The geometrical diffraction theory, in the sense of Keller, is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main pr
Differential Geometrical Foundations of Information Geometry Applications of Reidemeister Torsions to 3-Dimensional Topology Mathematical Analysis for Engineers Kähler Geometry of Loop Spaces The Hyperboloidal Foliation Method Probabilistic Approach to Geometry Wolf Prize in Mathematics Inspired by S S Chern ...
However in the cross-domain scenarios, the meta-train set is from one dataset while the meta-validation and the meta-test sets are from a different dataset. Thereby the effect of domain shift in our Conclusion In this paper, we have employed Riemannian (constrained) geometry and its related ...
4, 5, 9 and 8 show a connection between the PDE-G-CNN framework with the theory of association fields from neurogeometry [37, 39]. Thereby, PDE-G-CNNs reveal improved geometrical interpretability, in comparison with existing convolution neural networks. In Appendix 1, we further clarify the...
Due to its unique geometric properties, the whole analysis of FCBN can be performed on the Riemannian geometry of the SPD space. The advantage of the analysis of FCBN on the SPD space is that it takes into account all the pairwise interdependencies as a whole. However, only a few ...
(generalized coherent states manifold hereafter noted G.C.S.M.) is studied in details; the geometrical properties of some wellknown G.C.S.M. are reviewed and an explicit expression for the scalar Riemannian curvature is given in the general case. The physical meaning of such Riemannian ...
2.In this article,taking smooth vector field on manilotd as state usctor field of dynamic system,we establishes differential dynamic systcm on theRiemann manifoldand discuss the existenceand uuiqueness of solution of ynamic system,an effect of geometrical structure on structure stability and sinpl...
We use symmetric positive definite matrices (SPD) as statistical features for describing the EEG signals, so the geometrical operations on the data points respect the intrinsic geometry of the SPD manifold.We have included two notebooks with examples of application of the RPA on data from two BCI...
(reduced)orbifoldswithfinitelymanysingularities.Mostofourresultsgothroughforcer-tainotherclassesofcriticalRiemannianmetrics.Contents1Introduction22AquickintroductiontoK¨ahlergeometry72.1Setupofnotations...72.2Historicbackgroundandmotivation...82.3Derivationofsomeusefulformulas...92.4Aprioriboundsontheextremalvectorfield...
3. Finite dimensional geometry 3.1. The finite dimensional geometrical objects Let P ¼ f0 ¼ s0os1o?osn ¼ 1g be a partition of I ¼ ½0; 1: We denote sÀ ¼ maxfsipsg and sþ ¼ minfsi > sg and if f is a function, Dif ¼ f ðsiþ1Þ À f ð...