Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

Positioning systems in Minkowski space-time: from emission to inertial coordinates

The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of an emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a `central' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.Comment: 20 pages; 1 figur

Null cone preserving maps, causal tensors and algebraic Rainich theory

A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the null cone on itself are causal. It is known that, to any tensor A on V there is a corresponding ``superenergy'' (s-e) tensor T{A} which always has the dominant property. We prove that, conversely, any symmetric rank-2 tensor with the dominant property can be written in a canonical way as a sum of N s-e tensors of simple forms. We show that the square of any rank-2 s-e tensor is proportional to the metric if N<5, and that this holds for the s-e tensor of any simple form for arbitrary N. Conversely, we prove that any symmetric rank-2 tensor T whose square is proportional to the metric must be, up to sign, the s-e of a simple p-form, and that the trace of T determines the rank p of the form. This generalises, both with respect to N and the rank p, the classical algebraic Rainich conditions, which are necessary and sufficient conditions for a metric to originate in some physical field, and has a geometric interpretation: the set of s-e tensors of simple forms is precisely the set of tensors which preserve the null cone and its time orientation. It also means that all involutory Lorentz transformations (LT) can be represented as s-e tensors of simple forms, and that any rank-2 s-e tensor is the sum of at most N conformally involutory LT. Non-symmetric null cone preserving maps are shown to have a causal symmetric part and are classified according to the null eigenvectors of the skew-symmetric part. We thus obtain a complete classification of all conformal LT and singular null cone preserving maps on V.Comment: 36 pages, no figures, LaTeX fil

Inhibition of cathepsin B by caspase-3 inhibitors blocks programmed cell death in <i>Arabidopsis</i>

Programmed cell death (PCD) is used by plants for development and survival to biotic and abiotic stresses. The role of caspases in PCD is well established in animal cells. Over the past 15 years, the importance of caspase-3-like enzymatic activity for plant PCD completion has been widely documented despite the absence of caspase orthologues. In particular, caspase-3 inhibitors blocked nearly all plant PCD tested. Here, we affinity-purified a plant caspase-3-like activity using a biotin-labelled caspase-3 inhibitor and identified Arabidopsis thaliana cathepsin B3 (AtCathB3) by liquid chromatography with tandem mass spectrometry (LC-MS/MS). Consistent with this, recombinant AtCathB3 was found to have caspase-3-like activity and to be inhibited by caspase-3 inhibitors. AtCathepsin B triple-mutant lines showed reduced caspase-3-like enzymatic activity and reduced labelling with activity-based caspase-3 probes. Importantly, AtCathepsin B triple mutants showed a strong reduction in the PCD induced by ultraviolet (UV), oxidative stress (H2O2, methyl viologen) or endoplasmic reticulum stress. Our observations contribute to explain why caspase-3 inhibitors inhibit plant PCD and provide new tools to further plant PCD research. The fact that cathepsin B does regulate PCD in both animal and plant cells suggests that this protease may be part of an ancestral PCD pathway pre-existing the plant/animal divergence that needs further characterisation

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

Contains fulltext : 172380.pdf (publisher's version ) (Open Access

Una experiencia de desarrollo profesional del docente universitario de Educación Física a través de una práctica crítica, reflexiva y colaborativa

Presentamos la experiencia realizada por un subgrupo de una red de evaluación formativa en docencia universitaria que desarrolla proyectos de innovación e investigación especialmente enfocados al proceso de convergencia europea. Se explicitan los referentes conceptuales, se describe el contexto de actuación, los participantes y el proceso seguido y se concretan los factores que han caracterizado su aplicación, desarrollo y evaluación. El objetivo es exponer de qué forma, participando en una red interuniversitaria que trabaja a partir de sucesivos ciclos de investigación-acción, se puede contribuir de manera eficaz a la formación y desarrollo profesional del profesorado. La concreción, tanto de los factores facilitadores como de los inconvenientes surgidos en el proceso, define las conclusiones así como las nuevas vías de trabajo.A programme undertaken by a subgroup of a university education evaluation network that carries out innovation and research projects focused on the process of European convergence is presented. The paper explains the programme’s conceptual framework, and describes the context of performance, the participants, the procedure followed, and those factors that have characterised its application, development and assessment. The objective is to show how, by participating in an interuniversity network that works on the basis of successive researchaction cycles, an efficient contribution can be made to the training and professional development of teaching staff. The specification of both facilitating factors and obstacles that arose in the study defines our conclusions as well as new ways to address work