self similar set identification in the time scale domain we study the wavelet transform of deterministic self similar signals and derive their properties as well as a new algorithm for identification of the self similarity parameter we also include such applications as characterization and analysis of real chaotic signals in the presence of additive noise

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

nonlinear structures in electroencephalogram signals abstract we apply a nonlinear prediction algorithm to investigate the presence of nonlinear structure in electroencephalogram eeg recordings the eeg signal could be modeled as a realization of a nonlinear model plus a residual noise uncorrelated gaussian noise using linear and nonlinear models we analyze the statistical nature of these residual noises in the case of epileptic patients and normal subjects we found that the residual noise presents gaussian distribution for epileptic patients if a nonlinear model is used whereas in the case of normal subjects the residual noise will exhibit a gaussian distribution only if a linear model autoregressive is used these results provide another evidence of the nonlinear character of the epileptic seizure recordings while the normal eeg seems to be better described as linearly correlated noise

uniformity of the phase space and fluctuations in thermal equilibrium abstract general relations are found between the measure of the uniformity of distributions on the phase space and the first moments and correlations of extensive variables for systems close to thermal equilibrium the role played by the parameter of the renyi entropy for the analysis of their fluctuations and correlations is studied analytical results are verified and illustrated by direct simulations of quantum systems of ideal fermions and bosons problems of finite statistics usual in experiments and simulations are addressed and discussed and solved by finding unbiased estimators for renyi entropies and uniformities

local methods in predicting occurrence of chaos in two well potential systems superharmonic frequency region abstract approximate criteria for chaos in two well potential systems excited by harmonic force are considered the excitation frequency is assumed to be close to 0 5 the natural frequency of the small orbit i e close to the second order superharmonic resonance computer simulations reveal a scenario of transition to chaos significantly different from that at the principal resonance here both periodic attractors of the small and large orbits lose stability and jointly turn into a strange attractor classical analytical approximate techniques are applied to analyze approximate periodic solutions and their higher order instabilities the symmetry breaking instabilities of the large orbit and the first order instability of the approximate non resonant small orbit solution are used to estimate the parameter region in which chaos may occur

nonlinear dynamics in driven damped sine gordon systems abstract many quasi one and two dimensional systems can be modeled by sine gordon equations illustrations are given for driven and damped sine gordon equations of behaviors that are typical of ways that complexity in time and space can be manifested examples include an ac response to a dc driver and spontaneous pattern formation and low dimensional chaos under the influence of ac or ac dc drivers the importance of the coexistence of coherence and chaos for transport phenomena is emphasized

nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

estimating dimension from small samples abstract details of a new algorithm to estimate the dimension of a measure from point samples are described the new algorithm emphasizes that dimension need not be the same at all scales that is there need not be a scaling region the algorithm is verified with gaussian measures and is found to be reliable and have less demanding data requirements than conventional estimators using certain convergence properties of gaussian measures it is shown that good estimates can be made from very small samples

dynamical complexity detection in short term physiological series using base scale entropy physiological systems generate complex fluctuations in their output signals that reflect the underlying dynamics the base scale entropy method was proposed as a complexity measure to investigate the complexity of time series the advantages of this method are simplicity and extremely fast calculation for very short data sets this method enables analyzing very short nonstationary and noisy data sets we employed this method for short term physiological time series for analysis of heart rate variability signals the results show that the simple and easily calculated measure can effectively detect the complexity dissimilarity of physiological time series in different physiological or pathological states which is convenient for clinical applications

a joint inter and intrascale statistical model for bayesian wavelet based image denoising this paper presents a new wavelet based image denoising method which extends a geometrical bayesian framework the new method combines three criteria for distinguishing supposedly useful coefficients from noise coefficient magnitudes their evolution across scales and spatial clustering of large coefficients near image edges these three criteria are combined in a bayesian framework the spatial clustering properties are expressed in a prior model the statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model the three main novelties with respect to related approaches are 1 the interscale ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated 2 a joint conditional model is introduced and 3 a novel anisotropic markov random field prior model is proposed the results demonstrate an improved denoising performance over related earlier techniques

a technique for measuring fractal dimensions from time series on a real time scale abstract a dedicated electronic instrument for measuring fractal dimension of chaotic systems called dimensiometer is described the pointwise correlation dimension can be obtained from experimental time series on a real time scale this technique employs a discrete sequence of the time intervals between the successive intersections of a single variable x t and an arbitrary level c the dimensiometer is tested by means of a simple electronic chaos oscillator the experimental results are compared with the numerical calculations carried out for the corresponding dynamical model

