{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T20:59:46Z","timestamp":1778533186408,"version":"3.51.4"},"reference-count":312,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["702410"],"award-info":[{"award-number":["702410"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005713","name":"Technische Universitat Munchen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005713","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009591","name":"Ministerium f\u00fcr Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009591","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1945584"],"award-info":[{"award-number":["DMS-1945584"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["RGFnEAn201074"],"award-info":[{"award-number":["RGFnEAn201074"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["UF150238"],"award-info":[{"award-number":["UF150238"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T013613\/1"],"award-info":[{"award-number":["EP\/T013613\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R018472\/1"],"award-info":[{"award-number":["EP\/R018472\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R005125\/1"],"award-info":[{"award-number":["EP\/R005125\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T001968\/1"],"award-info":[{"award-number":["EP\/T001968\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1137\/21m1414024","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T08:42:43Z","timestamp":1691484163000},"page":"686-731","source":"Crossref","is-referenced-by-count":293,"title":["What Are Higher-Order Networks?"],"prefix":"10.1137","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5238-1146","authenticated-orcid":true,"given":"Christian","family":"Bick","sequence":"first","affiliation":[]},{"given":"Elizabeth","family":"Gross","sequence":"additional","affiliation":[]},{"given":"Heather A.","family":"Harrington","sequence":"additional","affiliation":[]},{"given":"Michael T.","family":"Schaub","sequence":"additional","affiliation":[]}],"member":"351","published-online":{"date-parts":[[2023,8,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1086\/284111"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.77.137"},{"key":"atypb3","first-page":"8","volume":"18","author":"Adams H.","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/ace39f"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1063\/1.4997385"},{"key":"atypb6","volume-title":"Elementary Concepts of Topology","author":"Alexandroff P.","year":"2012"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1014428108"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-020-01024-1"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/dvdy.175"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2015.7446987"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-21-07750.2003"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1186\/s13408-015-0033-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2016.02.009"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02429852"},{"key":"atypb15","volume-title":"36th International Symposium on Computational Geometry (SoCG 2020","author":"Aukerman A.","year":"2020"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.03.016"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2010-00677-7"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005055"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000437"},{"key":"atypb20","volume-title":"Network Science","author":"Barab\u00e1si A.-L.","year":"2016"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2020.3014067"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2020.2981920"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1109\/DSW.2018.8439885"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2016.7472914"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1038\/nn.4502"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2020.05.004"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780317"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOAS886"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1800683115"},{"key":"atypb30","volume-title":"Fueled by Classical Ideas and New Data, preprint, https:\/\/arxiv.org\/abs\/2103.05031","author":"Benson A. R.","year":"2021"},{"key":"atypb31","first-page":"118","volume-title":"Proceedings of the 2015 SIAM International Conference on Data Mining, SIAM, 2015","author":"Benson A. R.","year":"1974"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.050201"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-019-09552-5"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1063\/1.4958928"},{"key":"atypb36","series-title":"SIAM J. Appl. Dynam. Syst., to appear.","volume-title":"Phase oscillator networks with nonlocal higher-order interactions: Twisted states, stability, and bifurcations","author":"Bick C."