Objective functions with redundant domains

Let (E,A) be a set system consisting of a finite collection A of subsets of a ground set E, and suppose that we have a function ϕ which maps A into some set S. Now removing a subset K from E gives a restriction A(K¯) to those sets of A disjoint from K, and we have a corresponding restriction ϕ|A(K¯) of our function ϕ. If the removal of K does not affect the image set of ϕ, that is Im(ϕ|A(X¯))=Im(ϕ), then we will say that K is a kernel set of A with respect to ϕ. Such sets are potentially useful in optimisation problems defined in terms of ϕ. We will call the set of all subsets of E that are kernel sets with respect to ϕ a kernel system and denote it by Kerϕ(A). Motivated by the optimisation theme, we ask which kernel systems are matroids. For instance, if A is the collection of forests in a graph G with coloured edges and ϕ counts how many edges of each colour occurs in a forest then Kerϕ(A) is isomorphic to the disjoint sum of the cocycle matroids of the differently coloured subgraphs; on the other hand, if A is the power set of a set of positive integers, and ϕ is the function which takes the values 1 and 0 on subsets according to whether they are sum-free or not, then we show that Kerϕ(A) is essentially never a matroid

ASAS/WHO ICF Core Sets for ankylosing spondylitis (AS): how to classify the impact of AS on functioning and health

Objective: To report on the results of a standardised consensus process agreeing on concepts typical and/or relevant when classifying functioning and health in patients with ankylosing spondylitis (AS) based on the International Classification of Functioning and Health (ICF).Methods: Experts in AS from different professional and geographical backgrounds attended a consensus conference and were divided into three working groups. Rheumatologists were selected from members of the Assessment of SpondyloArthritis international Society (ASAS). Other health professionals were recommended by ASAS members. The aim was to compose three working groups with five to seven participants to allow everybody's contribution in the discussions. Experts selected ICF categories that were considered typical and/or relevant for AS during a standardised consensus process by integrating evidence from preceding studies in alternating working group and plenary discussions. A Comprehensive ICF Core Set was selected for the comprehensive classification of functioning and a Brief ICF Core Set for application in trials.Results: The conference was attended by 19 experts from 12 countries. Eighty categories were included in the Comprehensive Core Set, which included 23 Body functions, 19 Body structures, 24 Activities and participation and 14 Environmental factors. Nineteen categories were selected for the Brief Core Set, which included 6 Body functions, 4 Body structures, 7 Activities and participation and 2 Environmental factors.Conclusion: The Comprehensive and Brief ICF Core Sets for AS are now available and aim to represent the external reference to define consequences of AS on functioning

Optimal Placement of Valves in a Water Distribution Network with CLP(FD)

This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design. We take the formulation of the problem by Giustolisi and Savic (2008) and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network. We believe that the area of the so-called hydroinformatics can benefit from the techniques developed in Constraint Logic Programming and possibly from other areas of logic programming, such as Answer Set Programming.Comment: Best paper award at the 27th International Conference on Logic Programming - ICLP 2011; Theory and Practice of Logic Programming, (ICLP'11) Special Issue, volume 11, issue 4-5, 201