a scaling law how an attractor s volume depends on noise level abstract we investigate the meaning of the dimension of a strange attractor for systems with noise more specifically we investigate the effect of adding noise of magnitude e to a deterministic system with d degrees of freedom if the attractor has dimension d and d d then its volume is zero the addition of noise may be an important physical probe for experimental situations useful for determining how much of the observed phenomena in a system is due to noise already present when the noise is added the attractor a e has positive volume we conjecture that the generalized volume of a e is proportional to e d d for e near 0 and show this relationship is valid in several cases for chaotic attractors there are a variety of ways of defining d and the generalized volume definition must be chosen accordingly

the hilbert phenomenon in chaotic motions abstract it is proved that chaotic dynamical systems have d 1 singularity due to such singularity and its periodicity in hausdorff metric spaces a chaotic dynamical system induces a hilbert iterated system which was discovered at the end of the 19th century this implies that the most puzzling discovery in nature in the 20th century can be put into deep correspondence with that in thoughts in the 19th century all this is verified by the numerical experiments of chaotic vibrations of a beam and a tension slack oscillator

computing connectedness disconnectedness and discreteness we consider finite point set approximations of a manifold or fractal with the goal of determining topological properties of the underlying set we use the minimal spanning tree of the finite set of points to compute the number and size of its connected components by extrapolating the limiting behavior of these quantities as 0 we can say whether the underlying set appears to be connected totally disconnected or perfect we demonstrate the effectiveness of our techniques for a number of examples including a family of fractals related to the sierpinski triangle cantor subsets of the plane the henon attractor and cantori from four dimensional symplectic sawtooth maps for zero measure cantor sets we conjecture that the growth rate of the number of components as 0 is equivalent to the box counting dimension 2000 elsevier science b v all rights reserved

multifractal analysis and topological properties of a new family of weighted koch networks abstract weighted complex networks especially scale free networks which characterize real life systems better than non weighted networks have attracted considerable interest in recent years studies on the multifractality of weighted complex networks are still to be undertaken in this paper inspired by the concepts of koch networks and koch island we propose a new family of weighted koch networks and investigate their multifractal behavior and topological properties we find some key topological properties of the new networks their vertex cumulative strength has a power law distribution there is a power law relationship between their topological degree and weight strength the networks have a high weighted clustering coefficient of 0 41004 which is independent of the scaling factor c in the limit of large generation t the second smallest eigenvalue 2 and the maximum eigenvalue n are approximated by quartic polynomials of the scaling factor c for the general laplacian operator while 2 is approximately a quartic polynomial of c and n 1 5 for the normalized laplacian operator then we find that weighted koch networks are both fractal and multifractal their fractal dimension is influenced by the scaling factor c we also apply these analyses to six real world networks and find that the multifractality in three of them are strong

dimension measurement on high dimensional systems abstract using experimental data from a variety of laboratory electrical systems the upper limits on dimension measurement are examined and it is shown that contrary to standard scaling estimates it can be possible to reliably measure correlation dimensions larger than 10 the practical implications of the constraints on such a measurement are examined including the role of statistical errors geometrical artifacts dimension algorithm metric choice and the process power spectrum these ideas are applied to electrical 1 f noise from both macroscopic and microscopic sources to show that it cannot be explained by a deterministic model with fewer than roughly 20 degrees of freedom

on the dynamic properties of axially moving systems abstract the objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems such important mechanical systems exhibit interesting dynamic behaviors homoclinic orbits sub harmonic responses amplitude modulations and chaos these dynamics have been obtained numerically and in some cases have been experimentally observed using recent techniques of the non linear time series analysis the response of axially moving systems has been studied for a large variety of test cases the correlation dimension of the time series which is deeply related to the minimal dimension of a system able to reproduce the dynamics is estimated lyapunov exponents are evaluated in order to quantify the response regularity the present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems the dynamical phenomena are analyzed within the unified framework of the non linear time series analysis in the case of experimental data the new non linear filtering techniques based on the embedding techniques have been applied to reduce high noise when classical techniques give bad results

fuzzy peer groups for reducing mixed gaussian impulse noise from color images the peer group of an image pixel is a pixel similarity based concept which has been successfully used to devise image denoising methods however since it is difficult to define the pixel similarity in a crisp way we propose to represent this similarity in fuzzy terms in this paper we introduce the fuzzy peer group concept which extends the peer group concept in the fuzzy setting a fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing the fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic based procedure we use the fuzzy peer group concept to design a two step color image filter cascading a fuzzy rule based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group both steps use the same fuzzy peer group which leads to computational savings the proposed filter is able to efficiently suppress both gaussian noise and impulse noise as well as mixed gaussian impulse noise experimental results are provided to show that the proposed filter achieves a promising performance

positiveness of dynamic systems with nonpositive coefficient matrices this note gives a dynamical solution for linear dynamical feasibility problems and applies this result to a generalization of the concept of positive systems more specifically we require the existence of a positive state and or output evolution for any initial state in a given set we give conditions for various sets of initial states finally by means of an example we illustrate our results

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

characterization of the spatial complex behavior and transition to chaos in flow systems abstract we introduce a spatial lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow sytems this complexity is of spatial type and is due to sensitivity to the boundary conditions we show that there exists a relation between the spatial complexity index we define and the comoving lyapunov exponents in such systems the transition to chaos i e the occurrence of a positive lyapunov exponent can manifest itself in two different ways in the first case from neither chaotic nor spatially complex behavior to chaos one observes the typical scenario i e as the system size grows up the spectrum of the lyapunov exponents gives rise to a density in the second case when the chaos develops from a convectively unstable situation one observes only a finite number of positive lyapunov exponents

feature based wavelet shrinkage algorithm for image denoising a selective wavelet shrinkage algorithm for digital image denoising is presented the performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings the improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods the denoising method incorporated in the proposed algorithm involves a two threshold validation process for real time selection of wavelet coefficients the two threshold criteria selects wavelet coefficients based on their absolute value spatial regularity and regularity across multiresolution scales the proposed algorithm takes image features into consideration in the selection process statistically most images have regular features resulting in connected subband coefficients therefore the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients in the proposed algorithm coefficients are selected due to their magnitude and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction therefore two thresholds are used in the coefficient selection process the first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity the performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques as well as being computationally efficient to facilitate real time image processing applications

the fractal dimension of the two well potential strange attractor abstract the dimension of the duffing holmes two well potential strange attractor has been measured using both numerical solutions and experimental data from chaotic vibrations of a buckled beam using numerical simulation the fractal dimension of the poincare section of the strange attractor has been calculated as a function of damping using a correlation function technique the dimension of the poincare section is between one and two with higher damping resulting in a smaller dimensional attractor an equivalent cantor set for the attractor is defined the dimension seems to be relatively insensitive to the phase of the poincare section an analytical expression for the dimension as a function of damping is proposed the dimension algorithm is applied to experimentally generated poincare maps from chaotic vibrations of a buckled beam the calculation yields a dimension of the poincare map between one and two and seems to be insensitive to the phase of the poincare section

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

linear cone invariant control systems and their equivalence abstractin this paper we study invariant control systems that generalise positive systems a characterisation of linear control systems invariant on polyhedral cones corner regions in the state space called cone invariant linear control systems is established both for the inputs taking values in a polyhedral cone in the control space and for the inputs taking values in an affine polyhedral cone the problem of equivalence between control systems invariant on corner regions is introduced for cone invariant linear control systems we study invariance preserving state equivalence and invariance preserving feedback equivalence and present characterisations of both notions of equivalence

chaos in a variable mass relaxation oscillator model for the leaky tap abstract a variable mass relaxation oscillator model for the behaviour of the leaky tap is numerically investigated different regions of its three dimensional parameter space have been searched and interesting dynamical behaviour has been found the dynamics of the system is thoroughly characterized using projections of phase space trajectories 2 and 3 dimensional time delay plots power spectra lyapunov exponents hausdorff and correlation dimensions and bifurcation diagrams dynamical variables obtained from the model like drop masses velocities and drip intervals are used for reconstructing attractors we found several periodic intermittent and chaotic attractors we conclude that the rich dynamics of the model investigated represents an improvement in describing the experimentally observed behaviour of the actual dripping faucet system

coherence and chaos in the driven damped sine gordon equation measurement of the soliton spectrum abstract a numerical procedure is developed which measures the sine gordon soliton and radiation content of any field t which is periodic in space the procedure is applied to the field generated by a damped driven sine gordon equation this field can be either temporally periodic locked to the driver or chaotic in either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized soliton wave train modes the numerical procedure quantitatively identifies the presence number and properties of these soliton wave trains for example an increase of spatial symmetry is accompanied by the injection of additional solitons into the field

