reconstructing state spaces from multivariate data using variable delays we study two methods for constructing a nonuniform embedding for multivariate data a nonuniform embedding is a state space reconstruction which is more flexible than the common delay coordinates with fixed delays since it contains variable delays using these methods we can extract causal relationships among many variables in a more suitable way we demonstrate that the proposed methods can give more precise predictions and simpler models than some previous methods

comparison of systems with complex behavior abstract we present a formalism for comparing the asymptotic dynamics of dynamical systems with physical systems that they model based on the spectral properties of the koopman operator we first compare invariant measures and discuss this in terms of a statistical takens theorem proved here we also identify the need to go beyond comparing only invariant ergodic measures of systems and introduce an ergodic theoretic treatment of a class of spectral functionals that allow for this the formalism is extended for a class of stochastic systems discrete random dynamical systems the ideas introduced in this paper can be used for parameter identification and model validation of driven nonlinear models with complicated behavior as an illustration we provide an example in which we compare the asymptotic behavior of a combustion system measured experimentally with the asymptotic behavior of a class of models that have the form of a random dynamical system

identification of composite local linear state space models using a projected gradient search an identification method is described to determine a weighted combination of local linear state space models from input and output data normalized radial basis functions are used for the weights

pitch strength of regular interval click trains with different length runs of regular intervals click trains were generated with first and second order statistics following kaernbach and demany j acoust soc am 104 2298 2306 1998 first order intervals are between successive clicks while second order intervals are those between every other click click trains were generated with a repeating alternation of fixed and random intervals which produce a pitch at the reciprocal of the duration of the fixed interval the intervals were then randomly shuffled and compared to the unshuffled alternating click trains in pitch strength comparison experiments in almost all comparisons for the first order interval stimuli the shuffled interval click trains had a stronger pitch strength than the unshuffled interval click trains the shuffled interval click trains only produced stronger pitches for second order interval stimuli when the click trains were unfiltered several experimental conditions and an analysis of runs of regular and random intervals in these click trains suggest that the auditory system is sensitive to runs of regular intervals in a stimulus that contains a mix of regular and random intervals these results indicate that fine structure regularity plays a more important role in pitch perception than randomness and that the long term autocorrelation function or spectra of these click trains are not good predictors of pitch strength

dissimilarity judgments in relation to temporal and spatial factors for the sound field in an existing hall in relation to the temporal and spatial factors of sound fields dissimilarity judgments for different source locations on a stage were performed this study is based on the model of the auditory brain system which consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemispheres there are three temporal factors 1 1 and e extracted from the autocorrelation function and four spatial factors ll iacc iacc and w iacc from the interaural crosscorrelation function of binaural signals in addition to these temporal and spatial factors the orthogonal factors of the subjective preference for sound field t 1 and t sub were taken into account the psychological distance between sound fields of different source locations on the stage were calculated by using these temporal spatial and orthogonal factors of sound fields using these distances and their linear combination dissimilarity can be calculated results of multivariable analysis show that the calculated scale values of dissimilarity agree well with the measured scale values

iterated rippled noise discrimination at long durations iterated rippled noise irn was used to study discrimination of irn stimuli with a lower number of iterations from irn stimuli with a higher number of iterations as a function of stimulus duration 100 2000 ms such irn stimuli differ in the strength of the repetition pitch in some cases the gain used to generate irn stimuli was adjusted so that both irn stimuli in the discrimination task had the same height of the first peak in the autocorrelation function or autocorrelogram in previous work involving short duration irn stimuli 500 ms listeners were not able to discriminate between irn stimuli that had different numbers of iterations but the same height of the first peak in the autocorrelation function in the current study irn discrimination performance improved with increases in duration even in cases when the height of the first peak in the autocorrelation was the same for the two irn stimuli thus future studies involving discrimination of irn stimuli may need to use longer durations 1 s or greater than those that have been used in the past

