strange nonchaotic attractors with wada basins a b s t r a c t we demonstrate strange nonchaotic attractors with wada basins snaswb and verify the abundance of snaswb in a quasiperiodically forced holmes map we identify the routes to the creation of the snaswb in a two parameter space the snaswb are characterized by the maximal lyapunov exponent by the estimation of the phase sensitivity exponent and by the singular continuous spectra we observe that the snas basins are totally wada basins in a large range of parameters the topological structures of the snas wada basins are distinguished by the basin cell method we investigate the underlying mechanism for the abundance of snaswb which is responsible for different types of basin cell in the absence of forcing this suggests that the snas cannot be predicted reliably for specific initial conditions these snaswb can thus be expected to occur more commonly in dynamical systems

delayed feedback based bifurcation control in an internet congestion model in this paper the control of hopf bifurcation in an internet congestion model with a single link accessed by a single source is presented by choosing the gain parameter as a bifurcation parameter it is found that the system without control cannot guarantee a stationary sending rate furthermore hopf bifurcation occurs when the positive gain parameter of the system exceeds a critical value for internet congestion model a control model based on delayed feedback is proposed and analyzed for delaying the onset of undesirable hopf bifurcation numerical simulations are given to justify the validity of delayed feedback controller in bifurcation control

quasipolynomial generalization of lotka volterra mappings in recent years it has been shown that lotka volterra mappings constitute a valuable tool from both the theoretical and the applied points of view with developments in very diverse fields such as physics population dynamics chemistry and economy the purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism originally conceived for the analysis of ordinary differential equations can be extended into the mapping domain the extension of the formalism into the discrete time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case it will be demonstrated that lotka volterra mappings play a central role in the quasipolynomial formalism for the discrete time case moreover the extension of the formalism into the discrete time domain allows a significant generalization of lotka volterra mappings as well as a whole transfer of algebraic methods into the discrete time context the result is a novel and more general conceptual framework for the understanding of lotka volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of lotka volterra mappings and their generalizations but also for the development of new applications

online segmentation of time series based on polynomial least squares approximations the paper presents swiftseg a novel technique for online time series segmentation and piecewise polynomial representation the segmentation approach is based on a least squares approximation of time series in sliding and or growing time windows utilizing a basis of orthogonal polynomials this allows the definition of fast update steps for the approximating polynomial where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window the coefficients of the orthogonal expansion of the approximating polynomial obtained by means of the update steps can be interpreted as optimal in the least squares sense estimators for average slope curvature change of curvature etc of the signal in the time window considered these coefficients as well as the approximation error may be used in a very intuitive way to define segmentation criteria the properties of swiftseg are evaluated by means of some artificial and real benchmark time series it is compared to three different offline and online techniques to assess its accuracy and runtime it is shown that swiftseg which is suitable for many data streaming applications offers high accuracy at very low computational costs

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

time series k means existing clustering algorithms are weak in extracting smooth subspaces for clustering time series data in this paper we propose a new k means type smooth subspace clustering algorithm named time series k means tskmeans for clustering time series data the proposed tskmeans algorithm can effectively exploit inherent subspace information of a time series data set to enhance clustering performance more specifically the smooth subspaces are represented by weighted time stamps which indicate the relative discriminative power of these time stamps for clustering objects the main contributions of our work include the design of a new objective function to guide the clustering of time series data and the development of novel updating rules for iterative cluster searching with respect to smooth subspaces based on a synthetic data set and five real life data sets our experimental results confirm that the proposed tskmeans algorithm outperforms other state of the art time series clustering algorithms in terms of common performance metrics such as accuracy fscore randindex and normal mutual information

numerics of gram schmidt orthogonalization abstract the gram schmidt gs orthogonalization is one of the fundamental procedures in linear algebra in matrix terms it is equivalent to the factorization a q1r where q1 rm n with orthonormal columns and r upper triangular for the numerical gs factorization of a matrix a two different versions exist usually called classical and modified gram schmidt cgs and mgs although mathematically equivalent these have very different numerical properties this paper surveys the numerical properties of cgs and mgs a key observation is that mgs is numerically equivalent to householder qr factorization of the matrix a augmented by an n n zero matrix on top this can be used to derive bounds on the loss of orthogonality in mgs and to develop a backward stable algorithm based on mgs the use of reorthogonalization and iterated cgs and mgs algorithms are discussed finally block versions of gs are described

kernel decomposition of time frequency distributions bilinear time frequency distributions tfds offer improved time frequency resolution over linear representations but suffer from difficult interpretation higher implementation cost and the lack of associated low cost signal synthesis algorithms in the paper the authors introduce some new tools for the interpretation and quantitative comparison of high resolution tfds these tools are used in related work to define low cost high resolution tfds and to define linear low cost signal synthesis algorithms associated with high resolution tfds first each real valued tfd is associated with a self adjoint linear operator spl psi the spectral representation of spl psi expresses the tfd as a weighted sum of spectrograms sps it is shown that the sp decomposition and weyl correspondence do not yield useful interpretations for high resolution tfds due to the fact that spl psi is not positive

