Journal of applied and computational topology最新文献

英文中文

Decorated merge trees for persistent topology 持久拓扑的装饰合并树

Journal of applied and computational topology

Pub Date : 2021-03-30 DOI: 10.1007/s41468-022-00089-3

J. Curry, Haibin Hang, W. Mio, Tom Needham, Osman Berat Okutan

引用次数: 22

On Vietoris–Rips complexes of hypercube graphs 关于超立方图的Vietoris-Rips复形

Journal of applied and computational topology

Pub Date : 2021-03-01 DOI: 10.1007/s41468-021-00083-1

Michal Adamaszek, Henry Adams

引用次数: 12

Geodesic complexity of motion planning 运动规划的测地线复杂性

Journal of applied and computational topology

Pub Date : 2021-01-12 DOI: 10.1007/s41468-020-00064-w

David Recio-Mitter

引用次数: 9

Improved approximate rips filtrations with shifted integer lattices and cubical complexes. 具有移位整数格和立方络合物的改进近似撕裂过滤。

Journal of applied and computational topology

Pub Date : 2021-01-01 Epub Date: 2021-05-15 DOI: 10.1007/s41468-021-00072-4

Aruni Choudhary, Michael Kerber, Sharath Raghvendra

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For n points in $R^{d}$ , we present a scheme to construct a 2-approximation of the filtration of the Rips complex in the $L_{\infty}$ -norm, which extends to a $2 d^{0.25}$ -approximation in the Euclidean case. The k-skeleton of the resulting approximation has a total size of $n 2^{O (d log k + d)}$ . The scheme is based on the integer lattice and simplicial complexes based on the barycentric subdivision of the d-cube. We extend our result to use cubical complexes in place of simplicial complexes by introducing cubical maps between complexes. We get the same approximation guarantee as the simplicial case, while reducing the total size of the approximation to only $n 2^{O (d)}$ (cubical) cells. There are two novel techniques that we use in this paper. The first is the use of acyclic carriers for proving our approximation result. In our application, these are maps which relate the Rips complex and the approximation in a relatively simple manner and greatly reduce the complexity of showing the approximation guarantee. The second technique is what we refer to as scale balancing, which is a simple trick to improve the approximation ratio under certain conditions.

撕裂复形是分析度量空间拓扑特征的重要结构。不幸的是，由于复合尺寸的组合爆炸，生成这些复合物是昂贵的。对于R d中的n个点，我们给出了在L∞范数下构造Rips复滤的2-近似的方案，该方案扩展到欧几里得情况下的2- d 0.25 -近似。所得到的近似的k骨架的总大小为n2o (d log k + d)。该方案基于整数点阵和基于d-立方体质心细分的简单复形。通过引入复形之间的三次映射，我们扩展了用三次复形代替简单复形的结果。我们得到了与简单情况相同的近似保证，同时将近似的总大小减小到只有n 2o (d)(立方)单元。我们在本文中使用了两种新颖的技术。第一个是使用无环载流子来证明我们的近似结果。在我们的应用中，这些映射以一种相对简单的方式将Rips复合体和近似值联系起来，并大大降低了显示近似值保证的复杂性。第二种技术是我们所说的尺度平衡，这是一种在特定条件下提高近似比的简单技巧。

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引用次数: 7

Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces 虚拟持久性图、有符号测度、Wasserstein距离和Banach空间

Journal of applied and computational topology

Pub Date : 2020-12-18 DOI: 10.1007/s41468-022-00091-9

Peter Bubenik, Alex Elchesen

引用次数: 9

Constructible sheaves and functions up to infinity 可构造的轴和函数，直到无穷大

Journal of applied and computational topology

Pub Date : 2020-12-17 DOI: 10.1007/s41468-023-00121-0

P. Schapira

引用次数: 8

On the persistent homology of almost surely C0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^0$$end{document} stoc On the persistent homology of almost surely C0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^0$$end{document} stoc

Journal of applied and computational topology

Pub Date : 2020-12-17 DOI: 10.1007/s41468-023-00132-x

Daniel Pérez

引用次数: 3

Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis. 耦合动力系统的进化同源性及其在蛋白质柔韧性分析中的应用。

Journal of applied and computational topology

Pub Date : 2020-12-01 Epub Date: 2020-07-29 DOI: 10.1007/s41468-020-00057-9

Zixuan Cang, Elizabeth Munch, Guo-Wei Wei

While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.

虽然空间拓扑持久性是由基于半径的过滤自然构建的，但它几乎没有从时间过滤中得到。大多数拓扑模型是为给定对象的整体拓扑而设计的。据我们所知，文献中没有关于对象中单个组件拓扑的方法报告。对于科学和工程中的许多问题，单个组件的拓扑结构对于描述其性质非常重要。我们提出了一种基于时间进化的过滤和拓扑持久性的进化同源性(EH)。我们的方法通过物理系统(如大分子)的相互作用耦合一组动态系统或混沌振荡器。相互作用用加权图拉普拉斯算子逼近。在混沌振子的耦合轨迹上定义了简单、简单复形、代数群和拓扑持久性。由此产生的EH产生了物理系统单个组件的随时间变化的拓扑不变量或进化条形码，揭示了其拓扑-功能关系。与Wasserstein度量相结合，提出的EH应用于蛋白质柔韧性分析，这是计算生物物理学中的一个重要问题。对364个蛋白质的基准集进行b因子预测的数值结果表明，所提出的EH优于该领域所有其他最先进的方法。

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引用次数: 11

Steady and ranging sets in graph persistence 图持久性中的稳定集和测距集

Journal of applied and computational topology

Pub Date : 2020-09-15 DOI: 10.1007/s41468-022-00099-1

Mattia G. Bergomi, M. Ferri, Antonella Tavaglione

引用次数: 5

Dominance complexes and vertex cover numbers of graphs 图的优势复合体与顶点覆盖数

Journal of applied and computational topology

Pub Date : 2020-09-09 DOI: 10.1007/s41468-022-00109-2

Takahiro Matsushita

引用次数: 1

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