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

learning the dynamical system behind sensory data this letter looks at the physics behind sensory data by identifying the parameters that govern the physical system and estimating them from sensory observations we extend takens s delay embedding theorem to the dynamical systems controlled by parameters an embedding of the product space of the phase and the parameter spaces of the dynamical system can be obtained by the delay embedding map provided that the parameter of the dynamical system changes slowly the reconstruction error is bounded for slowly varying parameters a manifold learning technique is applied to the embedding obtained to extract a low dimensional global coordinate system representing the product space the phase space of the deterministic dynamics can be contracted by using the adjacency relationship in time which enables recovery of only the parameter space as examples the manifolds of synthetic and real world vowels with time varying fundamental frequency f0 are analyzed and the f0 contours are extracted by an unsupervised algorithm experimental results show that the proposed method leads to robust performance under various noise conditions and rapid changes of f0 compared with the current state of the art f0 estimation algorithms

phase space embedding of electrocardiograms we study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable against this background we discuss the possibility of using the phase space embedding method for this kind of signal in particular the specific nature of the stochastic or high dimensional component allows us to use phase space embeddings for certain signal processing tasks as practical applications we discuss noise filtering fetal ecg extraction and the automatic detection of clinically relevant features the main purpose of the paper is to connect results of embedding theory that have not been previously applied in practice and practical applications that have not yet been justified theoretically

an algorithm of uniform ultimate boundedness for a class of switched linear systems uniform ultimate boundedness of a class of switched linear systems is studied a switched linear system in this class consists of m subsystems and none of the individual subsystems need to be stabilizable the switched linear system is shown to be uniformly ultimately bounded for any pre given bound if the union of individual controllable subspaces covers the entire state space an algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy

stochastic analysis of recurrence plots with applications to the detection of deterministic signals recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems denoising as well as detection of deterministic signals embedded in noise though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise computations using examples from harmonic processes autoregressive models and outputs from nonlinear systems are shown to illustrate this relationship finally the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub optimal when compared to well known detectors based on the likelihood ratio

finding metastable states in real world time series with recurrence networks in the framework of time series analysis with recurrence networks we introduce a self adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real world time series as initial step we introduce a way to set the embedding parameters used to reconstruct the state space from the time series we set them as the ones giving the maximum shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and shannon entropy to identify metastable states as well as the transitions between them we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability we illustrate our method with a complex time series example finally we show the robustness of our method for identifying metastable states our results suggest that our method is robust for identifying metastable states in complex time series even when introducing considerable levels of noise and missing data points

extinction risk and structure of a food web model we investigate in detail the model of a trophic web proposed by amaral and meyer phys rev lett 82 652 1999 we focus on small size systems that are relevant for real biological food webs and for which the fluctuations play an important role we show using monte carlo simulations that such webs can be nonviable leading to extinction of all species in small and or weakly coupled systems estimations of the extinction times and survival chances are also given we show that before the extinction the fraction of highly connected species omnivores is increasing viable food webs exhibit a pyramidal structure where the density of occupied niches is higher at lower trophic levels and moreover the occupations of adjacent levels are closely correlated we also demonstrate that the distribution of the lengths of food chains has an exponential character and changes weakly with the parameters of the model on the contrary the distribution of avalanche sizes of the extinct species depends strongly on the connectedness of the web for rather loosely connected systems we recover the power law type of behavior with the same exponent as found in earlier studies while for densely connected webs the distribution is not of a power law type

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

stability of a model food web we investigate numerically the stability of a model food web introduced by nunes amaral and meyer phys rev lett 82 652 1999 the model describes a system of species located in niches at several levels upper level species are predating on those from a lower level we show that the model web is more stable when it is larger although the number of niches is more important than the number of levels the food web is self organizing itself trying to reach a certain degree of complexity i e number of species and links among them if the system cannot achieve this state it will go extinct we demonstrate that the average number of links per species and the reduced number of species depend in the same way on the number of niches we also determine how the stability of the food web depends on another parameter of the model the killing probability despite keeping the ratio of the creation and killing probabilities constant increasing the latter reduces significantly the stability of the model food web we show that connectance dependence on the number of niches has a power type character which agrees with the field data and that it decreases with the number of species also as a power type function

