A schema mapping is a declarative specification of the relationship between instances of a source schema and a target schema. The data exchange (or data translation) problem asks: given an instance over the source schema, materialize an instance (or solution) over the target schema that satisfies the schema mapping. In general, a given source instance may have numerous different solutions. Amon...

In this paper we propose an algorithm for computing large primes p and q such that q divides p4 + p3 + p2 + p+ 1 or p4 − p3 + p2 − p+ 1. Such primes are key parameters for the GiulianiGong Public Key System.

Preterm birth has a critical influence on interactive, communicative, and expressive child behaviour, particularly during the first years of life. Few studies have stressed the assessment of mother-father-child interaction in families with preterm children, generating contradictory results. The present study wished to develop these fields: (i) comparing the quality of family interactions betwee...

Despite recent efforts to develop automated protein structure determination protocols, structural genomics projects are slow in generating fold assignments for complete proteomes, and spatial structures remain unknown for many protein families. Alternative cheap and fast methods to assign folds using prediction algorithms continue to provide valuable structural information for many proteins. Th...

A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the type axmod b ≤ cx . We give a new presentation for these semigroups and we relate them with a type of affine full semigroups. Next, we describe explicitly the minimal generating system for the affine full semigroups we are considering. As a consequence, we obtain generatin...

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes...

We solve three enumerative problems concerning the families of planar maps. More precisely, we establish algebraic equations for the generating function of loopless triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}. The originality of the problem lies in the fact that degree restrictions are placed both on vertices and faces. Our proofs first...

A Coxeter group element w is fully commutative if any reduced expression for w can be obtained from any other via the interchange of commuting generators. For example, in the symmetric group of degree n, the number of fully commutative elements is the nth Catalan number. The Coxeter groups with finitely many fully commutative elements can be arranged into seven infinite families An , Bn , Dn , ...

Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play important rôles in themselves and in their diverse applications. Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing some (presumably new) gene...