Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown be Whitney stratified space. Each stratum Riemannian manifold which naturally yields geodesic distance across strata. resulting metric comp...

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each 3-manifold in the has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces 3-manifolds obtained. normal Gauß map its harmonicity are discussed.

In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general lowdegree functions, with no constraints on the influences. We show that any real-valued function on the slice, whose degree when written as a harmonic multi-linear polynomial is o( √ n), has approximately the same dis...

In this paper, we propose a novel approach to harmonicpercussive sound separation (HPSS) using Non-negative Matrix Factorization (NMF) with sparsity and harmonicity constraints. Conventional HPSS methods have focused on temporal continuity of harmonic components and spectral continuity of percussive components. However, it may not be appropriate to use them to separate time-varying harmonic sig...

Neuroimaging studies have shown that the perception of auditory stimuli involves occipital cortical regions traditionally associated with visual processing, even in the absence of any overt visual component to the task. Analogous behavioral evidence of an interaction between visual and auditory processing during purely auditory tasks comes from studies of short-term visual deprivation on the pe...

Harmonic complex tones are a particularly important class of sounds found in both speech and music. Although these sounds contain multiple frequency components, they are usually perceived as a coherent whole, with a pitch corresponding to the fundamental frequency (F0). However, when two or more harmonic sounds occur concurrently, e.g., at a cocktail party or in a symphony, the auditory system ...

The holomorphicity property of N = 1 superpotentials or of N = 2 F-terms involving vector multiplets is generalized to the case of N = 4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N = 4 Weyl superfield, computed by N = 4 topolog...

This article presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) in a Bayesian framework. A model of superimposed Gaussian components including harmonicity is proposed, while temporal continuity is enforced through an inverse-Gamma Markov chain prior. We then exhibit a space-alternating generalized expectation-maximization (SAGE) algorithm to ...

This paper is concerned with the approximate reconstruction of the earth’s potential field from geometric and gravimetric data. This is an ill-posed problem involving typically large amounts of data which are to be continued by a harmonic function. The standard approach in geodesy is based on spherical harmonics which are globally supported. Thus, a least squares approach for the data fitting y...