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

analysis of an adaptive control scheme for a partially observed controlled markov chain the authors consider an adaptive finite state controlled markov chain with partial state information motivated by a class of replacement problems they present parameter estimation techniques based on the information available after actions that reset the state to a known value are taken it is proved that the parameter estimates converge w p 1 to the true unknown parameter under the feedback structure induced by a certainty equivalent adaptive policy it is shown that the adaptive policy is self optimizing in a long run average sense for any measurable sequence of parameter estimates converging w p 1 to the true parameter

pixelwise adaptive blind optical flow assuming nonstationary statistics we address some of the major issues in optical flow within a new framework assuming nonstationary statistics for the motion field and for the errors problems addressed include the preservation of discontinuities model data errors outliers confidence measures and performance evaluation in solving these problems we assume that the statistics of the motion field and the errors are not only spatially varying but also unknown we thus derive a blind adaptive technique based on generalized cross validation for estimating an independent regularization parameter for each pixel our formulation is pixelwise and combines existing first and second order constraints with a new second order temporal constraint we derive a new confidence measure for an adaptive rejection of erroneous and outlying motion vectors and compare our results to other techniques in the literature a new performance measure is also derived for estimating the signal to noise ratio for real sequences when the ground truth is unknown

a new approach to the prediction of passenger flow in a transit system a non linear model is proposed for predicting the rate of passenger flow in a transit system and its chaotic characteristic is observed using wavelets analysis the passenger flow data for a whole day are decomposed in a multi scale way to obtain decomposition sequences subsequently a neural network approach is used to predict the sequences finally the passenger flow value can be predicted when the predicted sequences are reconstructed results show that the present approach is a feasible method for passenger flow prediction

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

optical flow computation using extended constraints several approaches for optical flow estimation use partial differential equations to model changes in image brightness throughout time a commonly used equation is the so called optical flow constraint ofc which assumes that the image brightness is stationary with respect to time more recently a different constraint referred to as the extended optical flow constraint eofc has been introduced which also contains the divergence of the flow field of image brightness there is no agreement in the literature about which of these constraints provides the best estimation of the velocity field two new solutions for optical flow computation are proposed which are based on an approximation of the constraint equations the two techniques have been used with both eofc and ofc constraint equations results achieved by using these solutions have been compared with several well known computational methods for optical flow estimation in different motion conditions estimation errors have also been measured and compared for different types of motion

certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to leqg lqg problems this paper is concerned with partially observed stochastic optimal control problems when nonlinearities enter the dynamics of the unobservable state and the observations as gradients of potential functions explicit representations for the information state are derived in terms of a finite number of sufficient statistics consequently the partially observed problem is recast as one of complete information with a new state generated by a modified version of the kalman filter when the terminal cost is quadratic in the unobservable state and includes the integral of the nonlinearities the optimal control laws are explicitly computed similar to linear exponential quadratic gaussian leqg and linear quadratic gaussian lqg tracking problems the results are applicable to filtering and control of hamiltonian systems

the equivalence between infinite horizon optimal control of stochastic systems with exponential of integral performance index and stochastic differential games a new method based on the theory of large deviations from the invariant measure is introduced for the analysis of stochastic systems with an infinite horizon exponential of integral performance index it is shown that the infinite horizon optimal exponential of integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system as an application of the developed technique the infinite horizon risk sensitive lqg problem is analyzed for both the completely observed and partially observed case

analysis of a risk sensitive control problem for hidden markov chains in this paper the risk sensitive control of partially observed markov decision processes is considered the replacement problem is analyzed in this context and the structure of risk sensitive optimal controllers is given

risk sensitive optimal control of hidden markov models structural results the authors consider a risk sensitive optimal control problem for finite state and action spaces hidden markov models hmm they present results of an investigation on the nature and structure of risk sensitive controllers for hmm several general structural results are presented as well as a particular case study of a popular benchmark problem for the latter they obtain structural results for the optimal risk sensitive controller and compare it to that of the risk neutral controller furthermore they show that indeed the risk sensitive controller and its corresponding information state converge to the known solutions for the risk neutral situation as the risk factor goes to zero they also study the infinite and general risk aversion cases

time series analysis and prediction on complex dynamical behavior observed in a blast furnace abstract this paper describes a strategy for building a predictive model for actual complex time series time series data of temperature fluctuations observed in a blast furnace for iron making are taken as an example chaotic features of the data are investigated with diagnostic algorithm for instability and parallelism of neighboring trajectories in phase space reconstructed from the time series data stationarity of the data is examined with diagnostic algorithm based on the km2o langevin equations developed by okabe a short time series for which no control actions were taken to the plant during measurement is diagnosed as possibly low dimensional chaos while for a long time series including many control actions during measurement determinism is less visible and its predicted behavior exhibits a scaling property similar to self affine random noise characteristic exponents are estimated from the scaling properties of the prediction error as a function of the prediction time interval such information is exploited as prior knowledge for designing a generalized gaussian radial basis function network as a predictor the performance of the network is improved when linear algebraic polynomials are added to the network the characteristic exponents estimated are used as reliability indices of forecasting future trends of the data

risk sensitive control of markov processes in countable state space in this paper we consider infinite horizon risk sensitive control of markov processes with discrete time and denumerable state space this problem is solved by proving under suitable conditions that there exists a bounded solution to the dynamic programming equation the dynamic programming equation is transformed into an isaacs equation for a stochastic game and the vanishing discount method is used to study its solution in addition we prove that the existence conditions are also necessary

