estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

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

generalized hyperelliptic surfaces this article presents some results on the surfaces of general type whose albanese morphism is a holomorphic fibre bundle

a class of fuzzy clusterwise regression models in this paper we introduce a class of fuzzy clusterwise regression models with lr fuzzy response variable and numeric explanatory variables which embodies fuzzy clustering into a fuzzy regression framework the model bypasses the heterogeneity problem that could arise in fuzzy regression by subdividing the dataset into homogeneous clusters and performing separate fuzzy regression on each cluster the integration of the clustering model into the regression framework allows us to simultaneously estimate the regression parameters and the membership degree of each observation to each cluster by optimizing a single objective function the class of models proposed here includes as special cases the fuzzy clusterwise linear regression model and the fuzzy clusterwise polynomial regression model we also introduce a set of goodness of fit indices to evaluate the fit of the regression model within each cluster as well as in the whole dataset finally we consider some cluster validity criteria that are useful in identifying the optimal number of clusters several applications are provided in order to illustrate the approach

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

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 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

support vector interval regression networks for interval regression analysis in this paper the support vector interval regression networks svirns are proposed for the interval regression analysis the svirns consist of two radial basis function networks one network identifies the upper side of data interval and the other network identifies the lower side of data intervals because the support vector regression svr approach is equivalent to solving a linear constrained quadratic programming problem the number of hidden nodes and the initial values of adjustable parameters can be easily obtained since the selection of a parameter e in the svr approach may seriously affect the modeling performance a two step approach is proposed to properly select the e value after the svr approach with the selected e an initial structure of svirns can be obtained besides outliers will not significantly affect the upper and lower bound interval obtained through the proposed two step approach consequently a traditional back propagation bp learning algorithm can be used to adjust the initial structure networks of svirns under training data sets without or with outliers due to the better initial structure of svirns are obtained by the svr approach the convergence rate of svirns is faster than the conventional networks with bp learning algorithms or with robust bp learning algorithms for interval regression analysis four examples are provided to show the validity and applicability of the proposed svirns

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

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

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 regression analysis using neural networks abstract in this paper we propose simple but powerful methods for fuzzy regression analysis using neural networks since neural networks have high capability as an approximator of nonlinear mappings the proposed methods can be applied to more complex systems than the existing lp based methods first we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input output patterns a nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms nonlinear fuzzy models whose h level sets approximately include all the given patterns can be derived last we show an application of the proposed methods to a real problem

new hermite orthogonal polynomial kernel and combined kernels in support vector machine classifier support vector machine is a desired method for classification of different types of data but the main obstacle to using this method is the considerable reduction of classification speed upon increase in the size of problem in this paper a new kernel function is proposed for svm which is derived from hermite orthogonal polynomials this function improves classification accuracy as well as reduction in the number of support vectors and increases the classification speed the overall kernel performance has been evaluated on real world data sets from uci repository by the ten fold cross validation method the combinations of hermite function with common kernels are proposed in this paper experimental results reveal that the hermite chebyshev kernel which is obtained from combination of hermite and chebyshev kernel has the best performance in the number of support vectors and hermite gussian kernel that is produced from combination hermite and gussian kernel has the first rank in the error rate among all experimental kernels on the other hand the hermite proposed method has the least number of support vectors and best performance in the error rate in comparison with common kernels and lowest required time among all kernels a new kernel function has been proposed by using hermite orthogonal polynomial new combined kernels resulted by combining hermite and common kernels have been proposed the proposed methods have been compared with three common kernels on real and synthetic data sets hermite kernel function has the lowest required time for classification the proposed methods yield better error rate and they have the best support vectors reduction significantly

