CCSR Technical Reports, 1988-89

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Technical Reports: 1989

Technical Reports: 1988

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CCSR Technical Reports,
with Abstracts: 1988-89

Technical Reports, with Abstracts: 1989

W. Li, Mutual Information Functions Versus Correlation Functions, Technical Report CCSR-89-1

Abstract: Mutual information functions M(d) can be used to analyze temporal or spatial sequences. Many aspects of M(d) are studied in this paper, especially in comparison with the more frequently used correlation function Γ(d). For binary sequences, a general relation between site-to-site M(d) and Γ(d) has been derived. Several block-to-block M(d) of sequences produced by some dynamical rules are numerically calculated. Also included is the estimation of errors in the numerical calculation of M(d) due to finite sequence lenghts. It is advocated that M(d) should be the quantity to use in analyzing symbolic sequences, such as language texts. The possibility of having symbolic 1/ f noise in English texts is discussed. Reprint
G. Mayer-Kress, A. Hübler, Time Evolution of Local Complexity Measures and Aperiodic Pertubations of Nonlinear Dynamical Systems, Technical Report CCSR-89-2

Abtract: We discuss numerical algorithms for estimating dimensional complexity of an observed time-series with special emphasis on biological and medical applications. Factors which enter the procedure are discussed and applied to a local estimate of the pointwise dimension or crowding index. We illustrate the concepts with the help of experimental time-series obtained from speech signals. The temporal evolution of the crowding index shows oscillations which can be correlated with properties of the time-series. We compare the time evolution of the dimensional complexity parameter with the original time-series and also with recurrence plots of the embedded time-series.
Besides the analysis of spontaneous activity of biological systems it is often more useful to study event related potentials. We have generalized our analysis code in a way that attractors can also be reconstructed from such non contiguous signals. Finally we discuss the possibility of nonlinear, aperiodic stimulation of nonlinear and chaotic systems as a method for very selective excitations of specific nonlinear modes. We discuss possible applications of this method to habituation phenomena and diagnostic use in connection with event-related potentials. Reprint
D. Bensen, M. Welge, A. Hübler, N. Packard, Characterization of Complex Systems by Aperiodic Driving Forces , Technical Report CCSR-89-3

Abtract: The response of a complex system is usually very complicated if it is pertubed by a sinusiodal driving force. We show, however, that for every complex system there is a special aperiodic driving force which produces a simple response. This special driving force is related to a certain nonlinear differential equation. We propose to use the parameters of this differential equation to describe the complexity of the system. Reprint
T. Meyer, A. Hübler, N. Packard, Reduction of Complexity by Optimal Driving Forces , Technical Report CCSR-89-4

Abtract: In general nonlinear waves are not stable in a chain of finite length. Since they have a finite lifetime, it is important to investigate the production of nonlinear waves, e.g. the production of solitons. A general feature of nonlinear waves is the amplitude frequency coupling, which causes the excitation by sinusoidal driving forces to be very inefficient. The response is usually very complex in addition. We present a method to calculate special aperiodic driving forces, which generates nonlinear waves very efficiently. The response to these driving forces is very simple. Reprint
K. Chang, A. Hübler, N. Packard, Universal Properties of the Resonance Curve of Complex Systems , Technical Report CCSR-89-5

Abtract: The dynamics of a large variety of complex systems are confined to a low-dimensional manifold. We show that the resonance curve of those systems has a universal shape. The parameters of the resonance curve can be used to characterize a complex system. Reprint
T. Eisenhammer, A. Hübler, T. Geisel, E. Lüscher, Scaling Behavior of the Maximum Energy Exchange Between Coupled Anharmonic Oscillators , Technical Report CCSR-89-6

Abtract: The maximum energy exchange of two harmonically coupled nonlinear oscillators is investigated. We calculate the maximum energy exchange close to resonance and show that the corresponding resonance curves have a universal shape and become broader and smaller when the amplitude-frequency coupling becomes large. Since there is a large variety of nonlinear oscillators where the trajectories are nearly homothetic curves in a phase space representation, we furthermore investigate the special situation where the oscillators are homothetic. We argue that in this case there is a scaling of the maximum energy exchange at resonance. Numerical investigations show that these relations remain valid if the oscillators are slightly damped or pertubed by random noise. Reprint
T. Eisenhammer, A. Hübler, N. Packard, J.A.S. Kelso, Modeling Experimental Time Series with Ordinary Differential Equations , Technical Report CCSR-89-7