phase relationships between two or more interacting processes from one dimensional time series i basic theory a general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system using one dimensional time series only it is based on the introduction of angles and radii of return times maps and on studying the dynamics of the angles an explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data it is valid under conditions of weak forcing this correspondence is confirmed numerically for a nonstationary process in a forced van der pol system a model describing the angles behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived to establish from experimental data whether or not two or more interacting processes are synchronized is an old and important problem in the absence of noise the existence of synchronization between two processes in interacting limit cycle oscillators was originally taken to imply that their basic frequencies of oscillation are related as integer numbers i e are rationally connected 1 2 and that their instantaneous phases are permanently locked this definition suggests that the detection of whether or not synchronization exists can be established by computation of the ratio of basic frequencies in the fourier spectrum of the signal from one of the sub systems involved even in this simplest case however the finite observation time and the discreteness of the digitiza tion steps used in practice will make it appear that all fre quencies are rationally connected thereby complicating the reliable estimation of their ratio furthermore the noise that is invariably present in all real macroscopic systems means that only effective synchronization 3 can normally take place meaning that the phases can remain locked only dur ing finite time intervals and that the basic frequencies may no longer be rationally connected 4 serious difficulties may also arise due to the nonstationarity of experimental data in view of these problems modern techniques for estab lishing the presence or absence of synchronization are based on the assumption that the behavior of each subsystem can be considered separately and that their individual time series can be compared by a variety of techniques e g by compu tation of the phase difference between them this approach has been justified theoretically 3 6 and is widely used to detect synchronization not only in periodic noisy but also in

cancellation model of pitch perception a model of pitch perception is presented involving an array of delay lines and inhibitory gating neurons in response to a periodic sound a minimum appears in the pattern of outputs of the inhibitory neurons at a lag equal to the period of the sound the position of this minimum is the cue to pitch the model is similar to the autocorrelation model of pitch multiplication being replaced by an operation similar to subtraction and maxima by minima the two models account for a wide class of pitch phenomena in very much the same way the principal goal of this paper is to demonstrate this fact several features of the cancellation model may be to its advantage it is closely related to the operation of harmonic cancellation that can account for segregation of concurrent harmonic stimuli it can be generalized to explain the perception of multiple pitches and it shows a greater degree of sensitivity to phase than autocorrelation which may allow it to explain certain phenomena that autocorrelation cannot account for

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

the dimensions of a non conformal repeller and an average conformal repeller in this paper using thermodynamic formalism for the sub additive potential upper bounds for the hausdorff dimension and the box dimension of non conformal repellers are obtained as the sub additive bowen equation the map f only needs to be c 1 without additional conditions we also prove that all the upper bounds for the hausdorff dimension obtained in earlier papers coincide this unifies their results furthermore we define an average conformal repeller and prove that the dimension of an average conformal repeller equals the unique root of the sub additive bowen equation

minimal attractors and bifurcations of random dynamical systems we consider attractors for certain types of random dynamical systems these are skew product systems whose base transformations preserve an ergodic invariant measure we discuss definitions of invariant sets attractors and invariant measures for deterministic and random dynamical systems under assumptions that include for example iterated function systems but that exclude stochastic differential equations we demonstrate how random attractors can be seen as examples of milnor attractors for a skew product system we discuss the minimality of these attractors and invariant measures supported by them as a further connection between random dynamical systems and deterministic dynamical systems we show how dynamical or d bifurcations of random attractors with multiplicative noise can be seen as blowout bifurcations and we relate the issue of branching at such d bifurcations to branching at blowout bifurcations