on the optimal choice of a wavelet for signal representation two techniques for finding the discrete orthogonal wavelet of support less than or equal to some given integer that leads to the best approximation to a given finite support signal up to a desired scale are presented the techniques are based on optimizing certain cost functions the first technique consists of minimizing an upper bound that is derived on the l sub 2 norm of error in approximating the signal up to the desired scale it is shown that a solution to the problem of minimizing that bound does exist and it is explained how the constrained minimization over the parameters that define discrete finite support orthogonal wavelets can be turned into an unconstrained one the second technique is based on maximizing an approximation to the norm of the projection of the signal on the space spanned by translates and dilates of the analyzing discrete orthogonal wavelet up to the desired scale both techniques can be implemented much faster than the optimization of the l sub 2 norm of either the approximation to the given signal up to the desired scale or that of the error in that approximation

subspace projection a unified framework for a class of partition based dimension reduction techniques similarity search in high dimensional space is a nontrivial problem due to the so called curse of dimensionality recent techniques such as piecewise aggregate approximation paa segmented means smean and mean standard deviation ms prove to be very effective in reducing data dimensionality by partitioning dimensions into subsets and extracting aggregate values from each dimension subset these partition based techniques have many advantages including very efficient multi phased approximation while being simple to implement they however are not adaptive to the different characteristics of data in diverse applications we propose subspace projection ssp as a unified framework for these partition based techniques ssp projects data onto subspaces and computes a fixed number of salient features with respect to a reference vector a study of the relationships between query selectivity and the corresponding space partitioning schemes uncovers indicators that can be used to predict the performance of the partitioning configuration accordingly we design a greedy algorithm to efficiently determine a good partitioning of the data dimensions the results of our extensive experiments indicate that the proposed method consistently outperforms state of the art techniques

multicavity formations and complexity modulation in a hyperchaotic discrete system abstract this paper introduces a novel and unified approach for controlling the directions and number of cavities of a two dimensional sine icmic modulation map 2d simm two controllers are added to the system for arranging the cavity fluctuations and translating the cavities respectively both the controllers can effectively redesign the dynamics of reproducing cavities in different directions with grid representations the dynamics of the proposed controlled model are investigated with bifurcation lyapunov and fuzzyen algorithms under various cavity formations in different directions a relationship is established for the complexity of the phase space with the directional control and various arrangements of the sinusoidal cavities the proposed model is overall hyperchaotic with the high complexity in the whole parameter plane the proposed scheme is effective for a dynamical model to reproduce the self phase structure in various arrangements for the optimization and modulation of complexity

estimation of intensive quantities in spatio temporal systems from time series abstract we study multivariate time series generated by coupled map lattices exhibiting spatio temporal chaos and investigate to what extent we are able to estimate various intensive measures of the underlying system without explicit knowledge of the system dynamics using the rescaling and interleaving properties of the lyapunov spectrum of systems in a spatio temporally chaotic regime and paying careful attention to errors introduced by sub system boundary effects we develop algorithms that are capable of estimating the lyapunov spectrum from time series we analyse the performance of these and find that the choice of basis used to fit the dynamics is crucial when the local dynamics at a lattice site is well approximated by this basis we are able to accurately determine the full lyapunov spectrum however as the local dynamics moves away from the space spanned by this basis the performance of our algorithm deteriorates

an efficient k nearest neighbor search for multivariate time series multivariate time series mts datasets are common in various multimedia medical and financial applications in order to efficiently perform k nearest neighbor searches for mts datasets we present a similarity measure eros extended frobenius norm an index structure muse multilevel distance based index structure for eros and a feature subset selection technique ropes recursive feature elimination on common principal components for eros eros is based on principal component analysis and computes the similarity between two mts items by measuring how close the corresponding principal components are using the eigenvalues as weights muse constructs each level as a distance based index structure without using the weights up to z levels which are combined at the query time with the weights ropes utilizes both the common principal components and the weights recursively in order to select a subset of features for eros the experimental results show the superiority of our techniques as compared to earlier approaches

oscillatory dynamics induced by time delay in an internet congestion control model with ring topology in this paper an n dimensional congestion control model with ring topology is considered to study delay induced oscillation via the hopf bifurcation the expression of the possible critical delay for the hopf bifurcation is obtained by analyzing the linear part of the system around the equilibrium and verified by the numerical simulation based on the linear analysis the method of multiple scales is employed to obtain the quantitative relation between the delay and the oscillation induced by it the analytical results agree well with those obtained by the numerical method furthermore the effects of other parameters are also studied the discussions reveal that excessive transfer times may cause the oscillation and that increasing the link capacity can control the oscillatory dynamics

dynamic time warping under limited warping path length dynamic time warping dtw is probably the most popular distance measure for time series data because it captures flexible similarities under time distortions however dtw has long been suffering from the pathological alignment problem and most existing solutions which essentially impose rigid constraints on the warping path are likely to miss the correct alignments a crucial observation on pathological alignment is that it always leads to an abnormally large number of links between two sequences based on this new observation we propose a novel variant of dtw called ldtw which limits the total number of links during the optimization process of dtw ldtw not only oppresses the pathological alignment effectively but also allows more flexibilities when measuring similarities it is a softer constraint because we still let the optimization process of dtw decide how many links to allocate to each data point and where to put these links in this paper we introduce the motivation and algorithm of ldtw and we conduct a nearest neighbor classification experiment on ucr time series archive to show its performance

