This paper describes an algorithm for melody detection in polyphonic recordings. Our approach starts by obtaining a set of pitch candidates for each time frame, with recourse to an auditory model. Trajectories of the most salient pitches are then constructed. Next, note candidates are obtained by trajectory segmentation (in terms of frequency and pitch salience variations). Too short, low-salie...

We study the effect of inflation on gaugino condensation in supergravity. Unless the Hubble scale H is significantly below the gaugino condensation scale, the gaugino condensate is a dynamical variable which cannot be integrated out. For a sufficiently high H, the gaugino condensate evolves to zero which in turn leads to dilaton/moduli destabilization. In practice, this often occurs at the Hubb...

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space Rn. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is (n − 2)-rectifiable. In this paper, we ...

In this study, we investigated the effect of viewpoint density and speed of motion on perceived smoothness of viewpoint transitions. The effect of viewpoint density was examined for two types of viewer motion: forward and lateral motion. In both cases, we found that perceived smoothness varies with viewpoint density. We also found the number of viewpoints required to maintain a certain level of...

In the recent literature on subdivision methods for approximation of manifold-valued data, a certain “proximity condition” comparing a nonlinear subdivision scheme to a linear subdivision scheme has proved to be a key analytic tool for analyzing regularity properties of the scheme. This proximity condition is now well-known to be a sufficient condition for the nonlinear scheme to inherit the re...

We formulate a version of the integral Hodge conjecture for categories, prove two-dimensional Calabi–Yau categories which are suitably deformation equivalent to derived category K3 or abelian surface, and use this deduce cases usual varieties. Along way, we variational families as well general smoothness result relative moduli spaces objects in such families. Our machinery also has applications...

Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties kernel in the so-called “flat limit,” which occurs when points close together relative scale kernel. We establish asymptotic expressions for determinants matrices, then leverage obtain main terms eigenvalues. Analyticity eigenprojectors yields limiting eigenvectors, strongly tie...

We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest to the analysis of convergence and smoothn...

Recently multiplicity M, K-regular, orthonormal wavelet bases (that have implications in transform coding applications) have been constructed by several authors 1, 2, 3]. This paper describes and parameterizes the cosine-modulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs (like in the general multiplicity 2 case in 4]), the scaling function uniquely determines the wavel...