Spectral clustering is a flexible clustering methodology that is applicable to a variety of data types and has the particular virtue that it makes few assumptions on cluster shapes. It has become popular in a variety of application areas, particularly in computational vision and bioinformatics. The approach appears, however, to be particularly sensitive to irrelevant and noisy dimensions in the...

Abstract Timbre characterizes the identity of a sound source. On psychoacoustic grounds, it has been described as a multidimensional perceptual attribute of complex sounds. Using Garner's interference paradigm, we found in a previous behavioral study that three timbral dimensions exhibited interactive processing. These timbral dimensions acoustically corresponded to attack time, spectral centro...

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the objective measure of the design performance (defined in the ...

PURPOSE The present study was designed to evaluate use of spectral and temporal cues under conditions in which both types of cues were available. METHOD Participants included adults with normal hearing and hearing loss. We focused on 3 categories of speech cues: static spectral (spectral shape), dynamic spectral (formant change), and temporal (amplitude envelope). Spectral and/or temporal dim...

We propose in this note a spectral method on triangles based on a new rectangle-to-triangle mapping, which leads to more reasonable grid distributions and efficient implementations than the usual approaches based on the collapsed transform. We present the detailed implementation for spectral approximations on a triangle and discuss the extension to spectral-element methods and three dimensions.

A spectral wave model coupling a quadtree-adaptive discretisation of the two spatial dimensions with a standard discretisation of the two spectral dimensions is described. The implementation is greatly simplified by reusing components of the Gerris solver (for spatial advection on quadtrees) and WAVEWATCH III (for spectral advection and source terms). Strict equivalence between the anisotropic ...

R 5 Tao produced a spectral set which is not a tile, while Kolountzakis and Matolcsi showed an example of a non-spectral tile. In search of lower dimensional nonspectral tiles we were led to investigate the Universal Spectrum Conjecture (USC) of Lagarias and Wang [13]. In particular, we prove here that the USC and the “tile → spectral” direction of Fuglede’s conjecture are equivalent in any dim...

We give an explicit construction of approximate eigenfunctions for linearized Euler operator in dimensions two and three with periodic boundary conditions, and an estimate from below for its spectral bound in terms of an appropriate Lyapunov exponent. As a consequence, we prove that in dimension 2 the spectral and growth bounds for the corresponding group are equal. Therefore, the linear hydrod...