Flexible and robust networks

Journal of Bioinformatics and Computational Biology

Volumn 10, Issue 2, 2012, Pages

  Vakulenko, Sergey A ^a   Radulescu, Ovidiu ^b  

^a INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

^b UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Gene networks; pattern formation; robustness

Indexed keywords

ARTICLE; COMPUTER SIMULATION; FEEDBACK SYSTEM; GENE REGULATORY NETWORK;

COMPUTER SIMULATION; FEEDBACK; GENE REGULATORY NETWORKS;

EID: 84859759888     PISSN: 02197200     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219720012410119     Document Type: Article

References (35)

1. Zhao J, Yu H, Luo JH, Cao ZW, Li YX, Hierarchical modularity of nested bow-ties in metabolic networks, BMC Bioinform 7:386, 2006.
2. Kauffman SA, Metabolic stability and epigenesis in randomly constructed genetic nets, J Theor Biol 22:437-467, 1969.
3. Aldana M, Boolean dynamics of networks with scale-free topology, Physica D 185:45-66, 2003.
4. He L, Hannon GJ, MicroRNAs: Small RNAs with a big role in gene regulation, Nat Rev Genet 5(7): 522-31, 2004. (Pubitemid 38868508)
5. Bartel DP, MicroRNAs: Target recognition and regulatory functions, Cell 136(2): 215-233, 2009.
6. Hendrickson DG, Hogan DJ, McCullogh HL, Myers JW, Herschlag D, Ferrell JE, Brown PO, Concordant regulation of translation and mRNA abundance for hundreds of targets of a human microRNA, PLOS Biol 7:2-19, 2009.
7. Ihui M, Martello G, Piccolo S, MicroRNA control of signal transduction, Nat Rev Mol Cell Biol 11:252-263, 2010.
8. Li L, Xu J, Yang D, Tan X, Wang H, Computational approaches for microRNA studies: A review, Mamm Genome 21:1-12, 2010.
9. Albert R, Barabási AL, Statistical mechanics of complex networks, Rev Modern Phys 74:47-97, 2002.
10. Lesne A, Complex networks: From graph theory to biology, Lett Math Phys 78:235-262, 2006. (Pubitemid 44878228)
11. Mjolness E, Sharp DH, Reinitz J, A connectionist model of development, J Theor Biol 152:429-453, 1991.
12. Reinitz J, Sharp DH, Mechanism of formation of eve stripes, Mech Develop 49:133-158, 1995.
13. D. Henry, Geometric Theory of Semiliniar Parabolic Equations, Springer, New York, 1981.
14. Dancer EN, Polácik P, Realization of Vector Fields and Dynamics of Spatially Homogeneous Parabolic Equations, American Mathematical Society, 1999.
15. Rybakowski KP, Realization of arbitrary vector fields on center manifolds of parabolic Dirichlet BVP's, J Diff Eq 114:199-321, 1994.
16. Vakulenko S, Dissipative systems generating any structurally stable chaos, Adv Diff Eq 5:1139-2178, 2000.
17. Babin AB, Vishik MI, Regular attractors of semigroups and evolution equations, J Math Pures Appl 62:441-491, 1983.
18. Ruelle D, Takens F, On the nature of turbulence, Comm Math Phys 20:167-192, 1971.
19. Newhouse R, Ruelle D, Takens F, Occurence of strange axiom A attractors from quasi periodic flows, Comm Math Phys 64:35-40, 1971.
20. Smale S, On the differential equations of species in competition, J Math Biol 3:5-7, 1976.
21. Anosov DV (ed.), Dynamical systems with hyperbolic behaviour, (Dynamical Systems 9), Encyclopedia of Mathematical Sciences, Vol. 66, translated from Russian, Springer V, Berlin, Heidelberg, New York, 1995.
22. Ruelle D, Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press, Boston, 1989.
23. Barron A, Universal Approximation Bounds for superpositions of a sigmoidal functions, IEEE Trans Inf Theor 39:930-945, 1993.
24. Funahashi K, Nakamura Y, Approximation of dynamical systems by continuous time recurrent neural networks, Neural Networks 6:801-806, 1993. (Pubitemid 23713279)
25. Hirsch MW, Stability and convergence in strongly monotone dynamical systems, J Reine Angew Math 383:1-58, 1988.
26. Keizer J, Statistical Thermodynamics of Nonequilibrium Processes, Springer Verlag, New York, 1997.
27. Reinitz J, Sharp DH, Mechanism of formation of eve stripes, Mechanisms of Development 49:133-158, 1995.
28. Li X, Cassidy JJ, Reinke CA, Fischboeck S, Carthew RW, A microRNA imparts robustness against environmental fluctuation during development, Cell 137:273-282, 2009.
29. Shalgi R, Lieber D, Oren M, Pilpel Y, Global and local architecture of the mammalian microRNA transcription factor regulatory network, PLoS Comput Biol 3:1291-1304, 2007. (Pubitemid 47196171)
30. Polácik P, Complicated dynamics in scalar semilinear parabolic equations in higher space dimensions, J Diff Eq 89:244-271, 1991.
31. Marion M, Approximate inertial manifolds for reaction-diffusion equations in high space dimension, J Dyn Diff Eq 1:245-267, 1989.
32. Mane R, Reduction of semilinear parabolic equations to finite dimensional C1-flow, Geometry and Topology, Lecture Notes in Mathematics, No. 597, Springer -Verlag, New York, pp. 361-378, 1977.
33. Constantin P, Foias C, Nicolaenko B, Temam R, Integral Manifolds and Inertial Manifolds for Dissipative Differential Equations, Springer, New York, 1989.
34. Chow SN, Lu K, Invariant manifolds for flows in Banach spaces, J Diff Eq 74:285-317, 1988.
35. Rabinovitch MI, Abarbanel HDI, The role of chaos in neural systems, Neuroscience 87(N1):5-14, 1998. (Pubitemid 28351165)