Asenjo, F. A., & Hojman, S. A. (2021). Reply to Comment on 'Do electromagnetic waves always propagate along null geodesics?' Reply. Class. Quantum Gravity, 38(23), 238002.
Abstract: A reply to the previous article commenting on nongeodesical propagation of electromagnetic fields on gravitational backgrounds and the eikonal limit are presented.

Barrera, J., & Fontbona, J. (2010). The Limiting MoveToFront SearchCost In Law Of Large Numbers Asymptotic Regimes. Ann. Appl. Probab., 20(2), 722–752.
Abstract: We explicitly compute the limiting transient distribution of the searchcost in the movetofront Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a “law of large numbers for random partitions,” a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting searchcost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting searchcost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.

Dang, C., Wei, P. F., Faes, M. G. R., Valdebenito, M. A., & Beer, M. (2022). Interval uncertainty propagation by a parallel Bayesian global optimization method. Appl. Math. Model., 108, 220–235.
Abstract: This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive blackbox function over a prescribed hyperrectangle. On this basis, a novel nonintrusive method, called `tripleengine parallel Bayesian global optimization', is proposed. The method begins by assuming a Gaussian process prior (which can also be interpreted as a surrogate model) over the response function. The main contribution lies in developing a novel infill sampling criterion, i.e., tripleengine pseudo expected improvement strategy, to identify multiple promising points for minimization and/or maximization based on the past observations at each iteration. By doing so, these identified points can be evaluated on the real response function in parallel. Besides, another potential benefit is that both the lower and upper bounds of the model response can be obtained with a single run of the developed method. Four numerical examples with varying complexity are investigated to demonstrate the proposed method against some existing techniques, and results indicate that significant computational savings can be achieved by making full use of prior knowledge and parallel computing.

Goles, E., Adamatzky, A., Montealegre, P., & RiosWilson, M. (2021). Generating Boolean Functions on Totalistic Automata Networks. Int. J. Unconv. Comput., 16(4), 343–391.
Abstract: We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are updated in parallel following a local totalistic rule, i.e., depending only on the sum of active states. Four families of totalistic rules are considered: linear or matrix defined rules (a node takes state 1 if each of its neighbours is in state 1), threshold rules (a node takes state 1 if the sum of its neighbours exceed a threshold), isolated rules (a node takes state 1 if the sum of its neighbours equals to some single number) and interval rule (a node takes state 1 if the sum of its neighbours belong to some discrete interval). We focus in studying the simulation capabilities of the dynamics of each of the latter classes. In particular, we show that totalistic automata networks governed by matrix defined rules can only implement constant functions and other matrix defined functions. In addition, we show that t by threshold rules can generate any monotone Boolean functions. Finally, we show that networks driven by isolated and the interval rules exhibit a very rich spectrum of boolean functions as they can, in fact, implement any arbitrary Boolean functions. We complement this results by studying experimentally the set of different Boolean functions generated by totalistic rules on random graphs.

Peters, A. A., Vargas, F. J., Garrido, C., Andrade, C., & Villenas, F. (2021). PLTOON: A LowCost Experimental Platform for Teaching and Research on Decentralized Cooperative Control. Sensors, 21(6), 2072.
Abstract: In this paper, we present the development of a lowcost multiagent system experimental platform for teaching, and research purposes. The platform consists of trainlike autonomous agents equipped with local speed estimation, distance sensing to their nearest predecessor, and wireless communications with other agents and a central coordinator. The individual agents can be used for simple PID experiments in a classroom or laboratory setting, while a collection of agents are capable of performing decentralized platooning with cooperative adaptive cruise control in a variety of settings, the latter being the main goal of the platform. The agents are built from low cost components and programmed with open source software, enabling teaching experiences and experimental work with a larger number of agents that would otherwise be possible with other existing solutions. Additionally, we illustrate with experimental results some of the teaching activities that the platform is capable of performing.

SotoEguibar, F., Asenjo, F. A., Hojman, S. A., & MoyaCessa, H. M. (2021). Bohm potential for the time dependent harmonic oscillator. J. Math. Phys., 62(12), 122103.
Abstract: In the MadelungBohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.
