Related papers: A Higher-Order Poincar\'e Ellipsoid representation…
We propose and experimentally demonstrate a novel interferometric approach to generate arbitrary cylindrical vector beams on the higher order Poincare sphere. Our scheme is implemented by collinear superposition of two orthogonal circular…
Recently, 3D Gaussian Splatting (3D-GS) has achieved significant success in real-time, high-quality 3D scene rendering. However, it faces several challenges, including Gaussian redundancy, limited ability to capture view-dependent effects,…
This note presents a procedure of constructing a higher dimensional sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given degree. As an application a new proof of a generalized…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
The Ince-Gaussian modes form a complete set of solutions to the paraxial wave equation parametrized by an ellipticity parameter {\epsilon}, enabling a continuous transition between Laguerre-Gaussian and Hermite-Gaussian modes While each…
Human pose estimation in complicated situations has always been a challenging task. Many Transformer-based pose networks have been proposed recently, achieving encouraging progress in improving performance. However, the remarkable…
An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit strength vortices is described. This…
The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the…
This manuscript presents an adaptive high order discretization technique for elliptic boundary value problems. The technique is applied to an updated version of the Hierarchical Poincar\'e-Steklov (HPS) method. Roughly speaking, the HPS…
Autonomous driving scenes range from empty highways to dense intersections with dozens of interacting road users, yet current 3D detection models apply a fixed computation budget to every frame, wasting resources on simple scenes while…
We address the problem of generating a high-resolution surface reconstruction from a single image. Our approach is to learn a Higher Order Function (HOF) which takes an image of an object as input and generates a mapping function. The…
3D Large Vision-Language Models (3D LVLMs) built upon Large Language Models (LLMs) have achieved remarkable progress across various multimodal tasks. However, their inherited position-dependent modeling mechanism, Rotary Position Embedding…
The ability to decompose complex multi-object scenes into meaningful abstractions like objects is fundamental to achieve higher-level cognition. Previous approaches for unsupervised object-oriented scene representation learning are either…
Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological…
Visual Place Recognition (VPR) enables coarse localization by comparing query images to a reference database of geo-tagged images. Recent breakthroughs in deep learning architectures and training regimes have led to methods with improved…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
High-dimensional photonic states have significantly advanced the fundamentals and applications of light. However, it remains huge challenges to quantify arbitrary states in high-dimensional Hilbert spaces with spin and orbital angular…
The propagation and Poincar\'e mapping of perturbed Keplerian motion is a key topic in celestial mechanics and astrodynamics, e.g. to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM)…
Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of…