measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

a new method to detect nonlinearity in a time series synthesizing surrogate data using a kolmogorov smirnoff tested hidden markov model abstract a way of statistically testing for nonlinearity in a time series is to employ the method of surrogate data this method often makes use of the fourier transform ft in order to generate the surrogate as various authors have shown this can lead to artefacts in the surrogates and spurious detection of nonlinearity can result this paper documents a new method to synthesize surrogate data using a 1st order hidden markov model hmm combined with a kolmogorov smirnoff test ks test to determine the required resolution of the hmm significance test results for a sinewave henon map and gaussian noise time series are presented it is demonstrated that ks tested hmm surrogates can be successfully used to distinguish between a deterministic and stochastic time series then by applying a simple test for linearity using linear and nonlinear predictors it is possible to determine the nature of the deterministic class and hence conclude whether the system is linear deterministic or nonlinear deterministic furthermore it is demonstrated that the method works for periodic functions too where ft surrogates break down

on the muskat problem with viscosity jump global in time results abstract the muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media in this paper we consider both the 2d and 3d setting of two fluids of different constant densities and different constant viscosities in this situation the related contour equations are non local not only in the evolution system but also in the implicit relation between the amplitude of the vorticity and the free interface among other extra difficulties no maximum principles are available for the amplitude and the slopes of the interface in l we prove global in time existence results for medium size initial stable data in critical spaces we also enhance previous methods by showing smoothing instant analyticity improving the medium size constant in 3d together with sharp decay rates of analytic norms the found technique is twofold giving ill posedness in unstable situations for very low regular solutions

self organizing dynamics of human erythrocytes under shear stress abstract the characterization of the erythrocytes viscoelastic properties is studied from the perspective of bounded correlated random walk brownian motion based on the assumption that diffractometric data involves both deterministic and stochastic components the photometric readings are obtained by ektacytometry over several millions of shear elongated cells using a home made device called erythrodeformeter the results suggest that the samples from healthy donors are intrinsically unpredictable ordinary brownian motion while when studying beta thalassemic samples these exhibit not only a great sensitivity to initial conditions fractional brownian motion but also chaotic behavior these results could allow us to claim that we have linked nonlinear tools with clinical aspects of the erythrocytes rheological properties

learning chaotic attractors by neural networks an algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series during training the algorithm learns to short term predict the time series at the same time a criterion developed by diks van zwet takens and de goede 1996 is monitored that tests the hypothesis that the reconstructed attractors of model generated and measured data are the same training is stopped when the prediction error is low and the model passes this test two other features of the algorithm are 1 the way the state of the system consisting of delays from the time series has its dimension reduced by weighted principal component analysis data reduction and 2 the user adjustable prediction horizon obtained by error propagation partially propagating prediction errors to the next time step the algorithm is first applied to data from an experimental driven chaotic pendulum of which two of the three state variables are known this is a comprehensive example that shows how well the diks test can distinguish between slightly different attractors second the algorithm is applied to the same problem but now one of the two known state variables is ignored finally we present a model for the laser data from the santa fe time series competition set a it is the first model for these data that is not only useful for short term predictions but also generates time series with similar chaotic characteristics as the measured data

contour dynamics of incompressible 3 d fluids in a porous medium with different densities we consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium which is known as the muskat problem and in two dimensions it is mathematically analogous to the two phase hele shaw cell we focus on a fluid interface given by a jump of densities being the equation of the evolution obtained using darcy s law we prove local well posedness when the smaller density is above stable case and in the unstable case we show ill posedness

fast recursive equalizers for 1d and 2d linear equalization we develop fast recursive equalizers to be used in the one dimensional 1d or two dimensional 2d linear minimum mean squared error equalization of a known linear finite length channel in particular these equalization algorithms address the communications scenario in which the channel or the prior information on the transmitted symbols may be time varying the latter case of time varying priors is especially pertinent for turbo equalization on which we focus here we first consider a 1d sliding window equalizer based on a cholesky factorization update and then generalize this approach to the 2d case finally we develop a 2d equalizer that is based on a recursive matrix inverse update we summarize each of these algorithms and describe their computational complexities

maximum likelihood estimation of the entropy of an attractor in this paper a maximum likelihood estimate of the kolmogorov entropy of an attractor is proposed that can be obtained directly from a time series also the relative standard deviation of the entropy estimate is derived it is dependent on the entropy and on the number of samples used in the estimation

