Entropy from AdS(3)/CFT(2)

We parametrize the (2+1)-dimensional AdS space and the BTZ black hole with Fefferman-Graham coordinates starting from the AdS boundary. We consider various boundary metrics: Rindler, static de Sitter and FRW. In each case, we compute the holographic stress-energy tensor of the dual CFT and confirm that it has the correct form, including the effects of the conformal anomaly. We find that the Fefferman-Graham parametrization also spans a second copy of the AdS space, including a second boundary. For the boundary metrics we consider, the Fefferman-Graham coordinates do not cover the whole AdS space. We propose that the length of the line delimiting the excluded region at a given time can be identified with the entropy of the dual CFT on a background determined by the boundary metric. For Rindler and de Sitter backgrounds our proposal reproduces the expected entropy. For a FRW background it produces a generalization of the Cardy formula that takes into account the vacuum energy related to the expansion.Comment: major revision with several clarifications and corrections, 22 page

Information-theoretic measures of music listening behaviour

We present an information-theoretic approach to the mea- surement of users’ music listening behaviour and selection of music features. Existing ethnographic studies of mu- sic use have guided the design of music retrieval systems however are typically qualitative and exploratory in nature. We introduce the SPUD dataset, comprising 10, 000 hand- made playlists, with user and audio stream metadata. With this, we illustrate the use of entropy for analysing music listening behaviour, e.g. identifying when a user changed music retrieval system. We then develop an approach to identifying music features that reflect users’ criteria for playlist curation, rejecting features that are independent of user behaviour. The dataset and the code used to produce it are made available. The techniques described support a quantitative yet user-centred approach to the evaluation of music features and retrieval systems, without assuming objective ground truth labels