Related papers: Uncertain Mode Surfaces in 3D Symmetric Second-Ord…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
We construct the tensor hierarchies of generic, bosonic, 5- and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor which tells us which vector is used for…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
Given a computer model of a physical object, it is often quite difficult to visualize and quantify any global effects on the shape representation caused by local uncertainty and local errors in the data. This problem is further amplified…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
Reconstructing 3D human heads in low-view settings presents technical challenges, mainly due to the pronounced risk of overfitting with limited views and high-frequency signals. To address this, we propose geometry decomposition and adopt a…
We explore the structure of entanglement edge modes on noncommutative backgrounds that arise from matrix quantum mechanics. For the fuzzy sphere, despite nonlocality and UV/IR mixing, we find area law behavior in the dominant $U(N)$…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
In the realm of diverse high-dimensional data, images play a significant role across various processes of manufacturing systems where efficient image anomaly detection has emerged as a core technology of utmost importance. However, when…
Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
Textured 3D meshes jointly represent geometry, topology, and appearance, yet their irregular structure poses significant challenges for deep-learning-based semantic segmentation. While a few recent methods operate directly on meshes without…
The introduction of synthetic dimensions in topological photonic systems enriches the exploration of topological phase of light in higher-dimensional space beyond three-dimensional real-space. Recently, the gapless corner modes of…
Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…
Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…
Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the…
This paper explores the problem of reconstructing temporally consistent surfaces from a 3D point cloud sequence without correspondence. To address this challenging task, we propose DynoSurf, an unsupervised learning framework integrating a…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
A hallmark feature of topologically ordered states of matter is the dependence of ground state degeneracy (GSD) on the topology of the manifold determined by the global shape of the system. Although the topology of a physical system is…
Reliable quantification of uncertainty in Mobile Laser Scanning (MLS) point clouds is essential for ensuring the accuracy and credibility of downstream applications such as 3D mapping, modeling, and change analysis. Traditional backward…