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

galois closure and lagrangian varieties abstract let x be a complex projective variety and consider the morphism k k h 0 x x 1 h 0 x x k we use galois closures of finite rational maps to introduce a new method for producing varieties such that k has non trivial kernel we then apply our result to the two dimensional case and we construct a new family of surfaces which are lagrangian in their albanese variety moreover we analyze these surfaces computing their chern invariants and proving that they are not fibred over curves of genus g 2 the topological index of these surfaces is negative and this provides a counterexample to a conjecture on lagrangian surfaces formulated in barja et al 2007 3

fibered algebraic surfaces with low slope the background of this paper is the following conjecture on complex surfaces of general type let s be a smooth projective minimal surface of general type over ti with c 2 throughout the paper

a study on reduced support vector machines recently the reduced support vector machine rsvm was proposed as an alternate of the standard svm motivated by resolving the difficulty on handling large data sets using svm with nonlinear kernels it preselects a subset of data as support vectors and solves a smaller optimization problem however several issues of its practical use have not been fully discussed yet for example we do not know if it possesses comparable generalization ability as the standard svm in addition we would like to see for how large problems rsvm outperforms svm on training time in this paper we show that the rsvm formulation is already in a form of linear svm and discuss four rsvm implementations experiments indicate that in general the test accuracy of rsvm are a little lower than that of the standard svm in addition for problems with up to tens of thousands of data if the percentage of support vectors is not high existing implementations for svm is quite competitive on the training time thus from this empirical study rsvm will be mainly useful for either larger problems or those with many support vectors experiments in this paper also serve as comparisons of 1 different implementations for linear svm and 2 standard svm using linear and quadratic cost functions

bayes estimators of generalized entropies the order q tsallis and renyi entropy receive broad applications in the statistical analysis of complex phenomena a generic problem arises however when these entropies need to be estimated from observed data the finite size of data sets can lead to serious systematic and statistical errors in numerical estimates in this paper we focus upon the problem of estimating generalized entropies from finite samples and derive the bayes estimator of the order q tsallis entropy including the order 1 i e the shannon entropy under the assumption of a uniform prior probability density the bayes estimator yields in general the smallest mean quadratic deviation from the true parameter as compared with any other estimator exploiting the functional relationship between and we use the bayes estimator of to estimate the renyi entropy we compare these novel estimators with the frequency count estimators for and we find by numerical simulations that the bayes estimator reduces statistical errors of order q entropy estimates for bernoulli as well as for higher order markov processes derived from the complete genome of the prokaryote haemophilus influenzae

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

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

assessing causality from multivariate time series in this work we propose a general nonparametric test of causality for weakly dependent time series more precisely we study the problem of attribution i e the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest we illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science

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

xiao s conjecture for general fibred surfaces we prove that the genus g the relative irregularity qf and the clifford index cf of a non isotrivial

interval regression analysis using quadratic loss support vector machine support vector machines svms have been very successful in pattern recognition and function estimation problems for crisp data this paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss svm this version of svm utilizes quadratic loss function unlike the traditional svm for data sets with crisp inputs and interval outputs the possibility and necessity models have been recently utilized which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one the quadratic loss svm also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression however this is not a computationally expensive way the quadratic loss svm allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space the proposed algorithm is a very attractive approach to modeling nonlinear interval data and is model free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output experimental results are then presented which indicate the performance of this algorithm

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

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

blind separation of post nonlinear mixtures using linearizing transformations and temporal decorrelation we propose two methods that reduce the post nonlinear blind source separation problem pnl bss to a linear bss problem the first method is based on the concept of maximal correlation we apply the alternating conditional expectation ace algorithm a powerful technique from non parametric statistics to approximately invert the componentwise non linear functions the second method is a gaussianizing transformation which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately gaussian distributed this heuristic but simple and efficient procedure works as good as the ace method using the framework provided by ace convergence can be proven the optimal transformations obtained by ace coincide with the sought after inverse functions of the nonlinearities after equalizing the nonlinearities temporal decorrelation separation tdsep allows us to recover the source signals numerical simulations testing ace td and gauss td on realistic examples are performed with excellent results