},{"key":"atypb37","volume-title":"Higher-Order Interactions in Phase Oscillator Networks through Phase Reductions of Oscillators with Phase Dependent Amplitude, preprint, https:\/\/doi.org\/10.48550\/arXiv.2305.04277","author":"Bick C.","year":"2023"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aa4f62"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1186\/s13408-020-00086-9"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-019-09562-3"},{"key":"atypb41","volume-title":"Simplex2Vec Embeddings for Community Detection in Simplicial Complexes, preprint, https:\/\/arxiv.org\/abs\/1906.09068","author":"Billings J. C. W.","year":"2019"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.052311"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-57072-3_87"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1007\/s41468-017-0010-0"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1232"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2005.10.009"},{"key":"atypb47","volume-title":"Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks, preprint, https:\/\/arxiv.org\/abs\/2103.03212","author":"Bodnar C.","year":"2021"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-016-0158-0"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1016\/j.socnet.2004.01.001"},{"key":"atypb50","volume-title":"The Embedded Homology of Hypergraphs and Applications, preprint, https:\/\/arxiv.org\/abs\/1610.00890","author":"Bressan S.","year":"2016"},{"key":"atypb51","volume-title":"Image Analysis for Alzheimer's Disease Prediction: Embracing Pathological Hallmarks for Model Architecture Design, preprint, https:\/\/arxiv.org\/abs\/2011.06531","author":"Br\u00fcningk S. C.","year":"2020"},{"key":"atypb52","first-page":"77","volume":"16","author":"Bubenik P.","year":"2015","journal-title":"J. Mach. Learn. Res."},{"key":"atypb53","volume-title":"Simplicial $2$-Complex Convolutional Neural Nets, preprint, https:\/\/arxiv.org\/abs\/2012.06010","author":"Bunch E.","year":"2020"},{"key":"atypb54","first-page":"206","volume-title":"Math. Today (Southend-on-Sea), 55","author":"Byrne H. M.","year":"2019"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abb2637"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1110.0500"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022308"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1088\/2632-072X\/aba8e1"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-09-01249-X"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-010-9066-0"},{"key":"atypb61","doi-asserted-by":"publisher","DOI":"10.1145\/1542362.1542408"},{"key":"atypb62","volume-title":"Persistent and Zigzag Homology: A Matrix Factorization Viewpoint, preprint, https:\/\/arxiv.org\/abs\/1911.10693","author":"Carlsson G.","year":"2019"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10631-6_74"},{"key":"atypb64","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-009-9176-0"},{"key":"atypb65","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1313480110"},{"key":"atypb66","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2019.07.024"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1145\/3178123"},{"key":"atypb68","volume-title":"First Betti Number of the Path Homology of Random Directed Graphs, preprint, https:\/\/arxiv.org\/abs\/2111.13493","author":"Chaplin T.","year":"2021"},{"key":"atypb69","first-page":"2143","volume-title":"International Conference on Machine Learning, PMLR","author":"Chazal F.","year":"2015"},{"key":"atypb70","first-page":"4","author":"Chazal F.","year":"2021","journal-title":"Frontiers Artificial Intell."},{"key":"atypb71","doi-asserted-by":"publisher","DOI":"10.1007\/b103930"},{"key":"atypb72","volume-title":"Helmholtzian Eigenmap: Topological Feature Discovery & Edge Flow Learning from Point Cloud Data, preprint, https:\/\/arxiv.org\/abs\/2103.07626","author":"Chen Y.-C.","year":"2021"},{"key":"atypb73","first-page":"871","volume-title":"International Conference on Artificial Intelligence and Statistics","author":"Chien I.","year":"2018"},{"key":"atypb74","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-020-0252-y"},{"key":"atypb75","volume-title":"Configuration Models of Random Hypergraphs, preprint, https:\/\/arxiv.org\/abs\/1902.09302","author":"Chodrow P. S.","year":"2019"},{"key":"atypb76","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abh1303"},{"key":"atypb77","first-page":"639","volume-title":"International Conference on Complex Networks and Their Applications","author":"Chowdhury S.","year":"2020"},{"key":"atypb78","first-page":"1152","volume-title":"Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2018","author":"Chowdhury