We show that BPP has p-measure zero if and only if BPP differs from EXP. The same holds when we replace BPP by any complexity class C that contains BPP and is closed under tt-reductions. The zero-one law for each of these classes C follows: Within EXP, C has either measure zero or else measure one.

The Ontology Engineering community widely agrees on the importance of helping the user understand the output of a DL reasoner. The most recent approaches to the problem [4] [3] are based on the notion of a Minimal Unsatisfiability Preserving SubTBoxes (MUPS). Roughly, a MUPS for an atomic concept A is a minimal fragment T ′ ⊆ T of a TBox T in which A is unsatisfiable. For example, given the TBox:

This paper describes the use of Ruby, a language of functions and relations, to develop serialised implementations of array-based architectures. Our Ruby expressions contain parameters which can be varied to produce a wide range of designs with diierent space-time trade-oos. Such expressions can be obtained by applying correctness-preserving transformations to an initial simple description. Thi...

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N−1/5. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigatio...

We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space and fibers. We give an application concerning scalar curvatures of smooth lim...

We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every homomorphism from an ergodic full group to a separable group is continuous. We also find bounds for the minimal number of topological generators (elements generating a dense subgroup) of full groups allowing us to dist...

Efforts have been directed at obtaining flexible learning procedures that optimally adapt to various possible characteristics of the data generating mechanism. A question that addresses the issue of how far one can go in this direction is: Given a regression procedure, however sophisticated it is, how many regression functions are estimated accurately? In this work, for a given sequence of pres...

We find a sharp combinatorial bound for the metric entropy of sets in R and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central Limit Theorem if the square root of its combinatorial dimension is integrable. 2. The uniform entropy is equivalent to the combinatorial dimension under minimal ...

We examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties. We compare our results with a number of traditional measures. The metric entropy is capable of detecting nonlinear dependence within the returns series, and is also capable of detecting nonlinear\a±nity" between the returns and their predictions obtain...

Hierarchical organisation is omnipresent in natural systems and is of special importance in connection with living systems. Thus far it is poorly understood what type of artificially created system is capable of replicating the emergent hierarchical structure of nature. This paper is an attempt to clarify what hierarchical struc-