Research interests

I'm interested in finite dynamical systems (Boolean networks mainly) and their application for the modeling of biological networks (gene networks mainly). The transversal question of interest, behind almost all my works, is the following: What can be said on a finite dynamical system according to the interaction graph of the system (that describes under the form of a graph the interaction between the component of the system)?
Below, I use this color for works concerning mainly the theory of finite dynamical systems, this color for works concerning mainly methods for the modeling of gene networks, and this color for works concerning mainly the modeling of particular biological networks.

Articles submitted in peerreviewed journals


J. Aracena, A. Richard and L. Salinas
Number of fixed points and disjoint cycles in monotone Boolean networks
(slides).

A. Richard.
Fixed points and connections between positive and negative cycles in Boolean networks.

J. Aracena, A. Richard and Lilian Salinas.
Fixed points in conjunctive networks and maximal independent sets in graph contractions.

G. Bernot, J.P. Comet, Z. Khalis, A. Richard and O. Roux.
A Genetically Modified Hoare Logic.

Articles in peerreviewed journals


M. Gadouleau, A. Richard and E. Fanchon.
Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability.
IEEE Transaction on Information Theory, 62(5):25042519, 2016.

M. Gadouleau and A. Richard.
Simple dynamics on graphs
(slides).
Theoretical Computer Science, 628:6277, 2016.

M. Gadouleau, A. Richard and S. Riis.
Fixed points of Boolean networks, guessing graphs, and coding theory.
SIAM Journal on Discrete Mathematics, 29(4):23122335, 2015.

A. Richard.
Fixed point theorems for Boolean networks expressed in terms of forbidden subnetworks.
Theoretical Computer Science, 583:126, 2015.

J. Aracena, A. Richard, L. Salinas.
Maximum number of fixed points in ANDORNOT networks.
Journal of Computer and System Sciences, 80(7):11751190, 2014.

S. Laurent, A. Richard, O. MulnerLorillon, J. Morales, D. Flament, V. Glippa, J. Bourdon, P. Gosselin, A. Siegel, P. Cormier, R. Bellé.
Modelisation of the regulation of protein synthesis following fertilization in sea urchin shows requirement of two processes: a destabilization of eIF4E:4EBP complex and a great stimulation of the 4EBPdegradation mechanism, both rapamycinsensitive.
Frontiers in Genetics, 5(117), 2014.

J.P. Comet, A. Richard, M. Noual, J. Aracena, L. Calzone, J. Demongeot, M. Kaufman, A. Naldi, E.H. Snoussi and D. Thieffry.
On circuit functionality in Boolean networks.
Bulletin of Mathematical Biology, 75(6):906919, 2013.

A. Richard and P. Ruet.
From kernels in directed graphs to fixed points and negative cycles in boolean networks.
Discrete Applied Mathematics, 161(78):11061117, 2013.

A. Richard, G. Rossignol, J.P. Comet, G. Bernot, J. GuespinMichel and A. Merieau.
Boolean models of biosurfactants production in Pseudomonas fluorescens.
PLoS ONE, 7(1):e24651, 2012.

M. Mabrouki, M. Aiguier, J.P. Comet, P. Le Gall and A. Richard.
Embedding of biological regulatory networks and properties preservation.
Mathematics in Computer Science , 5(3):263288, 2011.

A. Richard and J.P. Comet.
Stable periodicities and negative circuits in differential systems.
Journal of Mathematical Biology, 63:593600, 2011.
Here is an ERRATUM to this article.

A. Richard.
Local negative circuits and fixed points in nonexpansive boolean networks.
Discrete Applied Mathematics, 159(11):10851093, 2011.

L. Paulevé and A. Richard.
Topological Fixed Points in Boolean Networks.
Comptes Rendus de l'Académie des Sciences  Series I  Mathematics, 348(1516):825  828, 2010.

A. Richard.
Negative circuits and sustained oscillations in asynchronous automata networks.
Advances in Applied Mathematics, 44(4):378392, 2010.

A. Richard.
Positive circuits and maximal number of fixed points in discrete dynamical systems.
Discrete Applied Mathematics, 157(15):32813288, 2009.

Z. Khalis, J.P. Comet, A. Richard and G. Bernot.
The smbionet method for discovering models of gene regulatory networks.
Genes, Genomes and Genomics, 3:1522, 2009.

A. Richard.
An extension of a combinatorial fixed point theorem of Shih and Dong.
Advances in Applied Mathematics, 41(4):620627, 2008.

J. Ahmad, O. Roux, G. Bernot, J.P. Comet and A. Richard.
Analysing Formal Models of Genetic Regulatory Networks with Delays: Applications to Lambda phage and Tcell Activation Systems.
International Journal of Bioinformatics Research and Applications, 4(3):240262, 2008.