strong laws for l and u statistics strong laws of large numbers are given for l statistics linear combinations of order statistics and for u statistics averages of kernels of random samples for ergodic stationary processes extending classical theorems of hoeffding and of helmers for lid sequences examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisfied and an application is given to estimation of correlation dimension of invariant measures

image denoising using svm classification in nonsubsampled contourlet transform domain for image denoising the main challenge is how to preserve the information bearing structures such as edges and textures to get satisfactory visual quality when improving the signal to noise ratio snr edge preserving image denoising has become a very intensive research topic in this paper we propose an image denoising using support vector machine svm classification in nonsubsampled contourlet transform nsct domain firstly the noisy image is decomposed into different subbands of frequency and orientation responses using the nsct secondly the feature vector for a pixel in a noisy image is formed by the spatial regularity in nsct domain and the least squares support vector machine ls m model is obtained by training then the nsct detail coefficients are divided into two classes edge related coefficients and noise related ones by ls svm training model finally the detail subbands of nsct coefficients are denoised by using shrink method in which the adaptive bayesian threshold is utilized extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state of the art denoising techniques especially the proposed method can preserve edges very well while removing noise

wavelet transform domain filters a spatially selective noise filtration technique wavelet transforms are multiresolution decompositions that can be used to analyze signals and images they describe a signal by the power at each scale and position edges can be located very effectively in the wavelet transform domain a spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced a high correlation is used to infer that there is a significant feature at the position that should be passed through the filter the authors have tested the technique on simulated signals phantom images and real mr images it is found that the technique can reduce noise contents in signals and images by more than 80 while maintaining at least 80 of the value of the gradient at most edges the authors did not observe any gibbs ringing or significant resolution loss on the filtered images artifacts that arose from the filtration are very small and local the noise filtration technique is quite robust there are many possible extensions of the technique the authors see its applications in spatially dependent noise filtration edge detection and enhancement image restoration and motion artifact removal they have compared the performance of the technique to that of the weiner filter and found it to be superior

about nonnegative realizations we will state sufficient conditions such that a discrete time time invariant finite dimensional system with a nonnegative impulse response has a nonnegative finite dimensional realization the conditions are in terms of the minimal polynomial

an approach for characterizing coupling in dynamical systems abstract the study of coupling in dynamical systems dates back to christian hyugens who in 1665 discovered that pendulum clocks with the same length pendulum synchronize when they are near to each other in that case the observed synchronous motion was out of phase in this paper we propose a new approach for measuring the degree of coupling and synchronization of a dynamical system consisting of interacting subsystems the measure is based on quantifying the active degrees of freedom e g correlation dimension of the coupled system and the constituent subsystems the time delay embedding scheme is extended to coupled systems and used for attractor reconstruction of the coupled dynamical system we use the coupled lorenz rossler and henon model systems with a coupling strength variable for evaluation of the proposed approach results show that we can measure the active degrees of freedom of the coupled dynamical systems and can quantify and distinguish the degree of synchronization or coupling in each of the dynamical systems studied furthermore using this approach the direction of coupling can be determined

fractal analysis of measure representation of large proteins based on the detailed hp model abstract the notion of measure representation of protein sequences is introduced based on the detailed hp model multifractal analysis and detrended fluctuation analysis are then performed on the measure representations of a large number of long protein sequences it is concluded that these protein sequences are not completely random sequences through the measure representations and the values of the d q spectra and related c q curves the values of the exponent from the detrended fluctuation analysis show that the k strings with the ordering in the measure representation exhibit strong long range correlation for substrings with length k 5 the d q spectra of all proteins studied are multifractal like and sufficiently smooth for the c q curves to be meaningful the c q curves of all proteins resemble a classical phase transition at a critical point an ifs model is found to simulate the measure representation of protein sequences very well from the estimated values of parameters in the ifs model we think the non polar residues and uncharged polar residues play a more important role than other kinds of residues in the protein folding process

denoising by singularity detection a new algorithm for noise reduction using the wavelet transform is proposed similar to mallat s 1992 wavelet transform modulus maxima denoising approach we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales however we do not perform maxima detection and processing therefore complicated reconstruction is avoided instead the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding cone of influence and the coefficients that correspond to the regular part of the signal for reconstruction are selected the algorithm gives an improved denoising result as compared with the previous approaches in terms of mean squared error and visual quality the new denoising algorithm is also invariant to translation it does not introduce spurious oscillations and requires very little a priori information of the signal or noise besides we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so called directional cone of influence the denoising technique is applied to tomographic image reconstruction where the improved performance of the new approach can clearly be observed

