{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T17:31:43Z","timestamp":1779384703926,"version":"3.53.1"},"reference-count":51,"publisher":"American Chemical Society (ACS)","issue":"8","license":[{"start":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T00:00:00Z","timestamp":1712188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100002491","name":"Bristol-Myers Squibb","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100002491","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007709","name":"Michigan State University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007709","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000104","name":"National Aeronautics and Space Administration","doi-asserted-by":"publisher","award":["80NSSC21M0023"],"award-info":[{"award-number":["80NSSC21M0023"]}],"id":[{"id":"10.13039\/100000104","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01AI164266"],"award-info":[{"award-number":["R01AI164266"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01GM126189"],"award-info":[{"award-number":["R01GM126189"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R35GM148196"],"award-info":[{"award-number":["R35GM148196"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1761320"],"award-info":[{"award-number":["DMS-1761320"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS2052983"],"award-info":[{"award-number":["DMS2052983"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1900473"],"award-info":[{"award-number":["IIS-1900473"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Chem. Inf. Model."],"published-print":{"date-parts":[[2024,4,22]]},"DOI":"10.1021\/acs.jcim.4c00132","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T09:24:46Z","timestamp":1712222686000},"page":"3558-3568","source":"Crossref","is-referenced-by-count":14,"title":["Hodge Decomposition of Single-Cell RNA Velocity"],"prefix":"10.1021","volume":"64","author":[{"given":"Zhe","family":"Su","sequence":"first","affiliation":[{"name":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiying","family":"Tong","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Michigan State University, East Lansing, Michigan 48824, United States"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5781-2937","authenticated-orcid":true,"given":"Guo-Wei","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States"},{"name":"Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, United States"},{"name":"Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan 48824, United States"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2024,4,4]]},"reference":[{"key":"ref1\/cit1","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-019-0654-x"},{"key":"ref2\/cit2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2021.04.048"},{"key":"ref3\/cit3","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-017-1382-0"},{"key":"ref4\/cit4","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-021-02519-4"},{"key":"ref5\/cit5","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bbae054"},{"key":"ref6\/cit6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2024.115842"},{"key":"ref7\/cit7","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2024.108211"},{"key":"ref8\/cit8","doi-asserted-by":"crossref","unstructured":"Huynh, T.; Cang, Z. Topological and geometric analysis of cell states in single-cell transcriptomic data. 2023, arXiv preprint arXiv:2309.07950.","DOI":"10.1093\/bib\/bbae176"},{"key":"ref9\/cit9","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-018-0414-6"},{"key":"ref10\/cit10","doi-asserted-by":"crossref","unstructured":"McInnes, L., Healy, J., Melville, J. Umap: Uniform manifold approximation and projection for dimension reduction. 2018, arXiv preprint arXiv:1802.03426","DOI":"10.21105\/joss.00861"},{"key":"ref11\/cit11","first-page":"2579","volume":"9","author":"Van der Maaten L.","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref12\/cit12","doi-asserted-by":"publisher","DOI":"10.1038\/s41587-020-0591-3"},{"key":"ref13\/cit13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2021.12.045"},{"key":"ref14\/cit14","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-021-01346-6"},{"key":"ref15\/cit15","doi-asserted-by":"crossref","unstructured":"Stam, J. Seminal Graphics Papers: Pushing the Boundaries; Association for Computing Machinery: New York, NY, USA, 2023; Vol. 2, pp 779\u2013786.","DOI":"10.1145\/3596711.3596793"},{"key":"ref16\/cit16","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1996.0039"},{"key":"ref17\/cit17","volume-title":"Quantitative Seismology","author":"Aki K.","year":"2002"},{"key":"ref18\/cit18","doi-asserted-by":"publisher","DOI":"10.1007\/s13137-010-0001-y"},{"key":"ref19\/cit19","first-page":"164","volume-title":"SOHO 14 Helio-and Asteroseismology: Towards a Golden Future","author":"Mansour