Completeness theory for the product of finite partial algebras

AbstractA general completeness criterion for the finite product ∏P(ki) of full partial clones P(ki) (composition-closed subsets of partial operations) defined on finite sets E(ki)(|E(ki)|⩾2,i=1,…,n,n⩾2) is considered and a Galois connection between the lattice of subclones of ∏P(ki), called partial n-clones, and the lattice of subalgebras of multiple-base invariant relation algebra, with operations of a restricted quantifier free calculus, is established. This is used to obtain the full description of all maximal partial n-clones via multiple-base invariant relations and, thus, to solve the general completeness problem in ∏P(ki)

CandidaDB: a multi-genome database for Candida species and related Saccharomycotina

CandidaDB (http://genodb.pasteur.fr/CandidaDB) was established in 2002 to provide the first genomic database for the human fungal pathogen Candida albicans. The availability of an increasing number of fully or partially completed genome sequences of related fungal species has opened the path for comparative genomics and prompted us to migrate CandidaDB into a multi-genome database. The new version of CandidaDB houses the latest versions of the genomes of C. albicans strains SC5314 and WO-1 along with six genome sequences from species closely related to C. albicans that all belong to the CTG clade of Saccharomycotina—Candida tropicalis, Candida (Clavispora) lusitaniae, Candida (Pichia) guillermondii, Lodderomyces elongisporus, Debaryomyces hansenii, Pichia stipitis—and the reference Saccharomyces cerevisiae genome. CandidaDB includes sequences coding for 54 170 proteins with annotations collected from other databases, enriched with illustrations of structural features and functional domains and data of comparative analyses. In order to take advantage of the integration of multiple genomes in a unique database, new tools using pre-calculated or user-defined comparisons have been implemented that allow rapid access to comparative analysis at the genomic scale

Partial R-clones

In [Romov, ISMVL 2013] the first author introduced a type of partial clones as the intersection of some special infinite descending chains similar to I. Rosenberg (1972) in the case of total clones. We provide a characterization of these clones in terms of their invariants, and propose a generalization of such clones, which we will call partial R-clones. We show that there are only finitely many partial R-clones. Furthermore, we investigate some properties related to their position in the lattice of partial clones