A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

UNIVERSALITY OF RANDOM GRAPHS

We prove that asymptotically (as n -> infinity) almost all graphs with n vertices and C(d)n(2-1/2d) log(1/d) n edges are universal with respect to the family of all graphs with maximum degree bounded by d. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs satisfying certain pseudorandom properties. We also prove a counterpart result for random bipartite graphs, where the threshold number of edges is even smaller but the embedding is randomized.

GPR applied to mapping utilities along the route of the Line 4 (yellow) subway tunnel construction in Sao Paulo City, Brazil

The rapid industrial development and disorganized population growth in huge cities bring about various urban problems due to intense use of physical space on and below the surface. Subsurface problems in metropolitan areas are caused by subway line construction, which often follows the routes of utility networks, such as electric and telephone cables, water and gas pipes, storm sewers, etc. Usually, the main problems are related to damage or destruction of preexisting utilities, often putting human lives at risk. With the purpose of minimizing risks. GPR-profiling with 200 MHz antennae was done at two sites, both located in downtown Sao Paulo, Brazil. The objectives of this work were to map utilities or existing infrastructure in the subsurface in order to orient the construction of the Line 4 (yellow) subway tunnel in Sao Paulo. GPR profiles can detect water pipes, utility networks in the subsurface, and concrete foundation columns or pilings in subsoil up to 2 m depth. In addition. the GPR profiles also provided details of the target shapes in the subsurface. GPR interpretations combined with lithological information from boreholes and trenches opened in the study areas were extremely important in mapping of the correct spatial distribution of buried utilities at these two sites in Sao Paulo. This information improves and updates maps of utility placement, serves as a basis for planning of the geotechnical excavation of the Line 4 (yellow) subway tunnel in Sao Paulo, helps minimize problems related to destruction of preexisting utilities in the subsoil, and avoids risk of dangerous accidents. (C) 2012 Elsevier B.V. All rights reserved.

Modeling and measuring the spatial relation "along": Regions, contours and fuzzy sets

The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or ID contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. (C) 2011 Elsevier Ltd. All rights reserved.