complexity and synchronization in chaotic fiber optic systems abstract in this work we investigate experimentally the complexity of chaotic attractors generated by a semiconductor laser subjected to optical feedback and associate their dimensionality with the synchronization efficiency of the corresponding chaotic transmitter receiver configuration the complexity is characterized by calculating the correlation dimension d 2 of experimental chaotic time series for different values of the optical feedback we present the effect of d 2 on the synchronization efficiency and determine the optimal operating condition that leads to the most complex chaotic carrier and simultaneously to the most successful synchronization lastly we associate and explain our experimental results with theoretical predictions in the research literature

turning waves and breakdown for incompressible flows we consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids specifically we study the muskat and water wave problems we show that starting with a family of initial data given by f0 the interface reaches a regime in finite time in which is no longer a graph therefore there exists a time t where the solution of the free boundary problem parameterized as f t blows up f l t in particular for the muskat problem this result allows us to reach an unstable regime for which the rayleigh taylor condition changes sign and the solution breaks down

on the hausdorff dimension of fractal attractors we consider such mappingsx n 1 f xn of an interval into itself for which the attractor is a cantor set for the same class of mappings for which the feigenbaum scaling laws hold we show that the hausdorff dimension of the attractor is universally equal tod 0 538

convergence of the k 2 entropy for random noises with power law spectra abstract we discuss a counter example to the traditional expectation that stochastic processes lead to a non convergence of the k 2 entropy in computed or measured time series we consider a simple class of colored random noises with power law spectra which have already been shown to generate finite and predictable values of the correlation dimension we show that the k 2 entropy of these random noises converges as well these results imply that the observation of a finite or null value of the k 2 entropy in the analysis of data is not enough to infer that the system is dominated by a deterministic process such as low dimensional chaos

noisy dynamic simulations in the presence of symmetry data alignment and model reduction abstract we process snapshots of trajectories of evolution equations with intrinsic symmetries and demonstrate the use of recently developed eigenvector based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise our illustrative examples include a one dimensional evolutionary partial differential the kuramoto sivashinsky equation with periodic boundary conditions as well as a stochastic simulation of nematic liquid crystals which can be effectively modeled through a nonlinear smoluchowski equation on the surface of a sphere this is a useful first step towards data mining the symmetry adjusted ensemble of snapshots in search of an accurate low dimensional parametrization and the associated reduction of the original dynamical system we also demonstrate a technique vector diffusion maps that combines in a single formulation the symmetry removal step and the dimensionality reduction step

a nine dimensional lorenz system to study high dimensional chaos we examine the dynamics of three dimensional cells with square planform in dissipative rayleigh benard convection by applying a triple fourier series ansatz up to second order we obtain a system of nine nonlinear ordinary differential equations from the governing hydrodynamic equations depending on two control parameters namely the rayleigh number and the prandtl number the asymptotic behaviour can be stationary periodic quasiperiodic or chaotic a period doubling cascade is identified as a route to chaos hereafter the asymptotic behaviour progressively evolves towards a hyperchaotic attractor for given values of control parameters beyond the accumulation point we observe a low dimensional chaotic attractor as is currently done for dissipative systems although the correlation dimension strongly suggests that this attractor could be embedded in a three dimensional space a topological characterization reveals that a higher dimensional space must be used thus we reconstruct a four dimensional model which is found to be in agreement with the properties of the original dynamics the nine dimensional lorenz model could therefore play a significant role in developing tools to characterize chaotic attractors embedded in phase space with a dimension greater than 3

a maximum principle for the muskat problem for fluids with different densities we study the fluid interface problem given by two incompressible fluids with different densities evolving by darcy s law this scenario is known as the muskat problem for fluids with the same viscosities being in two dimensions mathematically analogous to the two phase hele shaw cell we prove in the stable case the denser fluid is below a maximum principle for the l norm of the free boundary

