Supersymmetric Renyi Entropy in CFT2CFT_2 and AdS3AdS_3

We show that in any two dimensional conformal field theory with (2, 2) supersymmetry one can define a supersymmetric analog of the usual Renyi entropy of a spatial region A. It differs from the Renyi entropy by a universal function (which we compute) of the central charge, Renyi parameter n and the geometric parameters of A. In the limit $n \to1$ it coincides with the entanglement entropy. Thus, it contains the same information as the Renyi entropy but its computation only involves correlation functions of chiral and anti-chiral operators. We also show that this quantity appears naturally in string theory on $AdS_3$.Comment: 15 pages; v2: reference adde

A Solvable Irrelevant Deformation of AdS3/CFT2AdS_3/CFT_2

Recently we proposed a universal solvable irrelevant deformation of $AdS_3/CFT_2$ duality, which leads in the ultraviolet to a theory with a Hagedorn entropy [1]. In this note we provide a worldsheet description of this theory as a coset CFT, and compare its spectrum to the field theory predictions of [2,3].Comment: 12 page

Stringy Horizons

We argue that classical $(\alpha')$ effects qualitatively modify the structure of Euclidean black hole horizons in string theory. While low energy modes experience the geometry familiar from general relativity, high energy ones see a rather different geometry, in which the Euclidean horizon can be penetrated by an amount that grows with the radial momentum of the probe. We discuss this in the exactly solvable SL(2,R)/U(1) black hole, where it is a manifestation of the black hole/Sine-Liouville duality.Comment: 14 page

Three-Charge Black Holes and Quarter BPS States in Little String Theory

We show that the system of $k$ NS5-branes wrapping $\mathbb{T}^4\times S^1$ has non-trivial vacuum structure. Different vacua have different spectra of 1/4 BPS states that carry momentum and winding around the $S^1$. In one vacuum, such states are described by black holes; in another, they can be thought of as perturbative BPS states in Double Scaled Little String Theory. In general, both kinds of states are present. We compute the degeneracy of perturbative BPS states exactly, and show that it differs from that of the corresponding black holes. We comment on the implication of our results to the black hole microstate program, UV/IR mixing in Little String Theory, string thermodynamics, the string/black hole transition, and other issues.Comment: 53 pages, 3 figure

Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Artificial neural network analysis of teachers��� performance against thermal comfort

This is an accepted manuscript of an article published by Emerald in International Journal of Building Pathology and Adaptation on 17/04/2020, available online at: https://doi.org/10.1108/IJBPA-11-2019-0098 The accepted manuscript may differ from the final published version.Purpose: The impact of thermal comfort in educational buildings continues to be of major importance in both the design and construction phases. Given this, it is also equally important to understand and appreciate the impact of design decisions on post-occupancy performance, particularly on staff and students. This study aims to present the effect of IEQ on teachers��� performance. This study would provide thermal environment requirements to BIM-led school refurbishment projects. Design: This paper presents a detailed investigation into the direct impact of thermal parameters (temperature, relative humidity and ventilation rates) on teacher performance. In doing so, the research methodological approach combines explicit mixed-methods using questionnaire surveys and physical measurements of thermal parameters to identify correlation and inference. It was conducted through a single case study using a technical college based in Saudi Arabia. Findings: Findings from this work were used to develop a model using an Artificial Neural Network to establish causal relationships. Research findings indicate an optimal temperature range between 23��C and 25��C, with a 65% relative humidity and 0.4m/s ventilation rate. This ratio delivered optimum results for both comfort and performance