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

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

Anderson localization on the Falicov-Kimball model with Coulomb disorder

The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phase diagrams of correlated and disordered electron systems are calculated within dynamical mean-field theory applied to the Bethe lattice, in which metal-insulator transitions led by structural and Coulomb disorders and correlation can be identified. Metallic, Mott insulator, and Anderson insulator phases, as well as the crossover between them are studied in this perspective. We show that Coulomb disorder has a relevant role in the phase-transition behavior as the system is led towards the insulator regime

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

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

Recording from two neurons: second order stimulus reconstruction from spike trains and population coding

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels - measured by a chi-squared averaged over the whole experiment - is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons

Metallicity inhomogeneities in local star-forming galaxies as sign of recent metal-poor gas accretion

We measure the oxygen metallicity of the ionized gas along the major axis of seven dwarf star-forming galaxies. Two of them, SDSSJ1647+21 and SDSSJ2238+14, show 0.5 dex metallicity decrements in inner regions with enhanced star-formation activity. This behavior is similar to the metallicity drop observed in a number of local tadpole galaxies by Sanchez Almeida et al. (2013) and interpreted as showing early stages of assembling in disk galaxies, with the star formation sustained by external metal-poor gas accretion. The agreement with tadpoles has several implications: (1) it proves that galaxies other than the local tadpoles present the same unusual metallicity pattern. (2) Our metallicity inhomogeneities were inferred using the direct method, thus discarding systematic errors usually attributed to other methods. (3) Taken together with the tadpole data, our findings suggest a threshold around one tenth the solar value for the metallicity drops to show up. Although galaxies with clear metallicity drops are rare, the physical mechanism responsible for them may sustain a significant part of the star-formation activity in the local Universe. We argue that the star-formation dependence of the mass-metallicity relationship, as well as other general properties followed by most local disk galaxies, are naturally interpreted as side effects of pristine gas infall. Alternatives to the metal poor gas accretion are examined too.Comment: Accepted for publication in ApJ. 10 pages. 5 Fig

First-principles characterisation of spectroscopic and bonding properties of cationic bismuth carbide clusters

Vibrational and electronic absorption spectra calculated at the (time-dependent) density functional theory level for the bismuth carbide clusters BinC2n+ (3≤n≤9) indicate significant differences in types of bonding that depend on cluster geometry. Analysis of the electronic charge densities of these clusters highlighted bonding trends consistent with the spectroscopic information. The combined data suggest that larger clusters (n>5) are likely to be kinetically unstable in agreement with the cluster mass distribution obtained in gas-aggregation source experiments. The spectral fingerprints of the different clusters obtained from our calculations also suggest that identification of specific BinC2n+ isomers of should be possible based on infra-red and optical absorption spectroscopy