These lecture notes are devoted to the spectral analysis of adjacency operators of graphs and random graphs. With the notion of unimodular random graphs, it is possible to define a natural notion of average spectral measure which corresponds to the density of states in the language of mathematical physics, to the Plancherel measure for Cayley graphs and, for finite graphs, to the empirical meas...

We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral MeasuresMφ the Pflug—Rockafellar—Uryasev methodology for the minimization of α—Expected Shortfall. The minimization problem of a spectral measure is shown to be equivalent to the minimization of a suitable function which contains additional parameters, but ...

A technique for searching in a spectral image database is proposed in this study. It is based on a similarity measure between spectral image features. New and convenient spectral image features are introduced and compared here. Nonnegative tensor factorization (NTF) and principal component analysis (PCA) are applied in a spectral image domain to characterize colors of a spectral image. A new wa...

In this article we show how to compute the semi-classical spectral measure associated with the Schrödinger operator on Rn, and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schrödinger operator on R2 with a radially symmetric electric potential, V , and magnetic potent...

The dependence structure of a max-stable random vector is characterized by its spectral measure. Using only the spectral measure, we present a method for approximating the conditional density of an unobserved component of a max-stable random vector given the other components of the vector. The approximated conditional density can be used for prediction. Additionally, we present a new parametric...

The lower and average spectral radii measure the minimal and average growth rates, respectively, of long products of matrices taken from a finite set. The logarithm of the average spectral radius is traditionally called the Lyapunov exponent. When one forms these products in the maxalgebra, we obtain quantities that measure the performance of Discrete Event Systems. We show that approximating t...

This paper proposes an innovative technique to incorporate the infor-mation of spectral dynamics into the line spectrum frequency (LSF) vec-tor quantization (VQ). This technique is based on a modified weightedlog-spectral distortion (MWLSD) measure. It can be used to shapethe spectral quantization distortion distribution into any frequency-dependent shaping curve, and simult...

Consider the empirical autocovariance matrices at given non-zero time lags, based on observations from a multivariate complex Gaussian stationary series. The spectral analysis of these can be useful in certain statistical problems, such as those related to testing for white noise. We study behavior their measure asymptotic regime where series dimension and observation window length both grow in...