Representing and absolutely representing systems

Absolutely Representing Systems, Uniform Smoothness and Type

Absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = ∑ i aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every ARS in a B-convex Banach ...

Combining and Representing Logical Systems

The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the model-theoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions). We propose a modiied notion of parchment together with a notion of pa...

Representing Complex Adaptive Spatial Systems

Representing Time in Multimedia Systems

As multimedia systems deal with a variety of temporally interrelated media items, synchronization is an important issue in those systems. One part of synchronization is the representation of temporal information. In contrast to traditional computing tasks, multimedia imposes new requirements on the representation of time. Specifically, a fine-grained and a flexible temporal model is required. T...

Representing Systems with Hidden State

Introduction Learning and planning under uncertainty is a crucial focus of modern AI research. In this paper, we address the issue of sequential decision making. Much of the work in this field is based on the framework of Partially Observable Markov Decision Processes (POMDPs) (Kaelbling et al., 1998). In this framework, problems are modeled using discrete states and actions. Actions cause stoc...