N. N.","year":"2004"},{"key":"ref20\/cit20","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882290"},{"key":"ref21\/cit21","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356546"},{"key":"ref22\/cit22","doi-asserted-by":"crossref","unstructured":"Gao, H.; Mandal, M. K.; Guo, G.; Wan, J. Singular point detection using discrete Hodge Helmholtz decomposition in fingerprint images. In  2010 IEEE International Conference on Acoustics, Speech and Signal Processing; IEEE, 2010, pp 1094\u20131097.","DOI":"10.1109\/ICASSP.2010.5495348"},{"key":"ref23\/cit23","doi-asserted-by":"crossref","unstructured":"Mochizuki, Y.; Imiya, A. Spatial reasoning for robot navigation using the Helmholtz-Hodge decomposition of omnidirectional optical flow. In  2009 24th International Conference Image and Vision Computing New Zealand; IEEE, 2009, pp 1\u20136.","DOI":"10.1109\/IVCNZ.2009.5378430"},{"key":"ref24\/cit24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02498-6_56"},{"key":"ref25\/cit25","volume-title":"The Mathematical Theory of Viscous Incompressible Flow","author":"Ladyzhenskaya O. A.","year":"1969"},{"key":"ref26\/cit26","doi-asserted-by":"crossref","unstructured":"Losasso, F.; Gibou, F.; Fedkiw, R. Acm Siggraph 2004 Papers; ACM, 2004, pp 457\u2013462.","DOI":"10.1145\/1015706.1015745"},{"key":"ref27\/cit27","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-020-00783-2"},{"key":"ref28\/cit28","doi-asserted-by":"publisher","DOI":"10.1002\/fld.598"},{"key":"ref29\/cit29","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0364-0","volume-title":"A Mathematical Introduction to Fluid Mechanics","volume":"3","author":"Chorin A. J.","year":"1990"},{"key":"ref30\/cit30","volume-title":"The Theory and Applications of Harmonic Integrals","author":"Hodge W. V. D.","year":"1989"},{"key":"ref31\/cit31","unstructured":"Shonkwiler, C. Poincar\u00e9 duality angles on Riemannian manifolds with boundary. Ph.D. thesis, University of Pennsylvania, 2009."},{"key":"ref32\/cit32","unstructured":"Desbrun, M.; Kanso, E.; Tong, Y. ACM SIGGRAPH 2006 Courses; ACM, 2006, pp 39\u201354."},{"key":"ref33\/cit33","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611975543","volume-title":"Finite Element Exterior Calculus","author":"Arnold D. N.","year":"2018"},{"key":"ref34\/cit34","unstructured":"Ribando-Gros, E.; Wang, R.; Chen, J.; Tong, Y.; Wei, G.W. Combinatorial and Hodge Laplacians: Similarity and Difference. 2023, arXiv preprint arXiv:2204.12218."},{"key":"ref35\/cit35","doi-asserted-by":"publisher","DOI":"10.1137\/18M1223101"},{"key":"ref36\/cit36","doi-asserted-by":"crossref","DOI":"10.1101\/592089","volume-title":"Modeling Latent Flows on Single-Cell Data Using the Hodge Decomposition","author":"Maehara K.","year":"2019"},{"key":"ref37\/cit37","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2312012"},{"key":"ref38\/cit38","unstructured":"Jia, J.; Chen, L. Velde: constructing cell potential landscapes by RNA velocity vector field decomposition. 2023, arXiv preprint arXiv:2311.10403."},{"key":"ref39\/cit39","doi-asserted-by":"publisher","DOI":"10.1038\/nbt.4314"},{"key":"ref40\/cit40","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-03232-9"},{"key":"ref41\/cit41","doi-asserted-by":"publisher","DOI":"10.1016\/j.crmeth.2022.100359"},{"key":"ref42\/cit42","doi-asserted-by":"publisher","DOI":"10.2307\/2372488"},{"key":"ref43\/cit43","doi-asserted-by":"publisher","DOI":"10.2307\/1969552"},{"key":"ref44\/cit44","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160080408"},{"key":"ref45\/cit45","doi-asserted-by":"publisher","DOI":"10.1038\/s41587-021-00870-2"},{"key":"ref46\/cit46","doi-asserted-by":"crossref","unstructured":"Kaminow, B.; Yunusov, D.; Dobin, A. STARsolo: accurate, fast and versatile mapping\/quantification of single-cell and single-nucleus RNA-seq data. 2021, Biorxiv.","DOI":"10.1101\/2021.05.05.442755"},{"key":"ref47\/cit47","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-019-1670-y"},{"key":"ref48\/cit48","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-022-01408-3"},{"key":"ref49\/cit49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.09.034"},{"key":"ref50\/cit50","doi-asserted-by":"publisher","DOI":"10.1063\/1.4953851"},{"key":"ref51\/cit51","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2020257"}],"container-title":["Journal of Chemical Information and Modeling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jcim.4c00132","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jcim.4c00132","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T08:12:19Z","timestamp":1713773539000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/doi\/10.1021\/acs.jcim.4c00132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,4]]},"references-count":51,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2024,4,22]]}},"alternative-id":["10.1021\/acs.jcim.4c00132"],"URL":"https:\/\/doi.org\/10.1021\/acs.jcim.4c00132","relation":{},"ISSN":["1549-9596","1549-960X"],"issn-type":[{"value":"1549-9596","type":"print"},{"value":"1549-960X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,4]]}}}