Comparing Probabilistic Models for Melodic Sequences

Modelling the real world complexity of music is a challenge for machine learning. We address the task of modeling melodic sequences from the same music genre. We perform a comparative analysis of two probabilistic models; a Dirichlet Variable Length Markov Model (Dirichlet-VMM) and a Time Convolutional Restricted Boltzmann Machine (TC-RBM). We show that the TC-RBM learns descriptive music features, such as underlying chords and typical melody transitions and dynamics. We assess the models for future prediction and compare their performance to a VMM, which is the current state of the art in melody generation. We show that both models perform significantly better than the VMM, with the Dirichlet-VMM marginally outperforming the TC-RBM. Finally, we evaluate the short order statistics of the models, using the Kullback-Leibler divergence between test sequences and model samples, and show that our proposed methods match the statistics of the music genre significantly better than the VMM.Comment: in Proceedings of the ECML-PKDD 2011. Lecture Notes in Computer Science, vol. 6913, pp. 289-304. Springer (2011

Vortex moment map for unsteady incompressible viscous flows

In this paper, a vortex moment map (VMM) method is proposed to predict the pitching moment on a body from the vorticity field. VMM is designed to identify the moment contribution of each given vortex in the flow field. Implementing this VMM approach in starting flows of a NACA0012 airfoil, it is found that, due to the rolling up of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs), the unsteady nose-down moment about the quarter chord is higher than the steady-state value. The time variation of the unsteady moment is closely related to the LEVs and TEVs near the body and the VMM gives an intuitive understanding of how each part of the vorticity field contributes to the pitching moment on the body