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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

BenitezLlambay, P., Krapp, L., Ramos, X. S., & Kratter, K. M. (2023). RAM: Rapid Advection Algorithm on Arbitrary Meshes. Astron. J., 952(2), 106.
Abstract: The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid Advection Algorithm on Arbitrary Meshes. RAM is a timeexplicit method to solve the advection equation in problems with large bulk velocity on arbitrary computational grids. In comparison with standard upwind algorithms, RAM enables advection with larger time steps and lower truncation errors. Our method is based on the operator splitting technique and conservative interpolation. Depending on the bulk velocity and resolution, RAM can decrease the numerical cost of hydrodynamics by more than one order of magnitude. To quantify the truncation errors and speedup with RAM, we perform one and twodimensional hydrodynamics tests. We find that the order of our method is given by the order of the conservative interpolation and that the effective speedup is in agreement with the relative increment in time step. RAM will be especially useful for numerical studies of disksatellite interaction, characterized by high bulk orbital velocities and nontrivial geometries. Our method dramatically lowers the computational cost of simulations that simultaneously resolve the global disk and potential well inside the Hill radius of the secondary companion.
Keywords: ORBITAL ADVECTION; MAGNETOHYDRODYNAMICS CODE; SCHEME; FLOWS; MHD; SIMULATIONS; FARGO; PPM

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.

Chang, M., Liu, B., Wang, B., MartinezVillalobos, C., Ren, G., & Zhou, T. (2022). Understanding future increases in precipitation extremes in global land monsoon regions. J. Clim., 35, 1839–1851.
Abstract: This study investigates future changes in daily precipitation extremes and the involved physics over the global land monsoon (GM) region using climate models from the Coupled Model Intercomparison Project Phase 6 (CMIP6). The daily precipitation extreme is identified by the cutoff scale, measuring the extreme tail of the precipitation distribution. Compared to the historical period, multimodel results reveal a continuous increase in precipitation extremes under four scenarios, with a progressively higher fraction of precipitation exceeding the historical cutoff scale when moving into the future. The rise of the cutoffscale by the end of the century is reduced by 57.8% in the moderate emission scenario relative to the highest scenario, underscoring the social benefit in reducing emissions. The cutoff scale sensitivity, defined by the increasing rates of the cutoff scale over the GM region to the global mean surface temperature increase, is nearly independent of the projected periods and emission scenarios, roughly 8.0% K−1 by averaging all periods and scenarios. To understand the cause of the changes, we applied a physical scaling diagnostic to decompose them into thermodynamic and dynamic contributions. We find that thermodynamics and dynamics have comparable contributions to the intensified precipitation extremes in the GM region. Changes in thermodynamic scaling contribute to a spatially uniform increase pattern, while changes in dynamic scaling dominate the regional differences in the increased precipitation extremes. Furthermore, the large intermodel spread of the projection is primarily attributed to variations of dynamic scaling among models.
Keywords: Precipitation; Extreme events; Monsoons; Climate prediction; Thermodynamics; Dynamics

Cisternas, J., Navarro, M., Duarte, S., & Concha, A. (2022). Equilibrium and symmetries of altitudinal magnetic rotors on a circle. Chaos, 32(12), 123120.
Abstract: Macroscopic magnets can easily be manipulated and positioned so that interactions between themselves and with external fields induce interesting dynamics and equilibrium configurations. In this work, we use rotating magnets positioned in a line or at the vertices of a regular polygon. The rotation planes of the magnets can be modified at will. The rich structure of stable and unstable configurations is dictated by symmetry and the side of the polygon. We show that both symmetric solutions and their symmetrybreaking bifurcations can be explained with group theory. Our results suggest that the predicted magnetic textures should emerge at any length scale as long as the interaction is polar, and the system is endowed with the same symmetries.
Keywords: ARTIFICIAL SPIN ICE; DYNAMICS

Cordova, S., Canizares, C. A., Lorca, A., & Olivares, D. E. (2022). FrequencyConstrained Energy Management System for Isolated Microgrids. IEEE Trans. Smart Grid, 13(5), 3394–3407.
Abstract: Secondtosecond power imbalances stemming from renewable generation can have a large impact on the frequency regulation performance of isolated microgrids, as these are characterized by low inertia and, more commonly nowadays, significant renewable energy penetration. Thus, the present paper develops a novel frequencyconstrained Energy Management System (EMS) that takes into account the impact of shortterm power fluctuations on the microgrid's operation and frequency regulation performance. The proposed EMS model is based on accurate linear equations describing frequency deviation, rateofchangeoffrequency, and regulation provision in daily microgrid operations. Dynamic simulations on a realistic CIGRE benchmark test system show the economic and reliability benefits of the presented EMS model, highlighting the need of incorporating fast power fluctuations and their impact on frequency dynamics in EMSs for sustainable isolated microgrids.

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.

