This book contains the proceedings of the workshop Uncertainty in Geomet ric Computations that was held in Sheffield, England, July 5-6, 2001. A total of 59 delegates from 5 countries in Europe, North America and Asia attended the workshop. The workshop provided a forum for the discussion of com putational methods for quantifying, representing and assessing the effects of uncertainty in geometric computations. It was organised around lectures by invited speakers, and presentations in poster form from participants. Computer simulations and modelling are used frequently in science and engi neering, in applications ranging from the understanding of natural and artificial phenomena, to the design, test and manufacturing stages of production. This widespread use necessarily implies that detailed knowledge of the limitations of computer simulations is required. In particular, the usefulness of a computer simulation is directly dependent on the user's knowledge of the uncertainty in the simulation. Although an understanding of the phenomena being modelled is an important requirement of a good computer simulation, the model will be plagued by deficiencies if the errors and uncertainties in it are not consid ered when the results are analysed. The applications of computer modelling are large and diverse, but the workshop focussed on the management of un certainty in three areas : Geometric modelling, computer vision, and computer graphics.

This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces as well as more practical topics.

Machinelearningis arapidlymaturing?eldthataims toprovidepracticalme- ods for data discovery, categorization and modelling. The She?eld Machine Learning Workshop, which was held 7-10 September 2004, brought together some of the leading international researchers in the ?eld for a series of talks and posters that represented new developments in machine learning and numerical methods. The workshop was sponsored by the Engineering and Physical Sciences - search Council (EPSRC) and the London Mathematical Society (LMS) through the MathFIT program,whose aim is the encouragementof new interdisciplinary research.AdditionalfundingwasprovidedbythePASCALEuropeanFramework 6 Network of Excellence and the University of She?eld. It was the commitment of these funding bodies that enabled the workshop to have a strong program of invited speakers,and the organizerswish to thank these funding bodies for their ?nancial support. The particular focus for interactions at the workshop was - vanced Research Methods in Machine Learning and Statistical Signal Processing. These proceedings contain work that was presented at the workshop, and ideas that were developed through, or inspired by, attendance at the workshop. The proceedings re?ect this mixture and illustrate the diversity of applications and theoretical work in machine learning. We would like to thank the presenters and attendees at the workshop for the excellent quality of presentation and discussion during the oral and poster sessions. We are also grateful to Gillian Callaghan for her support in the orga- zation of the workshop, and ?nally we wish to thank the anonymous reviewers for their help in compiling the proceedings.