S.","year":"1975"},{"key":"atypb79","volume-title":"CBMS Reg. Conf. Ser. Math. 92","author":"Chung F. R.","year":"1997"},{"key":"atypb80","doi-asserted-by":"publisher","DOI":"10.37236\/8611"},{"key":"atypb81","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-006-1276-5"},{"key":"atypb82","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.006"},{"key":"atypb83","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20857"},{"key":"atypb84","doi-asserted-by":"publisher","DOI":"10.1142\/S179352531650014X"},{"key":"atypb85","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-31580-5_6"},{"key":"atypb86","doi-asserted-by":"publisher","DOI":"10.1142\/S1793525317500170"},{"key":"atypb87","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216517400107"},{"key":"atypb88","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2012.05.005"},{"key":"atypb89","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.93.062311"},{"key":"atypb90","volume-title":"Topological Summaries of Tumor Images Improve Prediction of Disease Free Survival in Glioblastoma Multiforme, preprint, https:\/\/arxiv.org\/abs\/1611.06818","author":"Crawford L.","year":"2016"},{"key":"atypb91","doi-asserted-by":"publisher","DOI":"10.1090\/bull\/1554"},{"key":"atypb92","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.023032"},{"key":"atypb93","first-page":"10","volume":"54","author":"De Silva V.","year":"2007","journal-title":"Notices Amer. Math. Soc."},{"key":"atypb94","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/12\/124003"},{"key":"atypb95","volume-title":"Consensus on Simplicial Complexes, or: The Nonlinear Simplicial Laplacian, preprint, https:\/\/arxiv.org\/abs\/2010.07421","author":"DeVille L.","year":"2020"},{"key":"atypb96","volume-title":"An Efficient Algorithm for $1 $-Dimensional (Persistent) Path Homology, preprint, https:\/\/arxiv.org\/abs\/2001.09549","author":"Dey T. K.","year":"2020"},{"key":"atypb97","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20404"},{"key":"atypb98","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511761942"},{"key":"atypb99","volume-title":"Simplicial Neural Networks, preprint, https:\/\/arxiv.org\/abs\/2010.03633","author":"Ebli S.","year":"2020"},{"key":"atypb100","doi-asserted-by":"publisher","DOI":"10.1007\/BF02566245"},{"key":"atypb101","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/453\/08802"},{"key":"atypb102","volume-title":"Computational Topology: An Introduction","author":"Edelsbrunner H.","year":"2010"},{"key":"atypb103","doi-asserted-by":"publisher","DOI":"10.1145\/1940475.1940516"},{"key":"atypb104","doi-asserted-by":"publisher","DOI":"10.1007\/s12064-020-00328-0"},{"key":"atypb105","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.12.002"},{"key":"atypb106","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1109521108"},{"key":"atypb107","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15398-8"},{"key":"atypb108","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2020.107065"},{"key":"atypb109","volume-title":"Random Simplicial Complexes, Duality and the Critical Dimension, preprint, https:\/\/arxiv.org\/abs\/1901.09578","author":"Farber M.","year":"2019"},{"key":"atypb110","volume-title":"Introduction to the R package TDA, preprint, https:\/\/arxiv.org\/abs\/1411.1830","author":"Fasy B. T.","year":"2014"},{"key":"atypb111","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1252"},{"key":"atypb112","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1972.21.21017"},{"key":"atypb113","volume-title":"Statistics of Geometric Random Simplicial Complexes","author":"Ferraz E.","year":"2011"},{"key":"atypb114","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.09.002"},{"key":"atypb115","doi-asserted-by":"publisher","DOI":"10.1137\/16M1087175"},{"key":"atypb116","volume-title":"Generalized Random Simplicial Complexes, preprint, https:\/\/arxiv.org\/abs\/1503.01831","author":"Fowler C. F.","year":"2015"},{"key":"atypb117","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-018-00056-9"},{"key":"atypb118","doi-asserted-by":"publisher","DOI":"10.1086\/229694"},{"key":"atypb119","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0086028"},{"key":"atypb120","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8438-9_2"},{"key":"atypb121","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.79.066118"},{"key":"atypb122","first-page":"397","author":"Ghoshdastidar D.","year":"2014","journal-title":"Advances in Neural Information Processing Systems"},{"key":"atypb123","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1453"},{"key":"atypb124","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-07-01191-3"},{"key":"atypb125","volume-title":"Elementary Applied Topology","volume":"1","author":"Ghrist