{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T22:44:32Z","timestamp":1760913872528,"version":"build-2065373602"},"publisher-location":"Cham","reference-count":14,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032039170","type":"print"},{"value":"9783032039187","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T00:00:00Z","timestamp":1760918400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T00:00:00Z","timestamp":1760918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-03918-7_3","type":"book-chapter","created":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T22:04:20Z","timestamp":1760911460000},"page":"24-33","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Universal Collection of\u00a0Euclidean Invariants Between Pairs of\u00a0Position-Orientations"],"prefix":"10.1007","author":[{"given":"Gijs","family":"Bellaard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bart M. N.","family":"Smets","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Remco","family":"Duits","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,20]]},"reference":[{"key":"3_CR1","unstructured":"Anderson, B., Hy, T.S., Kondor, R.: Cormorant: covariant molecular neural networks. In: NeurIPS, vol.\u00a032. Curran Associates, Inc. (2019). https:\/\/papers.neurips.cc\/paper_files\/paper\/2019\/hash\/03573b32b2746e6e8ca98b9123f2249b-Abstract.html"},{"key":"3_CR2","unstructured":"Bekkers, E.J., Vadgama, S., Hesselink, R., van der Linden, P.A., Romero, D.W.: Fast, expressive SE(3) equivariant networks through weight-sharing in position-orientation space. In: ICLR (2024). https:\/\/openreview.net\/forum?id=dPHLbUqGbr"},{"key":"3_CR3","doi-asserted-by":"publisher","unstructured":"Christensen, A.S., von Lilienfeld, O.A.: On the role of gradients for machine learning of molecular energies and forces. Mach. Learn. Sci. Technol. 1(4) (2020). https:\/\/doi.org\/10.1088\/2632-2153\/abba6f","DOI":"10.1088\/2632-2153\/abba6f"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Deng, H., Birdal, T., Ilic, S.: PPF-FoldNet: unsupervised learning of rotation invariant 3D local descriptors (2018). arxiv:1808.10322","DOI":"10.1007\/978-3-030-01228-1_37"},{"key":"3_CR5","unstructured":"Fuchs, F., Worrall, D., Fischer, V., Welling, M.: SE(3)-transformers: 3D roto-translation equivariant attention networks. In: NeurIPS, vol.\u00a033 (2020). https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/15231a7ce4ba789d13b722cc5c955834-Abstract.html"},{"key":"3_CR6","unstructured":"Gasteiger, J., Becker, F., G\u00fcnnemann, S.: GemNet: universal directional graph neural networks for molecules. In: NeurIPS (2021). https:\/\/openreview.net\/forum?id=HS_sOaxS9K-"},{"key":"3_CR7","doi-asserted-by":"publisher","unstructured":"Lee, J.M.: Introduction to smooth manifolds. In: Introduction to Smooth Manifolds. Springer New York (2012). https:\/\/doi.org\/10.1007\/978-1-4419-9982-5","DOI":"10.1007\/978-1-4419-9982-5"},{"key":"3_CR8","unstructured":"Liu, Y., et al.: Spherical message passing for 3D molecular graphs. In: ICLR (2022). https:\/\/openreview.net\/forum?id=givsRXsOt9r"},{"key":"3_CR9","doi-asserted-by":"publisher","unstructured":"Ramakrishnan, R., Dral, P.O., Rupp, M., von Lilienfeld, O.A.: Quantum chemistry structures and properties of 134 kilo molecules. Sci. Data 1(1) (2014). https:\/\/doi.org\/10.1038\/sdata.2014.22","DOI":"10.1038\/sdata.2014.22"},{"issue":"11","key":"3_CR10","doi-asserted-by":"publisher","first-page":"2864","DOI":"10.1021\/ci300415d","volume":"52","author":"L Ruddigkeit","year":"2012","unstructured":"Ruddigkeit, L., van Deursen, R., Blum, L.C., Reymond, J.L.: Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17. J. Chem. Inf. Model. 52(11), 2864\u20132875 (2012). https:\/\/doi.org\/10.1021\/ci300415d","journal-title":"J. Chem. Inf. Model."},{"key":"3_CR11","doi-asserted-by":"publisher","unstructured":"Suk, J., de Haan, P., Lippe, P., Brune, C., Wolterink, J.M.: Mesh neural networks for SE(3)-equivariant hemodynamics estimation on the artery wall. Comput. Biol. Med. 173 (2024). https:\/\/doi.org\/10.1016\/j.compbiomed.2024.108328","DOI":"10.1016\/j.compbiomed.2024.108328"},{"key":"3_CR12","doi-asserted-by":"publisher","unstructured":"Suk, J., Imre, B., Wolterink, J.M.: Lab-GATR: geometric algebra transformers for large biomedical surface and volume meshes. In: MICCAI, pp. 185\u2013195 (2024). https:\/\/doi.org\/10.1007\/978-3-031-72390-2_18","DOI":"10.1007\/978-3-031-72390-2_18"},{"key":"3_CR13","unstructured":"Thomas, N., et al.: Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds. arXiv preprint (2018). arxiv:1802.08219"},{"key":"3_CR14","unstructured":"Weiler, M., Geiger, M., Welling, M., Boomsma, W., Cohen, T.S.: 3D steerable CNNs: learning rotationally equivariant features in volumetric data. In: NeurIPS, vol.\u00a031. Curran Associates, Inc. (2018). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2018\/file\/488e4104520c6aab692863cc1dba45af-Paper.pdf"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-03918-7_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T22:04:21Z","timestamp":1760911461000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-03918-7_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,20]]},"ISBN":["9783032039170","9783032039187"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-03918-7_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,20]]},"assertion":[{"value":"20 October 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GSI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Geometric Science of Information","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Saint-Malo","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conference-gsi.org\/gsi-2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}