Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity

We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $\Lambda$. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Now however, the underlying colored graph $\Gamma$ lives in a two-dimensional spacelike surface $\Sigma$, and some of its links cross the black hole horizon, which is viewed as a circular boundary of $\Sigma$. Each link $\ell$ crossing the horizon is colored by a spin $j_\ell$ (at the kinematical level), and the length $L$ of the horizon is given by the sum $L=\sum_\ell L_\ell$ of the fundamental length contributions $L_\ell$ carried by the spins $j_\ell$ of the links $\ell$. We propose an estimation for the number $N^\text{BTZ}_\Gamma(L,\Lambda)$ of the Euclidean BTZ black hole microstates (defined on a fixed graph $\Gamma$) based on an analytic continuation from the case $\Lambda>0$ to the case $\Lambda<0$. In our model, we show that $N^\text{BTZ}_\Gamma(L,\Lambda)$ reproduces the Bekenstein-Hawking entropy in the classical limit. This asymptotic behavior is independent of the choice of the graph $\Gamma$ provided that the condition $L=\sum_\ell L_\ell$ is satisfied, as it should be in three-dimensional quantum gravity.Comment: 14 pages. 1 figure. Paragraph added on page 7 to clarify the horizon conditio

Hypersymmetry bounds and three-dimensional higher-spin black holes

We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric.Comment: 26 page

Combining absolute and relative information in studies on food quality

A common problem in food science concerns the assessment of the quality of food samples. Typically, a group of panellists is trained exhaustively on how to identify different quality indicators in order to provide absolute information, in the form of scores, for each given food sample. Unfortunately, this training is expensive and time-consuming. For this very reason, it is quite common to search for additional information provided by untrained panellists. However, untrained panellists usually provide relative information, in the form of rankings, for the food samples. In this paper, we discuss how both scores and rankings can be combined in order to improve the quality of the assessment

Achieving Very High PV Penetration

This article argues that optimally deployed intermittency solutions could affordably transform solar power generation into the firm power delivery system modern economies require, thereby enabling very high solar penetration and the displacement conventional power generation. The optimal deployment of these high‐penetration enabling solutions imply the existence of a healthy power grid, and therefore imply a central role for utilities and grid operators. This article also argues that a value‐based electricity compensation mechanism, recognizing the multifaceted, penetration‐dependent value and cost of solar energy, and capable of shaping consumption patterns to optimally match resource and demand, would be an effective vehicle to enable high solar penetration and deliver affordable firm power generation

Aircraft conflict detection using data mining and statistical tools

&#65532;Nowadays and taking into account the different indicators and the forecast of the air traffic volume from Eurocontrol, it is accepted the idea that the traffic will be doubled by 2030, that is why it is so important to find new and efficient methods which allow the infrastructure absorb such a huge demand. Hence the importance of designs a plan in order to increase the actual capacity. This is the example of ATM MASTER PLAN included inside SESAR (Single European Sky and Research). The main aim of this project is to test a different tool which could lead to detect conflicts on the airspace and find which is its performance compared to a traditional 4D forecast trajectory software. It will be entirely developed on the environment of Python and the Scikitlearn library will be used in order to make the machine learn which is a conflict situation and which not