Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

Stochastic model of hysteresis

The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic evolution of the process. It has been shown that the branches of the hysteresis loop are converging to fixed limit curves when the number of cyclic back-and-forth variations of the control parameter between two consecutive reversal points is large enough. This convergence to limit curves gives a clear explanation of the accommodation process. The accommodated minor loops show the return-point memory property but this property is obviously absent in the case of non-accommodated minor loops which are not congruent and generally not closed. In contrast to the traditional Preisach model the reversal point susceptibilities are non-zero finite values. The stochastic model can provide a good approximation of the Raylaigh quadratic law when the external parameter varies between two sufficiently small values.Comment: 13 pages, 14 figure

Monitoring of arthropod infestations on high quality hard wheat in southern Italy

The results of a survey in 2006-2009 on high quality hard wheat, coming from 31 different storage centers located in Southern Italy, are reported. About 300 samples were analyzed by visual test, while 891 by both sieving and biological test. For the three different kinds of test the infesting species are listed and their relative incidence on the samples is reported. The most widespread species in the samples belonged to the order Coleoptera, i.e. Sitophilus granarius, Rhyzopertha dominica and Oryzaephilus spp., while Lepidoptera were less abundant. The results are discussed with the aim of providing the storage centre operators with helpful information on the correct monitoring strategies to adopt in case of arthropod infestations in high-quality hard-wheat warehouses.Keywords: Stored grain, Insects, Sampling, Coleoptera, Ital

PRET: Prerequisite-enriched terminology. A case study on educational texts

In this paper we present PRET, a gold dataset annotated for prerequisite relations between educational concepts extracted from a computer science textbook, and we describe the language and domain independent approach for the creation of the resource. Additionally, we have created an annotation tool to support, validate and analyze the annotation

Visualisation analysis for exploring prerequisite relations in textbooks

Building automatic strategies for organising knowledge contained in textbooks has a tremendous potential to enhance meaningful learning. Automatic identification of prerequisite relation (PR) between concepts in a textbook is a well-known way for knowledge structuring, yet it is still an open issue. Our research contributes for better understanding and exploring the phenomenon of PR in textbooks, by providing a collection of visualisation techniques for PR exploration and analysis, that we used for the design of and then the refinement of our algorithm for PR extraction

Gravitational Waves: Just Plane Symmetry

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.Comment: 10 pages, TeX, uses IOP style file

The interaction of aluminum with catecholamine-based neurotransmitters: Can the formation of these species be considered a potential risk factor for neurodegenerative diseases?

The potential neurotoxic role of Al(iii) and its proposed link with the insurgence of Alzheimer's Disease (AD) have attracted increasing interest towards the determination of the nature of bioligands that are propitious to interact with aluminum. Among them, catecholamine-based neurotransmitters have been proposed to be sensitive to the presence of this non-essential metal ion in the brain. In the present work, we characterize several aluminum-catecholamine complexes in various stoichiometries, determining their structure and thermodynamics of formation. For this purpose, we apply a recently validated computational protocol with results that show a remarkably good agreement with the available experimental data. In particular, we employ Density Functional Theory (DFT) in conjunction with continuum solvation models to calculate complexation energies of aluminum for a set of four important catecholamines: l-DOPA, dopamine, noradrenaline and adrenaline. In addition, by means of the Quantum Theory of Atoms in Molecules (QTAIM) and Energy Decomposition Analysis (EDA) we assessed the nature of the Al-ligand interactions, finding mainly ionic bonds with an important degree of covalent character. Our results point at the possibility of the formation of aluminum-catecholamine complexes with favorable formation energies, even when proton/aluminum competition is taken into account. Indeed, we found that these catecholamines are better aluminum binders than catechol at physiological pH, because of the electron withdrawing effect of the positively-charged amine that decreases their deprotonation penalty with respect to catechol. However, overall, our results show that, in an open biological environment, the formation of Al-catecholamine complexes is not thermodynamically competitive when compared with the formation of other aluminum species in solution such as Al-hydroxide, or when considering other endogenous/exogenous Al(iii) ligands such as citrate, deferiprone and EDTA. In summary, we rule out the possibility, suggested by some authors, that the formation of Al-catecholamine complexes in solution might be behind some of the toxic roles attributed to aluminum in the brain. An up-to-date view of the catecholamine biosynthesis pathway with sites of aluminum interference (according to the current literature) is presented. Alternative mechanisms that might explain the deleterious effects of this metal on the catecholamine route are thoroughly discussed, and new hypotheses that should be investigated in future are proposed