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Author (up) Aracena, J.; Demongeot, J.; Fanchon, E.; Montalva, M. pdf  doi
openurl 
  Title On the number of update digraphs and its relation with the feedback arc sets and tournaments Type
  Year 2013 Publication Discrete Applied Mathematics Abbreviated Journal Discret Appl. Math.  
  Volume 161 Issue 10-11 Pages 1345-1355  
  Keywords Update digraph; Feedback arc set; Tournament; Update schedule  
  Abstract An update digraph corresponds to a labeled digraph that indicates a relative order of its nodes introduced to define equivalence classes of deterministic update schedules yielding the same dynamical behavior of a Boolean network. In Aracena et al. [1], the authors exhibited relationships between update digraphs and the feedback arc sets of a given digraph G. In this paper, we delve into the study of these relations. Specifically, we show differences and similarities between both sets through increasing and decreasing monotony properties in terms of their structural characteristics. Besides, we prove that these sets are equivalent if and only if all the digraph circuits are cycles. On the other hand, we characterize the minimal feedback arc sets of a given digraph in terms of their associated update digraphs. In particular, for complete digraphs, this characterization shows a close relation with acyclic tournaments. For the latter, we show that the size of the associated equivalence classes is a power of two. Finally, we determine exactly the number of update digraphs associated to digraphs containing a tournament. (C) 2013 Elsevier B.V. All rights reserved.  
  Address Univ Concepcion, CI2 MA & Dept Ingn Matemat, Concepcion, Chile, Email: jaracena@ing-mat.udec.cl;  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0166-218x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000319029300005 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 282  
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Author (up) Aracena, J.; Demongeot, J.; Fanchon, E.; Montalva, M. pdf  doi
openurl 
  Title On the number of different dynamics in Boolean networks with deterministic update schedules Type
  Year 2013 Publication Mathematical Biosciences Abbreviated Journal Math. Biosci.  
  Volume 242 Issue 2 Pages 188-194  
  Keywords Boolean network; Update schedule; Update digraph; Dynamics  
  Abstract Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction digraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics. (C) 2013 Elsevier Inc. All rights reserved.  
  Address Univ Concepcion, CI2MA, Concepcion, Chile, Email: jaracena@ing-mat.udec.cl;  
  Corporate Author Thesis  
  Publisher Elsevier Science Inc Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0025-5564 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000317164700008 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 275  
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Author (up) Demongeot, J.; Goles, E.; Morvan, M.; Noual, M.; Sene, S. pdf  doi
openurl 
  Title Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems Type
  Year 2010 Publication Plos One Abbreviated Journal PLoS One  
  Volume 5 Issue 8 Pages 18 pp  
  Keywords  
  Abstract One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally.  
  Address [Demongeot, Jacques] Univ Grenoble 1, TIMC IMAG, CNRS, UMR 5525, La Tronche, France, Email: Sylvain.Sene@ibisc.univ-evry.fr  
  Corporate Author Thesis  
  Publisher Public Library Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1932-6203 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000280605400002 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 92  
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