Related papers: Moving frames and compatibility conditions for thr…

For a conformal theory it is natural to seek the conformal moduli space, M_c to which it belongs, generated by the exactly marginal deformations. By now we should have the tools to determine M_c in the presence of enough supersymmetry. Here…

We propose a geometric perspective to describe the motion of self-propelled particles moving at constant speed in d dimensions. We exploit the fact that the vector that conveys the direction of motion of the particle performs a random walk…

We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…

Navigating cluttered environments is a challenging task for any mobile system. Existing approaches for ground-based mobile systems primarily focus on small wheeled robots, which face minimal constraints with overhanging obstacles and cannot…

The aim of this paper is to provide a discussion on current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is presented. The main purpose of this work is to describe the…

Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This…

LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent…

Reducing domain divergence is a key step in transfer learning problems. Existing works focus on the minimization of global domain divergence. However, two domains may consist of several shared subdomains, and differ from each other in each…

In this paper, we propose a novel method for monocular depth estimation in dynamic scenes. We first explore the arbitrariness of object's movement trajectory in dynamic scenes theoretically. To overcome the arbitrariness, we use assume that…

Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering…

We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modelling, that they are governed by the local profile of the orientational…

The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…

We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We…

Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…

Accurate 3D scene description is fundamental to robotic navigation and augmented reality, yet current dense captioning methods face significant limitations in processing sparse point cloud data. % Existing approaches that apply Euclidean…

Structured meshes, composed of quadrilateral elements in 2D and hexahedral elements in 3D, are widely used in industrial applications and engineering simulations due to their regularity and superior accuracy in finite element analysis.…

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an…

The underlying structural disorder renders the concept of topological defects in amorphous solids difficult to apply and hinders a first-principle identification of the microscopic carriers of plasticity and of the regions more prone to…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in terms of evaluation metrics such as the pixel-wise relative error, most methods neglect the…