Correspondence between neural threshold networks and Kauffman Boolean cellular automata
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For an asymmetric version of the McCulloch-Pitts neural network (1943) and for Kauffman's infinite-range Boolean network model (1984), the time evolution of the Hamming distances between two different initial configurations are compared in the thermodynamic limit. It is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their Hamming distances can have the same time evolution leading to quantitatively the same dynamics, as known from time-dependent Landau theory for phase transitions.
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The basic McCulloch-Pitts design is common to many other living systems, including gene regulatory networks, immune networks, collective intelligence or some aneural systems, such as quorum-sensing decisions in microbial communities.
“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 [257]
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- Authors
- Kurten, K. E.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1988-06-07
- Volume
- 21
- Issue
- 11
- Pages
- L615-L619
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1998479249
- Cited by
- 83
- References
- 0
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 1 · 2022: 3 · 2021: 2 · 2020: 1 · 2019: 6 · 2018: 1 · 2017: 2 · 2016: 1 · 2015: 3 · 2014: 10 · 2013: 3 · 2012: 5
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- McCulloch-Pitts neuron, Hamming distance, phase transitions, thermodynamic limit, infinite-range interactions
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