In this paper, a method for automatic transcription of music signals using a convolutive probabilistic model is proposed, by extending the shift-invariant Probabilistic Latent Component Analysis method. Several note templates from multiple orchestral instruments are extracted from monophonic recordings and are used for training the transcription system. By incorporating shift-invariance into th...

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

Mappings from a master element to the physical mesh element, in conjunction with local metrics such as those appearing in the Target-matrix paradigm, are used to measure quality at points within an element. The approach is applied to both linear and quadratic triangular elements; this enables, for example, one to measure quality within a quadratic finite element. Quality within an element may a...

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...