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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 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 ...
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.
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.
The parameter B displayed on each spectral plot is the function's noise equivalent bandwidth metric, in units of DFT bins. [16]: p.56 eq.(16) See spectral leakage §§ Discrete-time signals and Some window metrics and Normalized frequency for understanding the use of "bins" for the x-axis in these plots.
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 ...
Spectral resolution: 15 m (bands 1–3); 30 m (bands 4–9); and 90 m (bands 10–14) Temporal resolution: 4-16 Days; Surface lithology mapping and mineral detection [7] Combined with digital elevation model for 3D analysis of land cover [38] Advanced Very-High-Resolution Radiometer Spaceborne; Multispectral imaging [6] Spatial resolution: 1.1 km