on a nonlinear kalman filter with simplified divided difference approximation abstract we present a new ensemble based approach that handles nonlinearity based on a simplified divided difference approximation through stirling s interpolation formula which is hence called the simplified divided difference filter sddf the sddf uses stirling s interpolation formula to evaluate the statistics of the background ensemble during the prediction step while at the filtering step the sddf employs the formulae in an ensemble square root filter ensrf to update the background to the analysis in this sense the sddf is a hybrid of stirling s interpolation formula and the ensrf method while the computational cost of the sddf is less than that of the ensrf numerical comparison between the sddf and the ensrf with the ensemble transform kalman filter etkf as the representative is conducted the experiment results suggest that the sddf outperforms the etkf with a relatively large ensemble size and thus is a good candidate for data assimilation in systems with moderate dimensions

global existence singular solutions and ill posedness for the muskat problem the muskat or muskat leibenzon problem describes the evolution of the interface between two immiscible fluids in a porous medium or hele shaw cell under applied pressure gradients or fluid injection extraction in contras t to the hele shaw problem the one phase version of the muskat problem there are few nontrivial exact solutions or analytic results for the muskat problem for the stable forward muskat problem in which the higher viscosity fluid ex pands into the lower viscosity fluid we show global in time existence for initial data that is a small perturbation of a flat interface the initial data in this result ma y contain weak e g curvature singularities for the unstable backwa rd problem in which the higher viscosity fluid contracts we construct singular solution s that start off with smooth initial data but develop a point of infinite curvature at fi nite time c 2004 wiley periodicals inc

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

on the detection of determinism in a time series the nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature chaoticity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process the distributions of the strengths of the modes for the data and the surrogate are compared statistically singular value decomposition is used for the implementation the ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series including linear and nonlinear stochastic noise and processes described by lorenz rossler and mackey glass equations henon map and ecological map and some real life examples

dependent variables in broad band continuous time series in this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series these methods are very broadly applicable and are particularly well suited to the study of continuous time series in which the value of the function may depend on derivatives of the function itself or on other quantities we apply our methods to a number of mathematical examples including the lorentz equation the h6non heiles equations the forced brusselator and the mackey glass equation we show that our methods are very successful at indicating deterministic dependencies in these systems even if the time series are highly chaotic statistical aspects of our procedure are discussed as are a number of interesting and surprising epistomological implications

error covariance matrix estimation of noisy and dynamically coupled time series we estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors we say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system the estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series the method is particularly powerful for short length time series with high uncertainties

uniform framework for the recurrence network analysis of chaotic time series we propose a general method for the construction and analysis of unweighted e recurrence networks from chaotic time series the selection of the critical threshold e c in our scheme is done empirically and we show that its value is closely linked to the embedding dimension m in fact we are able to identify a small critical range e numerically that is approximately the same for the random and several standard chaotic time series for a fixed m this provides us a uniform framework for the nonsubjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors we explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes n we also present two practical applications of the scheme detection of transition between two dynamical regimes in a time delayed system and identification of the dimensionality of the underlying system from real world data with a limited number of points through recurrence network measures the merits limitations and the potential applications of the proposed method are also highlighted

danco an intrinsic dimensionality estimator exploiting angle and norm concentration abstract in the past decade the development of automatic intrinsic dimensionality estimators has gained considerable attention due to its relevance in several application fields however most of the proposed solutions prove to be not robust on noisy datasets and provide unreliable results when the intrinsic dimensionality of the input dataset is high and the manifold where the points are assumed to lie is nonlinearly embedded in a higher dimensional space in this paper we propose a novel intrinsic dimensionality estimator danco and its faster variant fastdanco which exploit the information conveyed both by the normalized nearest neighbor distances and by the angles computed on couples of neighboring points the effectiveness and robustness of the proposed algorithms are assessed by experiments on synthetic and real datasets by the comparative evaluation with state of the art methodologies and by significance tests

intrinsic dimension estimation of manifolds by incising balls dimensionality reduction is a very important tool in data mining intrinsic dimension of data sets is a key parameter for dimensionality reduction however finding the correct intrinsic dimension is a challenging task in this paper a new intrinsic dimension estimation method is presented the estimator is derived by finding the exponential relationship between the radius of an incising ball and the number of samples included in the ball the method is compared with the previous dimension estimation methods experiments have been conducted on synthetic and high dimensional image data sets and on data sets of the santa fe time series competition and the results show that the new method is accurate and robust