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

motion field and optical flow qualitative properties it is shown that the motion field the 2 d vector field which is the perspective projection on the image plane of the 3 d velocity field of a moving scene and the optical flow defined as the estimate of the motion field which can be derived from the first order variation of the image brightness pattern are in general different unless special conditions are satisfied therefore dense optical flow is often ill suited for computing structure from motion and for reconstructing the 3 d velocity field by algorithms which require a locally accurate estimate of the motion field a different use of the optical flow is suggested it is shown that the smoothed optical flow and the motion field can be interpreted as vector fields tangent to flows of planar dynamical systems stable qualitative properties of the motion field which give useful informations about the 3 d velocity field and the 3 d structure of the scene usually can be obtained from the optical flow the idea is supported by results from the theory of structural stability of dynamical systems

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

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

image flow segmentation and estimation by constraint line clustering image flow is the velocity field in the image plane caused by the motion of the observer objects in the scene or apparent motion and can contain discontinuities due to object occlusion in the scene an algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusions is described the constraint line clustering algorithm uses a statistical test to estimate the image flow velocity field in the presence of step discontinuities in the image irradiance or velocity field particular emphasis is placed on motion estimation and segmentation in situations such as random dot patterns where motion is the only cue to segmentation experimental results on a demanding synthetic test case and a real image are presented a smoothing algorithm for improving the velocity field estimate is also described the smoothing algorithm constructs a smooth estimate of the velocity field by approximating a surface between step discontinuities it is noted that the velocity field estimate can be improved using surface reconstruction between velocity field boundaries

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

coarse grained embeddings of time series random walks gaussian random processes and deterministic chaos a new method for studying time series is described based on a statistic indicating the degree to which trajectories passing through a small region of an embedding space are parallel the method is particularly suited to time series with a significant correlation time analytic results are presented for brownian motion and gaussian random processes these are generally different from the results for chaotic systems allowing a test for deterministic dynamics in a time series a variety of examples are presented of the application of the method to low and high dimensional systems

evaluation of nonlinearity and validity of nonlinear modeling for complex time series even if an original time series exhibits nonlinearity it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria therefore we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria through numerical simulations we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model the measures are also robust against observational noises we also analyze some real time series the difference of the number of chickenpox and measles patients the number of sunspots five japanese vowels and the chaotic laser we can confirm that the nonlinear model is effective for the japanese vowel a the difference of the number of measles patients and the chaotic laser

brief risk sensitive and minimax control of discrete time finite state markov decision processes this paper analyzes a connection between risk sensitive and minimax criteria for discrete time finite state markov decision processes mdps we synthesize optimal policies with respect to both criteria both for the finite horizon and the discounted infinite horizon problem a generalized decision making framework is introduced which includes as special cases a number of approaches that have been considered in the literature the framework allows for discounted risk sensitive and minimax formulations leading to stationary optimal policies on the infinite horizon we illustrate our results with a simple machine replacement problem

on a constraint equation for the estimation of displacement rates in image sequences the commonly used constraint equation delta g sup t u g sub t 0 for the estimation of optical flow can only be justified by assumptions that are in general far too restrictive for image sequences of real world scenes b g schunck 1985 86 recently argued that a constraint equation for the estimation of what he called image flow has to include a term containing the divergence of this image flow without presenting however a stringent derivation based on perspective projection from 3 d scene space the present author derives a constraint equation based on a combination of perspective projection and notions from differential geometry in addition he demonstrates the quantitive effects of taking into account radiometric considerations based on the use of lambertian reflection properties and isotropic illumination in scene space

on the relationship between generalization error hypothesis complexity and sample complexity for radial basis functions feedforward networks together with their training algorithms are a class of regression techniques that can be used to learn to perform some task from a set of examples the question of generalization of network performance from a finite training set to unseen data is clearly of crucial importance in this article we first show that the generalization error can be decomposed into two terms the approximation error due to the insufficient representational capacity of a finite sized network and the estimation error due to insufficient information about the target function because of the finite number of samples we then consider the problem of learning functions belonging to certain sobolev spaces with gaussian radial basis functions using the above mentioned decomposition we bound the generalization error in terms of the number of basis functions and number of examples while the bound that we derive is specific for radial basis functions a number of observations deriving from it apply to any approximation technique our result also sheds light on ways to choose an appropriate network architecture for a particular problem and the kinds of problems that can be effectively solved with finite resources i e with a finite number of parameters and finite amounts of data

analysis of optical flow constraints different constraint equations have been proposed in the literature for the derivation of optical flow despite of the large number of papers dealing with computational techniques to estimate optical flow only a few authors have investigated conditions under which these constraints exactly model the velocity field that is the perspective projection on the image plane of the true 3 d velocity these conditions are analyzed under different hypotheses and the departures of the constraint equations in modeling the velocity field are derived for different motion conditions experiments are also presented giving measures of these departures and of the induced errors in the estimation of the velocity field

embedding hmms based models in a euclidean space the topological hidden markov models current extensions of hidden markov models such as structural hierarchical coupled and others have the power to classify complex and highly organized patterns however one of their major limitations is the inability to cope with topology when applied to a visible observation vo sequence the traditional hmm based techniques have difficulty predicting the n dimensional shape formed by the symbols of the vo sequence to fulfill this need we propose a novel paradigm named topological hidden markov models thmms that classifies vo sequences by embedding the nodes of an hmm state transition graph in a euclidean space this is achieved by modeling the noise embedded in the shape generated by the vo sequence we cover the first and second level topological hmms we describe five basic problems that are assigned to a second level topological hidden markov model 1 sequence probability evaluation 2 statistical decoding 3 structural decoding 4 topological decoding and 5 learning to show the significance of this research we have applied the concept of thmms to i predict the ascii class assigned to a handwritten numeral and ii map protein primary structures to their 3d folds the results show that the second level thmms outperform the shmms and the multi class svm classifiers significantly

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