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Author Goles, E.; Salinas, L. pdf  doi
openurl 
  Title (up) 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 Salinas, L.; Goles, E. pdf  doi
openurl 
  Title (up) Covering by squares Type
  Year 2008 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.  
  Volume 396 Issue 1-3 Pages 10-27  
  Keywords discrete geometry; covering; tiling  
  Abstract In this paper we introduce the “do not touch” condition for squares in the discrete plane. We say that two squares “do not touch” if they do not share any vertex or any segment of an edge. Using this condition we define a covering of the discrete plane, the covering can be strong or weak, regular or non-regular. For simplicity, in this article, we will restrict our attention to regular coverings, i.e., only a size is allowed for the squares and all the squares have the same number of adjacent squares. We establish minimal conditions for the existence of a weak or strong regular covering of the discrete plane, and we give a bound for the number of adjacent squares with respect to the size of the squares in the regular covering. (C) 2007 Elsevier B.V. All rights reserved.  
  Address [Salinas, L.] Univ Chile, Dept Engn Math, Santiago, Chile, Email: lsalinas@dim.uchile.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:000256199100002 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 31  
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Author Aracena, J.; Goles, E.; Moreira, A.; Salinas, L. pdf  doi
openurl 
  Title (up) 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.; Salinas, L. pdf  doi
openurl 
  Title (up) Sequential operator for filtering cycles in Boolean networks Type
  Year 2010 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.  
  Volume 45 Issue 3 Pages 346-358  
  Keywords  
  Abstract Given a Boolean network without negative circuits, we propose a polynomial algorithm to build another network such that, when updated in parallel, it has the same fixed points than the original one, but it does not have any dynamical cycle. To achieve that, we apply a network transformation related to the sequential update. As a corollary, we can find a fixed point in polynomial time for this kind of networks. (C) 2010 Elsevier Inc. All rights reserved.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language 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:000281294000004 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 94  
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