. Dans-le-cadre-de-l'approche-dite-dynamique, les études se sont fondées sur l'hypothèse que les profils d'expression biologique fournissent des intuitions fortes sur les relations entre les régulateurs. Les modules peuvent alors être révélés à partir des corrélations existant entre les éléments. À titre d'exemple, en utilisant des données d'expression génétique de la levure, des travaux ont inféré des modules en fonction des co-régulations et des conditions sous lesquelles se passent les régula-tions

, Ces études soulignent notamment que la découverte d'une organisation modulaire dans les réseaux est liée aux régulations entre les éléments au cours du temps et par conséquent aux dynamiques d'expression, vol.99

, Une autre approche Nous pensons, avec d'autres [BT09, Sie09], que l'étude de la modularité ne peut pas se contenter d'être menée en suivant l

M. Noual, D. Regnault, and S. Sené, About non-monotony in Boolean automata networks, Theoretical Computer Science, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00736641

J. Demongeot, M. Noual, and S. Sené, Combinatorics of Boolean automata circuits dynamics, vol.160, pp.398-415, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00666297

J. Demongeot, A. Elena, M. Noual, S. Sené, and F. Thuderoz, Immunetworks", intersecting circuits and dynamics, Journal of Theoretical Biology, vol.280, pp.18-33, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666298

J. Demongeot, E. Goles, M. Morvan, M. Noual, and S. Sené, Attraction basins as gauges of the robustness against boundary conditions in biological complex systems, PLoS One, vol.5, p.11793, 2010.

J. Demongeot, E. Drouet, A. Elena, A. Moreira, Y. Rechoum et al., MicroRNAs: viral genome and robustness of gene expression in the host, Philosophical Transactions of the Royal Society A, vol.367, pp.4941-4965, 2009.

J. Demongeot, H. Ben-amor, A. Elena, P. Gillois, M. Noual et al., Robustness in regulatory interaction networks. A generic approach with applications at different levels: physiologic, metabolic and genetic, International Journal of Molecular Sciences, vol.10, pp.4437-4473, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02007708

J. Demongeot, C. Jézéquel, and S. Sené, Boundary conditions and phase transitions in neural networks. Theoretical results. Neural Networks, vol.21, pp.971-979, 2008.

J. Demongeot and S. Sené, Boundary conditions and phase transitions in neural networks. Simulation results. Neural Networks, vol.21, pp.962-970, 2008.

J. Demongeot, A. Elena, and S. Sené, Robustness in regulatory networks: a multidisciplinary approach, Acta Biotheoretica, vol.56, pp.27-49, 2008.

M. Noual, D. Regnault, and S. Sené, Boolean networks synchronism sensitivity and XOR circulant networks convergence time, de Electronic Proceedings in Theoretical Computer Science, vol.90, pp.37-52, 2012.

S. Sené, A necessary condition for boundary sensitivity of attractive non-linear stochastic cellular automata in Z 2, Exploratory Papers Proceedings of Automata, pp.1-10, 2012.

F. Delaplace, H. Klaudel, T. Melliti, and S. Sené, Analysis of modular organisation of interaction networks based on asymptotic dynamics, Proceedings of CMSB, vol.7605, pp.148-165, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00750180

J. Demongeot and S. Sené, The singular power of the environment on stochastic nonlinear threshold Boolean automata networks, Proceedings of CMSB, pp.55-64, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666582

J. Demongeot, A. Elena, M. Noual, and S. Sené, Random Boolean networks and attractors of their intersecting circuits, Proceedings of WAINA, pp.41-50, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666589

J. Demongeot, M. Noual, and S. Sené, On the number of attractors of positive and negative Boolean automata circuits, Proceedings of WAINA, pp.782-789, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00647877

J. Demongeot, E. Goles, and S. Sené, Loss of linearity and symmetrisation in regulatory networks, Proceedings of WAINA, pp.908-913, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01499511

H. Ben-amor, J. Demongeot, and S. Sené, Structural sensitivity of neural and genetic networks, Proceedings of MICAI, vol.5317, pp.973-986, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00346566

J. Demongeot, M. Morvan, and S. Sené, Robustness of dynamical systems attraction basins against state perturbations: theoretical protocol and application in systems biology, Procedings of CISIS, pp.675-681, 2008.

J. Demongeot, M. Morvan, and S. Sené, Impact of fixed boundary conditions on the basins of attraction in the flower's morphogenesis of Arabidopsis thaliana, Proceedings of AINAW, pp.782-789, 2008.

M. Morvan and S. Sené, A distributed trust diffusion protocol for ad hoc networks, Proceedings of ICWMC, pp.87-92, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00353071

J. Demongeot, M. Morvan, and S. Sené, Influence des conditions de bord dans les réseaux d'automates booléens à seuil et application à la biologie, Proceedings of JOBIM, pp.111-116, 2008.

M. Noual, D. Regnault, and S. Sené, Non-monotony and Boolean automata networks. Rapport technique, 2011.

F. Delaplace, H. Klaudel, T. Melliti, and S. Sené, Modular organisation of interaction networks based on asymptotic dynamics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00750180

M. Noual and S. Sené, Towards a theory of modelling with Boolean automata networks -I. Theorisation and observations. Rapport technique, 2011.

