The hidden geometric character of relativistic quantum mechanics

The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in an hyperbolic space this fact leads inevitably to a wave equation with plane-like solutions. This is also true for 5-dimensional spacetime and we will explore those solutions, establishing a parallel with the solutions of the Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that don't belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate 4-fold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.Comment: 29 pages. Small changes in V3 suggested by refere

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Microlensing path parametrization for Earth-like Exoplanet detection around solar mass stars

We propose a new parametrization of the impact parameter u0 and impact angle {\alpha} for microlensing systems composed by an Earth-like Exoplanet around a Solar mass Star at 1 AU. We present the caustic topology of such system, as well as the related light curves generated by using such a new parametrization. Based on the same density of points and accuracy of regular methods, we obtain results 5 times faster for discovering Earth-like exoplanet. In this big data revolution of photometric astronomy, our method will impact future missions like WFIRST (NASA) and Euclid (ESA) and they data pipelines, providing a rapid and deep detection of exoplanets for this specific class of microlensing event that might otherwise be lost.Comment: 8 pages, 7 figures, accepted to be published in The Astronomical Journa

Temporal Analysis of Activity Patterns of Editors in Collaborative Mapping Project of OpenStreetMap

In the recent years Wikis have become an attractive platform for social studies of the human behaviour. Containing millions records of edits across the globe, collaborative systems such as Wikipedia have allowed researchers to gain a better understanding of editors participation and their activity patterns. However, contributions made to Geo-wikis_wiki-based collaborative mapping projects_ differ from systems such as Wikipedia in a fundamental way due to spatial dimension of the content that limits the contributors to a set of those who posses local knowledge about a specific area and therefore cross-platform studies and comparisons are required to build a comprehensive image of online open collaboration phenomena. In this work, we study the temporal behavioural pattern of OpenStreetMap editors, a successful example of geo-wiki, for two European capital cities. We categorise different type of temporal patterns and report on the historical trend within a period of 7 years of the project age. We also draw a comparison with the previously observed editing activity patterns of Wikipedia.Comment: Submitte

Polarization of the changing-look quasar J1011+5442

If the disappearance of the broad emission lines observed in changing-look quasars were caused by the obscuration of the quasar core through moving dust clouds in the torus, high linear polarization typical of type 2 quasars would be expected. We measured the polarization of the changing-look quasar J1011+5442 in which the broad emission lines have disappeared between 2003 and 2015. We found a polarization degree compatible with null polarization. This measurement suggests that the observed change of look is not due to a change of obscuration hiding the continuum source and the broad line region, and that the quasar is seen close to the system axis. Our results thus support the idea that the vanishing of the broad emission lines in J1011+5442 is due to an intrinsic dimming of the ionizing continuum source that is most likely caused by a rapid decrease in the rate of accretion onto the supermassive black hole.Comment: Accepted for publication in Astronomy and Astrophysics Letter