reduced support vector machines a statistical theory in dealing with large data sets the reduced support vector machine rsvm was proposed for the practical objective to overcome some computational difficulties as well as to reduce the model complexity in this paper we study the rsvm from the viewpoint of sampling design its robustness and the spectral analysis of the reduced kernel we consider the nonlinear separating surface as a mixture of kernels instead of a full model the rsvm uses a reduced mixture with kernels sampled from certain candidate set our main results center on two major themes one is the robustness of the random subset mixture model the other is the spectral analysis of the reduced kernel the robustness is judged by a few criteria as follows 1 model variation measure 2 model bias deviation between the reduced model and the full model and 3 test power in distinguishing the reduced model from the full one for the spectral analysis we compare the eigenstructures of the full kernel matrix and the approximation kernel matrix the approximation kernels are generated by uniform random subsets the small discrepancies between them indicate that the approximation kernels can retain most of the relevant information for learning tasks in the full kernel we focus on some statistical theory of the reduced set method mainly in the context of the rsvm the use of a uniform random subset is not limited to the rsvm this approach can act as a supplemental algorithm on top of a basic optimization algorithm wherein the actual optimization takes place on the subset approximated data the statistical properties discussed in this paper are still valid

measuring statistical dependences in a time series we propose two methods to measure all linear and nonlinear statistical dependences in a stationary time series presuming ergodicity the measures can be obtained from efficient numerical algorithms

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

linear and non linear fuzzy regression evolutionary algorithm solutions given some data which consists of pairs of fuzzy numbers our evolutionary algorithm searches our library of fuzzy functions which includes linear polynomial exponential and logarithmic for a fuzzy function which best fits the data tests of our fuzzy regression package are given for each of the four cases linear polynomial exponential and logarithmic for the linear model we also consider multiple independent variables in all cases we use data generated with and without noise we prove that fuzzy polynomial regression can model the extension principle extension of continuous real valued functions

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

a reduced support vector machine approach for interval regression analysis the support vector machine svm has been shown to be an efficient approach for a variety of classification problems it has also been widely used in pattern recognition regression and distribution estimation for separable data however there are two problems with using the svm model 1 large scale when dealing with large scale data sets the solution may be difficult to find when using svm with nonlinear kernels 2 unbalance the number of samples from one class is much larger than the number of samples from the other classes it causes the excursion of separation margin under these circumstances developing an efficient method is necessary recently the use of the reduced support vector machine rsvm was proposed as an alternative to the standard svm it has been proven more efficient than the traditional svm in processing large scaled data in this paper we introduce the principle of rsvm to evaluate interval regression analysis the main idea of the proposed method is to reduce the number of support vectors by randomly selecting a subset of samples

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

family of curves with large unitary summand in the hodge bundle in this note we construct non isotrivial families of curves of genus g ge 2 where the rank of the unitary summand contained in the hodge bundle can be as large as 2g 1 3 and hence disprove xiao s conjecture for the unitary rank

a revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals conventional fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets however some limitations still exist this paper deals with a revisited approach for possibilistic fuzzy regression methods indeed a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property moreover this model output can have any kind of spread tendency in this framework the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution the potential of the proposed method with regard to the conventional approach is illustrated by simulation examples

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

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

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 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

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

robust fuzzy regression analysis in this paper we propose a robust fuzzy linear regression model based on the least median squares weighted least squares lms wls estimation procedure the proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions we also define suitable goodness of fit indices useful to evaluate the performances of the proposed model the effectiveness of our model in reducing the outliers influence is shown by using applicative examples based both on simulated and real data and by a simulation study

dual possibilistic regression analysis using support vector networks abstract this study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine svm theory the dual regression model which comprises an upper model and a lower model approximates the observed fuzzy phenomena from the outside and inside directions respectively such that the inclusion relationship between those two models holds the proposed dual regression model better explains the inherent vagueness that exists in a given dataset it provides the outer and inner bounds for the estimated vagueness region and allows an estimation of the degree of confidence in the predicted fuzzy output using the principles for a twin support vector machine tsvm the upper and lower models are estimated by solving two smaller svm type quadratic programming problems qpps instead of a single larger qpp this strategy significantly increases the learning speed for the proposed algorithm the structural risk minimization principle of svm makes the proposed method to yield better generalization ability the kernel function method offers a model independent framework for the proposed dual regression model this paper focuses on the class of radial kernels which enables the proposed method to conquer the problem of increasing spreads the radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs the experimental results verify the effectiveness and efficiency of the proposed method in comparison with previous svm based dual regression model the proposed approach significantly improves the sparsity prediction speed and training speed