J. Demongeot and S. Sené, Nonlinear threshold Boolean automata networks and phase transitions, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00538953

J. Demongeot, M. Noual, and S. Sené, On the number of attractors of Boolean automata circuits, p.424722, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00424722

M. Morvan and S. Sené, A distributed trust diffusion protocol for ad hoc networks, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00353071

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Reviews of Modern Physics, vol.74, pp.47-97, 2002.

P. Aloy, B. Böttcher, H. Ceulemans, C. Leutwein, C. Mellwig et al., Structure-based assembly of protein complexes in yeast, Science, vol.303, pp.2026-2029, 2004.

J. Ahmad, J. Bourdon, D. Eveillard, J. Fromentin, O. Roux et al., Temporal constraints of a gene regulatory network: refining a qualitative simulation, Biosystems, vol.98, pp.149-159, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00423353

]. J. Ablm-+-03, S. Aracena, O. Ben-lamine, O. Mermet, J. Cohen et al., Mathematical modeling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits, IEEE Transactions on Systems, Man, and Cybernetics, vol.33, pp.825-834, 2003.

J. Aracena, J. Demongeot, and E. Goles, Fixed points and maximal independent sets in AND-OR networks, Discrete Applied Mathematics, vol.138, pp.277-288, 2004.

J. Aracena, J. Demongeot, and E. Goles, Positive and negative circuits in discrete neural networks, IEEE Transactions on Neural Networks, vol.15, pp.77-83, 2004.

J. Aracena, É. Fanchon, M. Montalva, and M. Noual, Combinatorics on update digraphs in Boolean networks, vol.159, pp.401-409, 2011.

J. Aracena, E. Goles, A. Moreira, L. Salinas, ;. Aracena et al., Regulatory network for cell shape changes during drosophila ventral furrow formation, Journal of Theoretical Biology, vol.239, pp.49-62, 2006.

D. H. Ackley, G. E. Hinton, and T. J. Sejnowski, A learning algorithm for Boltzmann machines, Cognitive science, vol.9, pp.147-169, 1985.

M. Aldana, Boolean dynamics of networks with scale-free topology, vol.185, pp.45-66, 2003.

U. Alon, Biological networks: The tinkerer as an engineer, Science, vol.301, pp.1866-1867, 2003.

T. M. , Apostol : Introduction to analytic number theory, 1976.

J. Aracena, Discrete mathematics models associated to biological systems. Application to the genetic regulatory networks, 2001.

J. Aracena, Maximum number of fixed points in regulatory Boolean networks, Bulletin of Mathematical Biology, vol.70, pp.1398-1409, 2008.

W. Adams and D. Shanks, Strong primality tests that are not sufficient. Mathematics of Computation, vol.39, pp.255-300, 1982.

H. Ben-amor, J. Demongeot, S. Sené, ;. L. Bowman, J. Alvarez et al., Structural sensitivity of neural and genetic networks, Control of flower development in Arabidopsis thaliana by apetala1 and interacting genes. Development, vol.5317, pp.721-743, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00346566

A. Bockmayr and A. Courtois, Using hybrid concurrent constraint programming to model dynamic biological systems, Proceedings of ICLP, vol.2401, pp.85-99, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00100783

G. Bernot, F. Cassez, J. Comet, F. Delaplace, C. Müller et al., Semantics of biological regulatory networks, vol.180, pp.3-14, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00339588

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning ways for your mathematical plays, 1982.

G. Bernot, J. Comet, A. Richard, and J. Guespin, A fruitful application of formal methods to biological regulatory networks : extending Thomas' asynchronous logical approach with temporal logic, Journal of Theoretical Biology, vol.229, pp.339-347, 2004.

A. Benecke, Chromatin code, local non-equilibrium dynamics, and the emergence of transcription regulatory programs, The European Physical Journal E : Soft Matter and Biological Physics, vol.19, pp.353-366, 2006.

C. Bernard, Introduction à l'étude de la médecine expérimentale, J. P. Baillière et fils, p.1865

C. L. Berge-;-c, H. B. Barrett, M. V. Hunt, S. S. Marathe, D. J. Ravi et al., Tosic : Gardens of Eden and fixed points in sequential dynamical systems, Graphes et hypergraphes. Dunod, pp.95-110, 1973.

Z. Bar-joseph, G. K. Gerber, T. I. Lee, N. J. Rinaldi, J. Y. Yoo et al., Computational discovery of gene modules and regulatory networks, Nature Biotechnology, vol.21, pp.1337-1342, 2003.

J. Berstel and D. Perrin, The origins of combinatorics on words, vol.28, pp.996-1022, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00619483

G. Butland, J. M. Peregrin-alvarez, J. Li, W. Yang, X. Yang et al., Interaction network containing conserved and essential protein complexes in Escherichia coli, Nature, vol.433, pp.531-537, 2005.

P. Bremaud, Markov chains: Gibbs fields, Monte Carlo simulations and queues, 1999.

S. A. Benner and S. M. , Sismour : Synthetic biology, Nature Reviews Genetics, vol.6, pp.533-543, 2005.

N. Barkai and B. , Shilo : Variability and robustness in biomolecular systems, Molecular Cell, vol.28, pp.755-760, 2007.

M. P. Butler and R. Silver, Basis of robustness and resilience in the suprachiasmatic nucleus: individual neurons form nodes in circuits that cycle daily, Journal of Biological Rhythms, vol.24, pp.340-352, 2009.