nonlinear scale space filtering and multiresolution system we derive and demonstrate a nonlinear scale space filter and its application in generating a nonlinear multiresolution system for each datum in a signal a neighborhood of weighted data is used for clustering the cluster center becomes the filter output the filter is governed by a single scale parameter that dictates the spatial extent of nearby data used for clustering this together with the local characteristic of the signal determines the scale parameter in the output space which dictates the influences of these data on the output this filter is thus adaptive and data driven it provides a mechanism for a removing impulsive noise b improved smoothing of nonimpulsive noise and c preserving edges comparisons with gaussian scale space filtering and median filters are made using real images using the architecture of the laplacian pyramid and this nonlinear filter for interpolation we construct a nonlinear multiresolution system that has two features 1 edges are well preserved at low resolutions and 2 difference signals are small and spatially localized this filter implicitly presents a new mechanism for detecting discontinuities differing from techniques based on local gradients and line processes this work shows that scale space filtering nonlinear filtering and scale space clustering are closely related and provides a framework within which further image processing image coding and computer vision problems can be investigated

a scaling exponent based detector of chaos in oscillatory circuits abstract in this paper a scaling exponent based approach is proposed to determine the state of chaotic circuits and the scaling exponent is calculated using detrended fluctuation analysis dfa the corresponding detector is designed using the fact that the scaling exponent changes for various states of chaotic circuits simulation examples in this paper are performed for chua s circuit and other chaotic systems and compared with the state of the art in the field the proposed detector outperforms existing techniques in ability to distinguish the chaotic and periodic states in the circuits for relatively high noise

positively invariant sets for constrained continuous time systems with cone properties this note deals with some properties of particular bounded sets w r t linear continuous time systems described by x spl dot t a 0 x t c t where c t spl isin spl omega spl sub r sup n spl omega a compact set and matrix e sup ta 0 has the property of leaving a proper cone k positively invariant that is e sup ta 0 k spl sub k the considered bounded sets spl dscr k a b are described as the intersection of shifted cones necessary and sufficient conditions are given they guarantee that such sets are positively invariant w r t the considered system the trajectories starting from x sub 0 spl isin r sup n spl dscr k a b respectively to x sub 0 spl isin r sup n are studied in terms of attractivity and contractivity of the set spl dscr k a b the results are applied to the study of the constrained state feedback regulator problem

reshape scale method a novel multi scale entropic analysis approach abstract the reshape scale rs method was introduced in this article as a novel approach to perform multi scale transition of sample entropy this method was able to quantify the orderliness in the signal by determining the distance over which the subsequent data points can remain affiliated to one another entropic half life enhl was introduced to characterize such an affiliation the method was tested for 1 f processes for different values furthermore the dependency of the multi scale entropy analysis developed by costa et al 2002 6 to the probability density function and the standard deviation of autoregressive signals was studied and discussed

on the exit times approach for e entropy and turbulent signals abstract we review a recently proposed approach to the computation of the e entropy of a given signal based on the exit time statistics i e one codes the signal by looking at the instants when the fluctuations are larger than a given threshold e moreover we show how the exit times statistics when applied to experimental turbulent data is able to highlight the intermediate dissipative range of turbulent fluctuations

a new algorithm for image noise reduction using mathematical morphology morphological openings and closings are useful for the smoothing of gray scale images however their use for image noise reduction is limited by their tendency to remove important thin features from an image along with the noise the paper presents a description and analysis of a new morphological image cleaning algorithm mic that preserves thin features while removing noise mic is useful for gray scale images corrupted by dense low amplitude random or patterned noise such noise is typical of scanned or still video images mic differs from previous morphological noise filters in that it manipulates residual images the differences between the original image and morphologically smoothed versions it calculates residuals on a number of different scales via a morphological size distribution it discards regions in the various residuals that it judges to contain noise mic creates a cleaned image by recombining the processed residual images with a smoothed version the paper describes the mic algorithm in detail discusses the effects of parametric variations presents the results of a noise analysis and shows a number of examples of its use including the removal of scanner noise it also demonstrates that mic significantly improves the jpeg compression of a gray scale image

