of noisy nonlinear maps are analyzed the bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically this equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points the scaling properties of the average value and of the variance are obtained with the help of this equation

map dependence of the fractal dimension deduced from iterations of circle maps every orientation preserving circle mapg with inflection points including the maps proposed to describe the transition to chaos in phase locking systems gives occasion for a canonical fractal dimensiond namely that of the associated set of for whichf g has irrational rotation number we discuss how this dimension depends on the orderr of the inflection points in particular in the smooth case we find numerically thatd r d r 1 r 1 8

renormalizations and rigidity theory for circle homeomorphisms with singularities of the break type circle homeomorphisms with singularities of the break type are considered in the case when rotation numbers have periodic continued fraction expansion we establish hyperbolicity for renormalizations and then use it in order to prove the following rigidity result namely we show that any two homeomorphisms with a single break point are smoothly conjugate to each other provided they have the same quadratic irrational rotation number and the same size of a break

a speaker independent label coding apparatus the present invention is related to speech recognition and particularly to a new type of vector quantizer and a new vector quantization technique in which the error rate of associating a sound with an incoming speech signal is drastically reduced to achieve this end the present invention technique groups the feature vectors in a space into different prototypes at least two of which represent a class of sound each of the prototypes may in turn have a number of subclasses or partitions each of the prototypes and their subclasses may be assigned respective identifying values to identify an incoming speech feature vector at least one of the feature values of the incoming feature vector is compared with the different values of the respective prototypes or the subclasses of the prototypes the class of sound whose group of prototypes or at least one of the prototypes whose combined value most closely matches the value of the feature value of the feature vector is deemed to be the class corresponding to the feature vector the feature vector is then labeled with the identifier associated with that class

attractors via random perturbations we discuss conditions which ensure that weak limits of invariant measures of small random perturbations of dynamical systems have their supports on attractors

scales interference and identification at the transition to chaos abstract the scaling at the transition to chaos is described by a linear autoregressive model the identification of the universal scales from experimental data generally suffers from the competition of statistical and model errors due to the presence of noise and scaling corrections respectively the dilemma is resolved through a two step least mean squares method as an application the parameter scaling data of hao and zhang j stat phys 28 1982 769 for the period doubling route to chaos of the forced brusselator are reanalysed combined with order detection methods the algorithm also provides a powerful tool to detect and analyse scales interference phenomena

information loss under coarse graining a geometric approach we use information geometry in which the local distance between models measures their distinguishability from data to quantify the flow of information under the renormalization group we show that information about relevant parameters is preserved with distances along relevant directions maintained under flow by contrast irrelevant parameters become less distinguishable under the flow with distances along irrelevant directions contracting according to renormalization group exponents we develop a covariant formalism to understand the contraction of the model manifold we then apply our tools to understand the emergence of the diffusion equation and more general statistical systems described by a free energy our results give an information theoretic justification of universality in terms of the flow of the model manifold under coarse graining

singularities of fluctuational paths for an overdamped two well system driven by white noise abstract noise induced escape from a metastable state in an overdamped double well system is investigated with the wkb approximation employed the pattern of fluctuational paths is given by using the action plot which gives rise to mpeps the pattern is divided into various regions where fluctuational paths inside show qualitatively distinguished characteristics the global quasi potential is calculated and its value at the saddle on the boundary agrees with the one obtained by action plot we show a contour and 3d plot of the quasi potential to illustrate the relative stabilities of metastable states the bifurcations of singularities as the system parameter varies are analyzed by the second order term of the wkb expansion in the vicinity of x axis its asymptotic behavior determines the positions of cusps and furthermore its evolution turns out to delineate the twisting structure of the lagrangian manifold

fluctuational transitions across different kinds of fractal basin boundaries we study fluctuational transitions in discrete and continuous dynamical systems that have two coexisting attractors in phase space separated by a fractal basin boundary which may be either locally disconnected or locally connected theoretical and numerical evidence is given to show that in each case the transition occurs via a unique accessible point on the boundary both in discrete systems and in flows the complicated structure of the escape paths inside the locally disconnected fractal basin boundary is determined by a hierarchy of homoclinic points the interrelation between the mechanism of transitions and the hierarchy is illustrated by consideration of fluctuational transitions in dynamical systems demonstrating fractal fractal basin boundary metamorphosis at some value of a control parameter the most probable escape path from an attractor which can be either regular or chaotic is found for each type of boundary using both statistical analysis of fluctuational trajectories and the hamiltonian theory of fluctuations

