The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time,...

on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies...

represent two spatial dimensions of the scene, and λ represents the spectral dimension (comprising a range of wavelengths). Technically speaking, there are...

evidence for dimensional reduction has come mainly, although not exclusively, from calculations of the spectral dimension. The spectral dimension is a measure...

statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction...

three-dimensional color space (which includes luminance), the spectral colors form a surface. When excluding luminance and considering a two-dimensional color...

one-dimensional space and in equal intervals for ease of visualization. Data binning may be used when small instrumental shifts in the spectral dimension...

communications, noise spectral density (NSD), noise power density, noise power spectral density, or simply noise density (N0) is the power spectral density of noise...

Multidimension spectral estimation is a generalization of spectral estimation, normally formulated for one-dimensional signals, to multidimensional signals...

candidate for dimensionality reduction of the dynamical system. While such manifolds are not guaranteed to exist in general, the theory of spectral submanifolds...

original spectral theorem was therefore conceived as a version of the theorem on principal axes of an ellipsoid, in an infinite-dimensional setting. The...

contexts are defined based on two neighboring coefficients in the spectral dimension and no neighboring coefficients in the same spatial plane. This contrasts...

3, Poetics of Fiction (1986), pp. 459–469. Rowe, W. W., Nabokov's Spectral Dimension, Ann Arbor: Ardis, 1981, ISBN 088233641X. Boyd 1991, p. 279. Pritzer...

stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by...

UV and NIR spectral elements can be separately recorded. Each CCD observes both the spectral dimension and the north–south spatial dimension. The instrument...

dimensional setting. In particular, the spectral theory of continuous self-adjoint linear operators on a Hilbert space generalizes the usual spectral...

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...

discussing the spectral properties of compact operators. The reader will see that most statements transfer verbatim from the matrix case. The spectral theory...

Waterfall plots are often used to show how two-dimensional phenomena change over time. A three-dimensional spectral waterfall plot is a plot in which multiple...

wide-by-narrow view, only one pixel tall and 64 pixels across. The spectral dimension was 1,024 pixels per spatial pixel. It could also take many images...

Spectral acceleration (SA) is a unit measured in g (the acceleration due to Earth's gravity, equivalent to g-force) that describes the maximum acceleration...

radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave...

dimensions and units: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz (W⋅m−2⋅Hz−1), while spectral irradiance of a...

many theorems known as the spectral theorem, but one in particular has many applications in functional analysis. Spectral theorem—Let A {\displaystyle...

on the direction from which it is being observed. The related quantity spectral radiance is the radiance of a surface per unit frequency or wavelength...

Spatio-spectral scanning is one of four techniques for hyperspectral imaging, the other three being spatial scanning, spectral scanning and non-scanning...

PMID 21405217 Sotiriou, Thomas P.; Visser, Matt; Weinfurtner, Silke (2011), "Spectral Dimension as a Probe of the Ultraviolet Continuum Regime of Causal Dynamical...

solutions in percolation and cluster counting problems and definition of spectral dimension of fractals." John J. Hopfield Princeton University "extending the...

fractal dimension of the random walk on an infinite incipient percolation cluster is given by d w {\displaystyle d_{w}} . The spectral dimension d ~ {\displaystyle...

understanding of the disciplines. He is credited with the introduction of spectral dimension concept in the studies of fractals and contributed to developing a...