G. Bernot and F. Tahi, Behaviour preservation of a biological regulatory network when embedded into a larger network, Fundamenta Informaticae, vol.91, pp.463-485, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00646001

D. C. Boyes, A. M. Zayed, R. Ascenzi, A. J. Mccaskill, N. E. Hoffman et al., Growth stage based phenotypic analysis of Arabidopsis : a model for high throughput functional genomics in plants, The Plant Cell, vol.13, pp.1499-1510, 2001.

M. Cosnard and J. Demongeot, On the definitions of attractors, Iteration theory and its functional equations, vol.1163, pp.23-31, 1985.

O. Cinquin and J. Demongeot, Positive and negative feedback: striking a balance between necessary antagonists, Journal of Theoretical Biology, vol.216, pp.229-241, 2002.

O. Cinquin and J. Demongeot, Roles of positive and negative feedback in biological systems, Comptes-Rendus Biologies, vol.325, pp.1085-1095, 2002.

G. Cattaneo, A. Dennunzio, E. Formenti, and J. Provillard, Non-uniform cellular automata, Proceedings of LATA, vol.5457, pp.302-313, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01297566

M. Cosnard, J. Demongeot, and A. L. Breton, éditeurs. Rhythms in biology and other fields of application, vol.49, 1983.

N. Chabrier and F. Fages, Symbolic model checking of biochemical networks, Proceedings of CMSB, vol.2602, pp.149-162, 2003.

A. Church, A set of postulates for the foundation of logic, Annals of Mathematics, vol.33, pp.346-366, 1932.

A. Church, An unsolvable problem of elementary number theory, American Journal of Mathematics, vol.58, pp.345-363, 1936.

P. Combe and H. Nencka, Frustration and overblocking on graphs. Mathematical and Computer Modelling, vol.26, pp.307-309, 1997.

M. Cook, Universality in elementary cellular automata, Complex Systems, vol.15, pp.1-40, 2004.

F. Corblin, S. Tripodi, É. Franchon, D. Ropers, and L. Trilling, A declarative constraint-based method for analyzing discrete genetic regulatory networks, Biosystems, vol.98, pp.91-104, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00793012

P. , Linear analysis of switching nets, Biological Cybernetics, vol.8, pp.31-39, 1971.

E. M. Clarke and J. , Wing : Formal methods: state of the art and future directions, ACM Computing Surveys, vol.28, pp.626-643, 1996.

J. Demongeot, J. Aracena, F. Thuderoz, T. Baum, and O. Cohen, Genetic regulation networks : circuits, regulons and attractors, vol.326, pp.171-188, 2003.

]. J. +-09, H. Demongeot, A. Ben-amor, P. Elena, M. Gillois et al., Robustness in regulatory interaction networks. A generic approach with applications at different levels : physiologic, metabolic and genetic, International Journal of Molecular Sciences, vol.10, pp.4437-4473, 2009.

M. Delbrück, Unités biologiques douées de continuité génétique, vol.8, pp.91-103, 1949.

J. Demongeot, Au sujet de quelques modèles stochastiques appliqués à la biologie, 1975.

J. Demongeot, Asymptotic inference for Markov random fields on Z d, Numerical methods in the study of critical phenomena, vol.9, pp.254-267, 1981.

J. Demongeot, A. Elena, M. Noual, S. Sené, and F. Thuderoz, Immunetworks", intersecting circuits and dynamics, Journal of Theoretical Biology, vol.280, pp.18-33, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666298

J. Demongeot, A. Elena, M. Noual, and S. Sené, Random Boolean networks and attractors of their intersecting circuits, Proceedings of WAINA, pp.41-50, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666589

J. Demongeot, A. Elena, and S. Sené, Robustness in regulatory networks: a multi-disciplinary approach, Acta Biotheoretica, vol.56, pp.27-49, 2008.

S. Diner, D. Frague, and G. Lochak, Dynamical systemsa renewal of mechanism: centennial of Georges David Birkhoff, 1986.

A. Dennunzio, E. Formenti, L. Manzoni, and G. , Mauri : mAsynchronous cellular automata, Proceedings of ACRI, vol.7495, pp.653-662, 2012.

A. Dennunzio, E. Formenti, J. Provillard, ;. Demongeot, E. Goles et al., Attraction basins as gauges of the robustness against boundary conditions in biological complex systems, Non-uniform cellular automata: classes, dynamics, and decidability. Information and Computation, vol.215, p.11793, 2010.

E. W. Dijkstra, A note on two problems in connexion with graphs, Numerische Mathematik, vol.1, pp.269-271, 1959.

J. Demongeot, C. Jézéquel, and S. Sené, Boundary conditions and phase transitions in neural networks. Theoretical results. Neural Networks, vol.21, pp.971-979, 2008.

F. Delaplace, K. Klaudel, and A. Cartier-michaud, Discrete causal model view of biological networks, Proceedings of CMSB, pp.4-13, 2010.

