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Author Goles, E.; Montalva-Medel, M.; MacLean, S.; Mortveit, H.
Title Block Invariance in a Family of Elementary Cellular Automata Type
Year 2018 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 13 Issue 1-2 Pages 15-32
Keywords Elementary cellular automata; block updates; periodic configurations; block invariance
Abstract We study the steady state invariance of elementary cellular automata (ECA) under different deterministic updating schemes. Specifically, we study a family of eleven ECA whose steady state invariance were left under conjecture in [2].
Address [Goles, Eric; Montalva-Medel, Marco; MacLean, Stephanie] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000410888100002 Approved
Call Number UAI @ eduardo.moreno @ Serial 782
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Author Goles, E.; Montalva-Medel, M.; Mortveit, H.; Ramirez-Flandes, S.
Title Block Invariance in Elementary Cellular Automata Type
Year 2015 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 10 Issue 1-2 Pages 119-135
Keywords Elementary cellular automata; block updates; periodic points; block invariance
Abstract Consider an elementary cellular automaton (ECA) under periodic boundary conditions. Given an arbitrary partition of the set of vertices we consider the block updating, i.e. the automaton's local function is applied from the first to the last set of the partition such that vertices belonging to the same set are updated synchronously. The automaton is said block-invariant if the set of periodic configurations is independent of the choice of the block updating. When the sets of the partition are singletons we have the sequential updating: vertices are updated one by one following a permutation pi. In [5] the authors analyzed the pi-invariance of the 2(8) = 256 possible ECA rules (or the 88 non-redundant rules subset). Their main result was that for all n > 3, exactly 41 of these non-redundant rules are pi-invariant. In this paper we determine the subset of these 41 rules that are block invariant. More precisely, for all n > 3, exactly 15 of these rules are block invariant. Moreover, we deduce that block invariance also implies that the attractor structure itself is independent of the choice of the block update.
Address [Goles, Eric; Montalva-Medel, Marco; Ramirez-Flandes, Salvador] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Penalolen, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000350183000006 Approved
Call Number UAI @ eduardo.moreno @ Serial 461
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Author MacLean, S.; Montalva-Medel, M.; Goles, E.
Title Block invariance and reversibility of one dimensional linear cellular automata Type
Year 2019 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.
Volume 105 Issue Pages 83-101
Keywords Cellular automata; Linear cellular automata; Block invariance; Reversibility
Abstract Consider a one-dimensional, binary cellular automaton f (the CA rule), where its n nodes are updated according to a deterministic block update (blocks that group all the nodes and such that its order is given by the order of the blocks from left to right and nodes inside a block are updated synchronously). A CA rule is block invariant over a family F of block updates if its set of periodic points does not change, whatever the block update of F is considered. In this work, we study the block invariance of linear CA rules by means of the property of reversibility of the automaton because such a property implies that every configuration has a unique predecessor, so, it is periodic. Specifically, we extend the study of reversibility done for the Wolfram elementary CA rules 90 and 150 as well as, we analyze the reversibility of linear rules with neighbourhood radius 2 by using matrix algebra techniques. (C) 2019 Elsevier Inc. All rights reserved.
Address [MacLean, Stephanie; Montalva-Medel, Marco; Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Diagonal Torres 2640, Penalolen, Chile, Email: stephanie.macleank@edu.uai.cl;
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:000459528000004 Approved
Call Number UAI @ eduardo.moreno @ Serial 983
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Author Montalva-Medel, M.; Ledger, T.; Ruz, G.A.; Goles, E.
Title Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements Type
Year 2021 Publication Mathematics Abbreviated Journal Mathematics
Volume 9 Issue 6 Pages 600
Keywords ELEMENTARY CELLULAR-AUTOMATA; CARBON CATABOLITE REPRESSION; GLUCOSE-LACTOSE DIAUXIE; ESCHERICHIA-COLI; BLOCK INVARIANCE; MAXIMUM SENSITIVITY; BETA-GALACTOSIDASE; BISTABLE BEHAVIOR; BISTABILITY; NETWORK
Abstract In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.
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 2227-7390 ISBN Medium
Area Expedition Conference
Notes WOS:000645324300001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1374
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