models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish two types of minimal models were used to study stochastic oscillations in sensory receptors composed of two coupled oscillators as in the electroreceptors of paddlefish they have populations of cells in sensory epithelia undergoing approximately 26 hz oscillations these are coupled unidirectionally via synaptic excitation to a few afferent neurons each of whose terminal contains a 30 70 hz oscillator expressed as a dominant peak in the power spectra of spontaneous afferent firing corresponding to the mean firing rate the two distinct types of internal noisy oscillators result in stochastic biperiodic firing patterns of the primary afferent sensory neurons however the functions of the oscillations have remained elusive motivating this study the models we used here are based on the circle map or on the ermentraut koppell canonical phase theta neuron model parameters were chosen according to experimental data we used the models to demonstrate that the presence of epithelial oscillations leads to extended negative correlations of afferent interspike intervals and to show that the correlation structure depends crucially on the ratio of the afferent to epithelial oscillation frequencies being most pronounced when this ratio is close to 2 as observed in experiments our studies of stochastic versions of these models are of general interest for a wide range of coupled excitable systems especially for understanding the functional roles of noisy oscillations in auditory and other types of hair cell primary afferent sensory receptors

incomparability entropy and mixing dynamics abstract boltzmann states are considered in a fundamentally new way specifically their mixing character the mixing character of these states is known to be partially ordered by majorization and thus contains information regarding their incomparability previously we showed that boltzmann entropy states had a huge range in the number of incomparable states here we phase average incomparability across boltzmann states we propose the consequent function as a new state variable complimentary to entropy that provides new insights to boltzmann systems this function can be related to a traditional complexity viewpoint and so we call it average boltzmann complexity abc the evolution of boltzmann complexity is explored via a monte carlo lattice dynamics approach and is shown to be consistent with the view of entropy as the arrow of time our report concludes with a discussion of the information contained in boltzmann complexity and offers suggestions for further studies

crossing the quasi threshold manifold of a noise driven excitable system we consider the noise induced escapes in an excitable system possessing a quasi threshold manifold along which there exists a certain point of minimal quasi potential in the weak noise limit the optimal escaping path turns out to approach this particular point asymptotically making it analogous to an ordinary saddle numerical simulations are performed and an elaboration on the effect of small but finite noise is given which shows that the ridges where the prehistory probability distribution peaks are located mainly within the region where the quasi potential increases gently the cases allowing anisotropic noise are discussed and we found that varying the noise term in the slow variable would dramatically raise the whole level of quasi potentials leading to significant changes in both patterns of optimal paths and exit locations

observations of order and chaos in nonlinear systems experiments on nonlinear electrical oscillators the belousov zhabotinskii reaction rayleigh benard convection and couette taylor flow have revealed several common routes to chaos that have also been found in numerical studies of models with a few degrees of freedom experimental results are presented illustrating the following transition sequences period doubling and the u sequence intermittency the periodic quasiperiodic chaotic sequence frequency locking and an alternating periodic chaotic sequence

harper equation the dissipative standard map and strange nonchaotic attractors relationship between an eigenvalue problem and iterated maps the almost periodic eigenvalue problem described by the harper equation is connected to other classes of quasiperiodic behavior the dissipative dynamics on critical invariant tori and quasiperiodically driven maps firstly the strong coupling limit of the supercritical harper equation and the strong dissipation limit of the critical standard map play equivalent role in describing the universal characteristics of these systems secondly a simple transformation is used to relate the harper equation to a quasiperiodically forced one dimensional map in this case the localized eigenstates of the supercritical harper equation correspond to strange but nonchaotic attractors of the driven map furthermore the existence of localization in the eigenvalue problem is associated with the appearance of homoclinic points in the corresponding map

escape from attracting sets in randomly perturbed systems the dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science previous studies of escape in chaotic systems have rather focused on the case of unbounded noise usually assumed to have gaussian distribution in this paper we address the problem of escape induced by bounded noise we show that the dynamics of escape from an attractor s basin is equivalent to that of a closed system with an appropriately chosen hole using this equivalence we show that there is a minimum noise amplitude above which escape takes place and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition we verify our analytical predictions through numerical simulations of two well known two dimensional maps with noise

universal properties of the transition from quasi periodicity to chaos in dissipative systems abstract an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi periodic regime is held at a fixed irrational value our approach is a natural extension of k a m theory to strong coupling most of our analysis is for analytic circle maps we have found a strong coupling fixed point where invertibility is lost which describes the universal features of the transition to chaos we find numerically that any two such critical maps with the same winding number are c 1 conjugate it follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency when the winding number has a periodic continued fraction our renormalization transform has a fixed point and spectra are self similar in addition for a set of non periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub space of all critical maps physically one finds singular and universal spectra that do not scale

