On the structure of symmetric self-dual Lie algebras

A finite-dimensional Lie algebra is called (symmetric) self-dual, if it possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric self-dual Lie algebras have been studied by Medina and Revoy, who have proven a very useful theorem about their structure. In this paper we prove a refinement of their theorem which has wide applicability in Conformal Field Theory, where symmetric self-dual Lie algebras start to play an important role due to the fact that they are precisely the Lie algebras which admit a Sugawara construction. We also prove a few corollaries which are important in Conformal Field Theory. (This paper provides mathematical details of results used, but only sketched, in the companion paper hep-th/9506151.)Comment: 19 pages, .dvi.uu (needs AMSFonts 2.1+

From sensorimotor dependencies to perceptual practices: making enactivism social

Proponents of enactivism should be interested in exploring what notion of action best captures the type of action-perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception, and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions, which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, music, etc. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and inter-modal perceptible material. I argue that perceptual practices explain three central features of socially dependent perception: attentional focus, aspects’ saliency, and modal-specific harmony-like relations

Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure