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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) Goles, E.; Montalva, M.; Ruz, G.A. pdf  doi
openurl 
  Title Deconstruction and Dynamical Robustness of Regulatory Networks: Application to the Yeast Cell Cycle Networks Type
  Year 2013 Publication Bulletin Of Mathematical Biology Abbreviated Journal Bull. Math. Biol.  
  Volume 75 Issue 6 Pages 939-966  
  Keywords Boolean networks; Attractors; Update robustness; Alliances; Dynamics  
  Abstract Analyzing all the deterministic dynamics of a Boolean regulatory network is a difficult problem since it grows exponentially with the number of nodes. In this paper, we present mathematical and computational tools for analyzing the complete deterministic dynamics of Boolean regulatory networks. For this, the notion of alliance is introduced, which is a subconfiguration of states that remains fixed regardless of the values of the other nodes. Also, equivalent classes are considered, which are sets of updating schedules which have the same dynamics. Using these techniques, we analyze two yeast cell cycle models. Results show the effectiveness of the proposed tools for analyzing update robustness as well as the discovery of new information related to the attractors of the yeast cell cycle models considering all the possible deterministic dynamics, which previously have only been studied considering the parallel updating scheme.  
  Address [Goles, Eric; Montalva, Marco; Ruz, Gonzalo A.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl;  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0092-8240 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000321220400005 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 288  
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Author (up) Ruz, G.A.; Goles, E.; Montalva, M.; Fogel, G.B. pdf  doi
openurl 
  Title Dynamical and topological robustness of the mammalian cell cycle network: A reverse engineering approach Type
  Year 2014 Publication Biosystems Abbreviated Journal Biosystems  
  Volume 115 Issue Pages 23-32  
  Keywords Gene regulatory networks; Boolean networks; Threshold networks; Update robustness; Topology robustness; Bees algorithm  
  Abstract A common gene regulatory network model is the threshold Boolean network, used for example to model the Arabidopsis thaliana floral morphogenesis network or the fission yeast cell cycle network. In this paper, we analyze a logical model of the mammalian cell cycle network and its threshold Boolean network equivalent. Firstly, the robustness of the network was explored with respect to update perturbations, in particular, what happened to the attractors for all the deterministic updating schemes. Results on the number of different limit cycles, limit cycle lengths, basin of attraction size, for all the deterministic updating schemes were obtained through mathematical and computational tools. Secondly, we analyzed the topology robustness of the network, by reconstructing synthetic networks that contained exactly the same attractors as the original model by means of a swarm intelligence approach. Our results indicate that networks may not be very robust given the great variety of limit cycles that a network can obtain depending on the updating scheme. In addition, we identified an omnipresent network with interactions that match with the original model as well as the discovery of new interactions. The techniques presented in this paper are general, and can be used to analyze other logical or threshold Boolean network models of gene regulatory networks. (C) 2013 Elsevier Ireland Ltd. All rights reserved.  
  Address [Ruz, Gonzalo A.; Goles, Eric; Montalva, Marco] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: gonzalo.ruz@uai.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:000330500100004 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 350  
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