dynamic time warping under pointwise shape context similarity measures are of fundamental importance in time series data mining dynamic time warping dtw is a quite popular measure because it handles time distortions well however dtw has an inherent shortcoming in that dtw can lead to pathological alignments between time series where a single point maps onto a large subsection of another time series to overcome this problem we propose a novel variant of dtw named sc dtw sc dtw employs shape context a rich local shape descriptor to replace the raw observed values considered by conventional dtw the main novelties of sc dtw are 1 it deeply explores both the numerical nature and shape nature of time series and 2 neighborhood information for each point is taken into account sc dtw can generate a more feature to feature alignment between time series and thus serves as a robust similarity measure we test the performance of sc dtw on ucr time series datasets using the one nearest neighbor 1nn classifier compared with other well established methods sc dtw provides better accuracy on 24 of 34 datasets

a multi dimensional indexing approach for timestamped event sequence matching abstract this paper addresses the problem of timestamped event sequence matching a new type of similar sequence matching that retrieves the occurrences of interesting patterns from timestamped sequence databases the sequential scan based method the trie based method and the method based on the iso depth index are well known approaches to this problem in this paper we point out their shortcomings and propose a new method that effectively overcomes these shortcomings the proposed method employs an r tree a widely accepted multi dimensional index structure that efficiently supports timestamped event sequence matching to build the r tree this method extracts time windows from every item in a timestamped event sequence and represents them as rectangles in n dimensional space by considering the first and last occurring times of each event type here n is the total number of disparate event types that may occur in a target application to resolve the dimensionality curse in the case when n is large we suggest an algorithm for reducing the dimensionality by grouping the event types our sequence matching method based on the r tree performs with two steps first it efficiently identifies a small number of candidates by searching the r tree second it picks out true answers from the set of candidates we prove its robustness formally and also show its effectiveness via extensive experiments

the weyl correspondence and time frequency analysis describes the weyl correspondence and its properties showing how it gives a window independent definition of time frequency concentration for use in models in signal detection the definition of concentration is justified by showing that it gives reasonable answers in certain intuitive cases the weyl correspondence expresses a linear transformation as a weighted superposition of time frequency shifts of the signal and then authors explain why this is not the same as transforming a signal into the time frequency domain multiplying by a weight in the transform domain and taking the inverse the investigation into time frequency concentration and the weyl correspondence is justified by a new result the authors show that convolving the wigner distribution with a general smoothing function is equivalent to evaluating a weighted sum of spectrograms this is a new interpretation of the process of smoothing the wigner distribution to reduce cross terms it relates smoothing of the wigner distribution to the multiple window technique pioneered by thomson 1982

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

an efficient qr based method for the computation of lyapunov exponents abstract an efficient and numerically stable method to determine all the lyapunov characteristic exponents of a dynamical system is developed numerical experiments are presented highlighting some aspects of convergence accuracy and efficiency in the computation of the lyapunov characteristic exponents

some phase transitions in coupled map lattices we study finite coupled map lattices of size d 2 with individual maps 0 1 0 1 and constant diffuse coupling for x 2x mod 1 we give sufficient conditions that the coupled system has a continuum of ergodic components in the case d 2 we determine the number of ergodic components for all coupling strengths if is a mixing tent map close to the transition from mixing to a periodic interval with period 2 the uncoupled system is mixing whereas numerical studies suggest that coupling with a suitable strength breaks up the phase space into domains which are interchanged with period 2 in case d 2 we prove this rigorously

piecewise aggregate representations and lower bound distance functions for multivariate time series abstract dimensionality reduction is one of the most important methods to improve the efficiency of the techniques that are applied to the field of multivariate time series data mining due to multivariate time series with the variable based and time based dimensions the reduction techniques must take both of them into consideration to achieve this goal we use a center sequence to represent a multivariate time series so that the new sequence can be seen as a univariate time series thus two sophisticated piecewise aggregate representations including piecewise aggregate approximation and symbolization applied to univariate time series are used to further represent the extended sequence that is derived from the center one furthermore some distance functions are designed to measure the similarity between two representations through being proven by some related mathematical analysis the proposed functions are lower bound on euclidean distance and dynamic time warping in this way false dismissals can be avoided when they are used to index the time series in addition multivariate time series with different lengths can be transformed into the extended sequences with equal length and their corresponding distance functions can measure the similarity between two unequal length multivariate time series the experimental results demonstrate that the proposed methods can reduce the dimensionality and their corresponding distance functions satisfy the lower bound condition which can speed up the calculation of similarity search and indexing in the multivariate time series datasets

stability switches bifurcation and multi stability of coupled networks with time delays abstract this paper reveals the dynamical behaviors of a network consisting of a pair of ring sub networks and two way couplings of neurons between the individual sub networks time delays are introduced into the internal connections within the individual sub networks and the couplings between the individual sub networks the stability and instability of the trivial equilibrium of the network are analyzed and the conditions for the existence of hopf bifurcation are obtained by discussing the associated characteristic equation the criterion for the global stability of the trivial equilibrium of the network is given by constructing a suitable lyapunov functional numerical simulations are performed to validate the theoretical results and rich dynamical behaviors are observed such as multiple stability switches of the network equilibrium synchronous asynchronous oscillations and multi stability

