Mapping the Education System in Northern Ireland

In this chapter we provide a broad overview of the education system discussing both the system of schooling and the network of both statutory and voluntary bodies that are responsible for the administration and management of the system. We begin with an examination of the administrative structures. This network of statutory and non-statutory bodies has increased in number over recent years, illustrating the diversity of vested interests in the system. This is followed by an examination of the system of schooling and the chapter concludes by exploring the significance of changes that have taken place in terms of its implications for a more pluralist society where each is accorded parity of esteem and equality of opportunity.

Mapping cosmopolis: moral topographies of the medieval city

Cosmopolis is a concept that has a long history in many cultures around the globe. It is a mirroring of the 'social' and 'natural' worlds, such that in one is seen the order and the structures of the other -- a mutual 'mapping'. In this paper I examine how the presence of cosmopolis -- a Christianised cosmopolis of the European Middle Ages -- was made evident in the representation and formation of cities at that time. I reveal a dualism between the social and spatial ordering of both city and cosmos which defined and reinforced social and spatial boundaries in urban landscapes, evident for example in the 11th and 12th centuries. Recently, Toulmin (1992) has taken the idea of cosmopolis to argue that it has been a persistent presence in Western - Enlightenment science, philosophy, and religion -- a 'hidden agenda of modernity'. I contend that, as an idea, cosmopolis has a much earlier circulation in European thinking, not least in the Middle Ages. Locating cosmopolis in the medieval and the modern periods then begs a question of what is it that really makes the two distinct and separate? All too often human geographers have emphasised discontinuities between the 'medieval' and 'modern' age, locating the 'rise of modernity' some time in the Enlightenment period. However, what 'mapping' cosmopolis reveals are continuities, binding time and space together, which when looked at begin to help query the modernity concept itself.

On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Dynamic Multivariate Statistical Process Control using Subspace Identification

This paper points out a serious flaw in dynamic multivariate statistical process control (MSPC). The principal component analysis of a linear time series model that is employed to capture auto- and cross-correlation in recorded data may produce a considerable number of variables to be analysed. To give a dynamic representation of the data (based on variable correlation) and circumvent the production of a large time-series structure, a linear state space model is used here instead. The paper demonstrates that incorporating a state space model, the number of variables to be analysed dynamically can be considerably reduced, compared to conventional dynamic MSPC techniques.