pitch shifts of mistuned partials a time domain model mistuning one partial of a complex harmonic tone makes that partial easier to hear as a tone separate from the complex at the same time two pitch shifts may be observed first the low pitch of the complex is shifted in the direction of the mistuning as if it were pulled by the partial second the mistuning of the partial is perceptually exaggerated as if the pitch of the partial were pushed away from the harmonic series defined by the complex this paper shows how the latter effect can emerge within a hypothetical neural circuit the circuit involves a gating neuron fed by three pathways one direct and excitatory and the other two delayed and inhibitory the neuron responds to any excitatory input spike unless it is accompanied by an inhibitory input spike on either delayed input thus acting as a kind of anticoincidence counter the first delay is fixed and tuned to the period of the background harmonic complex its purpose is to weaken correlates of in tune components and allow the mistuned partial to stand out the second delay is variable and used to estimate the period of the mistuned partial by searching for a minimum output as a function of delay with an appropriate choice of parameters the estimate is subject to shifts that are of the same sign as the mistuning and that peak at about 4 mistuning and decrease beyond as observed experimentally

pitch strength and pitch dominance of iterated rippled noises in hearing impaired listeners reports using a variety of psychophysical tasks indicate that pitch perception by hearing impaired listeners may be abnormal contributing to difficulties in understanding speech and enjoying music pitches of complex sounds may be weaker and more indistinct in the presence of cochlear damage especially when frequency regions are affected that form the strongest basis for pitch perception in normal hearing listeners in this study the strength of the complex pitch generated by iterated rippled noise was assessed in normal hearing and hearing impaired listeners pitch strength was measured for broadband noises with spectral ripples generated by iteratively delaying a copy of a given noise and adding it back into the original octave band pass versions of these noises also were evaluated to assess frequency dominance regions for rippled noise pitch hearing impaired listeners demonstrated consistently weaker pitches in response to the rippled noises relative to pitch strength in normal hearing listeners

the metric entropy of diffeomorphisms soit m une variete de riemann compacte c sans bord soit f un diffeomorphisme c 2 de m et soit m une mesure de probabilite de borel f invariante sur m soit h m f l entropie de f on donne des relations entre h m f et les proprietes geometriques de f et de m

temporal dynamics of pitch strength in regular interval noises the pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function j acoust soc am 100 3329 3335 1996 the current study compares the pitch strengths and autocorrelation functions of rippled noise rn and another regular interval noise aabb rn is generated by delaying a copy of a noise sample and adding it to the undelayed version aabb with the same pitch is generated by taking a sample of noise a with the same duration as the rn delay and repeating it to produce aa and then concatenating many of these once repeated sequences to produce aabbccdd the height of the first peak h1 in the normalized autocorrelation function of aabb is 0 5 identical to that of rn the current experiments show the following 1 aabb and rn can be discriminated when the pitch is less than about 250 hz 2 for these low pitches the pitch strength of aabb is greater than that for rn

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

calculation of a narrowed autocorrelation function a method of calculating an autocorrelation function with extremely narrow peaks is described this is done by including terms in the autocorrelation expression corresponding to delays at 2 3 etc in addition to the usual term with delay implications in the frequency domain are explored graphs of this autocorrelation function for a number of violin sound samples including a two octave scale vibrato and glissando are presented graphs of the autocorrelation function for some synthetic sound samples are also included

criticality and unpredictability in macroevolution a recently presented model of large scale evolution exhibiting self organized criticality is explored from the dynamical point of view it is shown that the system approaches the critical state in an anomalous way with a dynamical exponent z50 at the same time the complexity of the interactions among species increases leading to higher unpredictability the dynamic evolution is able to generate phylogenetic fractal trees with dimension close to the one obtained from real taxonomy some analytic results are presented and an interesting interpretation of the macroevolutionary process is suggested s1063 651x 97 15503 9

