On spectral techniques in analysis of Boolean networks

Physica D: Nonlinear Phenomena

Volumn 206, Issue 1-2, 2005, Pages 49-61

  Kesseli, Juha ^a   Rämö, Pauli ^a   Yli Harja, Olli ^a  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Boolean networks; Gene regulatory network; Phase transition; Scale free topology; Spectral methods

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; COMPUTATIONAL METHODS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; PHASE TRANSITIONS; RANDOM PROCESSES; SAMPLING; SPECTRUM ANALYSIS; TOPOLOGY; WALSH TRANSFORMS;

BOOLEAN NETWORKS; GENE REGULATORY NETWORKS; SCALE-FREE TOPOLOGY; SPECTRAL METHODS;

BOOLEAN ALGEBRA;

EID: 19944370198     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.04.016     Document Type: Article

References (22)

1. S.A. Kauffman The Origins of Order 1993 Oxford University Press New York
2. M.D. Stern Emergence of homeostasis and 'noise imprinting' in an evolutionary model Evolution 96 1999 10746 10751
3. M. Aldana, S. Coppersmith, L.P. Kadanoff, Boolean dynamics with random couplings, in: E. Kaplan, J.E. Marsden, K.R. Sreenivasan (Eds.), Perspectives and Problems in Nonlinear Science, A celebratory volume in honor of Lawrence Sirovich, Springer Applied Mathematical Sciences Series, 2003, pp. 23-89.
4. B. Derrida, and Y. Pomeau Random networks of automata: a simple annealed approximation Europhys. Lett. 1 1986 45 49
5. B. Derrida, and D. Stauffer Phase transitions in two dimensional Kauffman cellular automata Europhys. Lett. 2 1986 739 745
6. B. Luque, C. Blanc, Order parameters, Lyapunov exponents and control in random Boolean networks, Santa Fe Institute, Working paper 97-11-084.
7. B.K. Sawhill, S. Kauffman, Phase transitions in logic networks, Santa Fe Institute, Working paper 97-05-038.
8. I. Shmulevich, S.A. Kauffman, Activities and sensitivities in Boolean network models, Phys. Rev. Lett. 93 (4) (2004) 048701(1-4).
9. I. Shmulevich, H. Lähdesmaki, E.R. Dougherty, W.Z. Jaakko Astola, The role of certain Post classes in Boolean network models of genetic networks, Proc. Natl. Acad. Sci. USA 100 (2003) 10734-10739.
10. A. Wuensche, Discrete dynamical networks and their attractor basins, Santa Fe Institute, Working paper 98-11-101.
11. A. Bernasconi, Mathematical techniques for the analysis of Boolean functions, Ph.D. thesis, University of Pisa, 1998.
12. R.J. Lechner, Recent Developments in Switching Theory, Electrical Science Series, Academic Press, New York, 1971. Ch. Harmonic Analysis of Switching Functions, 122-229.
13. M.G. Karpovsky Spectral Techniques and Fault Detection 1985 Academic Press Orlando, Florida
14. F.J. MacWilliams, and N.J. Sloane The Theory of Error-Correcting Codes 1977 North-Holland Publishing
15. J.L. Shanks Computation of the fast Walsh-Fourier transform IEEE Trans. Comp. C18 1969 457 459
16. R. Albert, and A. Barabasi Statistical mechanics of complex networks Rev. Mod. Phys. 47 2002 47 97
17. M. Aldana Boolean dynamics of networks with scale-free topology Physica D 185 2003 45 66
18. S.A. Kauffman The ensemble approach to understand genetic regulatory networks Physica A 340 2004 733 740
19. W. Just, I. Shmulevich, and J. Konvalina The number and probability of canalizing functions Physica D 197 2004 211 221
20. B. Samuelsson, and C. Troein Superpolynomial growth in the number of attractors in Kauffman networks Phys. Rev. Lett. 90 2003 098701
21. S.E. Harris, B.K. Sawhill, A. Wuenche, and S.A. Kauffman A model of transcriptional regulatory networks based on biases in the observed regulation rules Complexity 7 4 2001 23 40
22. S.A. Kauffman, C. Peterson, B. Samuelsson, and C. Troein Random Boolean network models and the yeast transcriptional network Proc. Natl. Acad. Sci. USA 100 2003 14796 14799