3,709 research outputs found
Voronoi-Based Region Approximation for Geographical Information Retrieval with Gazetteers
Gazetteers and geographical thesauri can be regarded as parsimonious spatial models that associate geographical location with place names and encode some semantic relations between the names. They are of particular value in processing information retrieval requests in which the user employs place names to specify geographical context. Typically the geometric locational data in a gazetteer are confined to a simple footprint in the form of a centroid or a minimum bounding rectangle, both of which can be used to link to a map but are of limited value in determining spatial relationships. Here we describe a Voronoi diagram method for generating approximate regional extents from sets of centroids that are respectively inside and external to a region. The resulting approximations provide measures of areal extent and can be used to assist in answering geographical queries by evaluating spatial relationships such as distance, direction and common boundary length. Preliminary experimental evaluations of the method have been performed in the context of a semantic modelling system that combines the centroid data with hierarchical and adjacency relations between the associated place names
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
Approximation results for a general class of Kantorovich type operators
We introduce and study a family of integral operators in the Kantorovich
sense for functions acting on locally compact topological groups. We obtain
convergence results for the above operators with respect to the pointwise and
uniform convergence and in the setting of Orlicz spaces with respect to the
modular convergence. Moreover, we show how our theory applies to several
classes of integral and discrete operators, as the sampling, convolution and
Mellin type operators in the Kantorovich sense, thus obtaining a simultaneous
approach for discrete and integral operators. Further, we derive our general
convergence results for particular cases of Orlicz spaces, as spaces,
interpolation spaces and exponential spaces. Finally we construct some concrete
example of our operators and we show some graphical representations.Comment: 23 pages, 5 figure
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