Related papers: Uncertain Mode Surfaces in 3D Symmetric Second-Ord…

It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…

In recent years, substantial progress has been achieved in learning-based reconstruction of 3D objects. At the same time, generative models were proposed that can generate highly realistic images. However, despite this success in these…

The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features.…

Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…

Motivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of complex dimension $n$ in general position.…

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization…

Accurate surface estimation is critical for downstream tasks in scientific simulation, and quantifying uncertainty in implicit neural 3D representations still remains a substantial challenge due to computational inefficiencies, scalability…

Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…

We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…

We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…

Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a…

We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…

How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…

Segmentation of curvilinear structures such as vasculature and road networks is challenging due to relatively weak signals and complex geometry/topology. To facilitate and accelerate large scale annotation, one has to adopt semi-automatic…