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Likewise, the LCP of A[2] = ab and A[3] = abaab is ab, so H[3] = 2. Augmenting the suffix array with the LCP array allows one to efficiently simulate top-down and bottom-up traversals of the suffix tree , [ 1 ] [ 2 ] speeds up pattern matching on the suffix array [ 3 ] and is a prerequisite for compressed suffix trees.
The conditional entropy measures the average uncertainty Bob has about Alice's state upon sampling from his own system. The min-entropy can be interpreted as the distance of a state from a maximally entangled state. This concept is useful in quantum cryptography, in the context of privacy amplification (See for example [1]).
The first 128 symbols of the Fibonacci sequence has an entropy of approximately 7 bits/symbol, but the sequence can be expressed using a formula [F(n) = F(n−1) + F(n−2) for n = 3, 4, 5, ..., F(1) =1, F(2) = 1] and this formula has a much lower entropy and applies to any length of the Fibonacci sequence.
Hirschberg's algorithm is a generally applicable algorithm for optimal sequence alignment. BLAST and FASTA are suboptimal heuristics.If and are strings, where = and =, the Needleman–Wunsch algorithm finds an optimal alignment in () time, using () space.
[1] [2] In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. [3] The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement.
Longest word coined by a major author, [4] the longest word ever to appear in literature [5] Contrived nonce word; not in dictionary; Ancient Greek transliteration
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have an expected code length greater than or equal to the entropy of the source. [1]
The similarity of two strings and is determined by this formula: twice the number of matching characters divided by the total number of characters of both strings. The matching characters are defined as some longest common substring [3] plus recursively the number of matching characters in the non-matching regions on both sides of the longest common substring: [2] [4]