Related papers: Introducing the Classical Method of Moving Frames
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…
Extracting discriminative local features that are invariant to imaging variations is an integral part of establishing correspondences between images. In this work, we introduce a self-supervised learning framework to extract discriminative…
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…
The technique requires the epipolar geometry to be pre-estimated between each image pair. It exploits the constraints which the camera movement implies, in order to apply a closed-form correction to the parameters of the input affinities.…
Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the…
Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…
We obtain some new results on classical solutions of two dimensional Euclidean sigma models. From earlier work of Din-Zakrzewski, Glaser-Stora, and numerous differential geometers, one knows explicit solutions in the case of the…
Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…
Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an…
For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix…
The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
Ubiquitous mobile devices are generating vast amounts of location-based service data that reveal how individuals navigate and utilize urban spaces in detail. In this study, we utilize these extensive, unlabeled sequences of user…
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…
For an accurate description of electromagneto-thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame…
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…