Modeling Temporal Structure in Music for Emotion Prediction using Pairwise Comparisons

The temporal structure of music is essential for the cognitive processes related to the emotions expressed in music. However, such temporal information is often disregarded in typical Music Information Retrieval modeling tasks of predicting higher-level cognitive or semantic aspects of music such as emotions, genre, and similarity. This paper addresses the specific hypothesis whether temporal information is essential for predicting expressed emotions in music, as a prototypical example of a cognitive aspect of music. We propose to test this hypothesis using a novel processing pipeline: 1) Extracting audio features for each track resulting in a multivariate "feature time series". 2) Using generative models to represent these time series (acquiring a complete track representation). Specifically, we explore the Gaussian Mixture model, Vector Quantization, Autoregressive model, Markov and Hidden Markov models. 3) Utilizing the generative models in a discriminative setting by selecting the Probability Product Kernel as the natural kernel for all considered track representations. We evaluate the representations using a kernel based model specifically extended to support the robust two-alternative forced choice self-report paradigm, used for eliciting expressed emotions in music. The methods are evaluated using two data sets and show increased predictive performance using temporal information, thus supporting the overall hypothesis

World-sheet dynamics of ZZ branes

We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2,2m-1) minimal model coupled to two-dimensional quantum gravity.Comment: 14 page

Pleba\'nski-Demia\'nski solution of general relativity and its expressions quadratic and cubic in curvature: analogies to electromagnetism

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Pleba\'nski--Demia\'nski (PD)---to demonstrate these analogies for a physically meaningful spacetime: The two quadratic curvature invariants $\bf{B}^2-\bf{E}^2$ and $\bf{E}\cdot\bf{B}$ are evaluated analytically. In the asymptotically flat case, the leading terms of $\bf{E}$ and $\bf{B}$ can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel--Robinson tensor reads $(\mathbf{B}^2+\mathbf{E}^2)^2$ for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy-momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel--Robinson 3-form, from which the Bel--Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: in the original polynomial PD coordinates, and in a modified Boyer--Lindquist-like version introduced by Griffiths and Podolsk\'y (GP) allowing for a more straightforward physical interpretation of the free parameters.Comment: 52 pages, 11 listings of computer algebra code; typos removed, and journal reference adde