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Spectral layout drawing of random small-world network. For comparison, the same graph plotted as spring graph drawing. Spectral layout is a class of algorithm for drawing graphs. The layout uses the eigenvectors of a matrix, such as the Laplace matrix of the graph, as Cartesian coordinates of the graph's vertices.
The cut-offs at the short- and long-wavelength side of the diagram are chosen somewhat arbitrarily; the human eye can actually see light with wavelengths up to about 810 nm, but with a sensitivity that is many thousand times lower than for green light. These color matching functions define what is known as the "1931 CIE standard observer".
Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc.
In Fluorescence lifetime and spectral imaging, phasor can be used to visualize the spectra and decay curves. [1] [2] In this method the Fourier transformation of the spectrum or decay curve is calculated and the resulted complex number is plotted on a 2D plot where the X-axis represents the real component and the Y-axis represents the imaginary ...
The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1]. The first example of cospectral graphs was reported by Collatz and Sinogowitz [2] in 1957. The smallest pair of polyhedral cospectral mates are enneahedra with eight vertices each ...
A diagram indicating the equivalent width corresponding to the absorption line, which is shown in red. The equivalent width of a spectral line is a measure of the area of the line on a plot of intensity versus wavelength in relation to underlying continuum level. It is found by forming a rectangle with a height equal to that of continuum ...
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory).Such graphs are excellent spectral expanders.
All forms share the same general layout: stars of greater luminosity are toward the top of the diagram, and stars with higher surface temperature are toward the left side of the diagram. The original diagram displayed the spectral type of stars on the horizontal axis and the absolute visual magnitude on the vertical axis.