Understanding Nonlinear Dynamics

Kaplan, Daniel T.; Glass, Leon

doi:10.1007/978-1-4612-0823-5

Cited by 525 publications

(270 citation statements)

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“…It can be shown that not all states of the system are equally stable (equally probable to occur) but that some network states, as dictated by the GRN, represent stable steady states, the attractor states, to which the similar ("nearby") states that are not stable will be "attracted" (2). Thus, GRNs exhibit multistability (coexistence of multiple attractors) (3). Stochastic fluctuations caused by molecular noise in gene expression (4)(5)(6) can allow the network to "jump" from attractor to attractor-hence, the latter is actually metastable.…”

mentioning

confidence: 99%

Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape

Wennborg

Aurell

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

111

100

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The observed intercellular heterogeneity within a clonal cell population can be mapped as dynamical states clustered around an attractor point in gene expression space, owing to a balance between homeostatic forces and stochastic fluctuations. These dynamics have led to the cancer cell attractor conceptual model, with implications for both carcinogenesis and new therapeutic concepts. Immortalized and malignant EBV-carrying B-cell lines were used to explore this model and characterize the detailed structure of cell attractors. Any subpopulation selected from a population of cells repopulated the whole original basin of attraction within days to weeks. Cells at the basin edges were unstable and prone to apoptosis. Cells continuously changed states within their own attractor, thus driving the repopulation, as shown by fluorescent dye tracing. Perturbations of key regulatory genes induced a jump to a nearby attractor. Using the Fokker-Planck equation, this cell population behavior could be described as two virtual, opposing influences on the cells: one attracting toward the center and the other promoting diffusion in state space (noise). Transcriptome analysis suggests that these forces result from high-dimensional dynamics of the gene regulatory network. We propose that they can be generalized to all cancer cell populations and represent intrinsic behaviors of tumors, offering a previously unidentified characteristic for studying cancer.cancer cell attractor | cell heterogeneity | edge cells | gene regulatory network | cell population dynamics

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confidence: 99%

Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape

Wennborg

Aurell

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

111

100

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“…the number of active degrees of freedom or invariants, such as the maximal Lyapunov exponent, of a particular system solely by analysing the time course of one of its variables. Thus, the theory of nonlinear time series analysis offers tools that bridge the gap between experimentally observed irregular behaviour and deterministic chaos theory [19][20][21][22]. Although, in this sense, the transition between deterministic chaos theory and the analysis of irregular experimental traces appears smooth, the reality is very different.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear time series analysis of the human electrocardiogram

Perc

2005

Eur. J. Phys.

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We analyse the human electrocardiogram with simple nonlinear time series analysis methods that are appropriate for graduate as well as undergraduate courses. In particular, attention is devoted to the notions of determinism and stationarity in physiological data. We emphasize that methods of nonlinear time series analysis can be successfully applied only if the studied data set originates from a deterministic stationary system. After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, we calculate the maximal Lyapunov exponent, thus providing interesting insights into the dynamics of the human heart. Moreover, to facilitate interest and enable the integration of nonlinear time series analysis methods into the curriculum at an early stage of the educational process, we also provide user-friendly programs for each implemented method.

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“…Fractal-based techniques are global methods that have been successfully applied to estimate the attractor dimension of the underlying dynamic system generating time series [44]. Unless other global methods, they can provide as ID estimation a non-integer value.…”

Section: Fractal-based Methodsmentioning

confidence: 99%

Data dimensionality estimation methods: a survey

Camastra¹

2003

Pattern Recognition

236

172

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In this paper, data dimensionality estimation methods are reviewed. The estimation of the dimensionality of a data set is a classical problem of pattern recognition. There are some good reviews [1] in literature but they do not include more recent developments based on fractal techniques and neural autoassociators. The aim of this paper is to provide an up-to-date survey of the dimensionality estimation methods of a data set, paying special attention to the fractal-based methods.

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Understanding Nonlinear Dynamics

Abstract: Mathematics Subject Classifications (1991): 39xx, 92Bxx, 35xx Library of Congress Cataloging-in-Publication Data Kaplan, Daniel, 1959-Understanding nonlinear dynamics I Daniel Kaplan and Leon Glass. p. cm. -(Texts in applied mathematics; 19) Includes bibliographica1 references and index.

Cited by 525 publications

References 0 publications

Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape

Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape

Nonlinear time series analysis of the human electrocardiogram

Data dimensionality estimation methods: a survey

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