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Aracena, J., Demongeot, J., Fanchon, E., & Montalva, M. (2013). On the number of different dynamics in Boolean networks with deterministic update schedules. Math. Biosci., 242(2), 188–194.
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 NPcomplete. 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.
Keywords: Boolean network; Update schedule; Update digraph; Dynamics

Canessa, E., & Chaigneau, S. (2014). The dynamics of social agreement according to Conceptual Agreement Theory. Qual. Quant., 48(6), 3289–3309.
Abstract: Many social phenomena can be viewed as processes in which individuals in social groups develop agreement (e.g., public opinion, the spreading of rumor, the formation of social and linguistic conventions). Conceptual Agreement Theory (CAT) models social agreement as a simplified communicational event in which an Observer and Actor exchange ideas about a concept , and where uses that information to infer whether 's conceptual state is the same as its own (i.e., to infer agreement). Agreement may be true (when infers that is thinking and this is in fact the case, event ) or illusory (when infers that is thinking and this is not the case, event ). In CAT, concepts that afford or become more salient in the minds of members of social groups. Results from an agentbased model (ABM) and probabilistic model that implement CAT show that, as our conceptual analyses suggested would be the case, the simulated social system selects concepts according to their usefulness to agents in promoting agreement among them (Experiment 1). Furthermore, the ABM exhibits more complex dynamics where similar minded agents cluster and are able to retain useful concepts even when a different group of agents discards them (Experiment 2). We discuss the relevance of CAT and the current findings for analyzing different social communication events, and suggest ways in which CAT could be put to empirical test.

Dumett, M. A., & Cominetti, R. (2018). On The Stability Of An Adaptive Learning Dynamics In Traffic Games. J. Dyn. Games, 5(4), 265–282.
Abstract: This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the RouthHurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.

Goles, E., Montalva, M., & Ruz, G. A. (2013). Deconstruction and Dynamical Robustness of Regulatory Networks: Application to the Yeast Cell Cycle Networks. Bull. Math. Biol., 75(6), 939–966.
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.
Keywords: Boolean networks; Attractors; Update robustness; Alliances; Dynamics

Goles, E., Montealegre, P., Perrot, K., & Theyssier, G. (2018). On the complexity of twodimensional signed majority cellular automata. J. Comput. Syst. Sci., 91, 1–32.
Abstract: We study the complexity of signed majority cellular automata on the planar grid. We show that, depending on their symmetry and uniformity, they can simulate different types of logical circuitry under different modes. We use this to establish new bounds on their overall complexity, concretely: the uniform asymmetric and the nonuniform symmetric rules are Turing universal and have a Pcomplete prediction problem; the nonuniform asymmetric rule is intrinsically universal; no symmetric rule can be intrinsically universal. We also show that the uniform asymmetric rules exhibit cycles of superpolynomial length, whereas symmetric ones are known to have bounded cycle length. (C) 2017 Elsevier Inc. All rights reserved.

Gonzalez, E., & Villena, M. J. (2020). On the spatial dynamics of vaccination: A spatial SIRSV model. Comput. Math. Appl., 80(5), 733–743.
Abstract: In this paper, we analyze the effects of vaccination from a spatial perspective. We propose a spatial deterministic SIRSV model, which considers a nonlinear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process. The model allows us to simulate numerically the spatial and temporal dynamics of an epidemic, considering different spatial strategies for the vaccination policy. In particular, in our first example we analyze the classical SIRSV evolution with the addition of movements due to diffusion, while in the second one we focus on modeling one ring vaccination policy. We expect this model can improve spatial predictions of SIR vaccination models by taking into account the spatial dimension of the problem. (C) 2020 Elsevier Ltd. All rights reserved.

Kapitanov, G., Alvey, C., VogtGeisse, K., & Feng, Z. L. (2015). An AgeStructured Model For The Coupled Dynamics Of Hiv And Hsv2. Math. Biosci. Eng., 12(4), 803–840.
Abstract: Evidence suggests a strong correlation between the prevalence of HSV2 (genital herpes) and the perseverance of the HIV epidemic. HSV2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the coinfection dynamics between the two diseases by incorporating a timesinceinfection variable to track the alternating periods of infectiousness of HSV2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.

