Applications of controlled surgery in dimension 4: Examples

The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goal of this paper is to show that this also holds for other fundamental groups which are not known to be good, and that it is best understood using controlled surgery theory of Pedersen--Quinn--Ranicki. We consider some examples of 4-manifolds which have the fundamental group either of a closed aspherical surface or of a 3-dimensional knot space. A more general theorem is stated in the appendix

GIS and regional development: Examples of applications

The recent development of Geographic Information Technologies (GIT), such as GIS, Remote Sensing and Desktop Mapping gives to the technicians of landscape management and regional development areas, access to a new powerful set of tools with an high potential for spatial analysis. Our project's ambition is to confirm that GIT can be useful tools for the definition and management of development policies. The ability of GIT to analyse geographical information (more or less 80 to 90% of the overall information that exists can be georeferenced) will create conditions to establish a model for economical development and with the support of this model decisions can be more accurate. By doing so, we will encourage the use of GIS in the regional science field. The results that we already had achieved with our project push us in front. That's why it is important to present them. In order to gather more people for this area. This paper will resume the activities and the major conclusions of some projects being developed since 1996 with the main purpose of establishing a theoretical background and create sample methodologies to support economic development through the use of GIS.

The duality diagram in data analysis: Examples of modern applications

Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses circles as the Duality Diagram Approach, put to new uses through the use of a variety of metrics and ways of combining different diagrams together. This issue of the Annals of Applied Statistics contains contemporary examples of how this approach provides solutions to hard problems in data integration. We present here the genesis of the technique and how it can be seen as a precursor of the modern kernel based approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS408 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org