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Author Aracena, J.; Goles, E.; Moreira, A.; Salinas, L.
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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Author Goles, E.; Noual, M.
Title Disjunctive networks and update schedules Type
Year 2012 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.
Volume 48 Issue 5 Pages 646-662
Keywords Regulation network; Linear Boolean network; Attractor; Limit cycle; Fixed point; Update schedule
Abstract In this paper, we present a study of the dynamics of disjunctive networks under all block-sequential update schedules. We also present an extension of this study to more general fair periodic update schedules, that is, periodic update schedules that do not update some elements much more often than some others. Our main aim is to classify disjunctive networks according to the robustness of their dynamics with respect to changes of their update schedules. To study this robustness, we focus on one property, that of being able to cycle dynamically. (C) 2012 Elsevier Inc. All rights reserved.
Address [Noual, Mathilde] Univ Lyon, Lab Informat Parallelisme, ENS Lyon, CNRS UMR5668, F-69342 Lyon 07, France, Email: mathilde.noual@ens-lyon.fr
Corporate Author Thesis
Publisher Academic Press Inc Elsevier Science Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0196-8858 ISBN Medium
Area Expedition Conference
Notes WOS:000304682200004 Approved
Call Number UAI @ eduardo.moreno @ Serial 217
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Author Goles, E.; Ruz, G.A.
Title Dynamics of neural networks over undirected graphs Type
Year 2015 Publication Neural Networks Abbreviated Journal Neural Netw.
Volume 63 Issue Pages 156-169
Keywords Neural networks; Undirected graphs; Discrete updating schemes; Attractors; Fixed points; Cycles
Abstract In this paper we study the dynamical behavior of neural networks such that their interconnections are the incidence matrix of an undirected finite graph G = (V, E) (i.e., the weights belong to {0, 1}). The network may be updated synchronously (every node is updated at the same time), sequentially (nodes are updated one by one in a prescribed order) or in a block-sequential way (a mixture of the previous schemes). We characterize completely the attractors (fixed points or cycles). More precisely, we establish the convergence to fixed points related to a parameter alpha(G), taking into account the number of loops, edges, vertices as well as the minimum number of edges to remove from E in order to obtain a maximum bipartite graph. Roughly, alpha(G') < 0 for any G' subgraph of G implies the convergence to fixed points. Otherwise, cycles appear. Actually, for very simple networks (majority functions updated in a block-sequential scheme such that each block is of minimum cardinality two) we exhibit cycles with nonpolynomial periods. (C) 2014 Elsevier Ltd. All rights reserved.
Address [Goles, Eric; Ruz, Gonzalo A.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0893-6080 ISBN Medium
Area Expedition Conference
Notes WOS:000349730800015 Approved
Call Number UAI @ eduardo.moreno @ Serial 460
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Author Goles, E.; Salinas, L.
Title Comparison between parallel and serial dynamics of Boolean networks Type
Year 2008 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.
Volume 396 Issue 1-3 Pages 247-253
Keywords Boolean network; synchronous update; asynchronous update; attractor; dynamical cycle; fixed point
Abstract In this article we study some aspects about the graph associated with parallel and serial behavior of a Boolean network. We conclude that the structure of the associated graph can give some information about the attractors of the network. We show that the length of the attractors of Boolean networks with a graph by layers is a power of two and under certain conditions the only attractors are fixed points. Also, we show that, under certain conditions, dynamical cycles are not the same for parallel and serial updates of the same Boolean network. (C) 2007 Elsevier B.V. All rights reserved.
Address [Salinas, L.] Univ Chile, Dept Engn Math, Santiago, Chile, Email: eric.chacc@uai.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 0304-3975 ISBN Medium
Area Expedition Conference
Notes WOS:000256199100019 Approved
Call Number UAI @ eduardo.moreno @ Serial 32
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Author Goles, E.; Montalva, M.; Ruz, G.A.
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 Ruz, G.A.; Goles, E.
Title Learning gene regulatory networks using the bees algorithm Type
Year 2013 Publication Neural Computing & Applications Abbreviated Journal Neural Comput. Appl.
Volume 22 Issue 1 Pages 63-70
Keywords Swarm intelligence; The bees algorithm; Simulated annealing; Boolean networks; Attractors
Abstract Learning gene regulatory networks under the threshold Boolean network model is presented. To accomplish this, the swarm intelligence technique called the bees algorithm is formulated to learn networks with predefined attractors. The resulting technique is compared with simulated annealing through simulations. The ability of the networks to preserve the attractors when the updating schemes is changed from parallel to sequential is analyzed as well. Results show that Boolean networks are not very robust when the updating scheme is changed. Robust networks were found only for limit cycle length equal to two and specific network topologies. Throughout the simulations, the bees algorithm outperformed simulated annealing, showing the effectiveness of this swarm intelligence technique for this particular application.
Address [Ruz, Gonzalo A.; Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago 2640, Chile, Email: gonzalo.ruz@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 0941-0643 ISBN Medium
Area Expedition Conference
Notes WOS:000313062100008 Approved
Call Number UAI @ eduardo.moreno @ Serial 261
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Author Ruz, G.A.; Timmermann, T.; Barrera, J.; Goles, E.
Title Neutral space analysis for a Boolean network model of the fission yeast cell cycle network Type
Year 2014 Publication Biological Research Abbreviated Journal Biol. Res.
Volume 47 Issue Pages 12 pp
Keywords Neutral graph; Boolean networks; Evolution strategy; Fission yeast cell cycle; Attractors
Abstract Background: Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle. Results: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G(1) fixed point was found for deterministic updating schemes. Conclusions: In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.
Address [Ruz, Gonzalo A.; Timmermann, Tania; Barrera, Javiera; Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: gonzalo.ruz@uai.cl
Corporate Author Thesis
Publisher Soc Biolgia Chile Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0716-9760 ISBN Medium
Area Expedition Conference
Notes WOS:000348529400004 Approved
Call Number UAI @ eduardo.moreno @ Serial 440
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