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Geometrical correlation indices using homological constructions on manifolds
Abstract The course of dimensionality is a common problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of problems. ...
Geometric goodness of fit measure to detect patterns in data point clouds
The curse of dimensionality is a commonly encountered problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of ...
Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples
There is an isomorphism between the moduli spaces of σ-stable holomorphic triples and some of the critical submanifolds of the moduli space of k-Higgs bundles of rank three, whose elements (E, ϕk ) correspond to variations ...
Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs
We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural C ∗ -action on the moduli space. For general rank we provide ...