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

a search for chaotic behavior in large and mesoscale motions in the pacific ocean the lagrangian trajectories of three satellite tracked bouys deployed in the pacific ocean for a one year period are studied from the standpoint of dynamical systems theory time series of the bouy positions are analyzed to estimate the correlation dimension and kolmogorov entropy we find a small finite value of correlation dimension near 1 4 and a finite kolmogorov entropy of about 0 2 day 1 these results at first suggest that the bouy motions may be dominated by a low dimensional chaotic attractor using standard ideas from the mathematics of fractals and a new method which we call multivariate scaling analysis we are able to demonstrate however that the bouy trajectories are instead fractal curves in the physical plane x y these results may be viewed from the standpoint of multivariate nongaussian convergence of the scales which occur when the fourier spectrum is described by a power law such systems can have a small finite value for the correlation dimension and are therefore fractal even when no underlying attractor is present systems of this type are more easily related to turbulent behavior stochastic many degrees of freedom rather than to strange attractor deterministic few degrees of freedom

active learning and basis selection for kernel based linear models a bayesian perspective we develop an active learning algorithm for kernel based linear regression and classification the proposed greedy algorithm employs a minimum entropy criterion derived using a bayesian interpretation of ridge regression we assume access to a matrix bbrn n for which the i j th element is defined by the kernel function k i j bbr with the observed data i bbrd we seek a model m i yi where yi is a real valued response or integer valued label which we do not have access to a priori to achieve this goal a submatrix il ib bbrn m is sought that corresponds to the intersection of n rows and m columns of indexed by the sets il and ib respectively typically m n and n n we have two objectives i determine the m columns of indexed by the set ib that are the most informative for building a linear model m 1 i ib t yi without any knowledge of yi i 1n and ii using active learning sequentially determine which subset of n elements of yi i 1n should be acquired both stopping values ib m and il n are also to be inferred from the data these steps are taken with the goal of minimizing the uncertainty of the model parameters x as measured by the differential entropy of its posterior distribution the parameter vector x bbrm as well as the model bias bbr is then learned from the resulting problem yil il ibx 1 the remaining n n responses labels not included in yil can be inferred by applying x to the remaining n n rows of ib we show experimental results for several regression and classification problems and compare to other active learning methods

global solutions for a supercritical drift diffusion equation abstract we study the global existence of solutions to a one dimensional drift diffusion equation with logistic term generalizing the classical parabolic elliptic keller segel aggregation equation arising in mathematical biology in particular we prove that there exists a global weak solution if the order of the fractional diffusion 1 c 1 2 where c 1 0 is an explicit constant depending on the physical parameters present in the problem chemosensitivity and strength of logistic damping furthermore in the range 1 c 2 2 with 0 c 2 c 1 the solution is globally smooth let us emphasize that when 1 the diffusion is in the supercritical regime

rayleigh taylor breakdown for the muskat problem with applications to water waves the muskat problem models the evolution of the interface between two different fluids in porous media the rayleigh taylor condition is natural to reach linear stability of the muskat problem we show that the rayleigh taylor condition may hold initially but break down in finite time as a consequence of the method used we prove the existence of water waves turning

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

a nonsmooth coulomb friction oscillator abstract a forced coulomb friction oscillator whose frictional force is allowed to vary with displacement is analyzed geometrically the equation of motion for the oscillator is piecewise linear we geometrically observe the nature of the flow in each region of solvability and then see how these solutions interact at the boundary of the regions the dynamics of the flow is viewed in terms of a map on the boundary between the regions for chaotic motion we geometrically construct the strange attractor and show that its exact behavior is that of a one dimensional map the following dynamical properties arise from the nonsmooth nature of the coulomb friction law the flow may not be invertible the flow may reach its attractor in finite time the dimension of the attractor may be less than or equal to two embeddings of an observable may not be diffeomorphic to the full phase flow

intrinsic dimension estimation via nearest constrained subspace classifier we consider the problems of classification and intrinsic dimension estimation on image data a new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation the distribution of the data in each class is modeled by a union of a finite number of affine subspaces of the feature space the affine subspaces have a common dimension which is assumed to be much less than the dimension of the feature space the subspaces are found using regression based on the 0 norm the proposed method is a generalisation of classical nn nearest neighbor nfl nearest feature line classifiers and has a close relationship to ns nearest subspace classifier the proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy we also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity experiments on publicly available datasets corroborate these claims highlightsa new classifier called ncsc and its fast version called ncsc ii are proposed classifiers of nn nfl and ns are the special cases of ncsc ncsc ncsc ii can be used as intrinsic dimension estimator using well tuned intrinsic parameter ncsc ncsc ii outperforms nn nfl and ns