Abtract: Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with sufficient long transient trajectory and relatively low noise level. Reprint
W. Li, N. Packard, The Structure of the Elemenatary Cellular Automata Rule Space , Technical Report CCSR-89-8

Abtract: The structure of the elementary cellular automata rule space is investigated. The probabilities for a rule to be connected to other rules in the same class, as well as rules in different classes, are determined. The intra-class connection probabilities vary from around 0.3 to 0.5, an indication of the strong tendency for rules with the similar behavior to be next to each other. Rules are also grouped according to the mean-field descriptions. The mean-field clusters are classified into three classes (non-linear, linear and inversely-linear) according to the "hot bits" in the rule table. It is shown that such classification provides another easy to describe the rule space. Reprint
W. Li, Problems in Complex Systems , Technical Report CCSR-89-9

Abtract: Five separate problems concerning nonlinear complex systems are studied in this thesis. Three of them concern studies of dynamical systems with spatial degrees of freedom and the remaining two concern dynamical systems in lower dimensions. The problems studied are (1) the spectra of regular languages with application to cellular automata, (2) the spectra of context-free languages and 1/f noise in open dynamical systems, (3) the structure of celllular automata rule spaces, (4) fractal dimension of Cantori, and (5) stabilizing and destabilizing effects of weighted time delay. Reprint
N. Packard, A Genetic Learning Algorithm for the Analysis of Complex Data , Technical Report CCSR-89-10

Abtract: A genetic learning algorithm modeled after biological evolution is presented to discern patterns relating one observable that is taken to be dependent on many others. The problem is reduced to to an optimization procedure over a space of conditions on the independent variables. The optimization is performed by a genetic learning algorithm, using an information theoretic fitness function on conditional probability distributions, all derived from data that has a very sparse distribution over a very high dimensional space. We will discuss applications in forecasting, management, weather, neuroanalysis, large scale modeling, and other areas. Reprint
B. Mel, MURPHY: A Neurally-Inspired Connectionist Approach to Learning and Performance in Vision-based Robot Motion Planning, Technical Report CCSR-89-17A

Abtract: Many aspects of intelligent animal behavior require an understanding of the complex spatial relationships between the body and its parts and the coordinate systems of the external world. This thesis deals specifically with the problem of guiding a multi-link arm to a visual target in the presence of obstacles. A simple vision-based kinematic controller and motion planner based on a connectionist network architecture has been developed, called MURPHY. The physical setup consists of a video camera and a Rhino XR-3 robot arm with three joints that move in the image plane of the camera. We assume no a priori model of arm kinematics or of the imaging characteristics of the camera/visual system, and no sophisticated built-in algorithms for obstacle avoidance. Instead, MURPHY builds a model of his arm through a combination of physical and "mental" practice, and then uses simple heuristic search with mental images of his arm to solve visually-guided reaching problems in the presence of obstacles whose traditional algorithmic solutions are extremely complex. MURPHY differs from previous approaches to robot motion-planning primarily in his use of an explicit full-visual-field representation of the workspace. Several other aspects of MURPHY's design are unusual, including the sigma-pi synaptic learning rule, the teacherless training paradigm, and the integration of sequential control within an otherwise connectionist architecture. In concluding sections we outline a series of strong correspondences between the representations and algorithms used by MURPHY, and the psychology, physiology, and neural bases for the programming and control of directed, voluntary arm movements in humans and animals. Reprint

Technical Reports, 1988

Gerald Tesauro, Robert Janssens, Scaling Relationships in Back-propagation Learning: Dependence on Predicate Order , Technical Report CCSR-88-01 Reprint
Wentian Li, Context-free Languages Can Give 1/f Spectra , Technical Report CCSR-88-10 Reprint
Norman H. Packard, Intrinsic Adaptation in a Simple Model of Evolution , July 18, 1988, in Artificial Life, ed. C. Langton, Addison-Wesley (1989), Technical Report CCSR-88-11 Reprint
Norman H. Packard, Dynamics of Development: A Simple Model for Dynmaics away from Attractors , Technical Report CCSR-88-12 Reprint
Subutai Ahmad A Study of Scaling and Generalization in Neural Networks , Sept 1988, Technical Report CCSR-88-13 Reprint

CCSR Technical Reports,with Abstracts: 1988-89

Technical Reports, with Abstracts: 1989

Technical Reports, 1988

CCSR Technical Reports,
with Abstracts: 1988-89