an efficient and stable approach for computation of lyapunov characteristic exponents of continuous dynamical systems this paper proposes a new approach for computing the lyapunov characteristic exponents lces for continuous dynamical systems in an efficient and numerically stable fashion the method is adapted to systems with small dimensions numerical examples illustrating the accuracy of method are presented

a note on the computation of the largest p lces of discrete dynamical systems two efficient and numerically stable methods for the computation of the largest p lyapunov characteristic exponents of an n dimensional discrete dynamical systems are presented the efficiencies of the proposed methods are compared with the efficiencies of other methods through an operation count and illustrated with an example

faster retrieval with a two pass dynamic time warping lower bound the dynamic time warping dtw is a popular similarity measure between time series the dtw fails to satisfy the triangle inequality and its computation requires quadratic time hence to find closest neighbors quickly we use bounding techniques we can avoid most dtw computations with an inexpensive lower bound lb keogh we compare lb keogh with a tighter lower bound lb improved we find that lb improved based search is faster as an example our approach is 2 3 times faster over random walk and shape time series

an experimental comparison of autoregressive and fourier based descriptors in 2d shape classification an experimental comparison of shape classification methods based on autoregressive modeling and fourier descriptors of closed contours is carried out the performance is evaluated using two independent sets of data images of letters and airplanes silhouette contours are extracted from non occluded 2d objects rotated scaled and translated in 3d space several versions of both types of methods are implemented and tested systematically the comparison clearly shows better performance of fourier based methods especially for images containing noise

distance measure with improved lower bound for multivariate time series abstract lower bound function is one of the important techniques used to fast search and index time series data multivariate time series has two aspects of high dimensionality including the time based dimension and the variable based dimension due to the influence of variable based dimension a novel method is proposed to deal with the lower bound distance computation for multivariate time series the proposed method like the traditional ones also reduces the dimensionality of time series in its first step and thus does not directly apply the lower bound function on the multivariate time series the dimensionality reduction is that multivariate time series is reduced to univariate time series denoted as center sequences according to the principle of piecewise aggregate approximation in addition an extended lower bound function is designed to obtain good tightness and fast measure the distance between any two center sequences the experimental results demonstrate that the proposed lower bound function has better tightness and improves the performance of similarity search in multivariate time series datasets

evolutionary compact embedding for large scale image classification effective dimensionality reduction is a classical research area for many large scale analysis tasks in computer vision several recent methods attempt to learn either graph embedding or binary hashing for fast and accurate applications in this paper we propose a novel framework to automatically learn the task specific compact coding called evolutionary compact embedding ece which can be regarded as an optimization algorithm combining genetic programming gp and a boosting trick as an evolutionary computation methodology gp can solve problems inspired by natural evolution without any prior knowledge of the solutions in our evolutionary architecture each bit of ece is iteratively computed using a binary classification function which is generated through gp evolving by jointly minimizing its empirical risk with the adaboost strategy on a training set we address this as greedy optimization leading to small hamming distances for similar samples and large distances for dissimilar samples we then evaluate ece on four image datasets usps digital hand writing cmu pie face cifar 10 tiny image and sun397 scene showing the accurate and robust performance of our method for large scale image classification

quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series we describe methods of estimating the entire lyapunov spectrum of a spatially extended system from multivariate time series observations provided that the coupling in the system is short range the jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions this circumvents the curse of dimensionality that prevents the accurate reconstruction of high dimensional dynamics from observed time series the technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying

robust anatomical correspondence detection by hierarchical sparse graph matching robust anatomical correspondence detection is a key step in many medical image applications such as image registration and motion correction in the computer vision field graph matching techniques have emerged as a powerful approach for correspondence detection by considering potential correspondences as graph nodes graph edges can be used to measure the pairwise agreement between possible correspondences in this paper we present a novel hierarchical graph matching method with sparsity constraint to further augment the power of conventional graph matching methods in establishing anatomical correspondences especially for the cases of large inter subject variations in medical applications specifically we first propose to measure the pairwise agreement between potential correspondences along a sequence of intensity profiles which reduces the ambiguity in correspondence matching we next introduce the concept of sparsity on the fuzziness of correspondences to suppress the distraction from misleading matches which is very important for achieving the accurate one to one correspondences finally we integrate our graph matching method into a hierarchical correspondence matching framework where we use multiple models to deal with the large inter subject anatomical variations and gradually refine the correspondence matching results between the tentatively deformed model images and the underlying subject image evaluations on both synthetic data and public hand x ray images indicate that the proposed hierarchical sparse graph matching method yields the best correspondence matching performance in terms of both accuracy and robustness when compared with several conventional graph matching methods

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

computational explorations into the dynamics of rings of coupled oscillators this paper deals with the response of homogeneous and inhomogeneous rings of coupled oscillators where each individual oscillator when uncoupled from the others is chaotic it is shown that coupling can bring about a wide variety of global responses and that there is a significant range of coupling values when the response of the ring is periodic despite the fact that each oscillator is chaotic in fact numerous periodic solutions can be found depending on the initial conditions the response of a coupled set of homogeneous and non homogeneous rings is also investigated showing that the behavior of such coupled compartmental models can be quite counterintuitive and sensitive to the parameters that describe the extent and nature of coupling

