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REVIEW ARTICLE: Dissipative systems
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This article is published in Reports on Progress in Physics.The article was published on 1986-08-01. It has received 55 citations till now. The article focuses on the topics: Boolean algebra & Dissipative system.read more
Citations
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Non-genetic heterogeneity of cells in development: more than just noise.
TL;DR: This Primer attempts to clarify the confusing terminologies used in an emerging field that often conflates heterogeneity with noise, and provides a qualitative introduction to the fundamental dynamic principles that underlie heterogeneity.
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Reprogramming cell fates: reconciling rarity with robustness.
Sui Huang,Sui Huang +1 more
TL;DR: A pedagogical primer to the fundamental principles of gene regulatory networks as integrated dynamic systems as well as recent insights in gene expression noise and fate determination are provided, thereby offering a formal framework that may help to understand why cell fate reprogramming events are inherently rare and yet so robust.
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The Molecular and Mathematical Basis of Waddington's Epigenetic Landscape: A Framework for post-Darwinian Biology?
TL;DR: The Neo‐Darwinian concept of natural selection is plausible when one assumes a straightforward causation of phenotype by genotype, but such simple 1:1 mapping must now give place to the modern concepts of gene regulatory networks and gene expression noise.
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The Potential Landscape of Genetic Circuits Imposes the Arrow of Time in Stem Cell Differentiation
TL;DR: The quasipotential landscape of the stochastic dynamics of a canonical gene circuit that governs branching cell fate commitment is computed and reveals the global dynamics and permits the calculation of potential barriers between cell phenotypes imposed by the circuit architecture.
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Quasi-potential landscape in complex multi-stable systems
Joseph X. Zhou,Joseph X. Zhou,Joseph X. Zhou,M. D. S. Aliyu,Erik Aurell,Erik Aurell,Sui Huang,Sui Huang,Sui Huang +8 more
TL;DR: An overview of currently available methods, their limitations and a new decomposition of vector fields that permits the computation of a quasi-potential function that is equivalent to the Freidlin–Wentzell potential but is not limited to two attractors are presented.
References
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Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
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Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
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Reciprocal Relations in Irreversible Processes. II.
TL;DR: In this article, a general reciprocal relation applicable to transport processes such as the conduction of heat and electricity, and diffusion, is derived from the assumption of microscopic reversibility, and certain average products of fluctuations are considered.
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Characterization of Strange Attractors
TL;DR: In this article, a measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable, and the relation of this measure to fractal dimension and information-theoretic entropy is discussed.