相关论文: Virtual Manifolds and Localization

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Numerical Relativity has been using orbifolds for a long time, although they appear under different names in the literature. We review orbifolds previously used in simulations also discuss some that have not been used yet but are likely to…

A basic task in the design of a robotic production cell is the relative placement of robot and workpiece. The fundamental requirement is that the robot can reach all process positions; only then one can think of further optimization.…

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…

In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…

We develop a theory for stable maps to curves with divisible ramification. For a fixed integer $r>0$, we show that the condition of every ramification locus being divisible by $r$ is equivalent to the existence of an $r$th root of a…

We construct virtual fundamental classes for dg-manifolds whose tangent sheaves have cohomology only in degrees 0 and 1. This condition is analogous to the existence of a perfect obstruction theory in the approach of Behrend-Fantechi [BF]…

We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [59] the problem is supposed to have a unique solution, but…

In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…

Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…

We address the problem of localisation of objects as bounding boxes in images with weak labels. This weakly supervised object localisation problem has been tackled in the past using discriminative models where each object class is localised…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

This paper introduces an efficient procedure to localize user-defined points on the surface of deformable objects and track their positions in 3D space over time. To cope with a deformable object's infinite number of DOF, we propose a…

Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…

In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.

These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…

Modular object-centric representations are essential for *human-like reasoning* but are challenging to obtain under spatial ambiguities, *e.g. due to occlusions and view ambiguities*. However, addressing challenges presents both theoretical…

Deep Learning based techniques have been adopted with precision to solve a lot of standard computer vision problems, some of which are image classification, object detection and segmentation. Despite the widespread success of these…