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

feature extraction using a fast null space based linear discriminant analysis algorithm the small sample size problem is often encountered in pattern recognition several algorithms for null space based linear discriminant analysis nlda have been developed to solve the problem however these algorithms for nlda have high computational cost in this paper we simplify the recently proposed algorithm for nlda in chu and thye 2010 5 with the assumption that all the training data vectors are linearly independent and propose a new and fast algorithm for nlda our main observation is that two steps of economic qr decomposition with column pivoting can be replaced by one step of economic qr decomposition without column pivoting if the related matrix is of full column rank the main features of our algorithm for nlda include i our nlda algorithm is carried out by only one step of economic qr decomposition and does not compute any singular value decomposition svd when all the training data vectors are linearly independent ii the main cost of our method is the cost of an economic qr decomposition of an mx n 1 matrix here m is the dimension of the training data and n is the number of samples our method is a fast one experimental studies on orl feret and pie face databases demonstrate the effectiveness of our new algorithm for nlda

characterizing the radar ambiguity functions ambiguity functions are expanded relative to cross ambiguity functions associated with a special orthonormal basis of signal space related to a rectangular pulse the cross ambiguity functions are simply related to the well known ambiguity function of a rectangular pulse the description of ambiguity functions in terms of these well known and interrelated cross ambiguity functions facilitates the ease with which desired calculations can be made indeed one can compute the ambiguity function of a signal as easily as taking the fourier series of a periodic function the characterization of ambiguity functions resulting from this expansion is applied to prove two general results about the set of all ambiguity functions we prove that the set of ambiguity functions is closed on the square integrable topology and that except in a trivial case the sum of two ambiguity functions is never an ambiguity function

automatic construction of correspondences for tubular surfaces statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing such as image segmentation and analysis a challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes especially for shapes of cylindrical topology very little work has been done this paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes the method starts from an initial correspondence which is provided by cylindrical parameterization the quality of the obtained correspondence measured in terms of the description length is then improved by deforming the parameterizations using cylindrical b spline deformations and by optimization of the spatial alignment of the shapes in order to allow efficient gradient guided optimization an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment a comparison is made between models obtained from the correspondences before and after the optimization the results show that in comparison with parameterization based correspondences this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error generalization ability and specificity

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

chaotic attractors in the four dimensional leslie gower competition model abstract we study the occurrence of the chaotic attractor in the four dimensional classical leslie gower competition model we find that chaos can be generated by a cascade of quasiperiod doubling bifurcations starting from a supercritical neimark sacker bifurcation of the positive fixed point in this model the chaotic attractor is contained in the three dimensional carrying simplex that is a globally attracting invariant manifold biologically the result implies that the invasion attempts by an invader into a trimorphic population under the leslie gower dynamics can lead to chaos

multiresolution sequence detection in rapidly fading channels based on focused wavelet decompositions the problem of detecting a sequence using the maximum likelihood strategy when the time varying multipath channel is unknown can be in principle solved using the generalized likelihood detector gld the gld metric involves finding the orthogonal projection of the received signal onto the subspace of the transmitted signal distorted by the multipath channel the faded signal corresponding to one of the transmitted sequences is in fact known to lie in a subspace but its exact location is not known because the channel parameters are unknown this detector which in the case of a static channel collapses to the per survivor processing method is also called a matched subspace detector because its statistic is matched to the a priori known signal subspace unfortunately the computation of the perfectly matched orthogonal projection of the received signal onto the multipath faded signal subspace is in the general time varying case impossible we introduce in this work the idea of using new wavelet based subspaces that approximate the original signal subspace the nested sequence of linear vector spaces defined by a wavelet based multiresolution decomposition of the fading channel time variations provides a set of subspaces that at an increasingly high level of detail are efficient representations of the original signal subspace for each of these representations sequence detection at different levels of resolution can be performed

eigenregions for image classification for certain databases and classification tasks analyzing images based on region features instead of image features results in more accurate classifications we introduce eigenregions which are geometrical features that encompass area location and shape properties of an image region even if the region is spatially incoherent eigenregions are calculated using principal component analysis pca on a database of 77 000 different regions obtained through the segmentation of 13 500 real scene photographic images taken by nonprofessional eigenregions improved the detection of localized image classes by a noticeable amount additionally eigenregions allow us to prove that the largest variance in natural image region geometry is due to its area and not to shape or position

weighted dynamic time warping for time series classification dynamic time warping dtw which finds the minimum path by providing non linear alignments between two time series has been widely used as a distance measure for time series classification and clustering however dtw does not account for the relative importance regarding the phase difference between a reference point and a testing point this may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition therefore we propose a novel distance measure called a weighted dtw wdtw which is a penalty based dtw our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers the rationale underlying the proposed distance measure is demonstrated with some illustrative examples a new weight function called the modified logistic weight function mlwf is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point by applying different weights to adjacent points the proposed algorithm can enhance the detection of similarity between two time series we show that some popular distance measures such as dtw and euclidean distance are special cases of our proposed wdtw measure we extend the proposed idea to other variants of dtw such as derivative dynamic time warping ddtw and propose the weighted version of ddtw we have compared the performances of our proposed procedures with other popular approaches using public data sets available through the ucr time series data mining archive for both time series classification and clustering problems the experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems

lyapunov exponents and transport in the zhang model of self organized criticality we discuss the role played by lyapunov exponents in the dynamics of zhang s model of self organized criticality we show that a large part of the spectrum the slowest modes is associated with energy transport in the lattice in particular we give bounds on the first negative lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time we then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites we use a finite size scaling ansatz for the lyapunov spectrum and relate the scaling exponent to the scaling of quantities such as avalanche size duration density of active sites etc

subxpca and a generalized feature partitioning approach to principal component analysis in this paper we propose a general feature partitioning framework to pca computation and raise issues of cross sub pattern correlation feature ordering dependence selection of sub pattern size overlap of sub patterns and selection of principal components these issues are critical to the design and performance of feature partitioning approaches to pca computation we show several open issues and present a novel algorithm subxpca which proposes a solution to the cross sub pattern correlation issue in the feature partitioning framework subxpca is shown to be a general technique since we derive pca and subpca as special cases of subxpca we show subxpca has theoretically better time complexity as compared to pca comprehensive experimentation on uci repository data and face data sets orl cmu yale confirms the superiority of subxpca with better classification accuracy subxpca not only has better time performance but is also superior in its summarization of variance as compared to subpca subxpca is shown to be robust in its performance with respect to feature ordering and overlapped sub patterns

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

k local hyperplane distance nearest neighbor classifier oriented local discriminant analysis k local hyperplane distance nearest neighbor hknn classifier is an improved k nearest neighbor knn algorithm that has been successfully applied to pattern classification this paper embeds the decision rule of hknn classifier into the discriminant analysis model to develop a new feature extractor the obtained feature extractor is called k local hyperplane distance nearest neighbor classifier oriented local discriminant analysis holda in which a regularization item is imposed on the original hknn algorithm to obtain a more reliable distance metric based on this distance metric the homo class and hetero class local scatters are characterized in holda by maximizing the ratio of the hetero class local scatter to the homo class local scatter we obtain a subspace which is suitable for feature extraction and classification in general this paper provides a framework for building a feature extractor from the decision rule of a classifier by this means the feature extractor and classifier can be seamlessly integrated experimental results on four databases demonstrate that the integrated pattern recognition system is effective

dynamics and the periodic solutions of the delayed non smooth internet tcp red congestion control system via hb aft abstract this paper has attended to obtain the approximate analytical expressions of periodic solutions in the delayed non smooth internet tcp red congestion control system employing the semi analytical method named as the harmonic balance method with alternating frequency time hb aft domain technique for the first time the methodology presented herein provides the accurate approximate analytical expressions of periodic solutions including the non impacting periodic solutions and impacting periodic solutions in the non smooth dynamical system with time delays they agree very well with the results of numerical simulations by matlab it implies that the proposed method in this paper is accurate and effective furthermore rich dynamics of this delayed non smooth system is discovered in the present paper three kinds of bi stability i e coexistence of asymptotically stable equilibrium and equilibrium equilibrium and periodic solution periodic solution and periodic solution have been found in the system with the variation of the delay and the grazing solution the impacting solution traversing both the lower threshold tmin and the larger threshold tmax and a route to chaos i e intermittent to chaos have been also obtained by varying the delay employing numerical method

kolmogorov n widths and wavelet representations for signal classes we address the problem of basis selection and wavelet representations for two important signal classes the ellipsoidal signal class and the bounded cone class we define time frequency concentrated signals in this paper as the class of signals whose wigner distributions are concentrated in some region of the wigner domain we use the concept of the kolmogorov n width and the constrained n width to quantitatively measure the ability of a basis to represent a signal class we select the best wavelet representation by comparing the constrained widths of different wavelet bases explicit formulas are given to compute the kolmogorov n width for both signal models a globally convergent algorithm is proposed to calculate the constrained n width for a given basis

dynamics of coupled nonlinear maps and its application to ecological modeling this paper investigates the behavior of coupled nonlinear dynamical systems we take two such dynamical systems or units couple them together and study the effect of coupling on the dynamics we demonstrate that coupling two chaotic units can indeed stabilize both of them several results describing the global dynamics of the coupled nonlinear system are established using them we show that by and large the presence of coupling appears to increase the orderliness of the coupled system s response producing periodicity synchronicity and quasi symmetry using exponential maps which are commonly used to simulate population dynamics we establish the applicability of our results to population dynamics

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

on line motif detection in time series with swiftmotif this article presents swiftmotif a novel technique for on line motif detection in time series with this technique frequently occurring temporal patterns or anomalies can be discovered for instance the motif detection is based on a fusion of methods from two worlds probabilistic modeling and similarity measurement techniques are combined with extremely fast polynomial least squares approximation techniques a time series is segmented with a data stream segmentation method the segments are modeled by means of normal distributions with time dependent means and constant variances and these models are compared using a divergence measure for probability densities then using suitable clustering algorithms based on these similarity measures motifs may be defined the fast time series segmentation and modeling techniques then allow for an on line detection of previously defined motifs in new time series with very low run times swiftmotif is suitable for real time applications accounts for the uncertainty associated with the occurrence of certain motifs e g due to noise and considers local variability i e uniform scaling in the time domain this article focuses on the mathematical foundations and the demonstration of properties of swiftmotif in particular accuracy and run time using some artificial and real benchmark time series

