Gaston H. Gonnet

On the LambertW function

The LambertW function is defined to be the multivalued inverse of the functionw →wew. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.

Maple V Library reference manual

An interactive system for symbolic computation, Maple was developed to perform hundreds of functions for use at all mathematical levels. This manual describes all of the functions that are available in the Maple library which is where the code for over 95% of Maples mathematical knowledge and expertise resides. Through the library, the Maple system and the algorithms that it use can be dynamically extended and customized. Each description of the Maple library routines includes a short explanation of the function, the parameters that it uses, and additional details about the function. The design and implementation of the Maple system is an on-going project of the Symbolic Computation Group at the University of Waterloo. The Maple Symbolic Computation System is currently being used at over 1000 sites worldwide. An accompanying manual, the Maple Language Reference Manual, which describes the Maple language and the Maple system itself is currently in preperation. This reference book on mathematics, physics/astronomy, engineering and computer science is intended for mathematicians, computer scientists and physicists.

A Role for Codon Order in Translation Dynamics

The genetic code is degenerate. Each amino acid is encoded by up to six synonymous codons; the choice between these codons influences gene expression. Here, we show that in coding sequences, once a particular codon has been used, subsequent occurrences of the same amino acid do not use codons randomly, but favor codons that use the same tRNA. The effect is pronounced in rapidly induced genes, involves both frequent and rare codons and diminishes only slowly as a function of the distance between subsequent synonymous codons. Furthermore, we found that in S. cerevisiae codon correlation accelerates translation relative to the translation of synonymous yet anticorrelated sequences. The data suggest that tRNA diffusion away from the ribosome is slower than translation, and that some tRNA channeling takes place at the ribosome. They also establish that the dynamics of translation leave a significant signature at the level of the genome.

A mechanism for asymmetric segregation of age during yeast budding

Ageing and the mortality that ensues are sustainable for the species only if age is reset in newborns. In budding yeast, buds are made young whereas ageing factors, such as carbonylated proteins and DNA circles, remain confined to the ageing mother cell. The mechanisms of this confinement and their relevance are poorly understood. Here we show that a septin-dependent, lateral diffusion barrier forms in the nuclear envelope and limits the translocation of pre-existing nuclear pores into the bud. The retention of DNA circles within the mother cell depends on the presence of the diffusion barrier and on the anchorage of the circles to pores mediated by the nuclear basket. In accordance with the diffusion barrier ensuring the asymmetric segregation of nuclear age-determinants, the barrier mutant bud6Δ fails to properly reset age in buds. Our data involve septin-dependent diffusion barriers in the confinement of ageing factors to one daughter cell during asymmetric cell division.

First leaves: a tutorial introduction to Maple V

This tutorial shows how to use Maple both as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding tasks. It covers topics such as the basic data types and statements in the Maple language. It explains the differences between numeric computation and symbolic computation and illustrates how both are used in Maple. Extensive how-to examples are used throughout the tutorial to show how common types of calculations can be expressed easily in Maple. The manual also uses many graphics examples to illustrate the way in which 2D and 3D graphics can aid in understanding the behavior of functions.

Fast text searching for regular expressions or automaton searching on tries

We present algorithms for efficient searching of regular expressions on preprocessed text, using a Patricia tree as a logical model for the index. We obtain searching algorithms that run in logarithmic expected time in the size of the text for a wide subclass of regular expressions, and in sublinear expected time for any regular expression. This is the first such algorithm to be found with this complexity.

OMA Browser—Exploring orthologous relations across 352 complete genomes

MOTIVATIONnInference of the evolutionary relation between proteins, in particular the identification of orthologs, is a central problem in comparative genomics. Several large-scale efforts with various methodologies and scope tackle this problem, including OMA (the Orthologous MAtrix project).nnnRESULTSnBased on the results of the OMA project, we introduce here the OMA Browser, a web-based tool allowing the exploration of orthologous relations over 352 complete genomes. Orthologs can be viewed as groups across species, but also at the level of sequence pairs, allowing the distinction among one-to-one, one-to-many and many-to-many orthologs.nnnAVAILABILITYnhttp://omabrowser.org.

The OMA orthology database in 2015: function predictions, better plant support, synteny view and other improvements

The Orthologous Matrix (OMA) project is a method and associated database inferring evolutionary relationships amongst currently 1706 complete proteomes (i.e. the protein sequence associated for every protein-coding gene in all genomes). In this update article, we present six major new developments in OMA: (i) a new web interface; (ii) Gene Ontology function predictions as part of the OMA pipeline; (iii) better support for plant genomes and in particular homeologs in the wheat genome; (iv) a new synteny viewer providing the genomic context of orthologs; (v) statically computed hierarchical orthologous groups subsets downloadable in OrthoXML format; and (vi) possibility to export parts of the all-against-all computations and to combine them with custom data for ‘client-side’ orthology prediction. OMA can be accessed through the OMA Browser and various programmatic interfaces at http://omabrowser.org.

Darwin v. 2.0: an interpreted computer language for the biosciences

MOTIVATIONnWe 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.nnnRESULTSnThis second release improves Darwin version 1.6 in several ways: it now contains (1) a larger set of libraries touching most of the classical problems from computational biology (pairwise alignment, all versus all alignments, tree construction, multiple sequence alignment), (2) an expanded set of general purpose algorithms (search algorithms for discrete problems, matrix decomposition routines, complex/long integer arithmetic operations), (3) an improved language with a cleaner syntax, (4) better on-line help, and (5) a number of fixes to user-reported bugs.nnnAVAILABILITYnDarwin is made available for most operating systems free of char ge from the Computational Biochemistry Research Group (CBRG), reachable at http://chrg.inf.ethz.ch.nnnCONTACTndarwin@inf.ethz.ch

Estimates of Positive Darwinian Selection Are Inflated by Errors in Sequencing, Annotation, and Alignment

Published estimates of the proportion of positively selected genes (PSGs) in human vary over three orders of magnitude. In mammals, estimates of the proportion of PSGs cover an even wider range of values. We used 2,980 orthologous protein-coding genes from human, chimpanzee, macaque, dog, cow, rat, and mouse as well as an established phylogenetic topology to infer the fraction of PSGs in all seven terminal branches. The inferred fraction of PSGs ranged from 0.9% in human through 17.5% in macaque to 23.3% in dog. We found three factors that influence the fraction of genes that exhibit telltale signs of positive selection: the quality of the sequence, the degree of misannotation, and ambiguities in the multiple sequence alignment. The inferred fraction of PSGs in sequences that are deficient in all three criteria of coverage, annotation, and alignment is 7.2 times higher than that in genes with high trace sequencing coverage, “known” annotation status, and perfect alignment scores. We conclude that some estimates on the prevalence of positive Darwinian selection in the literature may be inflated and should be treated with caution.