Phase transition in the assignment problem for random matrices

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=ep

Finite entanglement entropy from the zero-point-area of spacetime

The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent. I argue that this divergence, which arises even in the case of Rindler horizon in flat spacetime, is yet another indication of a deep connection between horizon thermodynamics and gravitational dynamics. In an emergent perspective of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area, of the order of L_P^2, which will act as a regulator for this divergence. In a particular prescription for incorporating L_P^2 as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S proportional to (A/L_P^2) in Einstein gravity. In more general models of gravity, the surface density of microscopic degrees of freedom is different which leads to a modified regularisation procedure and the possibility that the entanglement entropy - when appropriately regularised - matches the Wald entropy.Comment: ver 2: minor clarifications added; reformatted with Sections; 11 page

Éthiopiques vs EthioSonic: sobre a world music e a música globalizada

This article deals with music influences post-WW2 between North and South and vice versa. It traces the concept of “World Music” emergence, then the adoption of African grooves by mixed bands as well as non-African musicians, opening the way to “globalized music”. Because Ethiopia remained never colonized over 3000 years (apart from five years under fascist Italian occupation), the modern part of the country’s musical culture remained totally unknown to the rest of the world. Recordings of modern (or urban) Ethiopian music were simply inexistent outside of the country before 1986, when other musics from Africa had kind of loud-speakers in the colonial capital cities Paris, London, Brussels or Lisbon, for example. A focus about Ethiopian musics through two music series (éthiopiques and ethioSonic) complete the scope of this study.Este artículo trata sobre las influencias musicales mutuas entre los hemisferios norte y sur después de la Segunda Guerra Mundial. Traza el concepto del surgimiento de la “World Music”, seguido de la adopción de ritmos africanos por bandas mixtas y también por músicos no africanos, allanando el camino para la “música globalizada”. Como Etiopía nunca fue colonizada durante más de 3.000 años (excepto durante cinco años bajo la ocupación fascista italiana), la parte moderna de la cultura musical del país permaneció totalmente desconocida para el resto del mundo. Las grabaciones de música etíope moderna (o urbana) simplemente no existían fuera del país antes de 1986, mientras que otras músicas africanas ya estaban presentes en capitales coloniales como París, Londres, Bruselas o Lisboa. Un enfoque en la música etíope a través de dos series musicales (éthiopiques y ethioSonic) completa el alcance de este estudio.Este artigo trata das influências musicais mútuas entre os hemisférios Norte e Sul pós-Segunda Guerra Mundial. Traça o conceito de surgimento da “World Music”, seguida da adoção de grooves africanos por bandas mistas e também por músicos não africanos, abrindo caminho para a “música globalizada”. Como a Etiópia nunca foi colonizada por mais de 3.000 anos (exceto cinco anos sob ocupação italiana fascista), a parte moderna da cultura musical do país permaneceu totalmente desconhecida para o resto do mundo. Gravações de música etíope moderna (ou urbana) simplesmente inexistiam fora do país antes de 1986, enquanto outras músicas da África já se encontravam presentes nas capitais coloniais como Paris, Londres, Bruxelas ou Lisboa. Um enfoque sobre as músicas etíopes por meio de duas séries musicais (éthiopiques e ethioSonic) completam o escopo deste estudo

Reduction of Lie--Jordan algebras: Quantum

In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties and the space of states. The reduced Lie--Jordan Banach algebra is characterized together with the Dirac states on the physical algebra of observables