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With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the function. The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal ...
In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2:1 ratio, are tuned slightly farther apart (a stretched octave). If the frequency ratios of octaves are greater than a factor of 2, the tuning is stretched ; if smaller than a factor of 2, it is compressed ."
One-way compression functions are often built from block ciphers. Block ciphers take (like one-way compression functions) two fixed size inputs (the key and the plaintext) and return one single output (the ciphertext) which is the same size as the input plaintext. However, modern block ciphers are only partially one-way.
(Note that if k > 1, then this really is a "stretch"; if k < 1, it is technically a "compression", but we still call it a stretch. Also, if k = 1, then the transformation is an identity, i.e. it has no effect.) The matrix associated with a stretch by a factor k along the x-axis is given by: []
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph with ...
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests. An example of graphs with treewidth at most 2 are the series–parallel graphs.
Together with F, this makes 2 N +1 files that all compress into one of the 2 N files of length N. But 2 N is smaller than 2 N +1, so by the pigeonhole principle there must be some file of length N that is simultaneously the output of the compression function on two different inputs. That file cannot be decompressed reliably (which of the two ...
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.