A logic for n-dimensional hierarchical refinement

Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.Comment: In Proceedings Refine'15, arXiv:1606.0134

Canalizing Kauffman networks: non-ergodicity and its effect on their critical behavior

Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.Comment: to be published in PR

Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.Comment: Accepted for publication in PLoS On

Unplugging the Universe: the neglected electromagnetic consequence of decoupling

This letter concentrates on the non-equilibrium evolution of magnetic field structures at the onset of recombination, when the charged particle current densities decay as neutrals are formed. We consider the effect that a decaying magnetic flux has on the acceleration of particles via the transient induced electric field. Since the residual charged-particle number density is small as a result of decoupling, we shall consider the magnetic and electric fields essentially to be imposed, neglecting the feedback from any minority accelerated population. We find that the electromagnetic treatment of this phase transition can produce energetic electrons scattered throughout the Universe. Such particles could have a significant effect on cosmic evolution in several ways: (i) their presence could delay the effective end of the recombination era; (ii) they could give rise to plasma concentrations that could enhance early gravitational collapse of matter by opposing cosmic expansion to a greater degree than neutral matter could; (iii) they could continue to be accelerated, and become the seed for reionisation at the later epoch $z \approx 10$.Comment: 4 pages, no figure

Is the equivalence for the response of static scalar sources in the Schwarzschild and Rindler spacetimes valid only in four dimensions?

It was shown recently that in four dimensions scalar sources with fixed proper acceleration minimally coupled to a massless Klein-Gordon field lead to the same responses when they are (i) uniformly accelerated in Minkowski spacetime (in the inertial vacuum) and (ii) static in the Schwarzschild spacetime (in the Unruh vacuum). Here we show that this equivalence is broken if the spacetime dimension is more than four.Comment: 4 pages, 1 figur

Introdução à análise probabilística simplificada da segurança estrutural

A análise da segurança de estruturas com vidas úteis diferentes das correntes, de estruturas existentes, de estruturas submetidas a acções invulgares, ou de estruturas reforçadas, é bastante complexa. A abordagem correcta deste problema não pode dispensar a utilização de modelos probabilísticos, que são desconhecidos da maioria dos engenheiros civis. Neste trabalho é apresentada uma breve introdução à análise probabilística simplificada da segurança, dando especial destaque à descrição dos modelos de acções e à análise de exemplos de aplicação

3D Simulations of Relativistic Precessing Jets Probing the Structure of Superluminal Sources

We present the results of a three-dimensional, relativistic, hydrodynamic simulation of a precessing jet into which a compact blob of matter is injected. A comparison of synthetic radio maps computed from the hydrodynamic model, taking into account the appropriate light travel time delays, with those obtained from observations of actual superluminal sources shows that the variability of the jet emission is the result of a complex combination of phase motions, viewing angle selection effects, and non-linear interactions between perturbations and the underlying jet and/or the external medium. These results question the hydrodynamic properties inferred from observed apparent motions and radio structures, and reveal that shock-in-jet models may be overly simplistic.Comment: Accepted for publication in ApJL. 4 pages, 5 figures (4 in color