boundary based lower bound functions for dynamic time warping and their indexing dynamic time warping dtw is a powerful technique in the time series similarity search however its performance on large scale data is unsatisfactory because of its high computational cost and the fact that it cannot be indexed directly the lower bound technique for dtw is an effective solution to this problem in this paper we explain the existing lower bound functions from a unified perspective and show that they are only special cases under our framework we then propose a group of lower bound functions for dtw and compare their performances through extensive experiments the experimental results show that the new methods are better than the existing ones in most cases and a theoretical explanation of the results is also given we further implement an index structure based on the new lower bound function experimental results demonstrate a similar conclusion

focused detection via multiresolution analysis in many applications there are strong discrepancies between the signal models assumed in the design phase and the actual signals encountered in the field these discrepancies penalize significantly the performance of the matched filter that is fine tuned to the preassumed conditions we propose a geometric framework that designs via wavelet multiresolution based techniques a receiver whose performance is to a large degree insensitive to these mismatches we say that the receiver is a focused detector the approach defines a signal set s that identifies the class of diverse conditions that are expected to arise we illustrate the method in the context of multipath problems the matched filter which is a simple receiver assumes that s is a singleton when this is not the case the matched filter experiences strong degradation on the other hand the optimal receiver for the signal set s is practically infeasible since it requires a multidimensional nonlinear optimization the paper designs the focused receiver as a good compromise between these two extremes we replace the signal set s by a linear subspace g the representation subspace that minimizes a measure of similarity with s we choose g to be a multiresolution subspace this choice resolves to satisfaction several issues the subspace design is reduced to the design of a single shiftable scaling function the similarity between s and g can be computed explicitly and the focused receiver that computes the energy of the orthogonal projection on g is implemented by a bank of correlators matched to scaled delayed versions of the reshaped scaling function followed by an energy detector we assume that the transmitted signal is a sample of a random process the signal set s becomes an ensemble of linear spaces we introduce the modified deflection as the appropriate similarity measure the paper details our algorithm describes how to compute the modified deflection and illustrates the performance results that can be obtained

performance analysis of a class of transient detection algorithms a unified framework the detection of short duration nonstationary signals which are commonly referred to as transients is often performed in the time frequency transform domain an analytical framework within which the performance of different detectors based on linear transforms can be easily compared for different classes of signals is developed a given class of transients is modeled as a signal existing in a linear subspace plus a mismatch signal closed form expressions are derived for the best and the worst detection performance for all possible transients in a given class using this framework the performance of detectors based on the gabor transform and on the short time fourier transform is evaluated and compared

a hyperplane based indexing technique for high dimensional data in this paper we propose a novel hyperplane based indexing method to support efficient processing of similarity search queries in high dimensional spaces the main idea of the proposed index is to improve data partitioning efficiency in a high dimensional space by using a hyperplane which further partitions a subspace and can also take advantage of the twin node concept used in the key dimension based index compared with the key dimension concept the hyperplane is more effective in data filtering high space utilization is achieved by dynamically performing data reallocation between twin nodes in addition a post processing step is used after index building to ensure effective filtration extensive experiments based on two types of real data sets are conducted and the results illustrate a significantly improved filtering efficiency because of the feature of hyperplane the proposed indexing method is only suitable to euclidean spaces

routes to chaos in high dimensional dynamical systems a qualitative numerical study this paper examines the most probable route to chaos a high dimensional dynamical systems function space time delay neural networks endowed with a probability measure in a computational setting the most probable route to chaos relative to the measure we impose on the function space as the dimension is increased is observed to be a sequence of neimark sacker bifurcations into chaos the analysis is composed of the study of an example dynamical system followed by a probabilistic study of the ensemble of dynamical systems from which the example was drawn a scenario depicting the decoupling of the stable manifolds of the torus leading up to the onset of chaos in high dimensional dissipative dynamical systems is also presented c 2006 elsevier b v all rights reserved

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

fuzzy clustering of time series in the frequency domain traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated hence in order to cluster time series data which are usually serially correlated one needs to extract features from the time series the values of which are uncorrelated the periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated additionally the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used in this paper we consider a fuzzy clustering approach for time series based on the estimated cepstrum the cepstrum is the spectrum of the logarithm of the spectral density function we show in our simulation studies for the typical generating processes that have been considered fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features

local bifurcation analysis of some dual congestion control algorithms we perform the necessary calculations to determine the stability and asymptotic forms of solutions bifurcating from steady state in a nonlinear delay differential equation with a single discrete delay the results are used to examine the loss of local stability in a selection of congestion control algorithms employed over a single link in particular we analyze the fair and the delay based dual algorithms explicit conditions are derived to ensure the onset of stable limit cycles as these algorithms just lose local stability further we are able to quantify the effect parameters of the system have on the amplitude of the bifurcating periodic solutions

automatic construction of parts geometry models for initializing groupwise registration groupwise nonrigid image registration is a powerful tool to automatically establish correspondences across sets of images such correspondences are widely used for constructing statistical models of shape and appearance as existing techniques usually treat registration as an optimization problem a good initialization is required although the standard initialization affine transformation generally works well it is often inadequate when registering images of complex structures in this paper we present a more sophisticated method that uses the sparse matches of a parts geometry model as the initialization we show that both the model and its matches can be automatically obtained and that the matches are able to effectively initialize a groupwise nonrigid registration algorithm leading to accurate dense correspondences we also show that the dense mesh models constructed during the groupwise registration process can be used to accurately annotate new images we demonstrate the efficacy of the approach on three datasets of increasing difficulty and report on a detailed quantitative evaluation of its performance

