Search results for "Manifold"
showing 10 items of 415 documents
The manifold communities of the We-ness
2013
International audience
Nonlinear data description with Principal Polynomial Analysis
2012
Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold learning based on the use of a sequence of Principal Polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA. Unlike recently proposed nonlinear methods (e.g. spectral/kernel methods and projection pursuit techniques, neural networks), PPA features are easily interpretable and the method leads to a fully invertible transform, which is a desirable property…
Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces
2020
This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a -hypersurface without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorff dimension 12, with…
The historical role played by the work of Ulisse Dini on implicit function theory in the modern differential geometry foundations: the case of the st…
2012
Nonlinear Time-Series Adaptation for Land Cover Classification
2017
Automatic land cover classification from satellite image time series is of paramount relevance to assess vegetation and crop status, with important implications in agriculture, biofuels, and food. However, due to the high cost and human resources needed to characterize and classify land cover through field campaigns, a recurrent limiting factor is the lack of available labeled data. On top of this, the biophysical–geophysical variables exhibit particular temporal structures that need to be exploited. Land cover classification based on image time series is very complex because of the data manifold distortions through time. We propose the use of the kernel manifold alignment (KEMA) method for…
An unbounded family of log Calabi–Yau pairs
2016
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective bundles over the Segre-Hirzebruch surfaces ${\mathbb F}_n$ for every positive integer $n$ big enough.
Reasons of irregularity of seed's distribution in the divider heads of air-seeders
2017
ISBN : 978-3-18-092300-0; International audience; Modern seeding equipment must allow to cultivate sizeable areas efficiently and finalize the seeding in a short amount of time. Air-seeder is a solution for a fast seeding: seeds are conveyed from the high-capacity seed hopper to the coulter-bar by an air-stream. Taking into account the complexity of this type of seed drills, they stay little-studied. Few developments have been done on divider headers responsible of distribution accuracy. This paper deals with a study on the influence of divider head geometry and functioning conditions on the seed's distribution accuracy. Moreover, observation of the seed's behaviour is done using a high-spe…
On the History of Differentiable Manifolds
2012
International audience; We discuss central aspects of history of the concept of an affine dif-ferentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.