This paper introduces a version of empirical likelihood based on the periodogram and spectral estimating equations. This formulation handles dependent data through a data transformation (i.e., a Fourier transform) and is developed in terms of the spectral distribution rather than a time domain probability distribution. The asymptotic properties of frequency domain empirical likelihood are studi...

We present a graph spectral approach in which melodies are represented as graphs, based on the intervals between the notes they are composed of. These graphs are then indexed into a database using their laplacian spectra as a feature vector. This laplacian spectrum is a good representative of the original melody. Consequently, range searching around the query spectrum returns similar melodies.

In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schem...

φ(t) = F (t, φ(t)), t ∈ [a, b], φ(a) = φa. (1.1) where φa, φ(t) ∈ C n and F : R × C → C. Let {t}n=0 be equally spaced nodes in the interval [a, b] with t0 = a, tN = b. Let {t j n} M j=0 be the Legendre-Gauss-Lobatto nodes in the subinterval [tn, tn+1] with t 0 n = tn, t M n = tn+1. Denote ∆n = t j+1 n − t j n. 1.1 Forward Euler Scheme The Picard integral equation in each [tn, tn+1] associated w...

We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding...

The effective use of complex fenestration systems in buildings requires knowledge of their optical spectral and directional properties. While the directional properties are commonly assessed by the measurement of bidirectional transmission or reflection distribution functions, the addition of spectral information would significantly aid in the design and analysis of such systems. This paper des...

In many applications of color technology such as spectral color reproduction it is of interest to represent the spectral data with lower dimensions than spectral space’s dimensions. It is more than half of a century that Principal Component Analysis PCA method has been applied to find the number of independent basis vectors of spectral dataset and representing spectral reflectance with lower di...

the main problem associated with the traditional approach to image classification for the mapping of hydrothermal alteration is that materials not associated with hydrothermal alteration may be erroneously classified as hydrothermally altered due to the similar spectral properties of altered and unaltered minerals. the major objective of this paper is to investigate the potential of a neuro-fuz...