Generalized Nonlinear Proca Equation and its Free-Particle Solutions

We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter $q$ (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit $q \rightarrow 1$. We derive the nonlinear Proca equation from a Lagrangian that, besides the usual vectorial field $\Psi^{\mu}(\vec{x},t)$, involves an additional field $\Phi^{\mu}(\vec{x},t)$. We obtain exact time dependent soliton-like solutions for these fields having the form of a $q$-plane wave, and show that both field equations lead to the relativistic energy-momentum relation $E^{2} = p^{2}c^{2} + m^{2}c^{4}$ for all values of $q$. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present $q$-generalized Proca theory reduces to Maxwell electromagnetism, and the $q$-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed

Constellation Queries over Big Data

A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation contexts. For example, a particularly interesting geometric pattern in astronomy is the Einstein cross, which is an astronomical phenomenon in which a single quasar is observed as four distinct sky objects (due to gravitational lensing) when captured by earth telescopes. Finding such crosses, as well as other geometric patterns, is a challenging problem as the potential number of sets of elements that compose shapes is exponentially large in the size of the dataset and the pattern. In this paper, we denote geometric patterns as constellation queries and propose algorithms to find them in large data applications. Our methods combine quadtrees, matrix multiplication, and unindexed join processing to discover sets of points that match a geometric pattern within some additive factor on the pairwise distances. Our distributed experiments show that the choice of composition algorithm (matrix multiplication or nested loops) depends on the freedom introduced in the query geometry through the distance additive factor. Three clearly identified blocks of threshold values guide the choice of the best composition algorithm. Finally, solving the problem for relative distances requires a novel continuous-to-discrete transformation. To the best of our knowledge this paper is the first to investigate constellation queries at scale

Radiatively induced leptogenesis in a minimal seesaw model

We study the possibility that the baryon asymmetry of the universe is generated in a minimal seesaw scenario where two right-handed Majorana neutrinos with degenerate masses are added to the standard model particle content. In the usual framework of thermal leptogenesis, a nonzero $CP$ asymmetry can be obtained through the mass splitting induced by the running of the heavy Majorana neutrino masses from their degeneracy scale down to the seesaw scale. Although, in the light of the present neutrino oscillation data, the produced baryon asymmetry turns out to be smaller than the experimental value, the present mechanism could be viable in simple extensions of the standard model.Comment: 6 pages, 2 figures, uses RevTeX4, calculations improved, comments adde

Task relevance modulates the behavioural and neural effects of sensory predictions

The brain is thought to generate internal predictions to optimize behaviour. However, it is unclear whether predictions signalling is an automatic brain function or depends on task demands. Here, we manipulated the spatial/temporal predictability of visual targets, and the relevance of spatial/temporal information provided by auditory cues. We used magnetoencephalography (MEG) to measure participants' brain activity during task performance. Task relevance modulated the influence of predictions on behaviour: spatial/temporal predictability improved spatial/temporal discrimination accuracy, but not vice versa. To explain these effects, we used behavioural responses to estimate subjective predictions under an ideal-observer model. Model-based time-series of predictions and prediction errors (PEs) were associated with dissociable neural responses: predictions correlated with cue-induced beta-band activity in auditory regions and alpha-band activity in visual regions, while stimulus-bound PEs correlated with gamma-band activity in posterior regions. Crucially, task relevance modulated these spectral correlates, suggesting that current goals influence PE and prediction signalling

Identificação das características dos clientes associadas ao risco de crédito

O processo da tomada de decisão sobre a avaliação de uma solicitação de crédito comercial é por vezes difícil para o julgamento humano, devido à imensidão de variáveis que estão em jogo e das suas inter- relações. Neste artigo propomo-nos identificar as características dos clientes associadas a alto e a baixo risco, com recurso a um modelo aplicacional. A partir de uma base de dados de um cartão de crédito, formada por variáveis de natureza qualitativa e quantitativa, ajustámos um modelo logit binário, com o objectivo de tornar o processo de decisão mais objectivo e quantificável. Em seguida, identificámos oito classes de risco através da aplicação de um método de classificação não hierárquica (K-means) sobre o vector da pontuação do modelo logit. Aferimos temporalmente o comportamento de cada classe de risco ao longo de 70 meses, verificando-se que probabilidades baixas de default estão associadas a classes de risco baixo. As características dos clientes tipicamente associadas ao risco de crédito foram identificadas através de uma Análise Factorial das Correspondências

Spin-Glass Attractor on Tridimensional Hierarchical Lattices in the Presence of an External Magnetic Field

A nearest-neighbor-interaction Ising spin glass, in the presence of an external magnetic field, is studied on different hierarchical lattices that approach the cubic lattice. The magnetic field is considered as uniform, or random (following either a bimodal or a Gaussian probability distribution). In all cases, a spin-glass attractor is found, in the plane magnetic field versus temperature, associated with a low-temperature phase. The physical consequences of this attractor are discussed, in view of the present scenario of the spin-glass problem.Comment: Accepted for publication in Physical Review

Thermostatistics of extensive and non-extensive systems using generalized entropies

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short-range and long-range interactions. The first method is quite general and it is based on the numerical evaluation of the density of states with a given energy. The second method is more specific for Tsallis thermostatistics and it is based on a standard Monte Carlo Metropolis algorithm along with a numerical integration procedure. We show here that both methods are robust and efficient. We present results of the application of the methods to the one-dimensional Ising model both in a short-range case and in a long-range (non-extensive) case. We show that the thermodynamic potentials for different values of the system size N and different values of the non-extensivity parameter q can be described by scaling relations which are an extension of the ones holding for the Boltzmann-Gibbs statistics (q=1). Finally, we discuss the differences in using standard or non-standard mean value definitions in the Tsallis thermostatistics formalism and present a microcanonical ensemble calculation approach of the averages.Comment: Submitted to Physica A. LaTeX format, 38 pages, 17 EPS figures. IMEDEA-UIB, 07071 Palma de Mallorca, Spain, http://www.imedea.uib.e

On the width of the last scattering surface

We discuss the physical effects of some accelerated world models on the width of the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). The models considered in our analysis are X-matter (XCDM) and a Chaplygin type gas. The redshift of the LSS does not depend on the kind of dark energy (if XCDM of Chaplygin). Further, for a Chaplygin gas, the width of the LSS is also only weakly dependent on the kind of scenario (if we have dark energy plus cold dark matter or the unified picture).Comment: 10 pages, 1 figure, 2 tables, accepted to IJMP

Water and chemical budgets at the catchment scale from intact forests and disturbed landscapes.

Poster 262

Purification of fructo-oligosaccharides

Este resumo faz parte de: Book of abstracts of the Meeting of the Institute for Biotechnology and Bioengineering, 2, Braga, Portugal, 2010. A versão completa do livro de atas está disponível em: http://hdl.handle.net/1822/1096