相关论文: Homology Computation of Large Point Clouds using Q…

Point clouds acquired in constrained, challenging, uncontrolled, and multi-sensor real-world settings are noisy, incomplete, and non-uniformly sparse. This presents acute challenges for the vital task of point cloud completion. Using tools…

We study the complexity of a classic problem in computational topology, the homology problem: given a description of some space $X$ and an integer $k$, decide if $X$ contains a $k$-dimensional hole. The setting and statement of the homology…

We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed…

We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…

We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…

Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying…

Given a loop or more generally 1-cycle $r$ of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave…

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…

In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…

We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…

High-throughput computational screening of polymers offers a powerful way to address the imbalance between the vast number of polymers synthesised for diverse applications and the relatively small subset that can be studied using atomistic…

We give an $O(n^2(k+\log n))$ algorithm for computing the $k$-dimensional persistent homology of a filtration of clique complexes of cyclic graphs on $n$ vertices. This is nearly quadratic in the number of vertices $n$, and therefore a…

We present a topology-informed approach for classifying particle jets using persistent homology, a framework that captures the structural properties of point clouds. Particle jets produced in proton-proton collisions consist of cascades of…