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The compressed exponential function (with β > 1) has less practical importance, with the notable exceptions of β = 2, which gives the normal distribution, and of compressed exponential relaxation in the dynamics of amorphous solids. [1] In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
Zopfli is a data compression library that performs Deflate, gzip and zlib data encoding. [2] It achieves higher compression ratios than mainstream Deflate and zlib implementations at the cost of being slower. [3] Google first released Zopfli in February 2013 under the terms of Apache License 2.0. [4]
Lloyd's algorithm starts by an initial placement of some number k of point sites in the input domain. In mesh-smoothing applications, these would be the vertices of the mesh to be smoothed; in other applications they may be placed at random or by intersecting a uniform triangular mesh of the appropriate size with the input domain.
for each pixel (Px, Py) on the screen do x0:= scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.5, 1)) y0:= scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1)) x:= 0.0 y:= 0.0 iteration:= 0 max_iteration:= 1000 // Here N = 2^8 is chosen as a reasonable bailout radius. while x*x + y*y ≤ (1 ...
Test whether the (k + 1)-vertex solution Y = X ∪ {v} to S can be compressed to a k-vertex solution. If it cannot be compressed, abort the algorithm: the input graph has no k-vertex solution. Otherwise, set X to the new compressed solution and continue the loop. This algorithm calls the compression subroutine a linear number of times.
Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, [1] making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.