Lagos, F., Schreiber, M. R., Parsons, S. G., Zurlo, A., Mesa, D., Gansicke, B. T., et al. (2020). The White Dwarf Binary Pathways Survey III. Contamination from hierarchical triples containing a white dwarf. Mon. Not. Roy. Astron. Soc., 494(1), 915–922.
Abstract: The White Dwarf Binary Pathways Survey aims at increasing the number of known detached A, F, G, and K mainsequence stars in close orbits with white dwarf companions (WD+AFGK binaries) to refine our understanding about compact binary evolution and the nature of Supernova Ia progenitors. These close WD+AFGK binary stars are expected to form through common envelope evolution, in which tidal forces tend to circularize the orbit. However, some of the identified WD+AFGK binary candidates show eccentric orbits, indicating that these systems are either formed through a different mechanism or perhaps they are not close WD+AFGK binaries. We observed one of these eccentric WD+AFGK binaries with SPHERE and find that the system TYC 72189341 is in fact a triple system where the WD is a distant companion. The inner binary likely consists of the Gtype star plus an unseen lowmass companion in an eccentric orbit. Based on this finding, we estimate the fraction of triple systems that could contaminate the WD+AFGK sample. We find that less than 15 per cent of our targets with orbital periods shorter than 100 d might be hierarchical triples.

RodriguezValdecantos, G., Manzano, M., Sanchez, R., Urbina, F., Hengst, M. B., Lardies, M. A., et al. (2017). Early successional patterns of bacterial communities in soil microcosms reveal changes in bacterial community composition and network architecture, depending on the successional condition. Appl. Soil Ecol., 120, 44–54.
Abstract: Soil ecosystem dynamics are influenced by the composition of bacterial communities and environmental conditions. A common approach to study bacterial successional dynamics is to survey the trajectories and patterns that follow bacterial community assemblages; however early successional stages have received little attention. To elucidate how soil type and chemical amendments influence both the trajectories that follow early compositional changes and the architecture of the community bacterial networks in soil bacterial succession, a time series experiment of soil microcosm experiments was performed. Soil bacterial communities were initially perturbed by dilution and subsequently subjected to three amendments: application of the pesticide 2,4dichlorophenoxyacetic acid, as a pesticideamended succession; application of cycloheximide, an inhibitor affecting primarily eukaryotic microorganisms, as a eukaryoticinhibition bacterial succession; or application of sterile water as a nonperturbed control. Terminal restriction fragment length polymorphism (TRFLP) analysis of the 16S rRNA gene isolated from soil microcosms was used to generate bacterial relative abundance datasets. BrayCurtis similarity and beta diversity partitionbased methods were applied to identify the trajectories that follow changes in bacterial community composition. Results demonstrated that bacterial communities exposed to these three conditions rapidly differentiated from the starting point (less than 12 h), followed different compositional change trajectories depending on the treatment, and quickly converged to a state similar to the initial community (4872 h). Network inference analysis was applied using a generalized LotkaVolterra model to provide an overview of bacterial OTU interactions and to follow the changes in bacterial community networks. This analysis revealed that antagonistic interactions increased when eukaryotes were inhibited, whereas cooperative interactions increased under pesticide influence. Moreover, central OTUs from soil bacterial community networks were also persistent OTUs, thus confirming the existence of a core bacterial community and that these same OTUs could plastically interact according to the perturbation type to quickly stabilize bacterial communities undergoing succession.

Ruivo, E. L. P., MontalvaMedel, M., de Oliveira, P. P. B., & Perrot, K. (2018). Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates. Chaos Solitons Fractals, 113, 209–220.
Abstract: Cellular automata are fullydiscrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different onestep trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their onestep maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's onestep trajectories also to change after one iteration. Although the onestep maximum sensitivity does not imply that the remainder of the timeevolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.

Schlecker, M., Kossakowski, D., Brahm, R., Espinoza, N., Henning, T., Carone, L., et al. (2020). A highly eccentric warm jupiter orbiting TIC 237913194. Astron. J., 160(6), 275.
Abstract: The orbital parameters of warm Jupiters serve as a record of their formation history, providing constraints on formation scenarios for giant planets on close and intermediate orbits. Here, we report the discovery of TIC.237913194b, detected in fullframe images from Sectors 1 and 2 of the Transiting Exoplanet Survey Satellite (TESS), groundbased photometry (ChileanHungarian Automated Telescope, Las Cumbres Observatory Global Telescope), and Fiberfed Extended Range Optical Spectrograph radial velocity time series. We constrain its mass to MP = 1.942(0.091)(+0.091) MJ and its radius to RP = 1.117(0.047)(+0.054) RJ, implying a bulk density similar to Neptune's. It orbits a Gtype star (M* = 1.026(0.055)(+0.057) Mcircle dot, V = 12.1 mag) with a period of 15.17 days on one of the most eccentric orbits of all known warm giants (e approximate to 0.58). This extreme dynamical state points to a past interaction with an additional, undetected massive companion. A tidal evolution analysis showed a large tidal dissipation timescale, suggesting that the planet is not a progenitor for a hot Jupiter caught during its higheccentricity migration. TIC.237913194b further represents an attractive opportunity to study the energy deposition and redistribution in the atmosphere of a warm Jupiter with high eccentricity.
