Practical implementation of nonlinear time series methods: The TISEAN package

doi:10.1063/1.166424

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Practical implementation of nonlinear time series methods: The TISEAN package

Journal Article•DOI•

Practical implementation of nonlinear time series methods: The TISEAN package

Rainer Hegger¹, Holger Kantz¹, Thomas Schreiber¹•Institutions (1)

Max Planck Society¹

30 Sep 1998-arXiv: Chaotic Dynamics-

TL;DR: A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters.

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Abstract: Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena despite the fact that very few natural systems have actually been found to be low dimensional deterministic in the sense of the theory. In order to evaluate the long term usefulness of the nonlinear time series approach as inspired by chaos theory, it will be important that the corresponding methods become more widely accessible. This paper, while not a proper review on nonlinear time series analysis, tries to make a contribution to this process by describing the actual implementation of the algorithms, and their proper usage. Most of the methods require the choice of certain parameters for each specific time series application. We will try to give guidance in this respect. The scope and selection of topics in this article, as well as the implementational choices that have been made, correspond to the contents of the software package TISEAN which is publicly available from this http URL . In fact, this paper can be seen as an extended manual for the TISEAN programs. It fills the gap between the technical documentation and the existing literature, providing the necessary entry points for a more thorough study of the theoretical background.

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Journal Article•DOI•

Surrogate time series

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Thomas Schreiber¹, Andreas Schmitz¹•Institutions (1)

University of Wuppertal¹

15 Aug 2000-Physica D: Nonlinear Phenomena

TL;DR: Specific as well as more general approaches to constrained randomisation, providing a full range of examples, and some implementational aspects of the realisation of these methods in the TISEAN software package are discussed.

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1,556 citations

Journal Article•DOI•

Protein Disorder Prediction: Implications for Structural Proteomics

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Rune Linding¹, Lars Juhl Jensen¹, Francesca Diella, Peer Bork¹, Toby J. Gibson¹, Robert B. Russell¹ - Show less +2 more•Institutions (1)

European Bioinformatics Institute¹

01 Nov 2003-Structure

TL;DR: DisEMBL is a computational tool for prediction of disordered/unstructured regions within a protein sequence that has developed parameters based on several alternative definitions and introduced a new one based on the concept of "hot loops," i.e., coils with high temperature factors.

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1,213 citations

Cites methods from "Practical implementation of nonline..."

...…is performed by an external open Subsequently, all loop regions with B factors below the median for source C module (sav_gol) from the TISEAN 2.1 (Hegger et al., 1999) secondary structure elements were labeled as ordered loops, while Nonlinear Time Series Analysis package…...
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Journal Article•DOI•

Synchronization and rhythmic processes in physiology

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Leon Glass¹•Institutions (1)

McGill University¹

08 Mar 2001-Nature

TL;DR: Molecular and physical techniques combined with physiological and medical studies are addressing questions concerning the dynamics of physiological rhythms and are transforming the understanding of the rhythms of life.

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Abstract: Complex bodily rhythms are ubiquitous in living organisms. These rhythms arise from stochastic, nonlinear biological mechanisms interacting with a fluctuating environment. Disease often leads to alterations from normal to pathological rhythm. Fundamental questions concerning the dynamics of these rhythmic processes abound. For example, what is the origin of physiological rhythms? How do the rhythms interact with each other and the external environment? Can we decode the fluctuations in physiological rhythms to better diagnose human disease? And can we develop better methods to control pathological rhythms? Mathematical and physical techniques combined with physiological and medical studies are addressing these questions and are transforming our understanding of the rhythms of life.

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1,204 citations

Cites background from "Practical implementation of nonline..."

...Likewise, the public availability of powerful data-processing methods should advance researc...
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Journal Article•DOI•

EEG dynamics in patients with Alzheimer's disease

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Jaeseung Jeong¹•Institutions (1)

Korea University¹

01 Jul 2004-Clinical Neurophysiology

TL;DR: EEG abnormalities of AD patients are characterized by slowed mean frequency, less complex activity, and reduced coherences among cortical regions, suggesting that the EEG has utility as a valuable tool for differential and early diagnosis of AD.

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1,100 citations

Cites background from "Practical implementation of nonline..."

