Generalized Hawking-Page Phase Transition

The issue of radiant spherical black holes being in stable thermal equilibrium with their radiation bath is reconsidered. Using a simple equilibrium statistical mechanical analysis incorporating Gaussian thermal fluctuations in a canonical ensemble of isolated horizons, the heat capacity is shown to diverge at a critical value of the classical mass of the isolated horizon, given (in Planckian units) by the {\it microcanonical} entropy calculated using Loop Quantum Gravity. The analysis reproduces the Hawking-Page phase transition discerned for anti-de Sitter black holes and generalizes it in the sense that nowhere is any classical metric made use of.Comment: 9 Pages, Latex with 2 eps figure

Minimizing Running Costs in Consumption Systems

A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently assumes that the energy source has an unbounded capacity, which is not always realistic. For example, an autonomous robotic device has a battery of finite capacity that has to be recharged periodically, and the total amount of energy consumed between two successive charging cycles is bounded by the capacity. Hence, a controller minimizing the mean-payoff must obey this restriction. In this paper we study the controller synthesis problem for consumption systems with a finite battery capacity, where the task of the controller is to minimize the mean-payoff while preserving the functionality of the system encoded by a given linear-time property. We show that an optimal controller always exists, and it may either need only finite memory or require infinite memory (it is decidable in polynomial time which of the two cases holds). Further, we show how to compute an effective description of an optimal controller in polynomial time. Finally, we consider the limit values achievable by larger and larger battery capacity, show that these values are computable in polynomial time, and we also analyze the corresponding rate of convergence. To the best of our knowledge, these are the first results about optimizing the long-run running costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission

A Multilayer Monte Carlo Model for the Investigation of Optical Path and Penetration Depth at Different Perfusion States of the Colon

There is a great interest in monitoring the oxygen supply delivered to the colon. Insufficient oxygen delivery may lead to hypoxia, sepsis, multiorgan dysfunction and death. For assessing colonic perfusion, more information and understanding is required relating to the light-interaction within the colonic tissue. A multilayer Monte Carlo model of a healthy human colon has been developed to investigate the light-tissue behavior during different perfusion states within the mucosal layer of the colon. Results from a static multilayer model of optical path and reflectance at two wavelengths, 660 nm and 880 nm, through colon tissue, containing different volume fractions of blood with a fixed oxygen saturation are presented. The effect on the optical path and penetration depth with varying blood volumes within the mucosa for each wavelength has been demonstrated. The simulation indicated both wavelengths of photons penetrated similar depths, entering the muscularis layer