相关论文: A Higher-Order Poincar\'e Ellipsoid representation…

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional…

We develop a geometric description of structured Gaussian beams, a form a structured light, by applying geometric quantisation and symplectic reduction to the 2D harmonic oscillator. Our results show that the geometric quantisation of the…

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk.…

We study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. We solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to…

We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing…

Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken,…

We develop a new method to estimate gravitational shear by adopting an elliptical weight function to measure background galaxy images. In doing so, we introduce a new concept of "zero plane" which is an imaginal source plane where shapes of…

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous…

In pose estimation for seen objects, a prevalent pipeline involves using neural networks to predict dense 3D coordinates of the object surface on 2D images, which are then used to establish dense 2D-3D correspondences. However, current…

Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce…

We geometrically derive the explicit form of the Unitary representation of the Poincare group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting…

Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…

Ever since the first observation of Bose-Einstein condensation in the nineties, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum…

In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of unit $2$-sphere is lower and upper bounded…

Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis…

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…

Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and…

Vector modes are well-defined field distributions with spatially varying polarisation states, rendering them irreducible to the product of a single spatial mode and a single polarisation state. Traditionally, the spatial degree of freedom…

A numerical method for variable coefficient elliptic problems on two dimensional domains is described. The method is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system of…