R. W.","year":"2014"},{"key":"atypb126","volume-title":"Surfaces and Homology: An Introduction to Algebraic Topology","author":"Giblin P.","year":"2013"},{"key":"atypb127","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1506407112"},{"key":"atypb128","volume-title":"Principled Simplicial Neural Networks for Trajectory Prediction, preprint, https:\/\/arxiv.org\/abs\/2102.10058","author":"Glaze N.","year":"2021"},{"key":"atypb129","doi-asserted-by":"publisher","DOI":"10.1137\/140976649"},{"key":"atypb130","doi-asserted-by":"publisher","DOI":"10.1137\/140985160"},{"key":"atypb131","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-43408-3_10"},{"key":"atypb132","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-290-2"},{"key":"atypb134","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-020-04897-9"},{"key":"atypb135","doi-asserted-by":"publisher","DOI":"10.1038\/nature23273"},{"key":"atypb136","volume-title":"Algebraic Statistics, Tables, and Networks: The Fienberg Advantage, preprint, https:\/\/arxiv.org\/abs\/1910.01692","author":"Gross E.","year":"2019"},{"key":"atypb137","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-016-0560-2"},{"key":"atypb138","volume-title":"Goodness-of-Fit Tests, and Applications to Biological Networks, preprint, https:\/\/arxiv.org\/abs\/2104.03167","author":"Gross E.","year":"2021"},{"key":"atypb139","volume-title":"k-simplex2vec: A Simplicial Extension of node2vec, preprint, https:\/\/arxiv.org\/abs\/2010.05636","author":"Hacker C.","year":"2020"},{"key":"atypb140","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.46.R7347"},{"key":"atypb141","volume-title":"Tech. report","author":"Harer J.","year":"2015"},{"key":"atypb142","doi-asserted-by":"publisher","DOI":"10.1137\/18M1224350"},{"key":"atypb143","volume-title":"Dynamic Biological Networks: The Stomatogastric Nervous System","author":"Harris-Warrick R.","year":"1992"},{"key":"atypb144","volume-title":"Cambridge University Press","author":"Hatcher A.","year":"2002"},{"key":"atypb145","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.94.022309"},{"key":"atypb146","first-page":"26","author":"Hein M.","year":"2013","journal-title":"Adv. Neural Inform. Process. Syst."},{"key":"atypb147","volume-title":"The Growing Topology of the C. Elegans Connectome, preprint, https:\/\/arxiv.org\/abs\/2101.00065","author":"Helm A.","year":"2020"},{"key":"atypb148","volume-title":"Matroid Filtrations and Computational Persistent Homology, preprint, https:\/\/arxiv.org\/abs\/1606.00199","author":"Henselman G.","year":"2016"},{"key":"atypb149","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-43408-3_11"},{"key":"atypb150","volume-title":"A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs, preprint, https:\/\/arxiv.org\/abs\/2102.06825","author":"Hickok A.","year":"2021"},{"key":"atypb151","doi-asserted-by":"publisher","DOI":"10.1137\/21M1440219"},{"key":"atypb152","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1520877113"},{"key":"atypb153","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnz077"},{"key":"atypb154","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.05.007"},{"key":"atypb155","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022305"},{"key":"atypb156","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v024.i03"},{"key":"atypb157","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-10431-6"},{"key":"atypb158","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.3977-14.2015"},{"key":"atypb159","doi-asserted-by":"publisher","DOI":"10.1145\/3292500.3330872"},{"key":"atypb160","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-010-0419-x"},{"key":"atypb161","volume-title":"Appl. Math. Sci. 157","author":"Kaczynski T.","year":"2006"},{"key":"atypb162","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.02.037"},{"key":"atypb163","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9319-3"},{"key":"atypb164","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2014.179.3.5"},{"key":"atypb165","first-page":"201","volume-title":"American Mathematical Society","author":"Kahle M.","year":"2014"},{"key":"atypb166","doi-asserted-by":"publisher","DOI":"10.4310\/HHA.2013.v15.n1.a17"},{"key":"atypb167","doi-asserted-by":"publisher","DOI":"10.1007\/s12021-017-9341-1"},{"key":"atypb168","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00464-2"},{"key":"atypb169","doi-asserted-by":"publisher","DOI":"10.1214\/17-EJS1235"},{"key":"atypb170","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOAS978"},{"key":"atypb171","volume-title":"Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration, preprint, https:\/\/arxiv.org\/abs\/1909.06503","author":"Ke