F. Delaplace, H. Klaudel, T. Melliti, and S. Sené, Analysis of modular organisation of interaction networks based on asymptotic dynamics, Proceedings of CMSB, vol.7605, pp.148-165, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00750180

J. Demongeot, M. Noual, and S. Sené, On the number of attractors of positive and negative Boolean automata circuits, Proceedings of WAINA, pp.782-789, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00647877

J. Demongeot, M. Noual, and S. Sené, Combinatorics of Boolean automata circuits dynamics, vol.160, pp.398-415, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00666297

R. L. Dobrushin, Existence of phase transitions in models of a lattice gas, Proceedings of the fifth Berkeley Symposium on Mathematical Statistics and Probabilities, pp.73-87, 1966.

R. L. Dobrushin, Gibbsian random fields for lattice systems with pairwise interactions. Functional Analysis and its Applications, vol.2, pp.292-301, 1968.

R. L. Dobrushin, The problem of uniqueness of a Gibbsian random field and the problem of phase transitions, Functional Analysis and its Applications, vol.2, pp.302-312, 1968.

J. Delahaye and F. Rechenman, La simulation par ordinateur change-t-elle les sciences ? Dossier Pour la Science, vol.52, pp.2-6, 2006.

J. Demongeot and S. Sené, Boundary conditions and phase transitions in neural networks. Simulation results. Neural Networks, vol.21, pp.962-970, 2008.

J. Demongeot and S. Sené, The singular power of the environment on stochastic nonlinear threshold Boolean automata networks, Proceedings of CMSB, pp.55-64, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00666582

H. Eisen, P. Brachet, L. Pereira-da-silva, and F. Jacob, Regulation of repressor expression in ?, Proceedings of the National Academy of Sciences of the USA, vol.66, pp.855-862, 1970.

A. Elena, Algorithme pour la simulation dynamique des réseaux de régulation génétique, 2004.

A. Elena, Robustesse des réseaux d'automates booléens à seuil aux modes d'itération. Application à la modélisation des réseaux de régu-lation génétique, 2009.

B. Elspas, The theory of autonomous linear sequential networks, IRE Transactions on Circuit Theory, vol.6, pp.45-60, 1959.

A. E. Ehrenhofer-murray, Chromatin dynamics at DNA replication, transcription and repair, European Journal of Biochemistry, vol.271, pp.2335-2349, 2004.

C. Espinosa-soto, P. Padilla-longoria, E. R. Alvarezbuylla, ;. E. Fanchon, L. Corblin et al., A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles, Proceedings of CMSB, vol.16, pp.104-118, 2004.

J. A. Feldman, Dynamic connections in neural networks, Biological Cybernetics, vol.46, pp.27-39, 1982.

P. Floréen, Computational complexity problems in neural associative memories, 1992.

N. Fatès and M. Morvan, Perturbing the topology of the game of life increases its robustness to asynchrony, Proceedings of ACRI, vol.3305, pp.111-120

. Springer, , 2004.

P. Floréen and P. Orponen, Counting stable states and sizes of attraction domains in Hopfield nets is hard, Proceedings of IJCNN, pp.395-399, 1989.

P. Floréen and P. Orponen, On the computational complexity of analyzing Hopfield nets, Complex Systems, vol.3, pp.577-587, 1989.

A. Fossey, Epigenetics: beyond genes. Southern Forests: a Journal of Forest Science, vol.71, pp.121-124, 2009.

F. Fogelman-soulié, E. Goles, and G. Weisbuch, Specific roles of different Boolean mappings in random networks, Bulletin of Mathematical Biology, vol.44, pp.715-730, 1982.

F. Fogelman-soulié, E. Goles, and G. Weisbuch, Transient length in sequential iteration of threshold functions, Discrete Applied Mathematics, vol.6, pp.95-98, 1983.

F. Soulié, Y. Robert, and M. Tchuente, éditeurs. Automata networks in computer science: theory and applications. Nonlinear Science: Theory and Applications, 1987.

M. Gardner, Mathematical games -the fantastic combinations of John Conway's new solitaire game, Life". Scientific American, vol.223, pp.120-123, 1970.

C. Gershenson, Classification of random Boolean networks, Proceedings of Artificial Life, pp.1-8, 2002.

C. Gershenson, Introduction to random Boolean networks, Proceedings of Workshop and Tutorial of Artificial Life, pp.160-173, 2004.

C. Gershenson, Updating schemes in random Boolean networks: do they really matter ?, Proceedings of Artificial Life, pp.238-243, 2004.

E. Goles, F. Fogelman-soulié, and D. Pellegrin, Decreasing energy functions as a tool for studying threshold networks, Discrete Applied Mathematics, vol.12, pp.261-277, 1985.

P. H. Guan and Y. He, Exact result for deterministic cellular automata with additive rules, Journal of Statistical Physics, vol.43, pp.463-478, 1986.

J. Gagneur, R. Krause, T. Bouwmeester, and G. Casari, Modular decomposition of protein-protein interaction networks, Genome Biology, vol.5, p.57, 2004.

R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete mathematics : a foundation for computer science, 1989.

E. Goles and S. Martínez, Neural and automata networks: dynamical behavior and applications, volume 58 de Mathematics and Its Applications, 1990.

J. Guespin-michel, Les bactéries, leur monde et nous : vers une biologie intégrative et dynamique. Dunod, 2011.

E. Goles and M. Noual, Block-sequential update schedules and Boolean automata circuits, Proceedings of Automata, pp.41-50
URL : https://hal.archives-ouvertes.fr/hal-01185498

. Dmtcs, , 2010.

