Gaston H. Gonnet

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The Lambert W function is de ned to be the multivalued inverse of the function w we It has many applications in pure and applied mathematics some of which are brie y described here We present a new discussion of the complex branches of W an asymptotic expansion valid for all branches an e cient numerical procedure for evaluating the function to arbitrary(More)
We introduce a family of simple and fast algorithms for solving the classical string matching problem, string matching with don't care symbols and complement symbols, and multiple patterns. In addition we solve the same problems allowing up to <italic>k</italic> mismatches. Among the features of these algorithms are that they are real time algorithms, they(More)
The entire protein sequence database has been exhaustively matched. Definitive mutation matrices and models for scoring gaps were obtained from the matching and used to organize the sequence database as sets of evolutionarily connected components. The methods developed are general and can be used to manage sequence data generated by major genome sequencing(More)
In aligning homologous protein sequences, it is generally assumed that amino acid substitutions subsequent in time occur independently of amino acid substitutions previous in time, i.e. that patterns of mutation are similar at low and high sequence divergence. This assumption is examined here and shown to be incorrect in an interesting way. Separate(More)
MOTIVATION We announce the availability of the second release of Darwin v. 2.0, an interpreted computer language especially tailored to researchers in the biosciences. The system is a general tool applicable to a wide range of problems. RESULTS This second release improves Darwin version 1.6 in several ways: it now contains (1) a larger set of libraries(More)
OMA (Orthologous MAtrix) is a database that identifies orthologs among publicly available, complete genomes. Initiated in 2004, the project is at its 11th release. It now includes 1000 genomes, making it one of the largest resources of its kind. Here, we describe recent developments in terms of species covered; the algorithmic pipeline--in particular(More)