Using methods introduced by Scargle we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble that started in August 2000.

I review some results of estimation of the power spectrum of density fluctuations from galaxy redshift surveys and discuss advances that may be possible with the Sloan Digital Sky Survey. I then examine the realities of power spectrum estimation in the presence of Galactic extinction, photometric errors, galaxy evolution, clustering evolution, and uncertainty about the background cosmology.

Current state-of-the-art fish monitoring systems are lack of intelligent in interpreting fishes behaviors automatically. To tackle these problems, we propose a vision-based method that automatically analyze behaviors of a group of fishes in an aquarium and detect abnormality precisely. Here we consider the problem in two steps. First, we propose a new incremental spectral clustering method to e...

In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering. Thus, we convert almost all results to the complex case, whenever ...

In this paper, we consider Chebyshev–Legendre Pseudo-Spectral (CLPS) method for solving coupled viscous Burgers (VB) equations. A leapfrog scheme is used in time direction, while CLPS method is used for space direction. Chebyshev–Gauss–Lobatto (CGL) nodes are used for practical computation. The error estimates of semi-discrete and fully-discrete of CLPS method for coupled VB equations are obtai...

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the “raw coordinates” encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization...

A high precision numerical analysis of the static, spherically symmetric SU (2) magnetic monopole equations is carried out. Using multi-shooting and multi-domain spectral methods , the mass of the monopole is obtained rather precisely as a function of β = M H /M W for a large β-interval (M H and M W denote the mass of the Higgs and gauge field respectively). The numerical results necessitated t...

Article history: Received 19 September 2007 Received in revised form 10 April 2008 Accepted 24 June 2008