adaptive nonlinear manifolds and their applications to pattern recognition dimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps multisensory information is processed fused and mapped to an essentially 2 d cortex in an information preserving manner data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition computational intelligence data mining information retrieval and image recognition dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields the topic of manifold learning has recently attracted a great deal of attention and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics geometry theory and adaptive neural networks this paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self organizing map som kernel pca principal manifold isomap local linear embedding and laplacian eigenmap many of them can be considered in a learning manifold framework the paper further elaborates on the biologically inspired som model and its metric preserving variant visom under the framework of adaptive manifold and their applications in dimensionality reduction with face recognition are investigated the experiments demonstrate that adaptive visom based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold

radial basis function approach to nonlinear granger causality of time series we consider an extension of granger causality to nonlinear bivariate time series in this frame if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one not all the nonlinear prediction schemes are suitable to evaluate causality indeed not all of them allow one to quantify how much knowledge of the other time series counts to improve prediction error we present an approach with bivariate time series modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally coupled chaotic maps and to physiological examples

a new separation measure for improving the effectiveness of validity indices many validity indices have been proposed for quantitatively assessing the performance of clustering algorithms one limitation of existing indices is their lack of generalizability due to their dependence on the specific algorithms and structures of the data space to handle large scale datasets with arbitrary structures this research study proposes a new cluster separation measure for improving the effectiveness of existing validity indices this is achieved by partitioning the original data space into a grid based structure which allows the introduction of a new measurement for assessing the true data distribution between any two clusters instead of the distance between the two cluster prototypes to validate the effectiveness of the proposed separation measure we adopt two commonly used validity indices the davies bouldin s function db and tibshirani s gap statistic gs these indices are denoted as r db 1 and r gs 1 for clusters with sphere shaped structures and r db 2 and r gs 2 for irregular shaped structures this integration enables the indices to evaluate both partitional algorithms and hierarchical algorithms partitional algorithms including c means cm fuzzy c means fcm and hierarchical algorithms including dbscan and clique are used to test the performance of the new indices two synthetic datasets with spherical structures and four synthetic datasets with irregular shapes are first compared five real datasets from the uci machine learning repository are then used to further test the measure s performance the experimental results provide evidence that the new indices outperform the original indices

kernel class wise locality preserving projection in the recent years the pattern recognition community paid more attention to a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel local structure based feature extraction method called class wise locality preserving projection clpp clpp utilizes class information to guide the procedure of feature extraction in clpp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper moreover a kernel version of clpp namely kernel clpp kclpp is developed through applying the kernel trick to clpp to increase its performance on nonlinear feature extraction experiments on orl face database and yale face database are performed to test and evaluate the proposed algorithm

stability and hopf bifurcation analysis on a ring of four neurons with delays we consider a four neuron ring with self feedback and delays by analyzing the associated characteristic equation linear stability is investigated and hopf bifurcations are demonstrated as well as the stability and direction of the hopf bifurcation are determined by employing the normal form method and the center manifold reduction numerical simulations are presented to illustrate the results

semisupervised multiview distance metric learning for cartoon synthesis in image processing cartoon character classification retrieval and synthesis are critical so that cartoonists can effectively and efficiently make cartoons by reusing existing cartoon data to successfully achieve these tasks it is essential to extract visual features that comprehensively represent cartoon characters and to construct an accurate distance metric to precisely measure the dissimilarities between cartoon characters in this paper we introduce three visual features color histogram shape context and skeleton to characterize the color shape and action respectively of a cartoon character these three features are complementary to each other and each feature set is regarded as a single view however it is improper to concatenate these three features into a long vector because they have different physical properties and simply concatenating them into a high dimensional feature vector will suffer from the so called curse of dimensionality hence we propose a semisupervised multiview distance metric learning ssm dml ssm dml learns the multiview distance metrics from multiple feature sets and from the labels of unlabeled cartoon characters simultaneously under the umbrella of graph based semisupervised learning ssm dml discovers complementary characteristics of different feature sets through an alternating optimization based iterative algorithm therefore ssm dml can simultaneously accomplish cartoon character classification and dissimilarity measurement on the basis of ssm dml we develop a novel system that composes the modules of multiview cartoon character classification multiview graph based cartoon synthesis and multiview retrieval based cartoon synthesis experimental evaluations based on the three modules suggest the effectiveness of ssm dml in cartoon applications

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

a novel document similarity measure based on earth mover s distance in this paper we propose a novel measure based on the earth mover s distance emd to evaluate document similarity by allowing many to many matching between subtopics first each document is decomposed into a set of subtopics and then the emd is employed to evaluate the similarity between two sets of subtopics for two documents by solving the transportation problem the proposed measure is an improvement of the previous om based measure which allows only one to one matching between subtopics experiments have been performed on the tdt3 dataset to evaluate existing similarity measures and the results show that the emd based measure outperforms the optimal matching om based measure and all other measures in addition to the texttiling algorithm the sentence clustering algorithm is adopted for document decomposition and the experimental results show that the proposed emd based measure does not rely on the document decomposition algorithm and thus it is more robust than the om based measure