The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Phase transitions in random networks: Simple analytic determination of critical points
Abstract
The standard method for determining the critical points in random networks (such as Boolean nets) is based on the Derrida approximation. This method leads to the critical points based on the so-called annealed approximation. In this paper, we present a very simple annealed approximation based on the study of damage spreading when single elements are modified. Several examples are analyzed.
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“Interestingly, the basic McCulloch–Pitts design is common to many other living systems, including gene regulatory networks [256–259], immune networks [260–262], collective intelligence [263–267] or some aneural systems, such as quorum-sensing decisions in microbial communities, where an explicit equivalence has been defined [268].”
From Fundamental constraints to the logic of living systems (2024) · cites this paper as [258]
Citations
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Random Networks of Automata: A Simple Annealed Approximation
Derrida, B., & Pomeau, Y. (1986) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/1/2/001 · Cited by 688
The Theory of Critical Phenomena: An Introduction to the Renormalization Group
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Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation
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Emergent properties in random complex automata
Kauffman, S. A. (1984) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(84)90257-4 · Cited by 256
The large scale structure and dynamics of gene control circuits
Kauffman, S. (1974) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(74)80037-8 · Cited by 232
Phase Transitions in Two-Dimensional Kauffman Cellular Automata
Derrida, B., & Stauffer, D. (1986) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/2/10/001 · Cited by 214
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- S. A. Kauffman, 1995, At Home in the Universe
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Raginsky, M. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0311045
Dynamical systems analysis of stack filtersPreprint
Nykter, M., Kesseli, J., & Ilya Shmulevich, C. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0907.4551
Dynamics and evolution of random Boolean networks
Mihaljev, T. (2008) · Technischen Universität Darmstadt · doi:10.26083/tuprints-00001188
Signal processing methods and information approach to systems biology
Nykter, M. (2006) · Tampere University Institutional Repository (Tampere University)
Chaos Control in Random Boolean Networks by Reducing Mean Damage Percolation Rate
Jiang, N., & Chen, S.-J. (2011) · Chinese Physics Letters · doi:10.1088/0256-307x/28/4/040504
Haruna, T., & Tanaka, S. (2014) · Conference on Artificial Life (ALIFE) · doi:10.1162/978-0-262-32621-6-ch068
Polacek, G. A., Verma, D., & Yang, S. Y. (2016) · INCOSE International Symposium · doi:10.1002/j.2334-5837.2016.00242.x
Reliability and Evolvability of Genetic Regulatory Networks
Braunewell, S. (2008) · State and University Library Bremen
Chaos control in random Boolean networks by reducing mean damage percolation rate∗Preprint
Jiang, N., & Chen, S. (2016)
The impact of sources and sinks on the dynamics of homogeneous and heterogeneous boolean networks
Agostini, L. (2021) · International Journal of Modern Physics C · doi:10.1142/s0129183122500826
Subpattern matching persistent homology for coupling complexity analysis of multivariate time series
Haruna, T. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0335719
Metadata
- Authors
- Luque, B., & Solé, R. V.
- Affiliations
- Universidad Nacional Autónoma de México (MX)
- Santa Fe Institute (US)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1997-01-01
- Volume
- 55
- Issue
- 1
- Pages
- 257-260
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1992555597
- Cited by
- 111
- References
- 12
- Citations by year
- 2026: 2 · 2024: 5 · 2023: 6 · 2022: 6 · 2021: 2 · 2020: 2 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 4 · 2015: 2 · 2014: 4 · 2013: 3 · 2012: 3
- FWCI
- 2.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Keywords
- random networks, phase transitions, critical points, Boolean networks, damage spreading, annealed approximation, spin glass
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