## Random Boolean Networks, Nk Networks

*01 Sep 2011 13:38*

See also: Adaptation; Artificial Life; Biological Order and Levels of Organization; Cellular Automata; Chaos and Non-linear Dynamics; Dissipative Structures; Edge of Chaos; Physical Principles in Biology; Self-organization; Statistical Mechanics

- Recommended (essential):
- Stuart Kauffman, The Origins of Order [Highly interesting, but to be read with some caution. The writing is often confused, and, frankly, after more than a decade many of the ideas have not panned out. Still extremely important.]

- Recommended, more specialized:
- Carlos Gershenson, Stuart A. Kauffman, and Ilya Shmulevich, "The Role of Redundancy in the Robustness of Random Boolean Networks", nlin.AO/0511018

- To read:
- Andrew Berdahl, Amer Shreim, Vishal Sood, Maya Paczuski, Joern Davidsen, "Random sampling vs. exact enumeration of attractors in random Boolean networks", arxiv:0904.3948
- Sourav Chatterjee, "Chaos, concentration, and multiple valleys", arxiv:0810.4221 ["Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers. They also arise in other areas, like fitness models in evolutionary biology. The ground state of a disordered system is the state with minimum energy. The system is said to be chaotic if a small perturbation of the energy landscape causes a drastic shift of the ground state. We present a rigorous theory of chaos in disordered systems that confirms long-standing physics intuition about connections between chaos, anomalous fluctuations of the ground state energy, and the existence of multiple valleys in the energy landscape."]
- Madalena Chaves, Reka Albert and Eduardo D. Sontag, "Robustness and fragility of Boolean models for genetic regulatory networks", q-bio.MN/0401037
- S. N. Coppersmith, "The computational complexity of Kauffman nets and the P versus NP problem", cond-mat/0510840
- L. Correale, M. Leone, A. Pagnani, M. Weigt, R. Zecchina, "Computational core and fixed-point organisation in Boolean networks", cond-mat/0512089
- Barbara Drossel, "On the number of attractors in random Boolean
networks", cond-mat/0503526
= Physical Review
E
**72**(2005): 016110 - Richard Durrett and Vlada Limic, "Rigorous Results for the NK
Model", The Annals of Probability
**31**(2003): 1713--1753 - Carlos Gershenson
- "Introduction to Random Boolean Networks", nlin.AO/0408006
- "Phase Transitions in Random Boolean Networks with Different Updating Schemes", nlin/0311008

- Florian Greil and Barbara Drossel, "The dynamics of critical
Kauffman networks under asynchronous stochastic update", cond-mat/0501081 = Physical Review
Letters
**95**(2005): 048701 - Leo Kadanoff, Susan Coppersmith and Maximino Aldana, "Boolean Dynamics with Random Couplings," nlin.AO/0204062
- Viktor Kaufman and Barbara Drossel, "Relevant components in critical random Boolean networks", cond-mat/0606507
- Viktor Kaufman, Tamara Mihaljev and Barbara Drossel, "Scaling in critical random Boolean networks", cond-mat/0506807
- Juha Kesseli, Pauli Rämö, and Olli Yli-Harja, "Tracking
perturbations in Boolean networks with spectral methods", Physical Review
E
**72**(2005):026137 - Constantin Klemm and Stefan Bornholdt, "Stable and unstable attractors in Boolean networks", cond-mat/0411102
- Michele Leone, Andrea Pagnani, Giorgio Parisi and Osvaldo Zagordi,
"Finite size corrections to random Boolean networks", Journal of
Statistical Mechanics: Theory and Experiment
**2006**: P12012 - Vlada Limic and Robin Pemantle, "More rigorous results on the
Kauffman-Levin model of evolution", Annals of
Probability
**32**(2004): 2149--2178 = math.PR/0308282 - Bartolo Luque, Fernando J. Ballesteros and Manuel Fernández,
"Variances as order paramaeter and complexity measure for random Boolean
networks", Journal
of Physics A: Mathematical and General
**38**(2005): 1031--1038 - James F. Lynch, "Critical Points for Random Boolean Networks," nlin.AO/0110036
- H. Mahmoudi, A. Pagnani, M. Weigt and R. Zecchina, "Propagation of
external regulation and asynchronous dynamics in random Boolean networks", Chaos
**17**(2007): 026109 - Christophe Malaterre, "Are self-organizing biochemical networks emergent?", phil-sci/5413
- Tamara Mihaljev, Barbara Drossel, "Scaling in a general class of
critical random Boolean
networks", cond-mat/0606612
= Physical
Review E
**74**(2006): 046101 - Andre A. Moreira and Luis A. N. Amaral, "Canalizing Kauffman
networks: non-ergodicity and its effect on their critical behavior", cond-mat/0504722 = PRL
**94**(2005): 218702 - U. Paul, V. Kaufman, B. Drossel, "The properties of attractors of canalyzing random Boolean networks", cond-mat/0511049
- Pauli Rämö, Juha Kesseli, and Olli Yli-Harja, "Stability
of functions in Boolean models of gene regulatory networks", Chaos
**15**(2005): 034101 - Cynthia J. Olson Reichhardt and Kevin E. Bassler, "Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks", q-bio.QM/0610011
- Chikoo Oosawa, Kazuhiro Takemoto, Shogo Matsumoto, Michael A. Savageau, "Local cause of coherence in Boolean networks", nlin.CG/0611049
- Bjoorn Samuelsson and Carl Troein, "Random maps and attractors in random Boolean networks", cond-mat/0505481
- Steffen Schober and Martin Bossert, "Analysis of random Boolean networks using the average sensitivity", arxiv:0704.0197
- C. Seshadhri, Yevgeniy Vorobeychik, Jackson R. Mayo, Robert C. Armstrong, and Joseph R. Ruthruff, "Influence and Dynamic Behavior in Random Boolean Networks", Physical Review Letters
**107**(2011): 108701 - Agnes Szejka and Barbara Drossel, "Evolution of Canalizing Boolean Networks", q-bio.PE/0701025