Notebooks
Random Boolean Networks, Nk Networks
06 May 2023 19:15
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