E. Goles and M. Noual, Disjunctive networks and update schedules, Advances in Applied Mathematics, vol.48, pp.646-662, 2012.

E. Goles and J. Olivos, Comportement itératif des fonctions à multiseuil. Information and Control, vol.45, pp.300-313, 1980.

S. W. Golomb, Shift register sequences, 1967.

E. Goles, Fixed point behavior of threshold functions on a finite set, SIAM Journal on Algebraic and Discrete Methods, vol.3, pp.529-531, 1982.

J. Gouzé, Positive and negative circuits in dynamical systems, Journal of Biological Systems, vol.6, pp.11-15, 1998.

N. Goto and R. P. , Pharis : Role of gibberellins in the development of floral organs of the gibberellin-deficient mutant, ga1-1, of Arabidopsis thaliana, Canadian Journal of Botany, vol.77, pp.944-954, 1999.

E. Goles and L. Salinas, Comparison between parallel and serial dynamics of Boolean networks, Theoretical Computer Science, vol.396, pp.247-253, 2008.

J. Gunawardena, Elements of computational systems biology, chapitre Models in systems biology: the parameter problem and the meanings of robustness, 2010.

K. F. Gödel, Kurt Gödel collected works, volume I -Publications 1929-1936, chapitre On undecidable propositions of formal mathematical systems, pp.346-372, 1986.

J. C. Hanse and J. Ausio, Chromatin dynamics and the modulation of genetic activity, Trends in Biochemical Sciences, vol.17, pp.187-191, 1992.

F. Harary, Graph theory, 1969.

I. Harvey and T. Bossomaier, Time out of joint: attractors in asynchronous random Boolean networks, Proceedings of ECAL, pp.67-75, 1997.

D. O. Hebb, The organization of behavior: a neuropsychological theory, 1949.

E. D. , Herzog : Neurons and networks in daily rhythms, Nature Reviews Neuroscience, vol.8, pp.790-802, 2007.

B. Hesper and P. Hogeweg, Bioinformatica: een werkconcept. Kameleon, vol.1, pp.18-29, 1970.

P. Hogeweg and B. Hesper, Interactive instruction on population interactions, Computers in Biology and Medicine, vol.8, pp.319-327, 1978.

L. H. Hartwell, J. J. Hopfield, S. Leibler, and A. W. Murray, From molecular to modular cell biology, Nature, vol.402, pp.47-52, 1999.

P. Hogeweg, The roots of bioinformatics in theoretical biology, PLoS Computational Biology, vol.7, p.1002021, 2011.

L. Hood, Systems biology: integrating technology, biology, and computation, vol.124, pp.9-16, 2003.

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the USA, vol.79, pp.2554-2558, 1982.

J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences of the USA, vol.81, pp.3088-3092, 1984.

G. E. Hinton and T. J. Sejnowski, Parallel distributed processing: explorations in the microstructure of cognition, chapitre Learning and relearning in Boltzmann machines, vol.1, pp.282-317, 1986.

D. A. Huffman, Canonical forms for information-lossless finite-state logical machines, IRE Transactions on Information Theory, vol.5, pp.41-59, 1959.

I. Ideker, T. Galistki, and L. Hood, A new approach to decoding life: systems biology, vol.2, pp.343-372, 2001.

E. Ising, Beitrag zur theorie des ferromagnetismus, Zeitschrift für Physik A Hadrons and Nuclei, vol.31, pp.253-258, 1925.

A. S. Jarrah, R. Laubenbacher, and A. Veliz-cuba, The dynamics of conjunctive and disjunctive Boolean network models, Bulletin of Mathematical Biology, vol.72, pp.1425-1447, 2010.

D. B. Johnson, Efficient algorithms for shortest paths in sparse networks, Journal of the ACM, vol.24, pp.1-13, 1977.

S. A. Kauffman, Homeostasis and differentiation in random genetic control networks, Nature, vol.224, pp.177-178, 1969.

S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of Theoretical Biology, vol.22, pp.437-467, 1969.

S. A. Kauffman, chapitre Gene regulation networks: A theory for their global structures and behaviors, Current topics in developmental biology, vol.6, pp.145-181, 1971.

S. A. Kauffman, The large scale structure and dynamics of gene control circuits: an ensemble approach, Journal of Theoretical Biology, vol.44, pp.167-190, 1974.

S. A. Kauffman, Origins of order: self-organization and selection in evolution, 1993.

S. A. Kauffman, C. Peterson, B. Samuelsson, and C. Troein, Random Boolean network models and the yeast transcriptional network, Proceedings of the National Academy of Sciences of the USA, vol.100, pp.14796-14799, 2003.

A. S. Khalil and J. J. Collins, Synthetic biology: applications come of age, Nature Reviews Genetics, 2010.

H. Kitano, Computational systems biology, Nature, vol.240, pp.206-210, 2002.

H. Kitano, Towards a theory of biological robustness, Molecular Systems Biology, vol.3, p.137, 2007.

H. T. Kung and C. E. , Leiserson : Introduction to VLSI systems, chapitre Algorithms for VLSI processor arrays, 1980.

S. C. , Kleene : Representation of events in nerve nets and finite automata. Project RAND RM-704, 1951.

S. C. Kleene, de Annals of Mathematics Studies, chapitre Representation of events in nerve nets and finite automata, Automata studies, vol.34, pp.3-41, 1956.

