We study a class of one-sided Hamiltonian operators with spectral measures given by invariant and ergodic measures of dynamical systems of the interval. We analyse dimensional properties of spectral measures, and prove upper bounds for the asymptotic spread in time of wavepackets. These bounds involve the Hausdorr dimension of the spectral measure, multiplied by a correction calculated from the...

The authors have recently defined the Rényi information dimension rate d({Xt}) of a stationary stochastic process {Xt, t ∈ Z} as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the quantizer step size 1/m in the limit as m → ∞ (B. Geiger and T. Koch, “On the information dimension rate of stochastic processes,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aa...

The spectra of color can represent a color in the most accurate way, but the dimension of the spectral data is too high to process. This paper aims to analyze the spectral reflectance curves of 1269 Munsell standard color samples with some influential algorithms in manifold learning. Experimental results reveal that the intrinsic dimension of the embedded manifold in the spectral Munsell color ...

In this article we continue our analysis of Schrödinger operators with a random potential using scattering theory. In particular the theory of Krein’s spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift funct...

In this work we prove that every locally symmetric smooth submanifoldM of Rn gives rise to a naturally defined smooth submanifold of the space of n × n symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs toM. We also present an explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic ...

We apply the feature selection technique of Fukunaga and Koontz an extension of the Karhunen Lo eve transformation to spoken letter recognition Feedforward networks trained for letter pair discrimination with the new features show up to reduction in classi er error rate relative to networks trained with spectral coe cients This performance increase is accompanyed by a reduction in feature dimen...

Riesz potentials and Laplacian of fractal measures in metric spaces are introduced. They deene self{adjoint operators in the Hilbert space L 2 () and the former are shown to be compact. In the euclidean case the corresponding spectral asymptotics are derived by Besov space methods. The inverses of the Riesz potentials are fractal pseudo-diierential operators. For the Laplace operator the spectr...

Abstract. We construct non-random bounded discrete half-line Schrödinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimensi...

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)dimensional case, the corresponding system can be extended to 2 × 2 matrix form. The factorization theorem of the Christoffel kernel for s...

We present an analysis of the effects of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we computed the harmonic spectrum within the Gaussian Network Model (GNM) and determined their spectral dimension, a parameter describing the low frequency behavior of the density of modes. We found a surpri...