quasiperiodicity in dissipative systems a renormalization group analysis abstract dynamical systems with quasiperiodic behavior i e two incommensurate frequencies may be studied via discrete maps which show smooth continuous invariant curves with irrational winding number in this paper these curves are followed using renormalization group techniques which are applied to a one dimensional system circle and also to an area contracting map of an annulus two fixed points are found representing different types of universal behavior a trivial fixed point for smooth motion and a nontrivial fixed point the latter representsthe incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow fixed point functions are determined numerically and via an e expansion and eigenvalues are calculated

weak noise approach to the logistic map using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1d maps we replace the noise driven 1d map by an area preserving 2d map modelling the poincare sections of a conserved dynamical system with unbounded energy manifolds we analyze the properties of the 2d map and draw conclusions concerning the interference of noise on the nonlinear time evolution we apply this technique to the standard period doubling sequence in the logistic map from the 2d area preserving analogue we in addition to the usual period doubling sequence obtain a series of period doubled cycles which are elliptic in nature these cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events

multiparameter definiteness conditions a previous attempt to systematize various conditions from multiparameter spectral theory is extended to weaker forms of definiteness the latter not only occur in the established literature but are also under active investigation at present several algebraic and geometrical formulations exist and questions concerning their equivalence are approached in a unified fashion where possible

noise and bifurcations the influence of while noise on bifurcating dynamical systems is investigated using both fokker planck and functional integral methods noise leads to fuzzy bifurcations where physically relevant quantities become smooth functions of the bifurcation parameters we study dynamical and probabilistic quantities such as invariant measures liapunov exponents correlation functions and exit times the behavior of these quantities near the deterministic bifurcation point changes for distinct values of the control parameter therefore the very concept of bifurcation point becomes meaningless and must be replaced by the notion of bifurcation region

renormalization horseshoe for critical circle maps we prove that the invariant horseshoe for the renormalization of critical circle maps is globally uniformly hyperbolic with one dimensional unstable direction this extends our earlier result on hyperbolicity of periodic orbits of the renormalization and completes the proof of lanford s program

quasipotentials for simple noisy maps with complicated dynamics the theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems leading to exponential estimates of invariant probabilities and mean first exit times in the present article we develop the mathematical foundation of this theory for discrete time systems following and extending the work of freidlin and wentzell and kifer we discuss strategies for calculating and estimating quasipotentials and show their application to one dimensionals unimodal maps the method proves to be especially suited for describing the noise scaling behavior of invariant probabilities e g for the map occurring as the limit of the feigenbaum period doubling sequence we show that the method allows statements about the scaling behavior in the case of localized noise too which does not originally lie within the scope of the quasipotential formalism

scaling exponents relations and order dependence for circle maps abstract scaling relations describing devil s staircase structures obtained by iterations of orientation preserving circle maps with minimal slope converging to zero have been investigated in the limit the circle map has a zero slope inflection point and the influence of the order at this point on the scaling exponents is analyzed we study the behavior of the step sizes and the minimal distance to an integer from a non zero cycle point for the super stable orbit and in particular we treat the average behavior this leads to a definition of an average crossover scale exponent and an average measure exponent besides the earlier defined average dimension d we find and d d moreover 1 d finally as the order increases we observe that hourglass structures evolve in the arnold tongues

noise induced escape through a fractal basin boundary we study noise induced escape within a discrete dynamical system that has two co existing chaotic attractors in phase space separated by a locally disconnected fractal basin boundary it is shown that escape occurs via a unique accessible point on the fractal boundary the structure of escape paths is determined by the original saddles forming the homoclinic structure of the system and by their hierarchical interrelations

the cumulant approach for investigating the noise influence on mode locking bifurcations the influence of noise on mode locking bifurcations is investigated for the circle map and for coupled logistic maps the technique based on the cumulant expansion is used for the bifurcation analysis of these systems it is shown that this cumulant analysis in gaussian approximation provides a suitable description of the influence of weak noise we find that the universal scaling properties for the circle map in the critical point for the golden mean sequence are the same as those obtained analytically using the path integral technique we find the same scaling behaviour in the case of weak multiplicative noise