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

loudness in relation to iterated rippled noise abstract this study examined the loudness of iterated rippled noises irns with different number of iterations under conditions of equal sound pressure the scale values of loudness were obtained using a paired comparison method the results showed that the loudness of irns was not constant even though the sound pressure level was equivalent the loudness of irns increased with increasing iteration number this indicated that repetitive components of sounds might affect their loudness

wasserstein distances in the analysis of time series and dynamical systems abstract a new approach based on wasserstein distances which are numerical costs of an optimal transportation problem allows us to analyze nonlinear phenomena in a robust manner the long term behavior is reconstructed from time series resulting in a probability distribution over phase space each pair of probability distributions is then assigned a numerical distance that quantifies the differences in their dynamical properties from the totality of all these distances a low dimensional representation in a euclidean space is derived in which the time series can be classified and statistically analyzed this representation shows the functional relationships between the dynamical systems under study it allows us to assess synchronization properties and also offers a new way of numerical bifurcation analysis the statistical techniques for this distance based analysis of dynamical systems are presented filling a gap in the literature and their application is discussed in a few examples of datasets arising in physiology and neuroscience and in the well known henon system

further evidence that fundamental frequency difference limens measure pitch discrimination difference limens for complex tones dlcs that differ in f0 are widely regarded as a measure of periodicity pitch discrimination however because f0 changes are inevitably accompanied by changes in the frequencies of the harmonics dlcs may actually reflect the discriminability of individual components to test this hypothesis dlcs were measured for complex tones the component frequencies of which were shifted coherently upward or downward by f 0 25 37 5 or 50 of the f0 yielding fully harmonic f 0 strongly inharmonic f 25 37 5 or odd harmonic f 50 tones if dlcs truly reflect periodicity pitch discriminability they should be larger worse for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch consistent with this prediction the results of two experiments showed a non monotonic dependence of dlcs on f with larger dlcs for f s of 25 or 37 5 than for f s of 0 or 50 of f0 these findings are consistent with

invariant graphs for forced systems abstract many applications of nonlinear dynamics involve forced systems we consider the case where for a fixed input the driven system is contracting this is for instance the situation in certain classes of filters and in the study of synchronization when such contraction is uniform it is well known that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space if the contraction is sufficiently strong then is smooth we describe the theoretical framework for such results and discuss a number of applications to the filtering of time series to synchronization and to quasiperiodically forced systems we go on to give recent generalizations to the case of non uniform contraction that is contraction measured by lyapunov exponent like quantities we conclude with a number of new results for quasiperiodic forcing a corollary of these is that a strange non chaotic attractor for such a system cannot be the graph of a continuous function nor roughly speaking can it have as open attracting neighbourhood in other words its closure must contain some repelling orbits

listening experience with iterated rippled noise alters the perception of pitch strength of complex sounds in the chinchilla behavioral responses obtained from chinchillas trained to discriminate a cosine phase harmonic tone complex from wideband noise indicate that the perception of pitch strength in chinchillas is largely influenced by periodicity information in the stimulus envelope the perception of pitch strength was examined in chinchillas in a stimulus generalization paradigm after animals had been retrained to discriminate infinitely iterated rippled noise from wideband noise retrained chinchillas gave larger behavioral responses to test stimuli having strong fine structure periodicity but weak envelope periodicity that is chinchillas learn to use the information in the fine structure and consequently their perception of pitch strength is altered behavioral responses to rippled noises having similar periodicity strengths but large spectral differences were also tested responses to these rippled noises were similar suggesting a temporal analysis can be used to account for the behavior animals were then retested using the cosine phase harmonic tone complex as the expected signal stimulus generalization gradients returned to those obtained originally in the naive condition suggesting that chinchillas do not remain fine structure listeners but rather revert back to being envelope listeners when the periodicity strength in the envelope of the expected stimulus is high

selecting nonlinear stochastic process rate models using information criteria we demonstrate how unknown process rates within a stochastic modelling framework based on markov processes can be approximated from time series data using polynomial basis functions the problem of model selection is considered by adapting basis function selection methods and the minimum description length information criteria which have previously been developed for nonlinear autoregressive models of time series under gaussian noise assumptions we investigate the effectiveness of the methods with application to stochastic biological population models

dimensions of invariant sets of expanding maps we consider a compact invariant set of an expanding map of a manifoldm and give upper and lowerbounds for the hausdorff dimension dimh and box dimensionsdimb and dimb these bounds are given in terms of the topological entropy topological pressure and uniform lyapunov exponents of the map

