Time in the theory of relativity: on natural clocks, proper time, the clock hypothesis, and all that

When addressing the notion of proper time in the theory of relativity, it is usually taken for granted that the time read by an accelerated clock is given by the Minkowski proper time. However, there are authors like Harvey Brown that consider necessary an extra assumption to arrive at this result, the so-called clock hypothesis. In opposition to Brown, Richard T. W. Arthur takes the clock hypothesis to be already implicit in the theory. In this paper I will present a view different from these authors by recovering Einstein's notion of natural clock and showing its relevance to the debate

Reusable Knowledge-based Components for Building Software Applications: A Knowledge Modelling Approach

In computer science, different types of reusable components for building software applications were proposed as a direct consequence of the emergence of new software programming paradigms. The success of these components for building applications depends on factors such as the flexibility in their combination or the facility for their selection in centralised or distributed environments such as internet. In this article, we propose a general type of reusable component, called primitive of representation, inspired by a knowledge-based approach that can promote reusability. The proposal can be understood as a generalisation of existing partial solutions that is applicable to both software and knowledge engineering for the development of hybrid applications that integrate conventional and knowledge based techniques. The article presents the structure and use of the component and describes our recent experience in the development of real-world applications based on this approach

Nonlinear approximation with nonstationary Gabor frames

We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions generalizes to the nonstationary case, providing perfect reconstruction and an FFT based implementation for compactly supported window functions sampled at a certain density. It is also known that for some signal classes, NSGFs with flexible time resolution tend to provide sparser expansions than can be obtained with classical Gabor frames. In this article we show, for the continuous case, that sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an associated decomposition space. In this way we characterize signals with sparse expansions relative to NSGFs with flexible time resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding the coefficients of both stationary and nonstationary Gabor expansions.Comment: 19 pages, 2 figure

Interchanging lexical resources on the Semantic Web

Lexica and terminology databases play a vital role in many NLP applications, but currently most such resources are published in application-specific formats, or with custom access interfaces, leading to the problem that much of this data is in ‘‘data silos’’ and hence difficult to access. The Semantic Web and in particular the Linked Data initiative provide effective solutions to this problem, as well as possibilities for data reuse by inter-lexicon linking, and incorporation of data categories by dereferencable URIs. The Semantic Web focuses on the use of ontologies to describe semantics on the Web, but currently there is no standard for providing complex lexical information for such ontologies and for describing the relationship between the lexicon and the ontology. We present our model, lemon, which aims to address these gap

Robust dual reconstruction systems and fusion frames

We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Weyl's search for a difference between `physical' and `mathematical' automorphisms

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.Comment: 30 p