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

a note on interface dynamics for convection in porous media we studied the fluid interface problem through porous media given by two incompressible 2 d fluids of different densities this problem is mathematically analogous to the dynamics interface for convection in porous media where the free boundary evolves between fluids with different temperatures we found a new formula for the evolution equation of the free boundary parameterized as a function in the periodic case in this formula there is not a principal value in the non local integral operator involved in the equation giving a simpler system using this formulation we perform numerical simulations in the stable case denser fluid below which shows a strong regularity effect in the periodic interface

fast techniques for computing finite length mimo mmse decision feedback equalizers multiple input multiple output mimo digital communication systems have received great attention due to their potential of increasing the overall system throughput in such systems mimo decision feedback equalization dfe schemes are often used to mitigate intersymbol interference isi resulting from channel multipath propagation in this context the existing computationally efficient methods for exact estimation of the dfe filters under minimum mean square error criteria mmse dfe rely on fast cholesky decomposition and backsubstitution or levinson techniques these methods may still present several difficulties in implementation as the demand on higher transmission rates increases and thus a simple solution is necessary in this paper new procedures for fast computation of the mimo mmse dfe are presented the new algorithms are obtained from a simple observation namely that the optimal feedforward filter fff is related to the well known kalman gain matrix commonly encountered in fast recursive least squares adaptive algorithms for which fast recursions exist and are readily applicable moreover the feedback filter can be easily computed via stable fast mimo convolution techniques as a result the proposed method is less complex more structured and can be as reliable in finite precision as known approaches in the literature

absence of long range order in one dimensional spin systems for a one dimensional ising model with interaction energy e left mu right sum limits 1 leqslant i j leqslant n j j i mu iota mu j left j k geqslant 0 mu iota pm 1 right it is proved that there is no long range order at any temperature when s n sum limits k 1 n kj left k right o left log n 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right the same result is shown to hold for the corresponding plane rotator model when s n o left left log n mathord left vphantom log n log log n right kern nulldelimiterspace log log n right right

analytical behavior of two dimensional incompressible flow in porous media in this paper we study the analytic structure of a two dimensional mass balance equation of an incompressible fluid in a porous medium given by darcy s law we obtain local existence and uniqueness by the particle trajectory method and we present different global existence criterions these analytical results with numerical simulations are used to indicate nonformation of singularities moreover blow up results are shown in a class of solutions with infinite energy

a pointwise estimate for fractionary derivatives with applications to partial differential equations this article emphasizes the role played by a remarkable pointwise inequality satisfied by fractionary derivatives in order to obtain maximum principles and lp decay of solutions of several interesting partial differential equations in particular there are applications to quasigeostrophic flows in two space variables with critical viscosity that model the eckman pumping see baroud ch n plapp b b she z s swinney h l 2002 phys rev lett 88 114501 and constantin p 2002 phys rev lett 89 184501

on chaotic graphs a different approach for characterizing aperiodic dynamics fractal worlds with limited connectivity are the topological result of growing graphs from chaotic series we show how this model presents original characteristics which cannot be detected by means of the standard network descriptors in detail intrinsic inaccessibility to the fully connected configuration is demonstrated to be a universal feature associated with this family of graphs and strictly related to the fractality of a specific chaotic source here we discuss the potential of our model to be a generator of fractal graphs and also a self consistent tool for differentiating chaotic dynamics from stochastic processes

a dual scale lattice gas automata model for gas solid two phase flow in bubbling fluidized beds modelling the hydrodynamics of gas solid flow is important for the design and scale up of fluidized bed reactors a novel gas solid dual scale model based on lattice gas cellular automata lgca is proposed to describe the macroscopic behaviour through microscopic gas solid interactions solid particles and gas pseudo particles are aligned in lattices with different scales for solid and gas in addition to basic lgca rules additional rules for collision and propagation are specifically designed for gas solid systems the solid s evolution is then motivated by the temporal and spatial average momentum gained through solid solid and gas solid interactions a statistical method based on the similarity principle is derived for the conversion between model parameters and hydrodynamic properties simulations for bubbles generated from a vertical jet in a bubbling fluidized bed based on this model agree well with experimental results as well as with the results of two fluid approaches and discrete particle simulations