a note on the behaviour of the correlation integral in the presence of a time series summary the behaviour of the correlation integral is well known when applied to simple chaotic regimes and to pure random noise the asymptotic behaviour of a chaotic system is represented by an infinite set of points called an attractor the dimension of which can be estimated by the correlation integral essentially the correlation integral of a time series is a normalized count of the number of close pairs of points of the series lying in phase space we examine the expected behaviour of the integral for some stochastic process models which place a weak structure on the noise such as simple autoregressive and moving average formulations

on invariant polyhedra of continuous time linear systems this note presents some conditions of existence of positively invariant polyhedra for linear continuous time systems these conditions are first described algebraically then interpreted on the basis of the system eigenstructure then a simple state feedback placement method is described for solving some linear regulation problems under constraints

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

combining spatial and scale space techniques for edge detection to provide a spatially adaptive wavelet based noise filtering algorithm new methods for detecting edges in an image using spatial and scale space domains are proposed a priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge an improved double thresholding technique is introduced for spatial domain filtering probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes gradient phases and edge connectivity the scale space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales a probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale space domain methods decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale these matched filters permit significant reduction in image noise without contributing to edge distortion the spatially adaptive wavelet noise filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images

on obtaining global nonlinear system characteristics through interpolated cell mapping abstract period doubling bifurcations and fractal basin boundaries are investigated by means of interpolated cell mapping icm icm is a new method to determine the continuous time trajectory of a nonlinear system by spatially discretizing the system and employing an interpolation procedure to estimate the system s response at any arbitrary point in phase space the parameter values at which period doubling occurs for a duffing s oscillator is found by both conventional time integration and two mapping techniques and the results compared the icm method is shown to very accurately determine the points of bifurcation the dimension of a fractal basin boundary is determined by icm and compared to an exact determination the icm procedure produces the same fractal dimension determination as the exact analysis but only requires one thousandth of the computation time

homoclinic and chaotic transitions in the rf squid abstract the results presented here are a continuation of recent work investigating the onset of homoclinic behavior in the rf squid the transition from periodic to chaotic behavior is studied through a calculation of the lyapunov exponents for the system and the threshold condition for the onset of chaotic behavior is compared with the melnikov condition for the homoclinic threshold the dimension calculated from the poincare section of the strange attracting set by means of the correlation function technique and the box counting technique is compared with the dimension derived from the lyapunov exponents

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

generalized synchronization of chaos in electronic circuit experiments abstract two examples of one way coupled electronic circuits displaying generalized synchronization of chaos are considered in one of them the dynamics of both the response and the driving systems represent a double scroll chaos oscillator in another example the double scroll oscillator is driven by an electronic analog of the mackey glass system to detect the generalized synchronization an auxiliary response system that is a replica of the original one is used in these systems we have discovered two types of generalized synchronization namely a strong and a weak synchronization which correspond to the existence of a smooth and a nonsmooth map from the trajectories of the driving attractor to the trajectories of the response system respectively

local positive reachability of nonlinear continuous time systems local positive reachability of positive nonlinear continuous time systems is investigated it is shown that the system is locally positively reachable from the origin if and only if in some neighborhood of the origin for each subface of the nonnegative cone of the state space there is a control value such that the vector field corresponding to this control value is tangent to the subface and nonzero this is a natural generalization of a characterization of positive reachability of positive linear continuous time systems contrary to discrete time systems positive reachability of continuous time systems requires that very restrictive conditions be satisfied

uniform partitions and a dimensions spectrum for lacunar measures a multifractal analysis has been proposed to investigate complex systems which exhibit a nonuniform local structure multifractal measures are normalized mass distributions inhomogeneous at every scale to every point p is associated the exponent of the power law r describing the asymptotic behaviour as r 0 of the mass of a sphere of radius r and centre p the measure properties are specified by the dimension spectrum f of the set of points p with the same scaling exponent this spectrum is nontrivial even when the mass distribution has no holes measure with euclidean support and the box counting dimension is an integer in this case it can be evaluated by considering a sequence of uniform grids whose spacing decreases as 2 n known as uniform partitions we consider here a family of iterated function system fractal measures with support on the unit square with random defects specified by three parameters a scale a probability p and an attenuation factor given a partition with a diameter less than any cell is chosen with probability p and its mass is multiplied by the corresponding pre measure is obtained after normalization in all the examples examined the f spectrum appears to widen monotonically as decreases this result suggests the possibility of using the method to detect the presence of defects in sponge like structures such as cancellous bone sponge like by analysing their radiographs since the grey intensity is related to the mass density of the structure a widening of the f spectrum is indeed observed in osteoporotic bone radiographs compared to normal bone radiographs this may be attributed to the rarefaction of the cancellous bone

