The computer program pret automatically constructs mathematical models of physical systems. A critical part of this task is automating the processing of sensor data. pret's intelligent data analyzer uses geometric reasoning to infer qualitative information from quantitative data; if critical variables are either unknown or cannot be measured, it uses delay-coordinate embedding to reconstruct the internal dynamics from the external sensor measurements. Successful modeling results for two sensor-equipped systems, a driven pendulum and a radio-controlled car, demonstrate the effectiveness of these techniques.

onfirm the integer values. These integers can be used to determine whether or not two dynamical systems are equivalent; in particular, they can determine whether a model developed from time-series data is an accurate representation of a physical system. Conversely, these integers can be used to provide a model for the dynamical mechanisms that generate chaotic data. In fact, the author has constructed a doubly discrete classification of strange attractors. The underlying branched manifold provides one discrete classification. Each branched manifold has an "unfolding" or perturbation in which some subset of orbits is removed. The remaining orbits are determined by a basis set of orbits that forces the presence of all remaining orbits. Branched manifolds and basis sets of orbits provide this doubly discrete classification of strange attractors. In this review the author describes the steps that have been developed to implement the topological-analysis procedure. In addition, th

In this chapter, I review the main methods and techniques of complex systems science. As a

Standard generative linguistic theory, which uses discrete symbolic models of cognition, has some strengths and weaknesses. It is strong on providing a network of outposts that make scientific travel in the jungles of natural language feasible. It is weak in that it currently depends on the elaborate and unformalized use of intuition to develop critical supporting assumptions about each data point. In this regard, it is not in a position to characterize natural language systems in the lawful terms that ecological psychologists strive for. Connectionist learning models offer some help: They define lawful relations between linguistic environments and language systems. But our understanding of them is currently weak, especially when it comes to natural language syntax. Fortunately, symbolic linguistic analysis can help connectionism if the two meet via dynamical systems theory. I discuss a case in point: Insights from linguistic explorations of natural language syntax appear to have identified information structures that are particularly relevant to understanding ecologically appealing but analytically mysterious connectionist learning models. This article is concerned with the relation between discrete, symbolic systems of the

Quantitative descriptions of a physical system’s behaviour form the backbone of the scientific method used in the natural sciences. They allow the principled determination of experimental parameters, a clear and unambiguous representation of experiments, and independent replication and verification of experimental results. In mobile robotics to date, quantitative descriptions of robot-environment interaction remain the exception, chiefly due to the lack of those descriptions. Instead, qualitative descriptions of experiments and existence proofs (i.e. unvalidated experimental results) are the norm. This paper discusses this problem, and presents a novel method of describing robot-environment interaction quantitatively — a first step towards scientific mobile robotics. The application of this novel method is illustrated on an example taken from mobile robotics: the comparison between a Nomad 200 mobile robot and its computer model.

A simple method for fitting differential equations to multi–wave panel data performs remarkably well in recovering parameters from underlying continuous models with as few as three waves of data. Two techniques for fitting models of intrinsic dynamics to intraindividual variability data are examined by testing these techniques ’ behavior in recovering the parameters from data generated by two simulated systems of differential equations. Each simulated data set contains 100 “subjects ” each of whom are measured at only three points in time. A local linear approximation of the first and second derivatives of the subject’s data accurately recovers the true parameters of each simulation. A state–space embedding technique for estimating the first and second derivatives does not recover the parameters as well. An optimum sampling interval can be estimated for this model as that interval at which multiple R 2 first nears its asymptotic value.

Motivated by the problem of the definition of a distance between two sequences of characters, we investigate the so-called learning process of a typical sequential data compression schemes. We focus on the problem of how a compression algorithm optimizes its features at the interface between two different sequences A and B while zipping the sequence A B obtained by simply appending B after A. We show the existence of a scaling function (the "learning function") which rules the way in which the compression algorithm learns a sequence B after having compressed a sequence A. In particular it turns out that there exists a cross-over length for the sequence B, which depends on the relative entropy between A and B, below which the compression algorithm does not learn the sequence B (measuring in this way the cross-entropy between A and B) and above which it starts learning B, i.e. optimizing the compression using the specific features of B. We check the scaling on three main classes of systems: Bernoulli schemes, Markovian sequences and the symbolic dynamic generated by a nontrivial chaotic system (the Lozi map). As a last application of the method we present the results of a recognition experiment, namely recognize which dynamical systems produced a given time sequence. We finally point out the potentiality of these results for segmentation purposes, i.e. the identification of homogeneous sub-sequences in heterogeneous sequences (with applications in various fields from genetic to time-series analysis).

A new framework for analyzing time series data called Time Series Data Mining (TSDM) is introduced. This framework adapts and innovates data mining concepts to analyzing time series data. In particular, it creates methods that reveal hidden temporal patterns that are characteristic and predictive of time series events. The TSDM framework, concepts, and methods, which use a genetic algorithm to search for optimal temporal patterns, are explained and the results are applied to real-world time series from the engineering and financial domains.

this paper (Mathematical Reviews:29 #648) with the words "This is a profound memoir." 9 will show in Chapter 3, there are simple algorithms for bounding the Lyapunov exponents in this setting. The advanced state of the theory for random matrix products is a peculiar situation because deterministic matrix products that govern sensitive dependence on initial conditions are barely understood; it is as if the strong law of large numbers were well understood without a satisfactory theory of convergence of infinite series. The elements of the theory of random matrix products are carefully explained in the beautiful monograph by Bougerol [16]. The basic result about Lyapunov exponents, lim

. The problem of extracting a signal xn from a noise-corrupted time series yn = xn + en is considered. The signal xn is assumed to be generated by a discrete-time, deterministic, chaotic dynamical system F -- in particular, xn = F n (x0 ), where the initial point x0 is assumed to lie in a compact hyperbolic F \Gammainvariant set. It is shown that (1) if the noise sequence en is gaussian then it is impossible to consistently recover the signal xn , but (2) if the noise sequence consists of i.i.d. random vectors uniformly bounded by a constant ffi ? 0, then it is possible to recover the signal xn provided ffi ! 5\Delta, where \Delta is a separation threshold for F . A filtering algorithm for the latter situation is presented. 1. Introduction Physical and numerical experiments carried out over the past 30+ years suggest that the phenomenon of deterministic chaos is ubiquitous in physical systems. Experience has shown that inference of the mathematical objects (the differential equati...