Partial Matrix Techniques.

Partial matrix techniques are those in which gravity models are fitted to a partially observed matrix of trips and journey costs, and used to infer the trips in the unobserved cells. This paper reviews the theoretical basis from which such techniques have been developed, and demonstrates the need to pay careful attention to the - underlying assumptions, which in effect require that the model be a good fit to be observed data (and also a good 'fit' to the unobserved data). Circumstances are described in which the estimates for the unobserved cells may not be uniquely determined, and the effects of data structure on the reliability of the estimates (assuming these to be unique) are discussed. Ways are suggested in which further theoretical and empirical research might demonstrate whether a given pattern of observations would lead to particularly error-prone estimates

The rational field is not universally definable in pseudo-exponentiation

We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field

How Can Speech Recognisers Help Applied Research in the Civil Engineering, Transport and Related Industries

BACKGROUND Speech recognition technology is rapidly advancing to the point here it can be usefully applied in a wide range of mtexts. For applications within the SERC Environment Committee's area of interest -civil engineering; construction; building; transport; water resources there are a number of kinds of recording situation in which one needs to keep one's eyes on the situation being studied; or in which the recording conditions (eg moving around with instruments) are unfavourable. The limitations of conventional pen and paper recording for these situations are obvious; and the limitations of hand-held data capture devices are also becoming apparent. Speech is therefore an easier medium to use; and a tape recorder a convenient means of recording the observations. For well defined recording tasks; speech recognisers might be a helpful way of transcribing the record. This seminar was convened to enable those who are potentially interested in such an application of information technology to hear of the latest developnents and assessments of the suitability of the technology

A note on the axioms for Zilber's pseudo-exponential fields

We show that Zilber's conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an example of a non-finitary abstract elementary class, answering a question of Kes\"al\"a and Baldwin.Comment: 10 pages, v2: substantial alteration

Efficient Compilation of a Class of Variational Forms

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.Comment: ACM Transactions on Mathematical Software 33(3), 20 pages (2007

A new look at Counterexamples in topology

The book Counterexamples in Topology is a useful catalogue of topological spaces and properties. This thesis extends that catalogue to the properties of sobriety and packedness, and describes some related theory. A purely topological account of sobriety and sober reflections is given, together with an account of the connection with point-free topology which motivates it. Concrete constructions of the sober, T0 and T1 reflections of a topological space are given, and these are calculated for each space in Counterexamples in Topology. These are used to study the relationship between sobriety and the T1 separation property. The notion of a specialization topology is introduced as a means of constructing topological spaces from quasiordered sets. The Alexandrov, Scott and weak topologies are described and shown to be examples of this notion. The sobriety and sober reflections of specialization topologies are considered, and these motivate a suggestion for a generalization of the notion of a topological space. The calculations in this thesis are summarized in two reference tables