invariant trajectory classification of dynamical systems with a case study on ecg an invariant pattern recognition framework for classification of phase space trajectories of nonlinear dynamical systems is presented using statistical shape theory known external influences can be discriminated from true changes of the system the external effects are modeled as a transformation group acting on the phase space and variation of the trajectories not explained by the transformations is accounted for using principal component analysis the approach suggested is highly adaptable to a wide range of situations and individual differences the methodology presented is applied to detect abnormalities in electrocardiograms results based on measured data indicate that the model developed is resistant to the effects of respiration and body position changes which are abundant in ambulatory conditions and cause significant morphological artifacts in the signal the results also show that the detection of an artificially induced acute myocardial infarction is achieved with high performance due to its low computational complexity the method developed can be implemented in real time the method developed also adapts to morphological changes caused by various heart conditions

the perceptual tone noise ratio of merged iterated rippled noises with octave harmonic and nonharmonic delay ratios the perceptual tone noise ratio was measured for merged iterated ripple noise stimuli irns in which one of the individual irns always had a delay of 16 ms the second irn was chosen to create merged irns with single octave delay ratios e g 16 ms 8 ms double octave delay ratios e g 16 ms 4 ms harmonic delay ratios e g 16 ms 12 ms and nonharmonic delay ratios e g 16 ms 3 9 ms all stimuli were high pass filtered at 800 hz the tone noise ratio was significantly enhanced for the octave ratios and there was a strong interaction between the single and double octave delay ratios and number of iterations but the perceptual tone noise ratio for nonoctave ratios was determined solely by the number of iterations the pattern of the results can be explained in terms of the height of the largest peak in the summary autocorrelogram meddis and hewitt j acoust soc am 89 2866 2882 1991 provided the model is modified to improve the simulation of the loss of phase locking

searching for the time constant of neural pitch extraction multichannel auditory models have been repeatedly used to explain many aspects of human pitch perception among the most successful ones are models where pitch is estimated based on an analysis of periodicity in the simulated auditory nerve firing this periodicity analysis is typically implemented as a running autocorrelation i e the autocorrelation is calculated within a temporal window which is shifted along the time axis the window was suggested to have an exponential decay with time constant estimates between 1 5 and 100 ms the window length determines the minimal integration time of pitch extraction the present experiments are designed to quantify the temporal window of pitch extraction using regular interval noises rins rins were generated by concatenating equal duration noise samples which produce a pitch corresponding to the reciprocal of the sample duration when the samples are identical periodic noise when the samples are independent the stimulus is gaussian noise and produces no pitch using rin stimuli where periodic portions interchange with aperiodic portions it is shown that the temporal window of pitch extraction cannot be modeled using a single time constant but that the size of the temporal window depends on the pitch itself

random walks on homeo s 1 in this paper we study random walks g n f n 1 ldots f 0 on the group homeo s 1 of the homeomorphisms of the circle where the homeomorphisms f k are chosen randomly independently with respect to a same probability measure nu we prove that under the only condition that there is no probability measure invariant by nu almost every homeomorphism the random walk almost surely contracts small intervals it generalizes what has been known on this subject until now since various conditions on nu were imposed in order to get the phenomenon of contractions moreover we obtain the surprising fact that the rate of contraction is exponential even in the lack of assumptions of smoothness on the f k s we deduce various dynamical consequences on the random walk g n finiteness of ergodic stationary measures distribution of the trajectories asymptotic law of the evaluations etc the proof of the main result is based on a modification of the avila viana s invariance principle working for continuous cocycles on a space fibred in circles

