On the hyperkaehler/quaternion Kaehler correspondence

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of A.Haydys. We construct in this paper the corresponding holomorphic line bundle on twistor space and compute many examples, including monopole and Higgs bundle moduli spaces. We also show that the bundle on twistor space has a natural meromorphic connection which realizes it as the quantum line bundle for the hyperkaehler family of holomorphic symplectic structures. Finally we give a twistor version of the HK/QK correspondence.Comment: 35 page

Storage of Natural Language Sentences in a Hopfield Network

This paper look at how the Hopfield neural network can be used to store and recall patterns constructed from natural language sentences. As a pattern recognition and storage tool, the Hopfield neural network has received much attention. This attention however has been mainly in the field of statistical physics due to the model's simple abstraction of spin glass systems. A discussion is made of the differences, shown as bias and correlation, between natural language sentence patterns and the randomly generated ones used in previous experiments. Results are given for numerical simulations which show the auto-associative competence of the network when trained with natural language patterns.Comment: latex, 10 pages with 2 tex figures and a .bib file, uses nemlap.sty, to appear in Proceedings of NeMLaP-

Manifolds with holonomy U*(2m)

We consider the geometry determined by a torsion-free affine connection whose holonomy lies in the subgroup U*(2m), a real form of GL(2m,C), otherwise denoted by SL(m,H).U(1). We show in particular how examples may be generated from quaternionic K\"ahler or hyperk\"ahler manifolds with a circle action.Comment: Based on the author's Santalo Lecture delivered in the Universidad Complutense, Madrid on October 10th 2013. To appear in the Revista Matem\'atica Complutens

Fingalian topographies: Ossian and the Highland Tour 1760-1805

If Ossian validated the Highland landscape for eighteenth-century tourists, the landscape, in turn, seemed to authenticate poems whose authenticity never ceased to be doubted; but text and topography alike ran the risk of dissolving into insubstantiality. Many tourists cited ‘local tradition’ in order to embroider existing (or to invent new) Fingalian place-names. Ranging over a wide variety of eighteenth-century travel-writers, this article casts new light on the relations between Ossian, travel-writing and Highland topography. It concludes by discussing the ‘fieldwork’ tradition of Ossianic tourism after 1800, which sought out local tradition bearers, rather than attempting to authenticate Macpherson's ‘translations’