A. Richard and J.P. Comet.
Necessary conditions for multistationarity in discrete dynamical systems.
Discrete Applied Mathematics, 155(18):24032413, 2007.

A. Richard, J.P. Comet and G. Bernot.
R. Thomas' modeling of biological regulatory networks: introduction of singular states in the qualitative dynamics.
Fundamenta Informaticae, 65(4):373392, 2005.

G. Bernot, J.P. Comet, A. Richard, J. GuespinMichel.
Application of Formal Methods to Biological Regulatory Networks: Extending Thomas' Asynchronous Logical Approach with Temporal Logic.
Journal of Theoretical Biology, 229(3):339347, 2004.

J. GuespinMichel, G. Bernot, J.P. Comet, A. Mérieau, A. Richard, C. Hulen and B. Polack.
Epigenesis and dynamic similarity in two regulatory networks in Pseudomonas aeruginosa.
Acta Biotheoretica. 52 (4): 379390, 2004.

Articles in peerreviewed conference proceedings


T. Melliti, D. Regnault, A. Richard and S. Sené.
Asynchronous simulation of Boolean networks by monotone Boolean networks.
Accepted in ACA 2016.

T. Melliti, D. Regnault, A. Richard and S. Sené.
On the convergence of Boolean automata networks without negative cycles.
In J. Kari, M. Kutrib, A. Malcher, Cellular Automata and Discrete Complex Systems (Proceeding of AUTOMATA 2013), Springer Berlin Heidelberg, LNCS 8155, 124138, 2013.

H. Gruber, A. Richard, and C. Soulé.
How to Knock out Feedback Circuits in Gene Networks?
In V. Capasso, M. Gromov, A. HarelBellan, N. Morozova, and L. Pritchard, editors, Pattern Formation in Morphogenesis  Problems and Mathematical Issues, volume 15 of Springer Proceedings in Mathematics, pages 175178, Springer, 2013.

A. Richard.
A fixed point theorem for boolean networks expressed in terms of forbidden subnetworks.
Proceeding of the 17th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2011), DMTCS Proceedings AP , 116, 2012.

L. Paulevé and A. Richard.
Static analysis of boolean networks based on interaction graphs: a survey.
Proceedings of The Second International Workshop on Static Analysis and Systems Biology (SASB 2011), ENTCS 284, 93104, 2012.

J. Bahi, J.F. Couchot, C. Guyeux and A. Richard.
On the link between strongly connected iteration graphs and chaotic Boolean discretetime dynamical systems.
Proceeding of the 18th International Symposium on Fundamentals of Computation Theory (FCT 2011), Lecture Note in Computer Science (LNCS), 6914, pp. 126137, 2011.

M. Dénès, B. Lesage, Y. Bertot and A. Richard.
Formal proof of theorems on genetic regulatory networks.
Synasc'09, IEEEXplore Digital Library, 2009.

A. Richard.
On the link between oscillations and negative circuits in discrete genetic regulatory networks.
Proceedings of JOBIM 2007, pp. 613618, 2007.

J. Ahmad, A. Richard, G. Bernot, J.P. Comet and O. Roux.
Delays in Biological Regulatory Networks.
In IWBRA 2006 / ICCS 2006: 6th International Conference, Proceedings, Part II , volume 3992 of LNCS, 887894, May 2006.

A. Richard, J.P. Comet, G. Bernot.
Graphbased Modeling of Biological Regulatory Networks : Introduction of Singular States.
International workshop on Computational Methods in Systems Biology (CMSB), Paris, France, May 2628,2004. In Proceedings CMSB 2004, LNBI 3082, pp. 5872, 2005.

Book chapters


G. Bernot, J.P. Comet, A. Richard, M. Chaves, J.L. Gouzé and F. Dayan.
Modeling and Analysis of Gene Regulatory Networks.
In Modeling in Computational Biology and Biomedicine, F. Cazals and P. Kornprobst (Ed.), Springer, pp 4780, 2013.

A. Richard, J.P. Comet and G. Bernot.
Formal methods for modeling biological regulatory networks.
In Modern Formal Methods and Applications, Gabbar Hossam A. (Ed.), pp. 83122, Springer, 2006.

Dissertation and Thesis


Modèles formels pour les réseaux de régulation génétiques et influence des circuits de rétroaction
PhD Dissertation in Computer Science, University of Evry Val d'Essonne, France, september 2006.

Organization of scientific events


Workshop sur la Théorie des réseaux booléens
et ses applications en biologie
Nice, 47 novembre 2014.

Ecole thématique CNRS Modélisation Formelle de Réseaux de Régulation Biologique
Ile de Porquerolles, 2428 juin 2013.
