Search results for "Affine"

showing 3 items of 183 documents

Robustifying principal component analysis with spatial sign vectors

2012

In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods. peerReviewed

robustisuusvaikutusfunktiospatiaalinen merkkivektoriefficiencyinfluence functionAffiinisti ekvivarianttisuustehokkuusAffine equivariancerobustnessspatial sign vector
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Stress sensitivity of stylolite morphology

2009

International audience; Stylolites are rough surfaces that form by localized stress-induced dissolution. Using a set of limestone rock samples collected at different depths from a vertical section in Cirque de Navacelles (France), we study the influence of the lithostatic stress on the stylolites morphology on the basis of a recent morphogenesis model. We measured the roughness of a series of bedding-parallel stylolites and show that their morphology exhibits a scaling invariance with two self-affine scaling regimes separated by a crossover-length (L) at the millimeter scale consistent with previous studies. The importance of the present contribution is to estimate the stylolite formation s…

self-affine scalingMorphology (linguistics)010504 meteorology & atmospheric sciences[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph]MineralogyMagnitude (mathematics)morphogenesisSurface finish010502 geochemistry & geophysics01 natural sciencesStress (mechanics)Geochemistry and Petrology[SDU.STU.GC]Sciences of the Universe [physics]/Earth Sciences/GeochemistryEarth and Planetary Sciences (miscellaneous)Geotechnical engineeringpaleo-stressScaling0105 earth and related environmental sciencesroughness[SDU.STU.TE]Sciences of the Universe [physics]/Earth Sciences/TectonicsDeformation (mechanics)stylolitesStress fieldGeophysicsSpace and Planetary ScienceStyloliteGeology[SDU.STU.MI]Sciences of the Universe [physics]/Earth Sciences/Mineralogy
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A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

torsorsaffine modificationsdifferential Galois groupsformal blowupsNéron blowups[MATH] Mathematics [math]Commutative Algebra (math.AC)shtukasMathematics - Algebraic Geometryaffine blowupsFOS: Mathematicsalgebraic dilatations[MATH]Mathematics [math]Algebraic Geometry (math.AG)multi-centered dilatationsdilatations of schemesA 1 -homotopy theoryKaliman-Zaidenberg modificationslevel structuresMoy-Prasad isomorphismrepresentations of p-adic groupsMathematics - Commutative Algebramono-centered dilatationslocalizations of ringscongruent isomorphismsTannakian groupsaffine geometry
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