A branch-and-bound methodology within algebraic modelling systems

Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\sc Minto} is an example of a system which offers the possibility to incorporate user-provided directives (written in {\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical programming models. The aim of this paper is to present a branch-and-bound methodology for particular combinatorial structures to be embedded inside an algebraic modelling language. One advantage is the increased scope of application. Another advantage is that directives are more easily implemented at the modelling level than at the programming level

The place of expert systems in a typology of information systems

This article considers definitions and claims of Expert Systems ( ES) and analyzes them in view of traditional Information systems (IS). It is argued that the valid specifications for ES do not differ fran those for IS. Consequently the theoretical study and the practical development of ES should not be a monodiscipline. Integration of ES development in classical mathematics and computer science opens the door to existing knowledge and experience. Aspects of existing ES are reviewed from this interdisciplinary point of view

The Micro-Electronic Revolution and its Impact on Labour and Employment

Series: Discussion Papers of the Institute for Economic Geography and GIScienc

Convex hulls of curves of genus one

Let C be a real nonsingular affine curve of genus one, embedded in affine n-space, whose set of real points is compact. For any polynomial f which is nonnegative on C(R), we prove that there exist polynomials f_i with f \equiv \sum_i f_i^2 (modulo I_C) and such that the degrees deg(f_i) are bounded in terms of deg(f) only. Using Lasserre's relaxation method, we deduce an explicit representation of the convex hull of C(R) in R^n by a lifted linear matrix inequality. This is the first instance in the literature where such a representation is given for the convex hull of a nonrational variety. The same works for convex hulls of (singular) curves whose normalization is C. We then make a detailed study of the associated degree bounds. These bounds are directly related to size and dimension of the projected matrix pencils. In particular, we prove that these bounds tend to infinity when the curve C degenerates suitably into a singular curve, and we provide explicit lower bounds as well.Comment: 1 figur

Non-cooperative Games

Non-cooperative games are mathematical models of interactive strategic decision situations.In contrast to cooperative models, they build on the assumption that all possibilities for commitment and contract have been incorporated in the rules of the game.This contribution describes the main models (games in normal form, and games in extensive form), as well as the main concepts that have been proposed to solve these games.Solution concepts predict the outcomes that might arise when the game is played by "rational" individuals, or after learning processes have converged.Most of these solution concepts are variations of the equilibrium concept that was proposed by John Nash in the 1950s, a Nash equilibrium being a combination of strategies such that no player can improve his payoff by deviating unilaterally.The paper also discusses the justifications of these concepts and concludes with remarks about the applicability of game theory in contexts where players are less than fully rational.noncooperative games