We consider the semi-flow defined by semi-linear parabolic equations in Lp-spaces and study the differentiable dependence on the initial data. Together with a spectral gap condition this implies existence of inertial manifolds in arbitrary space dimensions. The spectral gap condition is satisfied by the Laplace-Beltrami operator for a class of manifolds. The simplest examples are products of sp...

We present a compact method to provide independent weighted interconnections between every pixel in a two-dimensional input array and every pixel in a two-dimensional output array. The two input dimensions and two output dimensions are connected by a four-dimensional weight matrix consisting of wavelength-multiplexed volume holograms that use cryogenic spectral hole burning in a single holograp...

We establish Lp bounds on L2 normalized spectral clusters for selfadjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all 2 ≤ p ≤ ∞, up to logarithmic losses for 6 < p ≤ 8. In higher dimensions we obtain best possible bounds for a limited range of p.

We describe a dimensionality reduction method for modulation spectral features, which keeps the time-varying information of interest to the classification task. Due to the varying degrees of redundancy and discriminative power of the acoustic and modulation frequency subspaces, we first employ a generalization of SVD to tensors (Higher Order SVD) to reduce dimensions. Projection of modulation s...

Characterization of urban radiance and reflectance is important for understanding the effects of solar energy flux on the urban environment as well as for satellite mapping of urban settlement patterns. Spectral mixture analyses of Landsat and Ikonos imagery suggest that the urban radiance field can very often be described with combinations of three or four spectral endmembers. Dimensionality e...

satellite imagery was used as a rapid and spatially explicit method to delineate crop residue cover and to estimate the use and intensity of conservation tillage. the potential of multispectral high-spatial resolution of worldview-2 local data was evaluated using 11 satellite spectral indices and linear spectral unmixing analysis (lsua). experimental plots were examined; residue cover was measu...

The plenoptic function was introduced as a convenient, ray-based model for light that includes the color spectrum as well as spatial, temporal, and directional variation [1]. Throughout the last decade, an ever increasing number of approaches to acquiring individual plenoptic dimensions have been proposed [4]. We discuss the acquisition of experimental datasets that capture a variety of differe...