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We compare and contrast from a geometric perspective a number of low-dimensional signal models that support stable information-preserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, stru ...
The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...
The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
Two global gyrokinetic codes are benchmarked against each other by comparing simulation results in the case of ion temperature gradient driven turbulence, in the adiabatic electron response limit The two codes are the Eulerian code GENE and the Lagrangian ...
In general, most porous materials are so complex that structural information cannot be easily observed with 3D visualization tools. To address this problem, we have developed a special abstract 2D representation to depict all important topological features ...
Over the past few decades we have been experiencing a data explosion; massive amounts of data are increasingly collected and multimedia databases, such as YouTube and Flickr, are rapidly expanding. At the same time rapid technological advancements in mobil ...
We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric. ...
The economic growth inherent to our nowadays society pushes the industries toward better performances. In the mechatronic context, the increasing competition results in more and more stringent specifications. Thus, the multiple objectives to track become h ...
In this chapter we describe the basic ideas of reduced basis (RB) approximation methods for rapid and reliable evaluation of input-output relationships in which the output is expressed as a functional of a field variable that is the solution of an input-pa ...
We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distance ...