...…presented in other technical review articles (Abarbanel and Rabinovich, 2001; Cerutti et al., 1996; Faure and Korn, 2001; Kantz and Schreiber, 1997; Schreiber, 1999), and C-code programs estimating nonlinear measures are available at many websites including one developed by Hegger et al. (1999)....
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Journal Article•DOI•

GlobPlot: exploring protein sequences for globularity and disorder

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Rune Linding¹, Robert B. Russell, Victor Neduva, Toby J. Gibson•Institutions (1)

European Bioinformatics Institute¹

01 Jul 2003-Nucleic Acids Research

TL;DR: A new tool for discovery of unstructured, or disordered regions within proteins, and examples with known proteins where it successfully identifies inter-domain segments containing linear motifs, and also apparently ordered regions that do not contain any recognised domain are presented.

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Abstract: A major challenge in the proteomics and structural genomics era is to predict protein structure and function, including identification of those proteins that are partially or wholly unstructured. Non-globular sequence segments often contain short linear peptide motifs (e.g. SH3-binding sites) which are important for protein function. We present here a new tool for discovery of such unstructured, or disordered regions within proteins. GlobPlot (http://globplot.embl.de) is a web service that allows the user to plot the tendency within the query protein for order/globularity and disorder. We show examples with known proteins where it successfully identifies inter-domain segments containing linear motifs, and also apparently ordered regions that do not contain any recognised domain. GlobPlot may be useful in domain hunting efforts. The plots indicate that instances of known domains may often contain additional N- or C-terminal segments that appear ordered. Thus GlobPlot may be of use in the design of constructs corresponding to globular proteins, as needed for many biochemical studies, particularly structural biology. GlobPlot has a pipeline interface--GlobPipe--for the advanced user to do whole proteome analysis. GlobPlot can also be used as a generic infrastructure package for graphical displaying of any possible propensity.

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988 citations

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References

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Journal Article•DOI•

Numerical recipes

[...]

William H. Press, Saul A. Teukolsky

01 Oct 1990-Computers in Physics

17,845 citations

"Practical implementation of nonline..." refers background in this paper

...The latter is numerically more stable but involves the singular value decomposition of an N ×m matrix for N data points embedded in m dimensions, which can easily exceed computational resources for time series of even moderate length [33]....
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Book Chapter•DOI•

Detecting strange attractors in turbulence

[...]

Floris Takens

01 Jan 1981

9,756 citations

"Practical implementation of nonline..." refers methods in this paper

...Celebrated embedding theorems by Takens [21] and by Sauer et al. [22] state that if the sequence {sn} does indeed consist of scalar measurements of the state of a dynamical system, then under certain genericity assumptions, the time delay embedding provides a one-toone image of the original set {x}, provided m is large enough....
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...Celebrated embedding theorems by Takens [21] and by Sauer et al....
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Journal Article•DOI•

Measuring the Strangeness of Strange Attractors

[...]

Peter Grassberger¹, Peter Grassberger², Itamar Procaccia¹•Institutions (2)

Weizmann Institute of Science¹, University of Wuppertal²

01 Oct 1983-Physica D: Nonlinear Phenomena

TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.

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5,239 citations

Journal Article•DOI•

Ergodic theory of chaos and strange attractors

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Jean-Pierre Eckmann¹, David Ruelle²•Institutions (2)

University of Geneva¹, Institut des Hautes Études Scientifiques²

01 Jul 1985-Reviews of Modern Physics

TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).

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Abstract: Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.

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4,619 citations

"Practical implementation of nonline..." refers background in this paper

...This exponential instability is characterized by the spectrum of Lyapunov exponents [67]....
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...The Hausdorff dimension is, from the mathematical point of view, the most natural concept to characterize fractal sets [67], whereas the information dimension takes into account the relative visitation frequencies and is therefore more attractive for physical systems....
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Journal Article•DOI•

Independent coordinates for strange attractors from mutual information.

[...]

Andrew M. Fraser¹, Harry L. Swinney¹•Institutions (1)

University of Texas at Austin¹

01 Feb 1986-Physical Review A

TL;DR: In this paper, the mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction.

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Abstract: The mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An N logN algorithm for calculating I is presented. As proposed by Shaw, a minimum in I is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function.

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4,160 citations

"Practical implementation of nonline..." refers methods in this paper

...The time delayed mutual information was suggested by Fraser and Swinney [25] as a tool to determine a reasonable delay: Unlike the autocorrelation function, the mutual information takes into account also nonlinear correlations....
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...The adaptive algorithm used in [25] is more data intensive....
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