B. A. Krizek and E. M. Meyerowitz, The Arabidopsis homeotic genes apetalata3 and pistillata are sufficient to provide the B class organ identity function, Development, vol.122, pp.11-22, 1996.

I. Koch, W. Reisig, and F. Schreiber, éditeurs. Modeling in systems biology: the Petri net approach, 2011.

M. D. , The expected number of components under a random mapping function, The American Mathematical Monthly, vol.61, pp.392-397, 1954.

I. M. Kuli? and H. Schiessel, Chromatin dynamics: nucleosomes go mobile through twist defects, Physical Review Letters, vol.91, p.148103, 2003.

M. Kaufman and R. Thomas, Towards a logical analysis of the immune response, Journal of Theoretical Biology, vol.114, pp.527-561, 1985.

A. Kashiwagi, I. Urabe, K. Kaneko, and T. Yomo, Adaptive response of a gene network to environmental changes by fitness-induced attractor selection, PLoS One, vol.1, p.49, 2006.

P. Kurka, Languages, equicontinuity and attractors in cellular automata. Ergodic Theory and Dynamical Systems, 1997.

M. Kaufman, J. Urbain, and R. Thomas, Model analysis of the basis of multistationarity in the humoral immune response, Journal of Theoretical Biology, vol.129, pp.141-162, 1987.

E. M. Lederberg, Lysogenicity in Escherichia coli strain K-12. Microbial Genetics Bulletin, vol.1, pp.5-9, 1950.

A. Lichnerowicz, La Recherche, vol.201, p.9, 1996.

N. M. Luscombe, M. Madan, H. Babu, M. Yu, S. A. Snyder et al., Genomic analysis of regulatory network dynamics reveals large topological changes, vol.431, pp.308-312, 2004.

M. Lothaire, Combinatorics on words, 1983.
URL : https://hal.archives-ouvertes.fr/hal-00620609

H. D. Landahl, R. I. Runge-;-t, N. J. Lee, F. Rinaldi, D. T. Robert et al., Outline of a matrix calculus for neural nets, Transcriptional regulatory networks in Saccharomyces cerevisiae. Science, vol.8, pp.799-804, 1946.

S. S. Lam and A. U. , Shankar : A relational notation for state transition systems, IEEE Transactions on Software Engineering, vol.16, pp.755-775, 1990.

É. Lucas, Le calcul des nombres entiers. Le calcul des nombres rationnels. La divisibilité arithmétique. Gauthier-Villars, 1891.

A. Lesne and J. Victor, Chromatin fiber functional organization: some plausible models, European Physical Journal E: Soft Matter and Biological Physics, vol.19, pp.279-290, 2006.

R. C. Lyndon, On Burnside's problem, Transactions of the American Mathematical Society, vol.77, pp.202-215, 1954.

L. Mendoza and E. R. Alvarez-buylla, Dynamics of the genetic regulatory network for Arabidopsis thaliana flower morphogenesis, Journal of Theoretical Biology, vol.193, pp.307-319, 1998.

P. A. Macmahon, Application of a theory of permutations in circular procession to the theory of numbers, Proceedings of the London Mathematical Society, vol.23, pp.305-313, 1892.

L. Manzini and G. Margara, Attractors of d-dimensional linear cellular automata, Proceedings of STACS, vol.1373, pp.128-138, 1998.

L. Manzoni, Asynchronous cellular automata and dynamical properties. Natural Computing, vol.11, pp.269-276, 2012.

B. Martin, Inherent generation of fractals by cellular automata, Complex Sytems, vol.8, pp.347-366, 1994.

W. Magnus, A. Karass, and D. Solitar, Combinatorial group theory: presentation of groups in terms of generators and relations, 1966.

J. Monod, Chance and necessity: an essay on the natural philosophy of modern biology, 1970.

W. S. Mcculloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Journal of Mathematical Biophysics, vol.5, pp.115-133, 1943.

M. Minsky and S. Papert, Perceptrons: an introduction to computational geometry, 1969.

R. Milo, S. Shen-orr, S. Itzkovitz, N. Kashtan, D. Chklovskii et al., Network motifs: simple building blocks of complex networks, vol.298, pp.824-827, 2002.

J. Neumann, Theory of self-reproducing automata, 1966.

M. E. Newman, The structure and function of complex networks, SIAM Review, vol.45, pp.167-256, 2003.

M. , Updating automata networks, 2012.

M. Noual, D. Regnault, and S. Sené, About non-monotony in Boolean automata networks, Theoretical Computer Science, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00736641

M. Noual, D. Regnault, and S. Sené, Boolean networks synchronism sensitivity and XOR circulant networks convergence time, Full Papers Proceedings of Automata, volume 90 de Electronic Proceedings in Theoretical Computer Science, pp.37-52, 2012.

M. Noual and S. Sené, Towards a theory of modelling with Boolean automata networks -I. Theorisation and observations. Rapport technique, 2011.

M. Noual and S. Sené, Towards a theory of modelling with Boolean automata networks -I. Theorisation and observations, 2012.

P. Orponen, Neural networks and complexity theory, Proceedings of MFCS, vol.629, pp.50-61, 1992.

E. Plahte, T. Mestl, and S. W. , Omholt : A methodological basis for description and analysis of systems with complex switch-like interactions, Journal of Mathematical Biology, vol.36, pp.321-348, 1998.

