Algorithms for computer graphics or computational geometry often infer the topological structure of geometrical objects from numerical data. Unavoidable errors (due to limited precision) affect these calculations so that their use may produce ambiguous or contradictory inferences.

This special issue collects enhanced and extended versions of papers that were presented at the Symposium on Spatial Vagueness, Uncertainty, and Granularity held in October 2001. The contributions examine fundamental problems in the analysis of spatial vagueness and uncertainty, and the editors hope this selection stimulates further investigation in this growing subfield of the theory of spatial information.

The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

Spatial technologies like GIS, CAD, and spatial DBMS have proved their applicability and usability in almost every sector of urban development. Urban Planning Systems, Public Participation Systems, and others have been continuously developed and improved contributing to better decision making, communicating ideas between different actors as well as

Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.