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

detection and characterization of changes of the correlation structure in multivariate time series we propose a method based on the equal time correlation matrix as a sensitive detector for phase shape correlations in multivariate data sets the key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix consequently detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors the performance of the technique is demonstrated by application to n f tori autoregressive models and coupled chaotic systems the high sensitivity the comparatively small computational effort and the excellent time resolution of the method recommend it for application to the analysis of complex spatially extended nonstationary systems

characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis structures in recurrence plots rps preserving the rich information of nonlinear invariants and trajectory characteristics have been increasingly analyzed in dynamic discrimination studies the conventional analysis of rps is mainly focused on quantifying the overall diagonal and vertical line structures through a method called recurrence quantification analysis rqa this study extensively explores the information in rps by quantifying local complex rp structures to do this an approach was developed to analyze the combination of three major rqa variables determinism laminarity and recurrence rate dlr in a metawindow moving over a rp it was then evaluated in two experiments discriminating 1 ideal nonlinear dynamic series emulated from the lorenz system with different control parameters and 2 data sets of human heart rate regulations with normal sinus rhythms n 18 and congestive heart failure n 29 finally the dlr was compared with seven major rqa variables in terms of discriminatory power measured by standardized mean difference d smd in the two experiments dlr resulted in the highest discriminatory power with d smd 2 53 and 0 98 respectively which were 7 41 and 2 09 times the best performance from rqa the study also revealed that the optimal rp structures for the discriminations were neither typical diagonal structures nor vertical structures these findings indicate that local complex rp structures contain some rich information unexploited by rqa therefore future research to extensively analyze complex rp structures would potentially improve the effectiveness of the rp analysis in dynamic discrimination studies

conditional entropies phase synchronization and changes in the directionality of information flow in neural systems we devised a novel measure that dynamically evaluates temporal interdependences between two coupled units based on the properties of the distributions of their relative interevent intervals we investigate its properties on the system of two coupled non identical r ossler oscillators and a system of non identical hindmarsh rose models of thalamocortical neurons and show that the measure highlights the properties of phase synchronization observed in those two systems we postulate that the observed properties of the phase lag in conjunction with the experimentally observed activity dependent synaptic modification in the neural systems may drive the changes of the direction of information flow in a neural network and thus the measure can play an important role in assessing those changes

time delay embedding increases estimation precision of models of intraindividual variability this paper investigates the precision of parameters estimated from local samples of time dependent functions we find that time delay embedding i e structuring data prior to analysis by constructing a data matrix of overlapping samples increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data we show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function hence we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions we support these conclusions both by mathematical analysis and two simulations

a permutation entropy based test for causality the volume stock price relation abstract the purpose of this paper is to propose a newly developed non parametric test for linear and nonlinear causality based on permutation entropy and to show its usefulness in analyzing the potential causal relationship between trading volume and security prices most of the empirical applications and tests for causality rely on using granger causality based test for linear models although these tests have high power in uncovering linear causal relations their power against nonlinear causal relations can be low our test is designed to deal with the detection of linear and non linear causality we also compare our permutation entropy based test with other granger causality tests monte carlo simulations show excellent performance in terms of size and power of the new test for detecting linear and non linear causality under different scenarios our conclusions point that there is a bidirectional causal relation from volume to price returns not only in the mean but also in the variance

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

binary intersymbol interference channels gallager codes density evolution and code performance bounds we study the limits of performance of gallager codes low density parity check ldpc codes over binary linear intersymbol interference isi channels with additive white gaussian noise awgn using the graph representations of the channel the code and the sum product message passing detector decoder we prove two error concentration theorems our proofs expand on previous work by handling complications introduced by the channel memory we circumvent these problems by considering not just linear gallager codes but also their cosets and by distinguishing between different types of message flow neighborhoods depending on the actual transmitted symbols we compute the noise tolerance threshold using a suitably developed density evolution algorithm and verify by simulation that the thresholds represent accurate predictions of the performance of the iterative sum product algorithm for finite but large block lengths we also demonstrate that for high rates the thresholds are very close to the theoretical limit of performance for gallager codes over isi channels if c denotes the capacity of a binary isi channel and if c sub i i d denotes the maximal achievable mutual information rate when the channel inputs are independent and identically distributed i i d binary random variables c sub i i d spl les c we prove that the maximum information rate achievable by the sum product decoder of a gallager coset code is upper bounded by c sub i i d the last topic investigated is the performance limit of the decoder if the trellis portion of the sum product algorithm is executed only once this demonstrates the potential for trading off the computational requirements and the performance of the decoder

