Entropy in Spin Foam Models: The Statistical Calculation

Recently an idea for computing the entropy of black holes in the spin foam formalism has been introduced. Particularly complete calculations for the three dimensional euclidean BTZ black hole were done. The whole calculation is based on observables living at the horizon of the black hole universe. Departing from this idea of observables living at the horizon, we now go further and compute the entropy of BTZ black hole in the spirit of statistical mechanics. We compare both calculations and show that they are very interrelated and equally valid. This latter behaviour is certainly due to the importance of the observables.Comment: 11 pages, 1 figur

BTZ Black Hole Entropy: A spin foam model description

We present a microscopical explanation of the entropy of the BTZ black hole using discrete spin foam models of quantum gravity. The entropy of a black hole is given in geometrical terms which lead us to think that its statistical description must be given in terms of a quantum geometry. In this paper we present it in terms of spin foam geometrical observables at the horizon of the black hole.Comment: 10 pages, 2 figures, Final Versio

Measurements and Information in Spin Foam Models

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy associated to the corresponding information. We present a general definition, compute the Shannon entropy of some examples, and find some interesting inequalities.Comment: 15 pages, 3 figures. Improved versio

Towards a spin foam model description of black hole entropy

We propose a way to describe the origin of black hole entropy in the spin foam models of quantum gravity. This stimulates a new way to study the relation of spin foam models and loop quantum gravity.Comment: 5 pages, 1 figur

Observables in 3-dimensional quantum gravity and topological invariants

In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model. Instead of giving a formal description of the observables, we just formulate the paper by examples. This means that we just show how an idea works with particular cases and give a way to compute 'expectation values' in general by a topological procedure.Comment: 24 pages, 47 figure

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

Analysis of protein-coding genetic variation in 60,706 humans

Large-scale reference data sets of human genetic variation are critical for the medical and functional interpretation of DNA sequence changes. We describe the aggregation and analysis of high-quality exome (protein-coding region) sequence data for 60,706 individuals of diverse ethnicities generated as part of the Exome Aggregation Consortium (ExAC). This catalogue of human genetic diversity contains an average of one variant every eight bases of the exome, and provides direct evidence for the presence of widespread mutational recurrence. We have used this catalogue to calculate objective metrics of pathogenicity for sequence variants, and to identify genes subject to strong selection against various classes of mutation; identifying 3,230 genes with near-complete depletion of truncating variants with 72% having no currently established human disease phenotype. Finally, we demonstrate that these data can be used for the efficient filtering of candidate disease-causing variants, and for the discovery of human “knockout” variants in protein-coding genes

Determinants of penetrance and variable expressivity in monogenic metabolic conditions across 77,184 exomes

Penetrance of variants in monogenic disease and clinical utility of common polygenic variation has not been well explored on a large-scale. Here, the authors use exome sequencing data from 77,184 individuals to generate penetrance estimates and assess the utility of polygenic variation in risk prediction of monogenic variants