enhancement of noise induced escape through the existence of a chaotic saddle we study the noise induced escape process in a prototype dissipative nonequilibrium system the ikeda map in the presence of a chaotic saddle embedded in the basin of attraction of the metastable state we find the novel phenomenon of a strong enhancement of noise induced escape this result is established by employing the theory of quasipotentials our finding is of general validity and should be experimentally observable

quasipotential approach to critical scaling in noise induced chaos when a dynamical system exhibits transient chaos and a nonchaotic attractor as in a periodic window noise can induce a chaotic attractor in particular when the noise amplitude exceeds a critical value the largest lyapunov exponent of the attractor of the system starts to increase from zero while a scaling law for the variation of the lyapunov exponent with noise was uncovered previously it is mostly based on numerical evidence and a heuristic analysis this paper presents a more general approach to the scaling law one based on the concept of quasipotentials besides providing deeper insights into the problem of noise induced chaos the quasipotential approach enables previously unresolved issues to be addressed the fractal properties of noise induced chaotic attractors and applications to biological systems are also discussed

universal scalings of universal scaling exponents in the last decades renormalization group rg ideas have been applied to describe universal properties of different routes to chaos quasi periodic period doubling or tripling siegel disc boundaries etc each of the rg theories leads to universal scaling exponents which are related to the action of certain rg operators the goal of this announcement is to show that there is a principle that organizes many of these scaling exponents we give numerical evidence that the exponents of different routes to chaos satisfy approximately some arithmetic relations these relations are determined by combinatorial properties of the route and become exact in an appropriate limit

on weyl titchmarsh theory for singular finite difference hamiltonian systems we develop the basic theory of matrix valued weyl titchmarsh m functions and the associated green s matrices for whole line and half line self adjoint hamiltonian finite difference systems with separated boundary conditions

singular hamiltonian system with several spectral parameters abstract in this paper the weyl titchmarsh theory has been constructed for the singular 2n dimensional even order hamiltonian system with several spectral parameters in particular we consider that the left end point of the interval is regular and the right end point of the interval is singular for the hamiltonian system with several parameters using the nested circles approach we prove that at least n linearly independent solutions are squarly integrable with respect to some matrix functions

noise induced failures of chaos stabilization large fluctuations and their control noise induced failures in the stabilization of an unstable orbit in the one dimensional logistic map are considered as large fluctuations from a stable state the properties of the large fluctuations are examined by determination and analysis of the optimal path and the optimal fluctuational force corresponding to the stabilization failure the problem of controlling noise induced large fluctuations is discussed and methods of control have been developed

continuation techniques and interactive software for bifurcation analysis of odes and iterated maps physics abstract we present a numerical technique for the analysis of local bifurcations which is based on the continuation of structurally unstable invariant sets in a suitable phase parameter space the invariant sets involved in our study are equilibrium points and limit cycles of autonomous odes periodic solutions of time periodic nonautonomous odes fixed points and periodic orbits of iterated maps the more general concept of a continuation strategy is also discussed it allows the analysis of various singularities of generic systems and of their mutual relationships the approach is extended to codimension three singularities we introduce several bifurcation functions and show how to use them to construct well posed continuation problems the described continuation technique is supported by an interactive graphical program called locbif we discuss briefly the concepts of the locbif interface and give some examples of typical applications

transition to topological chaos for circle maps abstract many biperiodic flows can be modelled by maps of a circle to itself for such maps the transition from zero to positive topological entropy can be achieved in several ways we describe all the possible routes for smooth circle maps and discuss the relevance of our results to the transition to chaos for two frequency systems

on the rank of the matrix radius of the limiting set for a singular linear hamiltonian system this paper is concerned with the rank of the matrix radius of the limiting set for a singular hamiltonian system with one singular end point the exact relationship between the rank of the matrix radius and the number of square integrable solutions is obtained and then the defect index of the corresponding minimal operator can be represented in terms of the rank of the matrix radius so two results obtained by allan m krall siam j math anal 20 1989 664 are improved in addition it is discussed that the rank of the matrix radius is independent of the spectral parameter and a certain matrix especially the classification of singular linear hamiltonian systems is present and several sufficient and necessary conditions for the limit point and limit circle cases are established

the w sequence for circle maps and misbehaved itineraries the w sequence an ordering of maximal itineraries for circle maps is constructed by means of the farey transformation and the gluing operation the similarity in the dynamical behaviour of the maps is explicitly described in terms of itineraries a class of badly ordered itineraries termed misbehaved is defined with the language of symbolic sequences a misbehaved itinerary is shown to imply a rotation interval

bifurcations from an invariant circle for two parameter families of maps of the plane a computer assisted study we consider a two parameter family of maps of the plane to itself each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point for certain parameter values there is a hopf bifurcation to an invariant circle which is smooth for parameter values in a neighborhood of the bifurcation point however computer simulations show that the corresponding invariant set fails to be even topologically a circle for parameter values far from the bifurcation point this paper is an attempt to elucidate some of the mechanisms involved in this loss of smoothness and alteration of topological type

perturbation theory analysis of chaos iii period doubling bifurcations in a simple model abstract by using the nonlinear scale method the asymptotic solution of a three dimensional differential system is calculated to elucidate the period doubling bifurcation route to chaos as an stochastic description of chaos a langevin type equation with a vacillation force is derived the stochastic and deterministic nature of the vacillation force is studied

weyl titchmarsh theory for a class of discrete linear hamiltonian systems abstract this paper is concerned with establishing the weyl titchmarsh theory for a class of discrete linear hamiltonian systems over a half line fundamental properties of solutions regular spectral problems and the corresponding maximal and minimal operators are first studied matrix disks are constructed and proved to be nested and converge to a limiting set some precise relationships among the rank of the matrix radius of the limiting set the number of linearly independent square summable solutions and the defect indices of the minimal operator are established based on the above results a classification of singular discrete linear hamiltonian systems is given in terms of the defect indices of the minimal operator and several equivalent conditions on the cases of limit point and limit circle are obtained respectively especially several problems in the limit point case are more carefully investigated including fundamental properties of square summable solutions properties of the weyl function which is the unique element in the limiting set in this case and inhomogeneous boundary problems self adjointness of the corresponding hamiltonian operator relationship between the spectrum of the hamiltonian operator and the analyticity of the weyl function as well as the dependence of the spectrum on the boundary data in which some interesting separation results for the spectrum are obtained finally another set of four equivalent conditions on the limit point case are established

collective chaos and noise in the globally coupled complex ginzburg landau equation abstract we study a globally coupled version of the complex ginzburg landau equation gc cgle which consists of a large number n of identical two dimensional oscillators coupled through their mean amplitude depending on parameter values different dynamical regimes are attained we focus particularly on an interesting regime where the individual oscillators follow erratic motion but in a sufficiently coherent way so that the average motion does not vanish when n becomes large and is also chaotic a simple description of this state is proposed by considering the motion of a single forced two dimensional system which has both a limit cycle and a fixed point as stable attractors determining which of these two deterministic attractors is selected by a weak noise and how this depends on the parameter of the reduced system allows us to determine self consistently the average amplitude and dominant frequency of the collective behaviour of the full system finally we show that adding a small noise to the gc cgle transforms the chaotic collective behaviour into a purely periodic one

noise induced escape from attractors the author deals with several aspects of kautz 1987 1988 minimum principle for the noise induced escape from attractors he presents a slightly simpler derivation points out a connection with lyapunov exponents and invariant manifolds and generalises to chaotic maps

speech recognition apparatus having a speech coder outputting acoustic prototype ranks a speech coding and speech recognition apparatus the value of at least one feature of an utterance is measured over each of a series of successive time intervals to produce a series of feature vector signals the closeness of the feature value of each feature vector signal to the parameter value of each of a set of prototype vector signals is determined to obtain prototype match scores for each vector signal and each prototype vector signal for each feature vector signal first rank and second rank scores are associated with the prototype vector signals having the best and second best prototype match scores respectively for each feature vector signal at least the identification value and the rank score of the first ranked and second ranked prototype vector signals are output as a coded utterance representation signal of the feature vector signal to produce a series of coded utterance representation signals for each of a plurality of speech units a probabilistic model has a plurality of model outputs and output probabilities for each model output each model output comprises the identification value of a prototype vector and a rank score for each speech unit a match score comprises an estimate of the probability that the probabilistic model of the speech unit would output a series of model outputs matching a reference series comprising the identification value and rank score of at least one prototype vector from each coded utterance representation signal in the series of coded utterance representation signals