El Aiss, H., Barbosa, K. A., & Peters, A. A. (2022). Nonlinear TimeDelay ObserverBased Control to Estimate Vehicle States: Lateral Vehicle Model. IEEE Access, 10, 110459–110472.
Abstract: This paper deals with the state estimation and control problem for nonlinear lateral vehicle dynamics with time delays. First, a novel timevarying delay vehicle model described as a TakagiSugeno fuzzy model is presented. In particular, it is considered that the lateral force contains an air resistance term which is assumed to be a quadratic function of the lateral vehicle velocity. A timevarying delay has been included in the vehicle states by a simple formula in order to capture brake actuation aspects or other practical aspects that may generate a delayed response, while the nonlinear part of the vehicle model is described as a Lipschitz function. A TakagiSugeno timedelay observerbased control that satisfies the Lipschitz condition is proposed to get closedloop stability conditions. These results generalize existing ones in the literature on lateral dynamics control. Additionally, we provide a new methodology for the controller and observer gains design that can be cast as linear matrix inequality constraints. Finally, we illustrate our results with numerical examples, which also reveal the negative effect of not considering the presence of delays in the controller design.

Goles, E., Maldonado, D., & Montealegre, P. (2021). On the complexity of asynchronous freezing cellular automata. Inf. Comput., 281, 104764.
Abstract: In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each timestep only one cell is updated. We define the problem ASYNCUNSTABILITY, which consists in deciding there exists a sequential updating scheme that changes the state of a given cell.
We begin showing that ASYNCUNSTABILITY is in NL for any onedimensional FCA. Then we focus on the family of lifelike freezing CA (LFCA). We study the complexity of ASYNCUNSTABILITY for all LFCA in the triangular and square grids, showing that almost all of them can be solved in NC, except for one rule for which the problem is NPComplete. (C) 2021 Elsevier Inc. All rights reserved. Area: 08905401

Goles, E., Medina, P., & Santivanez, J. (2023). Majority networks and local consensus algorithm. Sci. Rep., 13(1), 1858.
Abstract: In this paper, we study consensus behavior based on the local application of the majority consensus algorithm (a generalization of the majority rule) over fourconnected bidimensional networks. In this context, we characterize theoretically every fourvicinity network in its capacity to reach consensus (every individual at the same opinion) for any initial configuration of binary opinions. Theoretically, we determine all regular grids with four neighbors in which consensus is reached and in which ones not. In addition, in those instances in which consensus is not reached, we characterize statistically the proportion of configurations that reach spurious fixed points from an ensemble of random initial configurations. Using numerical simulations, we also analyze two observables of the system to characterize the algorithm: (1) the quality of the achieved consensus, that is if it respects the initial majority of the network; and (2) the consensus time, measured as the average amount of steps to reach convergence.
Keywords: REGULATORY NETWORKS, DYNAMICS; BEHAVIOR; SYSTEMS

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.

GutierrezJara, J. P., VogtGeisse, K., Cabrera, M., CordovaLepe, F., & MunozQuezada, M. T. (2022). Effects of human mobility and behavior on disease transmission in a COVID19 mathematical model. Sci. Rep., 12(1), 10840.
Abstract: Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a SusceptibleExposedAsymptomaticInfectiousRecoveredSusceptible mathematical model with quarantine and socialdistancedependent transmission rates, to study COVID19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID19 is attributed to the “home” location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting.
Keywords: INFECTIOUSDISEASE; EPIDEMIC MODEL; DYNAMICS; CHALLENGES; RESISTANCE; DISTANCES; AWARENESS

Jackson, J. M., Dawson, R. I., Shannon, A., & Petrovich, C. (2021). Observable Predictions from Perturbercoupled Higheccentricity Tidal Migration of Warm Jupiters. Astron. J., 161(4), 200.
Abstract: The origin of warm Jupiters (gas giant planets with periods between 10 and 200 days) is an open question in exoplanet formation and evolution. We investigate a particular migration theory in which a warm Jupiter is coupled to a perturbing companion planet that excites secular eccentricity oscillations in the warm Jupiter, leading to periodic close stellar passages that can tidally shrink and circularize its orbit. If such companions exist in warm Jupiter systems, they are likely to be massive and closein, making them potentially detectable. We generate a set of warm Jupiterperturber populations capable of engaging in higheccentricity tidal migration and calculate the detectability of the perturbers through a variety of observational metrics. We show that a small percentage of these perturbers should be detectable in the Kepler light curves, but most should be detectable with precise radial velocity measurements over a 3 month baseline and Gaia astrometry. We find these results to be robust to the assumptions made for the perturber parameter distributions. If a highprecision radial velocity search for companions to warm Jupiters does not find evidence of a significant number of massive companions over a 3 month baseline, it will suggest that perturbercoupled higheccentricity migration is not the predominant delivery method for warm Jupiters.

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.

