On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold $M$, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the $C^k$-topology, $k=2,...,\infty$, in the set of metrics of a given index on $M$. A higher order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.Comment: 17 page

Genericity of nondegenerate geodesics with general boundary conditions

Let M be a possibly noncompact manifold. We prove, generically in the C^k-topology (k=2,...,\infty), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of the product MxM that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal of MxM. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C^k-generic are given.Comment: LaTeX2e, 21 pages, no figure

Variadic genericity through linguistic reflection : a performance evaluation

This work is partially supported by the EPSRC through Grant GR/L32699 “Compliant System Architecture” and by ESPRIT through Working Group EP22552 “PASTEL”.The use of variadic genericity within schema definitions increases the variety of databases that may be captured by a single specification. For example, a class of databases of engineering part objects, in which each database instance varies in the types of the parts and the number of part types, should lend itself to a single definition. However, precise specification of such a schema is beyond the capability of polymorphic type systems and schema definition languages. It is possible to capture such generality by introducing a level of interpretation, in which the variation in types and in the number of fields is encoded in a general data structure. Queries that interpret the encoded information can be written against this general data structure. An alternative approach to supporting such variadic genericity is to generate a precise database containing tailored data structures and queries for each different instance of the virtual schema.1 This involves source code generation and dynamic compilation, a process known as linguistic reflection. The motivation is that once generated, the specific queries may execute more efficiently than their generic counter-parts, since the generic code is “compiled away”. This paper compares the two approaches and gives performance measurements for an example using the persistent languages Napier88 and PJama.Postprin

Typological parameters of genericity

Different languages employ different morphosyntactic devices for expressing genericity. And, of course, they also make use of different morphosyntactic and semantic or pragmatic cues which may contribute to the interpretation of a sentence as generic rather than episodic. [...] We will advance the strong hypo thesis that it is a fundamental property of lexical elements in natural language that they are neutral with respect to different modes of reference or non-reference. That is, we reject the idea that a certain use of a lexical element, e.g. a use which allows reference to particular spatio-temporally bounded objects in the world, should be linguistically prior to all other possible uses, e.g. to generic and non-specific uses. From this it follows that we do not consider generic uses as derived from non-generic uses as it is occasionally assumed in the literature. Rather, we regard these two possibilities of use as equivalent alternative uses of lexical elements. The typological differences to be noted therefore concern the formal and semantic relationship of generic and non-generic uses to each other; they do not pertain to the question of whether lexical elements are predetermined for one of these two uses. Even supposing we found a language where generic uses are always zero-marked and identical to lexical sterns, we would still not assume that lexical elements in this language primarily have a generic use from which the non-generic uses are derived. (Incidentally, none of the languages examined, not even Vietnamese, meets this criterion.

Genericity aspects in gravitational collapse to black holes and naked singularities

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.Comment: 24 pages, 6 figures, some changes in text and figures to match the version accepted for publication by IJMP

From types to type requirements: Genericity for model-driven engineering

The final publication is available at Springer via http://dx.doi.org/10.1007/s10270-011-0221-0Model-driven engineering (MDE) is a software engineering paradigm that proposes an active use of models during the development process. This paradigm is inherently type-centric, in the sense that models and their manipulation are defined over the types of specific meta-models. This fact hinders the reuse of existing MDE artefacts with other meta-models in new contexts, even if all these meta-models share common characteristics. To increase the reuse opportunities of MDE artefacts, we propose a paradigm shift from type-centric to requirement-centric specifications by bringing genericity into models, meta-models and model management operations. For this purpose, we introduce so-called concepts gathering structural and behavioural requirements for models and meta-models. In this way, model management operations are defined over concepts, enabling the application of the operations to any meta-model satisfying the requirements imposed by the concept. Model templates rely on concepts to define suitable interfaces, hence enabling the definition of reusable model components. Finally, similar to mixin layers, templates can be defined at the meta-model level as well, to define languages in a modular way, as well as layers of functionality to be plugged-in into other meta-models. These ideas have been implemented in MetaDepth, a multi-level meta-modelling tool that integrates action languages from the Epsilon family for model management and code generation.This work has been sponsored by the Spanish Ministry of Science and Innovation with projects METEORIC (TIN2008-02081) and Go Lite (TIN2011-24139), and by the R&D program of the Community of Madrid with project “e-Madrid” (S2009/TIC-1650)