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Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...
In this thesis we are interested in the following problem : given two differential k–forms g and f, most of the time they will be assumed closed, on what conditions can we pullback g to f by a map φ ? In other words we ask when it is possible to solve the ...
Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...
Phase and intensity of light are detected simultaneously using a fully digital imaging technique: single-photon synchronous detection. This approach has been theoretically and experimentally investigated in this paper. We designed a fully integrated camera ...
We present a novel, automated way to find differential paths for MD5. As an application we have shown how, at an approximate expected cost of 2 50 calls to the MD5 compression function, for any two chosen message prefixes P and P′, suffixe ...
The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect produ ...
In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...
Reliable quantification of the macromolecule signals in short echo-time H-1 MRS spectra is particularly important at high magnetic fields for an accurate quantification of metabolite concentrations (the neurochemical profile) due to effectively increased s ...
In this work we do a theoretical analysis of the local sampling conditions for points lying on a quadratic embedding of a Riemannian manifold in a Euclidean space. The embedding is assumed to be quadratic at a reference point P. Our analysis is based on ...
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold’s structure. For this purp ...