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

correlation functions of an autonomous stochastic system with time delays abstract the auto correlation function and the cross correlation function of an autonomous stochastic system with time delays are investigated we obtain the distribution curves of the auto correlation function c x s and c y s and the cross correlation function c x y s and c y x s of the stochastic dynamic variables by the stochastic simulation method the delay time changes prominently the behaviors of the dynamical variables of an autonomous stochastic system which makes the auto correlation and the cross correlation of the autonomous stochastic system alternate oscillate periodically from positive to negative or from negative to positive decrease gradually and finally tends to zero with the decay time the delay time and the noise strength have important impacts for the auto correlation and the cross correlation of the autonomous stochastic delay system the delay time enhances the auto correlation and the cross correlation on the contrary the noise strength lowers the auto correlation and the cross correlation under the time delay by comparison we further show differences of the auto correlation and the cross correlation between the dynamical variables x and y

remarks on strongly flow invariant sets abstract conditions ensuring the strong flow invariance property for a compact set m with respect to the differential system x t x are considered an answer to a question raised in gard applicable anal 10 1980 285 293 is given in the case of autonomous systems

measure representation and multifractal analysis of complete genomes this paper introduces the notion of measure representation of dna sequences spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes the main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria from the measure representations and the values of the dq spectra and related cq curves it is concluded that these complete genomes are not random sequences in fact spectral analyses performed indicate that these measure representations considered as time series exhibit strong long range correlation here the long range correlation is for the k strings with dictionary ordering and it is different from the base pair correlations introduced by other people for substrings with length k58 the dq spectra of all organisms studied are multifractal like and sufficiently smooth for the cq curves to be meaningful with the decreasing value of k the multifractality lessens the cq curves of all bacteria resemble a classical phase transition at a critical point but the analogous phase transitions of chromosomes of nonbacteria organisms are different apart from chromosome 1 of c elegans they exhibit the shape of double peaked specific heat function a classification of genomes of bacteria by assigning to each sequence a point in two dimensional space d21 d1 and in three dimensional space d21 d1 d22 was given bacteria that are close phylogenetically are almost close in the spaces d21 d1 and d21 d1 d22

some results on the behavior and estimation of the fractal dimensions of distributions on attractors the strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation in this paper we first provide a rigorous mathematical framework for the study of dimension focusing on pointwise dimension x and the generalized renyi dimensionsd q and give a rigorous proof of inequalities first derived by grassberger and procaccia and hentschel and procaccia we then specialize to the problem of statistical estimation of the correlation dimension and information dimension it has been recognized for some time that the error estimates accompanying the usual procedures which generally involve least squares methods and nearest neighbor calculations grossly underestimate the true statistical error involved in least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates we then develop an estimation procedure for which corrects for an important bias term the local measure density and provides confidence intervals for the general applicability of this method is illustrated with various numerical examples

correlation dimension of financial market abstract in this paper correlation dimension is applied to financial data analysis we calculate the correlation dimensions of some real market data and find that the dimensions are significantly smaller than those of the simulation data based on geometric brownian motion based on the analysis of the chinese and us stock market data the main results are as follows first by calculating three data sets for the chinese and us market we find that large market volatility leads to a significant decrease in the dimensions second based on 5 min stock price data we find that the chinese market dimension is significantly larger than the us market this shows a significant difference between the two markets for high frequency data third we randomly extract stocks from a stock set and calculate the correlation dimensions and find that the average value of these dimensions is close to the dimension of the original set in addition we analyse the intuitional meaning of the relevant dimensions used in this paper which are directly related to the average degree of the financial threshold network the dimension measures the speed of the average degree that varies with the threshold value a smaller dimension means that the rate of change is slower

