Related papers: From Dimension-Free Manifolds to Dimension-varying…
We introduce a class of diffeological spaces, called elastic, on which the left Kan extension of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of Rosicky. On elastic spaces there is a natural…
Volumetric visualization has long been dominated by Direct Volume Rendering (DVR), which operates on dense voxel grids and suffers from limited scalability as resolution and interactivity demands increase. Recent advances in 3D Gaussian…
Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive,…
Camera and LiDAR sensor modalities provide complementary appearance and geometric information useful for detecting 3D objects for autonomous vehicle applications. However, current end-to-end fusion methods are challenging to train and…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Topology change is a challenging problem for 4D reconstruction of dynamic scenes. In the classic volumetric fusion-based framework, a mesh is usually extracted from the TSDF volume as the canonical surface representation to help estimating…
Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection…
The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These are the natural extension of the two-dimensional divergence…
This work develops a unified, dimensionless framework for comparing geometrically similar reacting porous-flow systems across scale, with emphasis on hydrometallurgical heap leaching, when particle size distribution (PSD) and intraparticle…
We show that long-distance quantum correlations probe short-distance physics. Two disjoint regions of the latticized, massless scalar field vacuum are numerically demonstrated to become separable at distances beyond the negativity sphere,…
Sequential dynamical systems (SDS) are used to model a wide range of processes occurring on graphs or networks. The dynamics of such discrete dynamical systems is completely encoded by their phase space, a directed graph whose vertices and…
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…
Unsigned distance functions (UDFs) have been a vital representation for open surfaces. With different differentiable renderers, current methods are able to train neural networks to infer a UDF by minimizing the rendering errors with the UDF…
A new mathematical structure, called the cross-dimensional mathematics (CDM), is proposed. The CDM considered in this paper consists of three parts: hyper algebra, hyper geometry, and hyper Lie group/Lie algebra. Hyper algebra proposes some…
Massless localized vector field is obtained in five-dimensional supersymmetric (SUSY) QED coupled to tensor multiplets as a half BPS solution. The four-dimensional gauge coupling is obtained as a topological charge. We also find all the…
Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is…
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
Given the high complexity of directly generating high-dimensional data such as 4D, we present 4DVD, a cascaded video diffusion model that generates 4D content in a decoupled manner. Unlike previous multi-view video methods that directly…