{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T01:04:07Z","timestamp":1768871047743,"version":"3.49.0"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid\/Lie algebroid case. <\/jats:p>","DOI":"10.1142\/s1230161220500158","type":"journal-article","created":{"date-parts":[[2020,12,28]],"date-time":"2020-12-28T02:50:31Z","timestamp":1609123831000},"page":"2050015","source":"Crossref","is-referenced-by-count":6,"title":["Information Geometry on Groupoids: The Case of Singular Metrics"],"prefix":"10.1142","volume":"27","author":[{"given":"Katarzyna","family":"Grabowska","sequence":"first","affiliation":[{"name":"Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02\u2013093 Warszawa, Poland"}]},{"given":"Janusz","family":"Grabowski","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Polish Academy of Sciences, ul. \u015aniadeckich 8, 00\u2013656 Warszawa, Poland"}]},{"given":"Marek","family":"Ku\u015b","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotnik\u00f3w 32\/46, 02-668 Warszawa, Poland"}]},{"given":"Giuseppe","family":"Marmo","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u201cEttore Pancini\u201d, Universit\u00e0 \u201cFederico II\u201d di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte Sant Angelo, Via Cintia, I-80126 Napoli, Italy"}]}],"member":"219","published-online":{"date-parts":[[2020,12,28]]},"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161220500158","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,28]],"date-time":"2020-12-28T02:50:32Z","timestamp":1609123832000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161220500158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":0,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S1230161220500158"],"URL":"https:\/\/doi.org\/10.1142\/s1230161220500158","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}