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

strange attractors and chaos control in periodically forced complex duffing s oscillators abstract an interesting and challenging research subject in the field of nonlinear dynamics is the study of chaotic behavior in systems of more than two degrees of freedom in this work we study fixed points strange attractors chaotic behavior and the problem of chaos control for complex duffing s oscillators which represent periodically forced systems of two degrees of freedom we produce plots of poincare map and study the fixed points and strange attractors of our oscillators the presence of chaotic behavior in these models is verified by the existence of positive maximal lyapunov exponent we also calculate the power spectrum and consider its implications regarding the properties of the dynamics the problem of controlling chaos for these oscillators is studied using a method introduced by pyragas phys lett a 170 1992 421 which is based on the construction of a special form of a time continuous perturbation the study of coupled periodically forced oscillators is of interest to several fields of physics mechanics and engineering the connection of our oscillators to the nonlinear schrodinger equation is discussed

reconstruction expansion as a geometry based framework for choosing proper delay times abstract the quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter here we develop a new computationally efficient approach to choosing that quantifies reconstruction expansion from the identity line of the embedding space we show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error thus reconstruction expansion represents a simple geometrical framework for choosing furthermore we describe the role of dynamical error in attractor expansion and argue that algorithms for determining should be considered as attempts at estimating an upper bound to the optimal delay

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

limit theorems for von mises statistics of a measure preserving transformation for a measure preserving transformation t of a probability space x mathcal f mu and some d ge 1 we investigate almost sure and distributional convergence of random variables of the form begin aligned x rightarrow frac 1 c n sum 0 le i 1 ldots i d n f t i 1 x ldots t i d x n 1 2 ldots end aligned where c 1 c 2 ldots are normalizing constants and the kernel f belongs to an appropriate subspace in some l p x d mathcal f otimes d mu d we establish a form of the individual ergodic theorem for such sequences using a filtration compatible with t and the martingale approximation we prove a central limit theorem in the non degenerate case for a class of canonical totally degenerate kernels and d 2 we also show that the convergence holds in distribution towards a quadratic form sum m 1 infty lambda m eta 2 m in independent standard gaussian variables eta 1 eta 2 ldots

exploring dynamic property of traffic flow time series in multi states based on complex networks phase space reconstruction versus visibility graph abstract a new method based on complex network theory is proposed to analyze traffic flow time series in different states we use the data collected from loop detectors on freeway to establish traffic flow model and classify the flow into three states based on k means method we then introduced two widely used methods to convert time series into networks phase space reconstruction and visibility graph furthermore in phase space reconstruction we discuss how to determine delay time constant and embedding dimension and how to select optimal critical threshold in terms of cumulative degree distribution in the visibility graph we design a method to construct network from multi variables time series based on logical or finally we study and compare the statistic features of the networks converted from original traffic time series in three states based on phase space and visibility by using the degree distribution network structure correlation of the cluster coefficient to betweenness and degree degree correlation

constrained regulation of linear continuous time dynamical systems abstract in this paper the linear constrained regulation problem lcrp for continuous time dynamical systems is studied the first part of the paper deals with the existence of linear state feedback control laws that transfer asymptotically to the origin all initial states belonging to a given polyhedral subset of the state space while respecting linear constraints on both state and control vectors then the lcrp is formulated as an optimization problem which can be solved by applying linear programming techniques

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

wavelet based image denoising using a markov random field a priori model this paper describes a new method for the suppression of noise in images via the wavelet transform the method relies on two measures the first is a classic measure of smoothness of the image and is based on an approximation of the local holder exponent via the wavelet coefficients the second novel measure takes into account geometrical constraints which are generally valid for natural images the smoothness measure and the constraints are combined in a bayesian probabilistic formulation and are implemented as a markov random field mrf image model the manipulation of the wavelet coefficients is consequently based on the obtained probabilities a comparison of quantitative and qualitative results for test images demonstrates the improved noise suppression performance with respect to previous wavelet based image denoising methods

the periodicity of chaotic impact oscillators in hausdorff phase spaces it is well known that non periodic behavior is one of the most puzzling characteristics of chaotic oscillators so far chaotic dynamical systems have been investigated in euclidean spaces in this paper the concept of non autonomous dynamical systems and that of hausdorff phase spaces are proposed the behavior of chaotic impact oscillators is investigated in hausdorff phase spaces it is discovered that although the non autonomous dynamical systems described by chaotic impact oscillators are non periodic in euclidean phase spaces they are periodic in hausdorff phase spaces this shows that euclidean spaces in which we stayed for hundreds of years may no longer be suitable for the investigation into chaotic phenomena in addition the periodicity of chaotic dynamical systems in hausdorff metric spaces induces a new class of strange invariant sets in euclidean spaces such strange invariant sets may be an ideal symbol of chaotic dynamical systems