Search results for "Euclidean spaces"

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Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below

2013

We show that in any infinitesimally Hilbertian CD* (K,N)-space at almost every point there exists a Euclidean weak tangent, i.e., there exists a sequence of dilations of the space that converges to Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian CD* (0,N)-spaces.

Mathematics - Differential GeometryPure mathematicsGeneral MathematicsSpace (mathematics)01 natural sciencesMeasure (mathematics)Mathematics - Metric Geometry0103 physical sciencesFOS: MathematicsMathematics::Metric Geometry0101 mathematics[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]tangent spaces; non-smooth geometryRicci curvatureMathematics51F99-53B99non-smooth geometrySequenceEuclidean spaceApplied MathematicsHilbertian spaces010102 general mathematicstangent spacesTangentMetric Geometry (math.MG)Euclidean spacesDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]weak tangentsBounded functionSplitting theorem010307 mathematical physics
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Projector operators in clustering

2016

In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which generates different clusters from a set of input data. Also, we consider what happens when the orthonormal bases first used in the definition of the projectors are replaced by frames, and how these can be useful when trying to connect some noised signal to a given cluster.

Mathematics - Functional AnalysisEngineering (all)FOS: MathematicsCluster analysis harmonic analysis on Euclidean spaces pattern recognitionMathematics (all)Settore MAT/07 - Fisica MatematicaFunctional Analysis (math.FA)
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