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The synthesis of topologically complex structures, such as links and knots, is one of the current challenges in supramolecular chemistry. The so-called Solomon link consists of two doubly interlocked rings. Despite being a rather simple link from a topolog ...
We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator when the Ricci curvature is bounded from below by a negative constant. We ...
The Deep City project at the École polytechnique fédérale de Lausanne has, for the past several years, been developing a method to identify and qualify the urban areas where underground development is high, particularly for human activities. The fourth dis ...
We consider the problem of trajectory generation for constrained differentially flat systems. Based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of ...
Understanding brain diseases can benefit from studying network organization of functional connectivity (FC) during resting state. Here we study the local topological properties of FC in minimally-disabled multiple sclerosis (MS) patients by comparison of t ...
The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2
Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H-T*(B) as a subring of H-T*(B-T). I ...
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 represent manifold data accurately while preserving the manifold's structure. For this purpo ...
When dealing with multi-angular image sequences, problems of reflectance changes due either to illumination and acquisition geometry, or to interactions with the atmosphere, naturally arise. These phenomena interplay with the scene and lead to a modificati ...
We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...