M. Pryczek, Neuronal groups and interrelations, Proceedings of IMCSIT, pp.221-227, 2008.

Y. Puri and T. Ward, A dynamical property unique to the Lucas sequence, The Fibonacci Quarterly, vol.39, pp.398-402, 2001.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, Journal of Integer Sequences, 2001.

P. E. Purnick and R. Weiss, The second wave of synthetic biology: from modules to systems, Nature Reviews Molecular Cell Biology, vol.10, pp.410-422, 2009.

Y. Qin and Z. R. Yang, Critical dynamics of the kinetic Ising model with triplet interaction on Sierpinski-gasket-type fractals, Physical Review B, vol.46, pp.11284-11289, 1992.

A. Richard and J. , Comet : Necessary conditions for multistationarity in discrete dynamical systems, Discrete Applied Mathematics, vol.155, pp.2403-2413, 2007.

A. W. Rives and T. Galitski, Modular organization of cellular networks, Proceedings of the National Academy of Sciences of the USA, vol.100, pp.1128-1133, 2003.

P. Ribenboim, The new book of prime number records, 1996.

A. Richard, Modèle formel pour les réseaux de régulation génétique & influence des circuits de rétroaction, 2006.

A. Richard, Positive circuits and maximal number of fixed points in discrete dynamical systems, Discrete Applied Mathematics, vol.157, pp.3281-3288, 2009.

A. Richard, Negative circuits and sustained oscillations in asynchronous automata networks, Advances in Applied Mathematics, vol.44, pp.378-392, 2010.

A. Richard, Local negative circuits and fixed points in nonexpansive Boolean networks, Discrete Applied Mathematics, vol.159, pp.1085-1093, 2011.

J. Riordan, Introduction to combinatorial analysis, 1958.

J. Riordan, An introduction to combinatorial analysis, 1962.

É. Remy, B. Mossé, C. Chaouyia, and D. Thieffry, A description of dynamical graphs associated to elementary regulatory circuits, Bioinformatics, vol.19, pp.172-178, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00311023

F. Robert, Blocs-H-matrices et convergence des méthodes itératives classiques par blocs, Linear Algebra and its Applications, vol.2, pp.223-265, 1969.

F. Robert, Contraction en norme vectorielle : convergence d'itéra-tions chaotiques pour des équations non linéaires de point fixe à plusieurs variables, Linear Algebra and its Applications, vol.13, pp.19-35, 1976.

F. Robert, Itérations sur des ensembles finis et automates cellulaires contractants, Linear Algebra and its Applications, vol.29, pp.393-412, 1980.

F. Robert, Discrete iterations: a metric study, Springer Series in Computational Mathematics, vol.6, 1986.

F. Robert, Les systèmes dynamiques discrets, vol.19, 1995.

F. Rosenblatt, The perceptron: a probabilistic model for information storage and organization in the brain, Psychological Review, vol.65, pp.386-408, 1958.

É. Remy and P. Ruet, From minimal signed circuits to the dynamics of Boolean regulatory networks, Bioinformatics, vol.24, pp.220-226, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01306956

É. Remy, P. Ruet, and D. Thieffry, Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Rapport technique, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00692086

É. Remy, P. Ruet, and D. Thieffry, Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework, Advances in Applied Mathematics, vol.41, pp.335-350, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00692086

D. Ruelle, Statistical mechanics of a one-dimensional lattice gas, Communications in Mathematical Physics, vol.9, pp.267-278, 1968.

D. Ruelle, Statistical mechanics: rigourous results. W. A. Benjamin, 1969.

F. Ruskey, Combinatorial generation. Book preliminary working draft, 2003.

H. Siebert and A. Bockmayr, Temporal constraints in the logical analysis of regulatory networks, Theoretical Computer Science, vol.391, pp.258-275, 2008.

D. R. Smyth, J. L. Bowman, and E. M. Meyerowitz, Early flower development in Arabidopsis, The Plant Cell, vol.2, pp.755-767, 1990.

A. L. Silverstone, C. N. Ciampaglio, and T. Sun, The Arabidopsis rga gene encodes a transcriptional regulator repressing the gibberellin signal transduction pathway, The Plant Cell, vol.10, pp.155-169, 1998.

A. K. Seth and G. M. Edelman, Environment and behavior influence the complexity of evolved neural networks, Adaptive Behavior, vol.12, pp.5-20, 2004.

S. Sené, Influence des conditions de bord dans les réseaux d'automates booléens à seuil et application à la biologie, 2008.

S. Sené, A necessary condition for boundary sensitivity of attractive non-linear stochastic cellular automata in Z 2, Exploratory Papers Proceedings of Automata, I3S/RR-2012-04-FR, pp.1-10, 2012.

H. Siebert, Dynamical and structural modularity of discrete regulatory networks, de Electronic Proceedings in Theoretical Computer Science, vol.6, pp.109-124, 2009.

V. Spirin and L. A. Mirny, Protein complexes and functional modules in molecular networks, Proceedings of the National Academy of Sciences of the USA, vol.100, pp.12123-12128, 2003.

