Journal of applied and computational topology最新文献_第7页

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

{"title":"Improved approximate rips filtrations with shifted integer lattices and cubical complexes.","authors":"Aruni Choudhary, Michael Kerber, Sharath Raghvendra","doi":"10.1007/s41468-021-00072-4","DOIUrl":"https://doi.org/10.1007/s41468-021-00072-4","url":null,"abstract":"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 <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> , we present a scheme to construct a 2-approximation of the filtration of the Rips complex in the <math><msub><mi>L</mi> <mi>∞</mi></msub> </math> -norm, which extends to a <math><mrow><mn>2</mn> <msup><mi>d</mi> <mrow><mn>0.25</mn></mrow> </msup> </mrow> </math> -approximation in the Euclidean case. The k-skeleton of the resulting approximation has a total size of <math><mrow><mi>n</mi> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <mi>d</mi> <mo>log</mo> <mi>k</mi> <mo>+</mo> <mi>d</mi> <mo>)</mo></mrow> </msup> </mrow> </math> . 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 <math><mrow><mi>n</mi> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <mi>d</mi> <mo>)</mo></mrow> </msup> </mrow> </math> (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.","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-021-00072-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39580559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

{"title":"Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.","authors":"Zixuan Cang, Elizabeth Munch, Guo-Wei Wei","doi":"10.1007/s41468-020-00057-9","DOIUrl":"https://doi.org/10.1007/s41468-020-00057-9","url":null,"abstract":"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.","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41468-020-00057-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39033436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

A directed persistent homology theory for dissimilarity functions 非相似函数的有向持久同调理论

Journal of applied and computational topology Pub Date : 2020-08-03 DOI: 10.1007/s41468-023-00124-x

D. M'endez, Rub'en J. S'anchez-Garc'ia

引用次数: 3

Stratifications of real vector spaces from constructible sheaves with conical microsupport 具有锥形微支撑的可构造轴的实向量空间分层

Journal of applied and computational topology Pub Date : 2020-07-31 DOI: 10.1007/s41468-023-00112-1

Ezra Miller

引用次数: 6