Nowadays, many factors support a growing production of information. In modern large environments, for the user’s point of view, it is desirable to have IRS that retrieve documents according to their relevance levels. Relevance levels have been studied in some previous IR works while some others (few) IR research works tackled the questions of IRS effectiveness and collections size. These latter...

We consider the mixed states of the two-qubit system under the action of the group G = SU(2) × SU(2) of local unitary transformations. The Hilbert space of this system is the tensor product H = C ⊗ C. Let P be the algebra of real polynomial functions on the affine space of all hermitian operators of trace 1 on H. The polynomials f ∈ P which are invariant under G form the subalgebra P ⊆ P. We co...

Let k be a field, let I be an ideal generated by monomials in the polynomial ring k[x1, . . . , xt] and let R = k[x1, . . . , xt]/I be the associated monomial ring. The k-vector spaces Tori (k, k) are N -graded. We derive a formula for the multigraded Poincaré series of R, PRk (x, z) = ∑ i≥0,α∈Nt dimk Tor R i,α(k, k)x z, in terms of the homology of certain simplicial complexes associated to sub...

Most test collections (like TREC and CLEF) for experimental research in information retrieval apply binary relevance assessments. This paper introduces a four-point relevance scale and reports the findings of a project in which TREC-7 and TREC8 document pools on 38 topics were reassessed. The goal of the reassessment was to build a subcollection of TREC for experiments on highly relevant docume...

We consider the problem of computing homogeneous coordinates points in a zero-dimensional subscheme compact, complex toric variety X X ....