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

efficient simplicial reconstructions of manifolds from their samples an algorithm for manifold learning is presented given only samples of a finite dimensional differentiable manifold and no a priori knowledge of the manifold s geometry or topology except for its dimension the goal is to find a description of the manifold the learned manifold must approximate the true manifold well both geometrically and topologically when the sampling density is sufficiently high the proposed algorithm constructs a simplicial complex based on approximations to the tangent bundle of the manifold an important property of the algorithm is that its complexity depends on the dimension of the manifold rather than that of the embedding space successful examples are presented in the cases of learning curves in the plane curves in space and surfaces in space in addition a case when the algorithm fails is analyzed

determination of the meter of musical scores by autocorrelation a single voice extracted from the scores of compositions from the baroque classical romantic and contemporary periods has been studied in order to determine the feasibility of the determination of musical meter by computer the method of autocorrelation is appropriate for this calculation since it is a measure of the frequency of occurrence of events following an event at time zero if a greater frequency of events occurs on the downbeat of a measure as predicted by palmer and krumhansl mental representations for musical meter j exp psychol hum percept perform 16 728 741 1990 then a peak in the autocorrelation function should indicate the time for a single measure the results of these computations indicate that computer determination of meter from score events is indeed possible an example is included to show that this method of analysis can be applied to live performance data as well

dimension theory of iterated function systems let si l i 1 be an iterated function system ifs on d with attractor k let denote the one sided full shift over the alphabet 1 l we define the projection entropy function h on the space of invariant measures on e associated with the coding map k and develop some basic ergodic properties about it this concept turns out to be crucial in the study of dimensional properties of invariant measures on k we show that for any conformal ifs respectively the direct product of finitely many conformal ifss without any separation condition the projection of an ergodic measure under is always exactly dimensional and its hausdorff dimension can be represented as the ratio of its projection entropy to its lyapunov exponent respectively the linear combination of projection entropies associated with several coding maps furthermore for any conformal ifs and certain affine ifss we prove a variational principle between the hausdorff dimension of the attractors and that of projections of ergodic measures 2008 wiley periodicals inc

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

generic observability of differentiable systems a dynamical system consists of a smooth vectorfield defined on a differentiable manifold and a smooth mapping from the manifold to the real numbers the vectorfield represents the dynamics of a physical system the mapping stands for a measuring device by which experimental information on the dynamics is made available the information itself is modeled as a sampled version of the image of the state trajectory under the smooth mapping in this paper the observability of this set up is discussed from the viewpoint of genericity first the observability property is expressed in terms of transversality conditions then the theory of transversal intersection is called upon to yield the desired results it is shown that almost any measuring device will combine with a given physical system to form an observable dynamical system if 2n 1 samples are taken and not fewer where n is the dimension of the manifold dually it is shown that almost any physical system will combine with a given measuring device

the role of the envelope in processing iterated rippled noise iterated rippled noise irn is generated by a cascade of delay and add the gain after the delay is 1 0 or delay and subtract the gain is 1 0 operations the delay and add subtract operations impart a spectral ripple and a temporal regularity to the noise the waveform fine structure is different in these two conditions but the envelope can be extremely similar four experiments were used to determine conditions in which the processing of irn stimuli might be mediated by the waveform fine structure or by the envelope in experiments 1 and 3 listeners discriminated among three stimuli in a single interval task irn stimuli generated with the delay and add operations g 1 0 irn stimuli generated using the delay and subtract operations g 1 0 and a flat spectrum noise stimulus in experiment 2 the listeners were presented two irn stimuli that differed in delay 4 vs 6 ms and a flat spectrum noise stimulus that was not an irn stimulus in experiments 1 and 2 both the envelope and waveform fine structure contained the spectral ripple and temporal regularity in experiment 3 only the envelope had this spectral and temporal structure in all experiments discrimination was determined as a function of high pass filtering the stimuli and listeners could discriminate between the two irn stimuli up to frequency regions as high as 4000 6000 hz listeners could discriminate the irn stimuli from the flat spectrum noise stimulus at even higher frequencies as high as 8000 hz but these discriminations did not appear to depend on the pitch of the irn stimuli a control experiment fourth experiment suggests that irn discriminations in high frequency regions are probably not due entirely to low frequency nonlinear distortion products the results of the paper imply that pitch processing of irn stimuli is based on the waveform fine structure