Lai, D., & Munoz, D. J. (2023). Circumbinary Accretion: From Binary Stars to Massive Binary Black Holes. Annu. Rev. Astron. Astrophys., 61, 517–560.
Abstract: We review recent works on the dynamics of circumbinary accretion, including time variability, angular momentum transfer between the disk and the binary, and the secular evolution of accreting binaries. These dynamics impact stellar binary formation/evolution, circumbinary planet formation/migration, and the evolution of (super)massive black hole binaries. We discuss the dynamics and evolution of inclined/warped circumbinary disks and connect with observations of protoplanetary disks. A special kind of circumbinary accretion involves binaries embedded in big disks, which may contribute to the mergers of stellarmass black holes in AGN disks. Highlights include the following:
Circumbinary accretion is highly variable, being modulated at Pb (the binary period) or similar to 5P(b), depending on the binary eccentricity e(b) and mass ratio q(b). The inner region of the circumbinary disk can develop coherent eccentric structure, which may modulate the accretion and affect the physical processes (e.g., planet migration) taking place in the disk. Over long timescales, circumbinary accretion steers binaries toward equal masses, and it does not always lead to binary orbital decay. The secular orbital evolution depends on the binary parameters (e(b) and q(b)) and on the thermodynamic properties of the accreting gas. A misaligned disk around a loweccentricity binary tends to evolve toward coplanarity due to viscous dissipation. But when e(b) is significant, the disk can evolve toward “polar alignment,” with the disk plane perpendicular to the binary plane. 
Leleu, A., Alibert, Y., Hara, N. C., Hooton, M. J., Wilson, T. G., Robutel, P., et al. (2021). Six transiting planets and a chain of Laplace resonances in TOI178. Astron. Astrophys., 649, A26.
Abstract: Determining the architecture of multiplanetary systems is one of the cornerstones of understanding planet formation and evolution. Resonant systems are especially important as the fragility of their orbital configuration ensures that no significant scattering or collisional event has taken place since the earliest formation phase when the parent protoplanetary disc was still present. In this context, TOI178 has been the subject of particular attention since the first TESS observations hinted at the possible presence of a near 2:3:3 resonant chain. Here we report the results of observations from CHEOPS, ESPRESSO, NGTS, and SPECULOOS with the aim of deciphering the peculiar orbital architecture of the system. We show that TOI178 harbours at least six planets in the superEarth to miniNeptune regimes, with radii ranging from
1.152(0.070)(+0.073)</textualform> 1.1520.070+0.073 to 2.87(0.13)(+0.14)</textualform> 2.870.13+0.14 Earth radii and periods of 1.91, 3.24, 6.56, 9.96, 15.23, and 20.71 days. All planets but the innermost one form a 2:4:6:9:12 chain of Laplace resonances, and the planetary densities show important variations from planet to planet, jumping from 1.02(0.23)(+0.28)</textualform> 1.020.23+0.28 to 0.177(0.061)(+0.055)</textualform> 0.1770.061+0.055 times the Earth's density between planets c and d. Using Bayesian interior structure retrieval models, we show that the amount of gas in the planets does not vary in a monotonous way, contrary to what one would expect from simple formation and evolution models and unlike other known systems in a chain of Laplace resonances. The brightness of TOI178 (H = 8.76 mag, J = 9.37 mag, V = 11.95 mag) allows for a precise characterisation of its orbital architecture as well as of the physical nature of the six presently known transiting planets it harbours. The peculiar orbital configuration and the diversity in average density among the planets in the system will enable the study of interior planetary structures and atmospheric evolution, providing important clues on the formation of superEarths and miniNeptunes. Keywords: HOT SUPEREARTHS; TESS INPUT CATALOG; RADIUS DISTRIBUTION; MASS; SYSTEM; MODEL; STARS; MIGRATION; DYNAMICS; TOOL

RamirezCuevas, F. V., Gurunatha, K. L., Parkin, I. P., & Papakonstantinou, I. (2022). Universal Theory of Light Scattering of Randomly Oriented Particles: A FluctuationalElectrodynamics Approach for Light Transport Modeling in Disordered Nanostructures. ACS Photonics, 9(2), 672–681.
Abstract: Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often constrained by the irregular geometry of the scatterers involved or the stochastic nature of the problem itself. In this Article, we resolve this conundrum by presenting a universal theory of averaged light scattering of randomly oriented objects. Specifically, we derive expansionbasisindependent formulas of the orientationandpolarizationaveraged absorption cross section, scattering cross section, and asymmetry parameter, for single or a collection of objects of arbitrary shape. These three parameters can be directly integrated into traditional unpolarized radiative energy transfer modeling, enabling a practical tool to predict multiple scattering and light transport in disordered nanostructured materials. Notably, the formulas of average light scattering can be derived under the principles of fluctuational electrodynamics, allowing the analogous mathematical treatment to the methods used in thermal radiation, nonequilibrium electromagnetic forces, and other associated phenomena. The proposed modeling framework is validated against optical measurements of polymer composite films with metaloxide microcrystals. Our work may contribute to a better understanding of lightmatter interactions in disordered systems, such as plasmonics for sensing and photothermal therapy, photocatalysts for water splitting and CO2 dissociation, photonic glasses for artificial structural colors, and diffuse reflectors for radiative cooling, to name just a few.