removing the stiffness from interfacial flows with surface tension a new formulation and new methods are presented for computing the motion of fluid interfaces with surface tension in two dimensional irrotational and incompressible fluids through the laplace young condition at the interface surface tension introduces high order terms both nonlinear and nonlocal into the dynamics this leads to severe stability constraints for explicit time integration methods and makes the application of implicit methods difficult this new formulation has all the nice properties for time integration methods that are associated with having a linear constant coefficient highest order term that is using this formulation we give implicit time integration methods that have no high order time step stability constraint associated with surface tension and are explicit in fourier space the approach is based on a boundary integral formulation and applies more generally even to problems beyond the fluid mechanical context here they are applied to computing with high resolution the motion of interfaces in hele shaw flows and the motion of free surfaces in inviscid flows governed by the euler equations one hele shaw computation shows the behavior of an expanding gas bubble over long time as the interface undergoes successive tip splittings and finger competition a second computation shows the formation of a very ramified interface through the interaction of surface tension with an unstable density stratification in euler flows the computation of a vortex sheet shows its roll up through the kelvin helmholtz instability this motion culminates in the late time self intersection of the interface creating trapped bubbles of fluid this is we believe a type of singularity formation previously unobserved for such flows in 2d finally computations of falling plumes in an unstably stratified boussinesq fluid show a very similar behavior

adaptation of nonlinear systems through dynamic entropy estimation we show that adaptation and control of the target system can be achieved by linking the modification of its dynamical properties to the estimated difference of the distribution of the dynamical characteristics of the control and target signals subsequently the target system which has initially different dynamical properties adjusts its dynamics via changes of its control parameters and synchronizes with the control one the differences in the evolving probability distributions are evaluated through entropy estimation causing the adaptation to be based solely on the statistical properties of the control and target signals without explicit knowledge of the underlying equations of the system

simulation of fluidized beds with lattice gas cellular automata this paper introduces an approach for the simulation of the hydrodynamic behaviour of gas solid fluidized beds via the use of lattice gas cellular automata this approach is based on a two speed model developed by u frisch b hasslacher and y pomeau simulation runs for different configurations of the automaton produce results that can be compared to actual data the simulations show when and how bubbling will occur values for the bubble diameters as a function of bed height as well as bed porosities in two horizontal planes have been obtained from the simulations from these results correlation diagrams and the kolmogorov entropy are calculated generally the results of the simulations are qualitatively in good agreement with experimental observations showing that this new approach could provide a useful tool in predicting the fluid dynamic behaviour of fluidized beds

kolmogorov sinai entropy from the ordinal viewpoint abstract in the case of ergodicity much of the structure of a one dimensional time discrete dynamical system is already determined by its ordinal structure we generally discuss this phenomenon by considering the distribution of ordinal patterns which describe the ups and downs in the orbits of a borel measurable map on a borel subset of the real line on this base we give a natural ordinal description of the kolmogorov sinai entropy of one dimensional dynamical systems and relate the kolmogorov sinai entropy to the permutation entropy recently introduced by bandt and pompe

the necessity for a time local dimension in systems with time varying attractors abstract we show that a simple non linear system for ordinary differential equations may possess a time varying attractor dimension this indicates that it is infeasible to characterize eeg and meg time series with a single time global dimension we suggest another measure for the description of non stationary attractors

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

on determining the dimension of chaotic flows abstract we describe a method for determining the approximate fractal dimension of an attractor our technique fits linear subspaces of appropriate dimension to sets of points on the attractor the deviation between points on the attractor and this local linear subspace is analyzed through standard multilinear regression techniques we show how the local dimension of attractors underlying physical phenomena can be measured even when only a single time varying quantity is available for analysis these methods are applied to several dissipative dynamical systems