E. H. Snoussi, Structure et comportement itératif de certains modèles discrets, 1980.

E. H. Snoussi, Necessary conditions for multistationarity and stable periodicity, vol.6, pp.3-9, 1998.

C. Soulé, Graphic requirements for multistationarity. Complexus, vol.1, pp.123-133, 2003.

L. E. Sieburth, M. P. Running, and E. M. Meyerowitz, Genetic separation of third and fourth whorl function of agamous, Plant Cell, vol.7, pp.1249-1258, 1995.

E. Segal, M. Shapira, D. Regev, A. Pe'er, D. Botstein et al., Module networks: discovering regulatory modules and their condition specific regulators from gene expression data, Robustness of cellular functions. Cell, vol.34, pp.675-685, 2003.

E. H. Snoussi and R. Thomas, Logical identification of all steady states : the concept of feedback loop characteristic states, Bulletin of Mathematical Biology, vol.55, pp.973-991, 1993.

S. H. Strogatz, Exploring complex networks, Nature, vol.410, pp.268-276, 2001.

L. Tournier and M. Chaves, Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics, Journal of Theoretical Biology, vol.260, pp.196-209, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00554625

R. Thomas and R. , Biological feedback, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00087681

R. Thom, Stabilité structurelle et morphogenèse : vers une théorie générale des modèles. Interéditions, 1972.

R. Thomas, Boolean formalization of genetic control circuits, Journal of Theoretical Biology, vol.42, pp.563-585, 1973.

R. Thom, Structural stability and morphogenesis. W. A. Benjamin, 1975.

R. Thomas, On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations, Numerical methods in the study of critical phenomena, vol.9, pp.180-193, 1981.

R. Thomas, Logical vs. continuous description of systems comprising feedback loops: the relation between time delays and parameters, Studies in Physical and Theoretical Chemistry, vol.28, pp.307-321, 1983.

R. Thomas, Regulatory networks seen as asynchronous automata: a logical description, Journal of Theoretical Biology, 1991.

R. Thomas and M. Kaufman, Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior, Chaos, vol.11, pp.170-179, 2001.

R. Thomas and M. Kaufman, Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits, Chaos, vol.11, pp.180-195, 2001.

R. A. Toledo, Linear finite dynamical systems, Communications in Algebra, vol.33, pp.2977-2989, 2005.

P. Tosic, Computational complexity of some enumeration problems about uniformly sparse Boolean network automata, Proceedings of ECCS, 2006.

G. Toulouse, Theory of the frustration effect in spin glasses, I. Communications on Physics, vol.2, pp.115-134, 1977.

R. Thomas and J. Richelle, Positive feedback loops and multistationarity, vol.19, pp.381-396, 1988.

D. Thieffry and D. Romero, The modularity of biological regulatory networks, Biosystems, vol.50, pp.49-59, 1999.

D. Thieffry and R. Thomas, Dynamical behaviour of biological regulatory networks -II. Immunity control in bacteriophage lambda, Bulletin of Mathematical Biology, vol.57, pp.277-297, 1995.

R. Thomas, D. Thieffry, and M. Kaufman, Dynamical behaviour of biological regulatory networks -I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state, Bulletin of Mathematical Biology, vol.57, pp.247-276, 1995.

A. M. Turing, On computable numbers, with an application to the entscheidungsproblem, Proceedings of the London Mathematical Society, vol.2, pp.230-265, 1936.

R. Thomas and P. Van-ham, Analyse formelle de circuits de régu-lation génétique : le contrôle de l'immunité chez les bactériophages lambdoïdes, Biochimie, vol.56, pp.1529-1547, 1975.

S. Ulam, On some mathematical problems connected with patterns of growth and figures, Proceedings of Symposia in Applied Mathematics, vol.14, pp.215-224, 1962.

A. Veliz-cuba and R. Laubenbacher, On the computation of fixed points in Boolean networks, Journal of Applied Mathematics and Computing, vol.39, pp.145-153, 2011.

H. Van-der-laan and ;. E. Brill, Le nombre plastique, quinze leçons sur l'ordonnance architectonique, 1960.

J. Vannimenus and G. Toulouse, Theory of the frustration effect in spin glasses. II. Ising spins on a square lattice, Journal of Physics C: Solid State Physics, vol.10, pp.537-542, 1977.

A. Wagner, Robustness and evolvability in living systems, 2005.

S. Wolfram, Universality and complexity in cellular automata, vol.10, pp.1-35, 1984.

F. Y. Wu, Rigorous results on the triangular Ising model with pair and triplet interactions, Physics Letters A, vol.153, pp.73-75, 1991.

X. N. Wu and F. Y. Wu, Exact results for lattice models with pair and triplet interactions, Journal of Physics A : Mathematical and Theoretical, vol.22, p.1031, 1989.

D. C. Weaver, C. T. Workman, and G. , Stormo : Modeling regulatory networks with weight matrices, Proceedings of PSB, pp.112-123, 1999.

J. Xing and G. L. , Gerstein : Networks with lateral connectivity. II. Development of neuronal grouping and corresponding receptive field changes, Journal of neurophysiology, vol.75, pp.200-216, 1996.

H. Yu, T. Ito, Y. Zhao, J. Peng, P. Kumar et al., Meyerowitz : Floral homeotic genes are targets of gibberellin signaling in flower development, Proceedings of the National Academy of Sciences of the USA, vol.101, pp.7827-7838, 2004.