In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability d...

In 1982, Drezner proposed the (1|1)-centroid problem on the plane, in which two players, called the leader and the follower, open facilities to provide service to customers in a competitive manner. The leader opens the first facility, and then the follower opens the second. Each customer will patronize the facility closest to him (ties broken in favor of the leader’s one), thereby decides the m...

This paper describes work done as part of the Oxford AGV (Autonomous Guided Vehicle) project [2] towards recognition of classes of objects to be encountered in a factory environment. \Ye address the problem of recognising an object from range-data observations as an instance of a parametric model class, and determining the values of the class parameters for that instance of the model, and the p...

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms tropical geometry. Applications include shortest paths traffic networks with variable link travel times.

IFC (Industry Foundation Classes) is the commonly accepted data exchange standard for Building Information Models (BIM). However, the geometric representation in IFC is restricted to explicit, extrusion and CSG (Constructive Solid Geometry) approaches. Accordingly, the exchange of parametric geometry between parametric design applications used in the AEC (Architecture, Engineering and Construct...