3,255 research outputs found
Formal study of plane Delaunay triangulation
This article presents the formal proof of correctness for a plane Delaunay
triangulation algorithm. It consists in repeating a sequence of edge flippings
from an initial triangulation until the Delaunay property is achieved. To
describe triangulations, we rely on a combinatorial hypermap specification
framework we have been developing for years. We embed hypermaps in the plane by
attaching coordinates to elements in a consistent way. We then describe what
are legal and illegal Delaunay edges and a flipping operation which we show
preserves hypermap, triangulation, and embedding invariants. To prove the
termination of the algorithm, we use a generic approach expressing that any
non-cyclic relation is well-founded when working on a finite set
Fractal Electromagnetic Showers
We study the self-similar structure of electromagnetic showers and introduce
the notion of the fractal dimension of a shower. Studies underway of showers in
various materials and at various energies are presented, and the range over
which the fractal scaling behaviour is observed is discussed. Applications to
fast shower simulations and identification, particularly in the context of
extensive air showers, are also discussed.Comment: Talk to be presented at the XI International Symposium on Very High
Energy Cosmic Ray Interaction
Formalized proof, computation, and the construction problem in algebraic geometry
An informal discussion of how the construction problem in algebraic geometry
motivates the search for formal proof methods. Also includes a brief discussion
of my own progress up to now, which concerns the formalization of category
theory within a ZFC-like environment
Persistent topology for natural data analysis - A survey
Natural data offer a hard challenge to data analysis. One set of tools is
being developed by several teams to face this difficult task: Persistent
topology. After a brief introduction to this theory, some applications to the
analysis and classification of cells, lesions, music pieces, gait, oil and gas
reservoirs, cyclones, galaxies, bones, brain connections, languages,
handwritten and gestured letters are shown
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