We present a very general geometrico-dynamical description of physical or more abstract entities, called the general tension-reduction (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable fluctuations in the...

Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both Hilbertian and non-Hilbertian settings; (ii) a compactness result for bounded sequences in a suitable Discontinuous Galerkin norm, together with a weak convergence property for some discrete gradients. The...

Hilbertian Deductive Systems, Infon Logic, and Datalog Andreas Blassa,1,∗, Yuri Gurevich aMathematics Department, University of Michigan, Ann Arbor, MI 48109, USA bMicrosoft Research, One Microsoft Way, Redmond, WA 98052, USA

Multidimensional codesign is a recently proposed paradigm for integrating different system dimensions in sensor networks. Examples of such dimensions are logical and physical mobility, continuous and discrete transitions, deterministic and random evolutions and features resulting from their interaction, like deterministic and stochastic hybrid behaviours. In this paper, we propose a unifying co...

We study some natural empirical processes determined by uniformly convex Banach spaces with modulus of convexity of power type 2. Results of this kind were extensively studied in a Hilbertian setting, and became an important tool for investigations, for example, of the behaviour of various random sets of vectors (as in [14, 15, 7, 16, 2, 6]). We then apply these results to address a problem of ...