Z. T.","year":"2019"},{"key":"atypb172","first-page":"207","volume-title":"2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX), SIAM, 2021","author":"Kerber M.","year":"1976"},{"key":"atypb173","doi-asserted-by":"publisher","DOI":"10.1109\/SAMPTA.2017.8024470"},{"key":"atypb174","volume-title":"Stable Signatures for Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence, preprint, https:\/\/arxiv.org\/abs\/1712.04064","author":"Kim W.","year":"2017"},{"key":"atypb175","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-019-00168-w"},{"key":"atypb176","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-43408-3_14"},{"key":"atypb177","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cnu016"},{"key":"atypb178","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000385"},{"key":"atypb179","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.020901"},{"key":"atypb180","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2009.5206846"},{"key":"atypb181","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/16\/8\/085013"},{"key":"atypb182","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abe3824"},{"key":"atypb183","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69689-3"},{"key":"atypb184","first-page":"3070","author":"Kwitt R.","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"key":"atypb185","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0459-y"},{"key":"atypb186","volume-title":"Modularity and Dynamics on Complex Networks","author":"Lambiotte R.","year":"2021"},{"key":"atypb187","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-019-0232-2"},{"key":"atypb188","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.012211"},{"key":"atypb189","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.L042201"},{"key":"atypb190","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2017.8006580"},{"key":"atypb191","volume-title":"Interactive Visualization of \\textup2-D Persistence Modules, preprint, https:\/\/arxiv.org\/abs\/1512.00180","author":"Lesnick M.","year":"2015"},{"key":"atypb192","doi-asserted-by":"publisher","DOI":"10.1038\/nature22898"},{"key":"atypb193","first-page":"3014","volume-title":"International Conference on Machine Learning, PMLR","author":"Li P.","year":"2018"},{"key":"atypb194","doi-asserted-by":"publisher","DOI":"10.1137\/18M1223101"},{"key":"atypb195","volume-title":"Weighted Path Homology of Weighted Digraphs and Persistence, preprint, https:\/\/arxiv.org\/abs\/1910.09891","author":"Lin Y.","year":"2019"},{"key":"atypb196","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0027-9"},{"key":"atypb197","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033410"},{"key":"atypb198","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-017-9938-z"},{"key":"atypb199","doi-asserted-by":"publisher","DOI":"10.1007\/s11192-018-2908-2"},{"key":"atypb200","doi-asserted-by":"publisher","DOI":"10.3390\/a13010019"},{"key":"atypb201","doi-asserted-by":"publisher","DOI":"10.1201\/b11431"},{"key":"atypb202","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1013213108"},{"key":"atypb203","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2017.07.007"},{"key":"atypb204","doi-asserted-by":"publisher","DOI":"10.1126\/science.aav7932"},{"key":"atypb205","volume-title":"Transl. Math. Monogr. 208","author":"Matsumoto Y.","year":"2002"},{"key":"atypb206","volume-title":"A Concise Course in Algebraic Topology","author":"May J. P.","year":"1999"},{"key":"atypb207","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1917763117"},{"key":"atypb208","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0909615107"},{"key":"atypb209","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002384"},{"key":"atypb210","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20238"},{"key":"atypb211","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.054302"},{"key":"atypb212","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.218301"},{"key":"atypb213","volume-title":"Data Structures for Real Multiparameter Persistence Modules, preprint, https:\/\/arxiv.org\/abs\/1709.08155","author":"Miller E.","year":"2017"},{"key":"atypb214","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-575X(02)80030-3"},{"key":"atypb215","first-page":"1024","volume-title":"Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems","author":"Muhammad A.","year":"2006"},{"key":"atypb216","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.062313"},{"key":"atypb217","unstructured":"E. Munch,Applications of Persistent Homology to Time Varying Systems, Doctoral dissertation, Duke University, Durham, NC, 2013."},{"key":"atypb218","doi-asserted-by":"publisher","DOI":"10.18608\/jla.2017.42.6"},{"key":"atypb219","doi-asserted-by":"publisher","DOI":"10.1201\/9780429493911"},{"key":"atypb220","doi-asserted-by":"publisher","DOI":"10.1080\/00107514.2015.1094987"},{"key":"atypb221","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1009094"},{"key":"atypb222","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20782"},{"key":"atypb223","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.032310"},{"key":"atypb224","volume-title":"Control and Optimization (NETGCOOP 2021)","author":"Neuh\u00e4user L.","year":"2021"},{"key":"atypb225","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198805090.001.0001"},{"key":"atypb226","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1102826108"},{"key":"atypb227","doi-asserted-by":"publisher","DOI":"10.1063\/5.0093842"},{"key":"atypb228","doi-asserted-by":"publisher","DOI":"10.1137\/18M1219977"},{"key":"atypb229","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aaaa07"},{"key":"atypb230","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2018.2820126"},{"key":"atypb231","doi-asserted-by":"publisher","DOI":"10.1140\/epjds\/s13688-017-0109-5"},{"key":"atypb232","volume-title":"Tech. report","author":"Page L.","year":"1999"},{"key":"atypb233","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20657"},{"key":"atypb234","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-014-3002-x"},{"key":"atypb235","doi-asserted-by":"publisher","DOI":"10.1140\/epjds\/s13688-017-0114-8"},{"key":"atypb236","doi-asserted-by":"publisher","DOI":"10.1140\/epjds\/s13688-017-0104-x"},{"key":"atypb237","first-page":"11","volume":"168","author":"Pattison P.","year":"2004","journal-title":"Math. Sci. Hum. Math. Soc. Sci."},{"key":"atypb238","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.2109"},{"key":"atypb239","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.013201"},{"key":"atypb240","doi-asserted-by":"publisher","DOI":"10.1090\/noti1869"},{"key":"atypb241","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2019.06.001"},{"key":"atypb242","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.2017.8296988"},{"key":"atypb243","doi-asserted-by":"publisher","DOI":"10.1017\/9781316671665"},{"key":"atypb244","first-page":"594","volume-title":"International Conference on Intelligent Networking and Collaborative Systems","author":"Ray J.","year":"2017"},{"key":"atypb245","volume-title":"Cycle Registration in Persistent Homology with Applications in Topological Bootstrap, preprint, https:\/\/arxiv.org\/abs\/2101.00698","author":"Reani Y.","year":"2021"},{"key":"atypb246","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2017.00048"},{"key":"atypb247","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab9338"},{"key":"atypb248","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216520430075"},{"key":"atypb249","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/11\/4\/009"},{"key":"atypb250","doi-asserted-by":"publisher","DOI":"10.1007\/s41468-017-0008-7"},{"key":"atypb251","doi-asserted-by":"publisher","DOI":"10.1090\/noti1867"},{"key":"atypb252","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP43922.2022.9747233"},{"key":"atypb253","doi-asserted-by":"publisher","DOI":"10.1109\/IEEECONF44664.2019.9049000"},{"key":"atypb254","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2015.10.008"},{"key":"atypb255","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms15082"},{"key":"atypb258","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2020.101623"},{"key":"atypb259","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0076939"},{"key":"atypb260","doi-asserted-by":"publisher","DOI":"10.1137\/18M1201019"},{"key":"atypb261","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-017-0023-6"},{"key":"atypb262","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-91374-8_12"},{"key":"atypb263","doi-asserted-by":"publisher","DOI":"10.1109\/GlobalSIP.2018.8646701"},{"key":"atypb264","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2021.108149"},{"key":"atypb265","volume-title":"Algebra and Topology for Data Analysis","author":"Schenck H.","year":"2020"},{"key":"atypb266","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579445"},{"key":"atypb267","volume-title":"High-order social interactions in groups of mice, eLife, 2","author":"Shemesh Y.","year":"2013"},{"key":"atypb268","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2012.2235192"},{"key":"atypb269","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2008.232"},{"key":"atypb270","doi-asserted-by":"publisher","DOI":"10.1162\/netn_a_00073"},{"key":"atypb271","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.248301"},{"key":"atypb272","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-020-00485-0"},{"key":"atypb273","doi-asserted-by":"publisher","DOI":"10.1111\/0081-1750.00066"},{"key":"atypb274","first-page":"12464","volume":"1","author":"Spagnuolo C.","year":"2020","journal-title":"Internet Math."},{"key":"atypb275","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.89.045001"},{"key":"atypb276","volume-title":"Proceedings of 21st International Conference on Computational Statistics","author":"Stasi D.","year":"2014"},{"key":"atypb277","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111103419896"},{"key":"atypb278","volume-title":"Master's thesis","author":"Stolz B.","year":"2014"},{"key":"atypb279","doi-asserted-by":"publisher","DOI":"10.1063\/1.4978997"},{"key":"atypb280","volume-title":"Multiscale Topology Characterises Dynamic Tumour Vascular Networks, preprint, https:\/\/arxiv.org\/abs\/2008.08667","author":"Stolz B. J.","year":"2020"},{"key":"atypb281","unstructured":"B. Stolz-Pretzer,Global and Local Persistent Homology for the Shape and Classification of Biological Data, Ph.D. thesis, University of Oxford, 2019."},{"key":"atypb282","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(00)00094-4"},{"key":"atypb283","volume-title":"Sync: The Emerging Science of Spontaneous Order","author":"Strogatz S. H.","year":"2004"},{"key":"atypb284","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2047541"},{"key":"atypb285","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.224101"},{"key":"atypb286","first-page":"1","volume":"6","author":"Taylor D.","year":"2015","journal-title":"Nature Commun."},{"key":"atypb287","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2319"},{"key":"atypb288","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/47\/34\/343001"},{"key":"atypb289","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0126383"},{"key":"atypb290","doi-asserted-by":"publisher","DOI":"10.1137\/20M1355896"},{"key":"atypb291","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-021-00704-2"},{"key":"atypb292","doi-asserted-by":"publisher","DOI":"10.3390\/a13110278"},{"key":"atypb293","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1001066"},{"key":"atypb294","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.066106"},{"key":"atypb295","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2009\/07\/P07006"},{"key":"atypb296","volume-title":"Hypergraph Cuts with General Splitting Functions, preprint, https:\/\/arxiv.org\/abs\/2001.02817","author":"Veldt N.","year":"2020"},{"key":"atypb297","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2102166118"},{"key":"atypb298","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.211361"},{"key":"atypb299","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(75)90042-8"},{"key":"atypb300","doi-asserted-by":"publisher","DOI":"10.1016\/j.socnet.2008.08.002"},{"key":"atypb301","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-statistics-031017-100045"},{"key":"atypb302","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2655"},{"key":"atypb303","volume-title":"Capturing Dynamics of Time-Varying Data via Topology, preprint, https:\/\/arxiv.org\/abs\/2010.05780","author":"Xian L.","year":"2020"},{"key":"atypb304","doi-asserted-by":"publisher","DOI":"10.1038\/nature24056"},{"key":"atypb305","doi-asserted-by":"publisher","DOI":"10.23919\/EUSIPCO54536.2021.9616185"},{"key":"atypb306","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2022.3207045"},{"key":"atypb307","unstructured":"X. Yang,Social Network Modeling and the Evaluation of Structural Similarity for Community Detection, Ph.D. thesis, Carnegie Mellon University, 2015."},{"key":"atypb308","doi-asserted-by":"publisher","DOI":"10.1109\/ICTAI.2013.61"},{"key":"atypb309","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.032312"},{"key":"atypb310","first-page":"240","volume-title":"Topology of 3-Manifolds and Related Topics","author":"Zeeman E. C.","year":"1962"},{"key":"atypb311","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2019.2950213"},{"key":"atypb312","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2010\/10\/P10005"},{"key":"atypb313","volume-title":"NIPS Workshop on Networks Across Disciplines: Theory and Applications","volume":"2","author":"Zheleva E.","year":"2010"},{"key":"atypb314","first-page":"19","author":"Zhou D.","year":"2006","journal-title":"Adv. Neural Inform. Process. Syst."},{"key":"atypb315","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-004-1146-y"},{"key":"atypb316","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/48\/46\/465002"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T12:42:39Z","timestamp":1692189759000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1414024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8]]},"references-count":312,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1137\/21M1414024"],"URL":"https:\/\/doi.org\/10.1137\/21m1414024","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8]]}}}