
Goles, E., & Gomez, L. (2018). Combinatorial game associated to the one dimensional Schelling's model of social segregation. Nat. Comput., 17(2), 427–436.
Abstract: In this paper we consider a finite onedimensional lattice with sites such that one of them is empty and the others have a black or white token. There are two players (one for each color), such that step by step alternately they move one of their tokens to the empty site trying to obtain a connected configuration. This game is related with the Schelling's social segregation model, where colors represent two different populations such that each one tries to take up a position with more neighbors as itself (same color). In this work we study strategies to play the game as well as their relation with the associated Schelling's onedimensional case (line and cycle graphs).



Goles, E., Lobos, F., Ruz, G. A., & Sene, S. (2020). Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks. Nat. Comput., 19(2), 295–319.
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.



MontalvaMedel, M., de Oliveira, P. P. B., & Goles, E. (2018). A portfolio of classification problems by onedimensional cellular automata, over cyclic binary configurations and parallel update. Nat. Comput., 17(3), 663–671.
Abstract: Decision problems addressed by cellular automata have been historically expressed either as determining whether initial configurations would belong to a given language, or as classifying the initial configurations according to a property in them. Unlike traditional approaches in language recognition, classification problems have typically relied upon cyclic configurations and fully paralell (twoway) update of the cells, which render the action of the cellular automaton relatively less controllable and difficult to analyse. Although the notion of cyclic languages have been studied in the wider realm of formal languages, only recently a more systematic attempt has come into play in respect to cellular automata with fully parallel update. With the goal of contributing to this effort, we propose a unified definition of classification problem for onedimensional, binary cellular automata, from which various known problems are couched in and novel ones are defined, and analyse the solvability of the new problems. Such a unified perspective aims at increasing existing knowledge about classification problems by cellular automata over cyclic configurations and parallel update.



Perrot, K., MontalvaMedel, M., de Oliveira, P. P. B., & Ruivo, E. L. P. (2020). Maximum sensitivity to update schedules of elementary cellular automata over periodic configurations. Nat. Comput., 19(1), 51–90.
Abstract: This work is a thoughtful extension of the ideas sketched in Montalva et al. (AUTOMATA 2017 exploratory papers proceedings, 2017), aiming at classifying elementary cellular automata (ECA) according to their maximal onestep sensitivity to changes in the schedule of cells update. It provides a complete classification of the ECA rule space for all period sizes n[ 9 and, together with the classification for all period sizes n <= 9 presented in Montalva et al. (Chaos Solitons Fractals 113:209220, 2018), closes this problem and opens further questionings. Most of the 256 ECA rule's sensitivity is proved or disproved to be maximum thanks to an automatic application of basic methods. We formalize meticulous case disjunctions that lead to the results, and patch failing cases for some rules with simple arguments. This gives new insights on the dynamics of ECA rules depending on the proof method employed, as for the last rules 45 and 105 requiring o0011THORN induction patterns.



Travisany, D., Goles, E., Latorre, M., Cort?s, M. P., & Maass, A. (2020). Generation and robustness of Boolean networks to model Clostridium difficile infection. Nat. Comput., 19(1), 111–134.
Abstract: One of the more common healthcare associated infection is Chronic diarrhea. This disease is caused by the bacterium Clostridium difficile which alters the normal composition of the human gut flora. The most successful therapy against this infection is the fecal microbial transplant (FMT). They displace C. difficile and contribute to gut microbiome resilience, stability and prevent further episodes of diarrhea. The microorganisms in the FMT their interactions and inner dynamics reshape the gut microbiome to a healthy state. Even though microbial interactions play a key role in the development of the disease, currently, little is known about their dynamics and properties. In this context, a Boolean network model for C. difficile infection (CDI) describing one set of possible interactions was recently presented. To further explore the space of possible microbial interactions, we propose the construction of a neutral space conformed by a set of models that differ in their interactions, but share the final community states of the gut microbiome under antibiotic perturbation and CDI. To begin with the analysis, we use the previously described Boolean network model and we demonstrate that this model is in fact a threshold Boolean network (TBN). Once the TBN model is set, we generate and use an evolutionary algorithm to explore to identify alternative TBNs. We organize the resulting TBNs into clusters that share similar dynamic behaviors. For each cluster, the associated neutral graph is constructed and the most relevant interactions are identified. Finally, we discuss how these interactions can either affect or prevent CDI.

