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Author Aracena, J.; Demongeot, J.; Fanchon, E.; Montalva, M.
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.; 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.; 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.; Lobos, F.; Ruz, G.A.; Sene, S.
Title Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks Type
Year 2020 Publication Natural Computing Abbreviated Journal Nat. Comput.
Volume 19 Issue 2 Pages 295-319
Keywords Discrete dynamical systems; Boolean networks; Biological network modeling
Abstract In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, i.e. any Boolean network with firing memory composed of m vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, i.e. the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-phage and that of the genetic control of the floral morphogenesis of the plant Arabidopsis thaliana.
Address [Goles, Eric; Lobos, Fabiola; 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 1567-7818 ISBN Medium
Area Expedition Conference
Notes WOS:000531210800001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1139
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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 Goles, E.; Montealegre, P.; Rios-Wilson, M.
Title On The Effects Of Firing Memory In The Dynamics Of Conjunctive Networks Type
Year 2020 Publication Discrete And Continuous Dynamical Systems Abbreviated Journal Discret. Contin. Dyn. Syst.
Volume 40 Issue 10 Pages 5765-5793
Keywords Discrete dynamical systems; boolean network; firing memory; conjunctive networks; prediction problem; and PSPACE
Abstract A boolean network is a map F : {0, 1}(n) -> {0, 1}(n) that defines a discrete dynamical system by the subsequent iterations of F. Nevertheless, it is thought that this definition is not always reliable in the context of applications, especially in biology. Concerning this issue, models based in the concept of adding asynchronicity to the dynamics were propose. Particularly, we are interested in a approach based in the concept of delay. We focus in a specific type of delay called firing memory and it effects in the dynamics of symmetric (non-directed) conjunctive networks. We find, in the caseis in which the implementation of the delay is not uniform, that all the complexity of the dynamics is somehow encapsulated in the component in which the delay has effect. Thus, we show, in the homogeneous case, that it is possible to exhibit attractors of non-polynomial period. In addition, we study the prediction problem consisting in, given an initial condition, determinate if a fixed coordinate will eventually change its state. We find again that in the non-homogeneous case all the complexity is determined by the component that is affected by the delay and we conclude in the homogeneous case that this problem is PSPACE-complete.
Address [Goles, Eric; Montealegre, Pedro] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Diagonal Torres 2650, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1078-0947 ISBN Medium
Area Expedition Conference
Notes WOS:000545661800006 Approved
Call Number UAI @ eduardo.moreno @ Serial 1183
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Author Goles, E.; Montealegre, P.; Salo, V.; Torma, I.
Title PSPACE-completeness of majority automata networks Type
Year 2016 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.
Volume 609 Issue Pages 118-128
Keywords Boolean network; Majority network; Prediction problem; PSPACE
Abstract We study the dynamics of majority automata networks when the vertices are updated according to a block sequential updating scheme. In particular, we show that the complexity of the problem of predicting an eventual state change in some vertex, given an initial configuration, is PSPACE-complete. (C) 2015 Elsevier B.V. All rights reserved.
Address [Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, 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:000367488400009 Approved
Call Number UAI @ eduardo.moreno @ Serial 572
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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.; Goles, E.; Montalva, M.; Fogel, G.B.
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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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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Author Ruz, G.A.; Zuniga, A.; Goles, E.
Title A Boolean network model of bacterial quorum-sensing systems Type
Year 2018 Publication International Journal Of Data Mining And Bioinformatics Abbreviated Journal Int. J. Data Min. Bioinform.
Volume 21 Issue 2 Pages 123-144
Keywords gene regulatory networks; quorum-sensing systems; Boolean networks; neural networks; network inference
Abstract There are several mathematical models to represent gene regulatory networks, one of the simplest is the Boolean network paradigm. In this paper, we reconstruct a regulatory network of bacterial quorum-sensing systems, in particular, we consider Paraburkholderia phytofirmans PsJN which is a plant growth promoting bacteria that produces positive effects in horticultural crops like tomato, potato and grape. To learn the regulatory network from temporal expression pattern of quorum-sensing genes at root plants, we present a methodology that considers the training of perceptrons for each gene and then the integration into one Boolean regulatory network. Using the proposed approach, we were able to infer a regulatory network model whose topology and dynamic exhibited was helpful to gain insight on the quorum-sensing systems regulation mechanism. We compared our results with REVEAL and Best-Fit extension algorithm, showing that the proposed neural network approach obtained a more biologically meaningful network and dynamics, demonstrating the effectiveness of the proposed method.
Address [Ruz, Gonzalo A.; Zuniga, Ana; Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Av Diagonal Torres 2640, Santiago, Chile, Email: gonzalo.ruz@uai.cl;
Corporate Author Thesis
Publisher Inderscience Enterprises Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1748-5673 ISBN Medium
Area Expedition Conference
Notes WOS:000451832900003 Approved
Call Number UAI @ eduardo.moreno @ Serial 933
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Author Timmermann, T.; Gonzalez, B.; Ruz, G.A.
Title Reconstruction of a gene regulatory network of the induced systemic resistance defense response in Arabidopsis using boolean networks Type
Year 2020 Publication Bmc Bioinformatics Abbreviated Journal BMC Bioinformatics
Volume 21 Issue 1 Pages 16 pp
Keywords Boolean networks; Differential evolution; Gene regulatory networks; Induced systemic resistance; Paraburkholderia phytofirmans; Pseudomonas syringae
Abstract Background An important process for plant survival is the immune system. The induced systemic resistance (ISR) triggered by beneficial microbes is an important cost-effective defense mechanism by which plants are primed to an eventual pathogen attack. Defense mechanisms such as ISR depend on an accurate and context-specific regulation of gene expression. Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRNs). Here, we explore the regulatory mechanism of the ISR defense response triggered by the beneficial bacterium Paraburkholderia phytofirmans PsJN in Arabidopsis thaliana plants infected with Pseudomonas syringae DC3000. To achieve this, a GRN underlying the ISR response was inferred using gene expression time-series data of certain defense-related genes, differential evolution, and threshold Boolean networks. Results One thousand threshold Boolean networks were inferred that met the restriction of the desired dynamics. From these networks, a consensus network was obtained that helped to find plausible interactions between the genes. A representative network was selected from the consensus network and biological restrictions were applied to it. The dynamics of the selected network showed that the largest attractor, a limit cycle of length 3, represents the final stage of the defense response (12, 18, and 24 h). Also, the structural robustness of the GRN was studied through the networks' attractors. Conclusions A computational intelligence approach was designed to reconstruct a GRN underlying the ISR defense response in plants using gene expression time-series data of A. thaliana colonized by P. phytofirmans PsJN and subsequently infected with P. syringae DC3000. Using differential evolution, 1000 GRNs from time-series data were successfully inferred. Through the study of the network dynamics of the selected GRN, it can be concluded that it is structurally robust since three mutations were necessary to completely disarm the Boolean trajectory that represents the biological data. The proposed method to reconstruct GRNs is general and can be used to infer other biologically relevant networks to formulate new biological hypotheses.
Address [Timmermann, Tania; Gonzalez, Bernardo; Ruz, Gonzalo A.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Lab Bioingn, Santiago, Chile, Email: gonzalo.ruz@uai.cl
Corporate Author Thesis
Publisher Bmc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1471-2105 ISBN Medium
Area Expedition Conference
Notes WOS:000529043500003 Approved
Call Number UAI @ eduardo.moreno @ Serial 1143
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