Isometric shifts and metric spaces

Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.Comment: 10 pages, LaTeX, no figure

Automatic Detection of Trends in Dynamical Text: An Evolutionary Approach

This paper presents an evolutionary algorithm for modeling the arrival dates of document streams, which is any time-stamped collection of documents, such as newscasts, e-mails, IRC conversations, scientific journals archives and weblog postings. This algorithm assigns frequencies (number of document arrivals per time unit) to time intervals so that it produces an optimal fit to the data. The optimization is a trade off between accurately fitting the data and avoiding too many frequency changes; this way the analysis is able to find fits which ignore the noise. Classical dynamic programming algorithms are limited by memory and efficiency requirements, which can be a problem when dealing with long streams. This suggests to explore alternative search methods which allow for some degree of uncertainty to achieve tractability. Experiments have shown that the designed evolutionary algorithm is able to reach the same solution quality as those classical dynamic programming algorithms in a shorter time. We have also explored different probabilistic models to optimize the fitting of the date streams, and applied these algorithms to infer whether a new arrival increases or decreases {\em interest} in the topic the document stream is about.Comment: 22 pages, submitted to Journal of Information Retrieva

Entropy in locally-de Sitter spacetimes

As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known "a priori", independently of Einstein equation. They represent different non-gravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincar\'e, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.Comment: 11 pages. V2: presentation changes aiming at clarifying the text. Version accepted for publication in Int. J. Mod. Phys.

Flat deformations of Pn{\mathbb P}^n

In this paper we study projective flat deformations of projective spaces. We prove that the singular fibers of projective flat deformations of projective spaces appear either in codimension 1 or over singular points of the base. We also describe projective flat deformations of projective spaces with smooth total space, and discuss flatness criteria.Comment: 6 page

NectaRSS, an RSS feed ranking system that implicitly learns user preferences

In this paper a new RSS feed ranking method called NectaRSS is introduced. The system recommends information to a user based on his/her past choices. User preferences are automatically acquired, avoiding explicit feedback, and ranking is based on those preferences distilled to a user profile. NectaRSS uses the well-known vector space model for user profiles and new documents, and compares them using information-retrieval techniques, but introduces a novel method for user profile creation and adaptation from users' past choices. The efficiency of the proposed method has been tested by embedding it into an intelligent aggregator (RSS feed reader), which has been used by different and heterogeneous users. Besides, this paper proves that the ranking of newsitems yielded by NectaRSS improves its quality with user's choices, and its superiority over other algorithms that use a different information representation method.Comment: Submitted to First Monday. 16 page

Gravitational wave background from neutron star phase transition

We study the generation of a stochastic gravitational wave (GW) background produced by a population of neutron stars (NSs) which go over a hadron-quark phase transition in its inner shells. We obtain, for example, that the NS phase transition, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of $h_{\rm BG} \sim 10^{-24}$, in the frequency band $\nu_{\rm{obs}} \simeq 20-2000 {\rm Hz}$ for stars forming at redshifts of up to $z\simeq 20.$ We study the possibility of detection of this isotropic GW background by correlating signals of a pair of Advanced LIGO observatories.Comment: 17 pages, 5 figure

de Sitter-invariant special relativity and the dark energy problem

The replacement of the Poincar\'e-invariant Einstein special relativity by a de Sitter-invariant special relativity produces concomitant changes in all relativistic theories, including general relativity. A crucial change in the latter is that both the background de Sitter curvature and the gravitational dynamical curvature turns out to be included in a single curvature tensor. This means that the cosmological term no longer explicitly appears in Einstein equation, and is consequently not restricted to be constant. In this paper, the Newtonian limit of such theory is obtained, and the ensuing Newtonian Friedmann equations are show to provide a good account of the dark energy content of the present-day universe.Comment: 14 pages. Accepted for publication in Class. Quantum Grav. V2: a few corrections and small presentation change

de Sitter invariant special relativity and galaxy rotation curves

Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincar\'e invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is used to study the circular velocity of stars around the galactic center. It is shown that the de Sitter modified Newtonian force---which includes corrections coming from the underlying local kinematics---could possibly explain the rotation curve of galaxies without the necessity of supposing the existence of a dark matter halo.Comment: 12 pages, 1 figure. V2: presentation changes aiming at clarifying the text, 13 pages, 1 figure; matches published version. arXiv admin note: text overlap with arXiv:1704.0212

On the volume of singular-hyperbolic sets

An attractor $\Lambda$ for a 3-vector field $X$ is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that $C^{1+\alpha}$ singular-hyperbolic attractors, for some $\alpha>0$, always have zero volume, thus extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular attractors. Moreover, we prove that if $\Lambda$ is a singular-hyperbolic attractor for $X$ then either it has zero volume or $X$ is an Anosov flow. We also present examples of $C^1$ singular-hyperbolic attractors with positive volume. In addition, we show that $C^1$ generically we have volume zero for $C^1$ robust classes of singular-hyperbolic attractors.Comment: 19 pages, 3 figures; references updated and minor correction

Stacked triangular lattice: Percolation properties

The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties have received few attention. We investigate several non-universal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is $p_c^\text{bond}=0.186\;02\pm0.000\;02$ for bonds and $p_c^\text{site}=0.262\;40\pm0.000\;05$ for sites. The number of clusters at the threshold per site is $n_c^\text{bond}=0.284\;58\pm0.000\;05$ and $n_c^\text{site}=0.039\;98\pm0.000\;05$. The stacked triangular lattice is a convenient choice to study the RGB model [Sci. Rep. {\bf 2}, 751 (2012)]. We present results on this model and its scaling behavior at the percolation threshold