speech coding apparatus and method using classification rules a speech coding apparatus and method uses classification rules to code an utterance while consuming fewer computing resources the value of at least one feature of an utterance is measured during each of a series of successive time intervals to produce a series of feature vector signals representing the feature values the classification rules comprise at least first and second sets of classification rules the first set of classification rules map each feature vector signal from a set of all possible feature vector signals to exactly one of at least two disjoint subsets of feature vector signals the second set of classification rules map each feature vector signal in a subset of feature vector signals to exactly one of at least two different classes of prototype vector signals each class contains a plurality of prototype vector signals according to the classification rules a first feature vector signal is mapped to a first class of prototype vector signals the closeness of the feature value of the first feature vector signal is compared to the parameter values of only the prototype vector signals in the first class of prototype vector signals to obtain prototype match scores for the first feature vector signal and each prototype vector signal in the first class at least the identification value of at least the prototype vector signal having the best prototype match score is output as a coded utterance representation signal of the first feature vector signal

limit point and limit circle classification for symplectic systems on time scales abstract in this paper we study the limit point and limit circle classification for symplectic systems on time scales which depend linearly on the spectral parameter in a broader context we develop a unified weyl titchmarsh theory for continuous and discrete linear hamiltonian and symplectic systems both separated and coupled boundary conditions are allowed our results include the study of the weyl disks and circles and their limiting behavior as well as a precise analysis of the number of linearly independent square integrable solutions we also prove an analogue of the famous weyl alternative we connect and unify many known results in the weyl titchmarsh theory for continuous discrete and special time scales systems and explain the differences between them some of our statements in particular those connected with coupled endpoints or the weyl alternative are new even in the continuous time setting

intermittent diffusion in the presence of noise abstract the diffusion coefficient for intermittent diffusion in the presence of weak additive gaussian white noise is calculated the recent result by tsimring physica d 63 1993 41 is shown to be correct only in a certain limit of the parameter values

noise induced escape through a chaotic saddle lowering of the activation energy the noise induced escape mechanism is investigated for a prototype time discrete nonequilibrium system describing a laser in a ring cavity with optical feedback the ikeda map for certain parameter values a chaotic saddle is embedded in the basin of attraction of the metastable state this results in a lowering of the escape threshold for the activation energy which is established by employing the theory of quasipotentials our findings are explained by the computation of the most probable exit path mpep which lies partly on the chaotic saddle the enhancement of escape turns out to be maximal if the mpep lies entirely on the chaotic saddle

algorithms for controlling chaotic motion application for the bvp oscillator the bvp oscillator is a biologically and physically important dynamical system exhibiting chaotic motion phaselocking phenomenon and so on in this paper we investigate the controlling of chaos in this system both when periodic and constant currents are present we use the various control algorithms and investigate their effectiveness in particular we study the controlling by the following mechanisms i adaptive control algorithm ii weak periodic perturbations iii ott grebogi yorke method iv weak feedback control and v addition of noise also we show the suppression of chaos by numerical models

universal behaviour of two coupled circle maps symmetric coupling of two critical circle maps near the golden mean rotation number is considered on the basis of a renormalization group method the three universal types of interaction are found the theoretical scaling predictions are confirmed by numerical calculations

generalization of the kramers langer theory decay of the metastable state in the case of strongly anisotropic friction the problem of escape of a classical particle from a multidimensional potential well due to the influence of random forces is studied a new solution to the problem is obtained which shows that with fairly large friction anisotropy the qualitative picture of the process principally differs from that underlying the conventional multidimensional kramers langer theory according to the new process picture particles escape the well before reaching the saddle point the limiting stage of the process is the particle attainment of the transition region i e well dynamics not during passage through the barrier regions as the conventional theory suggests the new expression for the rate constant predicts a slower process rate in comparison with the kramers langer theory with decreasing friction anisotropy the new expression coincides with the conventional one

fractal properties of critical invariant curves we examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers through both the thermodynamic formalism and numerical computation the maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed our results indicate that the dimension is universal for a given type of singularity and rotation number and that among all rotation numbers the golden mean produces the largest dimension

combination laws for scaling exponents and relation to the geometry of renormalization operators the principle of approximate combination of scaling exponents renormalization group has become a standard tool for describing universal properties of different routes to chaos period doubling in unimodal maps quasiperiodic transitions in circle maps dynamics on the boundaries of siegel disks destruction of invariant circles of area preserving twist maps and others the universal scaling exponents for each route are related to the properties of the corresponding renormalization operators

on the existence of fixed points of the composition operator for circle maps in the theory of circle maps with golden ratio rotation number formulated by feigenbaum kadanoff and shenker fks and by ostlund rand sethna and siggia orss a central role is played by fixed points of a certain composition operator in map space we define a common setting for the problem of proving the existence of these fixed points and of those occurring in the theory of maps of the interval we give a proof of the existence of the fixed points for a wide range of the parameters on which they depend