Number restrictions are concept constructors that are available in almost all implemented Description Logic systems. However, they are mostly available only in a rather weak form, which considerably restricts their expressive power. On the one hand, the roles that may occur in number restrictions

We consider expressive Description Logics (ALCN ) allowing for number restrictions on complex roles built with combinations of role constructors.

We present the atomic decomposition tech-nique as a general method for reducing reason-ing about cardinalities of sets, in the DL case the cardinalities of role llers, to equation solv-ing problems. Then we apply the technique to a particular description logic with complex role terms and role hierarchies and a strong arith-metic component. 1

algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result

In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors

Number restrictions are concept constructors that are available in almost all implemen-ted description logic systems. However, even though there has lately been considerable ef-fort on integrating expressive role construc-tors into description logics, the roles that may occur in number restrictions

In this extended abstract an optimization technique, the so-called signature calculus, for reasoning with number restrictions in description logics is investigated. The calculus is used to speed-up ABox (and TBox) reasoning in the description logic

Abstract not found

Number restrictions are concept constructors that are available in almost all implemented description logic systems. However, even though there has lately been considerable effort on integrating expressive role constructors into description logics, the roles that may occur in number restrictions

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso