Conjunctions of Among Constraints

Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some given bounds. It is known that domain filtering algorithms can benefit from reasoning about the interaction of among constraints so that values can be filtered out taking into consideration several among constraints simultaneously. The present pa- per embarks into a systematic investigation on the circumstances under which it is possible to obtain efficient and complete domain filtering algorithms for conjunctions of among constraints. We start by observing that restrictions on both the scope and the range of the among constraints are necessary to obtain meaningful results. Then, we derive a domain flow-based filtering algorithm and present several applications. In particular, it is shown that the algorithm unifies and generalizes several previous existing results.Comment: 15 pages plus appendi

On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings

We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described in [14] for the stationary problem and leads to the finite difference scheme introduced by Achdou and Capuzzo-Dolcetta in [3]. In order to solve the finite dimensional variational problems, in [14] the authors implement the primal-dual algorithm introduced by Chambolle and Pock in [20], whose core consists in iteratively solving linear systems and applying a proximity operator. We apply that method to time-dependent MFG and, for large viscosity parameters, we improve the linear system solution by replacing the direct approach used in [14] by suitable preconditioned iterative algorithms

Brachypodium distachyon as a model for defining the allergen potential of non-prolamin proteins

Epitope databases and the protein sequences of published plant genomes are suitable to identify some of the proteins causing food allergies and sensitivities. Brachypodium distachyon, a diploid wild grass with a sequenced genome and low prolamin content, is the closest relative of the allergen cereals, such as wheat or barley. Using the Brachypodium genome sequence, a workflow has been developed to identify potentially harmful proteins which may cause either celiac disease or wheat allergy-related symptoms. Seed tissue-specific expression of the potential allergens has been determined, and intact epitopes following an in silico digestion with several endopeptidases have been identified. Molecular function of allergen proteins has been evaluated using Gene Ontology terms. Biologically overrepresented proteins and potentially allergen protein families have been identified. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s10142-012-0294-z) contains supplementary material, which is available to authorized users

Undirected Forest Constraints

Abstract. We present two constraints that partition the vertices of an undirected n-vertex, m-edge graph G = (V, E) into a set of vertex-disjoint trees. The first is the resource-forest constraint, where we assume that a subset R ⊆ V of the vertices are resource vertices. The constraint specifies that each tree in the forest must contain at least one resource vertex. This is the natural undirected counterpart of the tree constraint [1], which partitions a directed graph into a forest of directed trees where only certain vertices can be tree roots. We describe a hybrid-consistency algorithm that runs in O(m + n) time for the resource-forest constraint, a sharp improvement over the O(mn) bound that is known for the directed case. The second constraint is proper-forest. In this variant, we do not have the requirement that each tree contains a resource, but the forest must contain only proper trees, i.e., trees that have at least two vertices each. We develop a hybrid-consistency algorithm for this case whose running time is O(mn) in the worst case, and O(m √ n) in many (typical) cases.