Various problems in machine learning, databases, and statistics involve pairwise distances among a set of objects. It is often desirable for these distances to satisfy the properties of a metric, especially the triangle inequality. Applications where metric data is useful include clustering, classification, metric-based indexing, and approximation algorithms for various graph problems. This pap...

Many practical applications in machine learning require pairwise distances among a set of objects. It is often desirable that these distance measurements satisfy the properties of a metric, especially the triangle inequality. Applications that could benefit from the metric property include data clustering and metric-based indexing of databases. In this paper, we present the metric nearness prob...

'Space and place are central to the strategies and meaning of protest’ (p. xi) reads the opening sentence of Katrina Navickas's latest study, Protest and the Politics of Space and Place 1789–1848. Written, in part, as a response to the 'spatial turn' in History, Navickas makes a cogent and persuasive argument for attending to the importance of the particularities of 'place' rather than the abst...

In this paper we present a new approach towards global passive approximation in order to find a passive real-rational transfer function G(s) that is an arbitrarily close approximation of the passive transfer function nearest to a non-passive square transfer function H(s). It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the ...

&bstract. The notions of a situation and a distance between situations in a narrow subject domain are introduced. ~ approach to the construction of an intellectual data base is suggested. The main task.of this data base is to find situations ~lhich are near to the one fixed by user. The theory of finite groups is considered as an example° I INTRODUCTION No~ information retrieval systems and esp...

We first prove the equivalence between some conditions of nearness and accretivity for nonlinear operators. Then we show an easier proof of a result of Tarsia regarding the equivalence of Cordes and Campanato conditions. 2000 Mathematics Subject Classification: 35H20, 46B20, 47H06.