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Author 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 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 Aracena, J.; Goles, E.; Moreira, A.; Salinas, L. pdf  doi
openurl 
  Title On the robustness of update schedules in Boolean networks Type
  Year 2009 Publication Biosystems Abbreviated Journal Biosystems  
  Volume 97 Issue 1 Pages 1-8  
  Keywords Boolean network; Update schedule; Robustness; Attractor; Dynamical cycle  
  Abstract Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems. (C) 2009 Elsevier Ireland Ltd. All rights reserved.  
  Address [Aracena, J.] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile, Email: jaracena@ing-mat.udec.cl  
  Corporate Author Thesis  
  Publisher Elsevier Sci Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0303-2647 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000267528900001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 29  
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