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

fuzzy regression methods a comparative assessment abstract the fundamental differences between fuzzy regression and ordinary regression are identified in this paper fuzzy regression can be used to fit fuzzy data and crisp data into a regression model whereas ordinary regression can only fit crisp data through a comprehensive literature review three approaches of fuzzy regression are summarized the first approach of fuzzy regression is based on minimizing fuzziness as an optimal criterion the second approach uses least squares of errors as a fitting criterion and two methods are summarized in this paper the third approach can be described as an interval regression analysis for each fuzzy regression method numerical examples and graphical presentations are used to evaluate their characteristic and differences with ordinary least squares regression based on the comparative assessment the fundamental differences between ordinary least squares regression and conventional fuzzy regression are concluded that is ordinary least squares regression modeling data with randomness type of uncertainty and conventional fuzzy regression modeling data with fuzziness type of uncertainty in order to integrate both randomness and fuzziness types of uncertainty into one regression model the concept of hybrid fuzzy least squares regression analysis is proposed in this paper and the details of its method are derived in the accompanying paper

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

fuzzy phoneme recognition abstract first a scheme for pattern recognition is given in a learning step a relation between acoustic characteristics and the corresponding phoneme is computed using an inference rule next the phonemes are recognised as result of a fuzzy relation equation then the recognition quality is analysed by means of uncertainty measures specially sugeno s and possibility measures

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

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

a set arithmetic based linear regression model for modelling interval valued responses through real valued variables a new linear regression model for an interval valued response and a real valued explanatory variable is presented the approach is based on the interval arithmetic comparisons with previous methods are discussed the new linear model is theoretically analyzed and the regression parameters are estimated some properties of the regression estimators are investigated finally the performance of the procedure is illustrated using both a real life application and simulation studies

information transfer in continuous processes we discuss a recently proposed quantity called transfer entropy which uses time series data to measure the amount of information transferred from one process to another in order to understand its foundation merits and limitations we review some aspects of information theoretic functionals while for symbol sequences these measures have an intuitive interpretation their application to continuous state processes and in particular their estimation from finite data sets is problematic for mutual information finite length scale estimates converge from below and can thus be used to reject the assumption that the observed processes are independent however mutual information does not provide any directional information conversely transfer entropy does resolve the directionality of information exchange but no similar monotonic convergence seems to hold thus only in the case of zero transfer entropy in one direction we can reliably infer an asymmetry of the information exchange

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

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

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

on the classification of irregular surfaces of general type with nonbirational bicanonical map the present paper is devoted to the classification of irregular surfaces of general type with pg 3 and nonbirational bicanonical map our main result is that if s is such a surface and if s is minimal with no pencil of curves of genus 2 then s is the symmetric product of a curve of genus 3 and therefore pg q 3 and k2 6 furthermore we obtain some results towards the classification of minimal surfaces with pg q 3 such surfaces have 6 kz 9 and we show that kz 6 if and only if s is the symmetric product of a curve of genus 3 we also classify the minimal surfaces with pg q 3 with a pencil of curves of genus 2 proving in particular that for those one has kz 8

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

fuzzy spline univariate regression with exact predictors and fuzzy responses abstract spline smoothing is a form of nonlinear regression when there is reason to believe that relationship between the predictor and the response is curvilinear in such cases the spline smoothing is an effective method to improve the performances of the conventional polynomial based regression models this paper proposed a fuzzy spline method based on a weighted absolute error distance measure with exact predictors and fuzzy responses unknown fuzzy coefficients tuning parameter were selected according to a hybrid optimization algorithm the effectiveness of the proposed method was also examined and compared with some well established fuzzy nonlinear regression models through some numerical examples including a simulation study for this purpose several common goodness of fit criteria were employed the numerical results clearly indicated that our prediction estimation gives more accurate results compared to other methods

support vector fuzzy regression machines support vector machine svm has been very successful in pattern recognition and function estimation problems in this paper we introduce the use of svm for multivariate fuzzy linear and nonlinear regression models using the basic idea underlying svm for multivariate fuzzy regressions gives computational efficiency of getting solutions