An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

Two-parameter non-linear spacetime perturbations: gauge transformations and gauge invariance

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Omega), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in Omega. Clearly, any interesting physics requires non-linear perturbations, as at least terms lambda Omega need to be considered. In this paper we analyse the gauge dependence of non-linear perturbations depending on two parameters, derive explicit higher order gauge transformation rules, and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory.Comment: 22 pages, 3 figures. Minor changes to match the version appeared in Classical and Quantum Gravit

A special irreducible matrix representation of the real Clifford algebra C(3,1)

4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. As a byproduct, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.Comment: 23 pages LaTeX, to appear in the J. Math. Phys. (v2: appendix B on Pauli matrices and references are added, minor other changes

On the Asymptotic Stability of De-Sitter Spacetime: a non-linear perturbative approach

We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the perturbations decay asymptotically in time and that the solutions converge to the De-Sitter solution. By induction, this result is valid for perturbations of arbitrary order. This is in agreement with the cosmic no-hair conjecture of Gibbons and Hawking.Comment: 11 pages, 2 figure

Safer in the Clouds (Extended Abstract)

We outline the design of a framework for modelling cloud computing systems.The approach is based on a declarative programming model which takes the form of a lambda-calculus enriched with suitable mechanisms to express and enforce application-level security policies governing usages of resources available in the clouds. We will focus on the server side of cloud systems, by adopting a pro-active approach, where explicit security policies regulate server's behaviour.Comment: In Proceedings ICE 2010, arXiv:1010.530

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl

The radiative transfer for polarized radiation at second order in cosmological perturbations

This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by using a tensor valued distribution function, the second order Boltzmann equation, including polarization, is derived without relying on the Stokes parameters.Comment: 4 pages, no figure; replaced to match published versio

Disability and multidimensional quality of life: A capability approach to health status assessment

This paper offers an approach to assessing quality of life, based on Sen's (1985) theory, which it uses to understand loss in quality of life due to mobility impairment. Specifically, it provides a novel theoretical analysis that is able to account for the possibility that some functionings may increase when a person's capabilities decrease, if substitution effects are large enough. We then develop new data consistent with our theoretical framework that permits comparison of quality of life between those with a disability (mobility impairment) and those without. Empirical results show that mobility impairment has widespread rather than concentrated impacts on capabilities and is associated with high psychological costs. We also find evidence that a small number of functionings are higher for those with a disability, as our theory allows. The paper concludes by discussing possible implications for policy and health assessment methods