Quantale Modules and their Operators, with Applications

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to be precisely the homomorphisms between free objects in those categories - find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology

Facts and Fictions about Anti deSitter Spacetimes with Local Qantum Matter

It is natural to analyse the AdS$_{d+1}$-CQFT$_{d}$ correspondence in the context of the conformal- compactification and covering formalism. In this way one obtains additional inside about Rehren's rigorous algebraic holography in connection with the degree of freedom issue which in turn allows to illustrates the subtle but important differences beween the original string theory-based Maldacena conjecture and Rehren's theorem in the setting of an intrinsic field-coordinatization-free formulation of algebraic QFT. I also discuss another more generic type of holography related to light fronts which seems to be closer to 't Hooft's original ideas on holography. This in turn is naturally connected with the generic concept of ``Localization Entropy'', a quantum pre-form of Bekenstein's classical black-hole surface entropy.Comment: this final version is identical to the one which appeared in Commun. Math. Phys. 219, (2001) 57-76, an issue of CMP dedicated to the memory of Harry Lehmann

Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy

It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT. This casts new light on the fundamental question whether the volume propotionality of heat bath entropy and the (logarithmically corrected) dimensionless area law obeyed by localization-induced thermal behavior are different geometric parametrizations which share a common primordeal algebraic origin. Strong arguments are presented that these two different thermal manifestations can be directly related, this is in fact the main aim of this paper. It will be demonstrated that QFT beyond the Lagrangian quantization setting receives crucial new impulses from holography onto horizons. The present paper is part of a project aimed at elucidating the enormous physical range of "modular localization". The latter does not only extend from standard Hamitonian heat bath thermal states to thermal aspects of causal- or event- horizons addressed in this paper. It also includes the recent understanding of the crossing property of formfactors whose intriguing similarity with thermal properties was, although sometimes noticed, only sufficiently understood in the modular llocalization setting.Comment: 42 pages, changes, addition of new results and new references, in this form the paper will appear in Foundations of Physic

Learning and tuning fuzzy logic controllers through reinforcements

A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing