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The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of two formalisms used for different purposes and in different research areas: graphical games and soft constraints. We relate the notion of optimality used in the area of soft constraint satisfaction problems (SCSPs) to that used in graphical games, showing that for a large class of SCSPs that includes weighted constraints every optimal solution corresponds to a Nash equilibrium that is also a Pareto efficient joint strategy. We also study alternative mappings including one that maps graphical games to SCSPs, for which Pareto efficient joint strategies and optimal solutions coincide.
Qualitative representations of spatial knowledge have been widely studied and a variety of frameworks are used to express relationships between static regions. Dynamic regions present a much greater challenge, but are important in practical applications such as describing crowds of people moving over time. Previous work has analysed changes as regions merge and split and as new regions are created and existing ones disappear. We present a novel framework for the qualitative description of spatial regions based on two levels of granularity. Introducing granularity yields significantly more informative qualitative descriptions than are available from a single level of detail. The formal model represents a region, which may have multiple components, as a bipartite graph where the nodes are the components of the region at a fine level of d...
We study a model in which a group of agents make a sequence of collective decisions on whether to remain in the current state of the system or switch to an alternative state, as proposed by one of them. Examples for instantiations of this model include the step-wise refinement of a bill of law by means of amendments to be voted on, as well as resource allocation problems, where agents successively alter the current allocation by means of a sequence of deals. We specifically focus on cases where the majority rule is used to make each of the collective decisions, as well as variations of the majority rule where different quotas need to be met to get a proposal accepted. In addition, we allow for cases in which the same proposal may be made more than once. As this can lead to infinite sequences, we investigate the effects of introducing a...
Modal and modal-like formalisms such as temporal or description logics go beyond propositional logic by introducing operators that allow for a guarded form of quantication over states or paths of transition systems. Thus, they are more expressive than propositional logic, yet computationally better behaved than rst-order logic. We propose constraint-based methods to model and solve modal satisability problems. We model the satisability of basic modal formulas via appropriate sets of nite constraint satisfaction problems, and then resolve these via constraint solvers. The domains of the constraint satisfaction problems contain other values than just the Boolean 0 or 1; for these values, we create specialised constraints that help us steer the decision procedure and so keep the modal search tree as small as possible. We show experimental...
A novel approach for the control of exciton-exciton Coulomb coupling in semiconductor macroatoms/molecules is proposed. We show that by applying properly tailored external fields, we can induce ---or significantly reinforce--- excitonic dipoles, which in turn allows to control and magnify intra- as well as inter-dot few-exciton effects. Such dipole-dipole interaction mechanism will be accounted for within a simple analytical model, which is found to be in good agreement with fully three-dimensional calculations. The proposed approach may play an important role for the design and realization of fully-optical quantum gates as well as ultrafast optical switches.
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