[{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2026.102598"}],"has_accepted_license":"1","dataavailabilitystatement":"The code used for the computational experiments is available in https://github.com/Cimagroup/IBloFunMatch","month":"06","article_type":"original","mathsc":["55N31","16G20"],"OA_place":"publisher","quality_controlled":"1","OA_type":"hybrid","department":[{"_id":"HeEd"}],"oa_version":"Published Version","arxiv":1,"article_processing_charge":"No","keyword":["Persistence module","Persistence map","Persistent homology"],"supplementarymaterial":"no","date_created":"2026-07-13T09:43:38Z","oa":1,"date_published":"2026-06-23T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","license":"https://creativecommons.org/licenses/by/4.0/","status":"public","fulldoi":"https://doi.org/10.1016/j.jsc.2026.102598","acknowledgement":"This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR, under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also like to thank Lars M Salbu for fruitful discussions regarding the operators from Definition 4.1 and their relation with the order relations introduced in Definition 3.2.","author":[{"first_name":"Rocio","full_name":"Gonzalez-Diaz, Rocio","last_name":"Gonzalez-Diaz"},{"last_name":"Soriano Trigueros","full_name":"Soriano Trigueros, Manuel","first_name":"Manuel","orcid":"0000-0003-2449-1433","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8"},{"first_name":"Alvaro","last_name":"Torras-Casas","full_name":"Torras-Casas, Alvaro"}],"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publisher":"Elsevier","external_id":{"arxiv":["2006.11100"]},"volume":138,"publication":"Journal of Symbolic Computation","corr_author":"1","title":"Additive partial matchings induced by persistence maps","year":"2026","_id":"22291","language":[{"iso":"eng"}],"PlanS_conform":"1","publication_status":"epub_ahead","day":"23","type":"journal_article","ddc":["500"],"abstract":[{"text":"Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available.","lang":"eng"}],"das_tickbox":"1","article_number":"102598","publication_identifier":{"eissn":["1095-855X"],"issn":["0747-7171"]},"date_updated":"2026-07-13T12:00:07Z","researchdata_availability":"yes","doi":"10.1016/j.jsc.2026.102598","citation":{"apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>","mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>.","ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.","ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>, vol. 138. Elsevier, 2026.","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>.","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138. doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>","short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic Computation 138 (2026)."},"intvolume":"       138"},{"intvolume":"        31","citation":{"short":"T. Vernet, Transformation Groups 31 (2026) 1047–1083.","ama":"Vernet T. Rational singularities for moment maps of totally negative quivers. <i>Transformation Groups</i>. 2026;31:1047-1083. doi:<a href=\"https://doi.org/10.1007/s00031-024-09873-0\">10.1007/s00031-024-09873-0</a>","chicago":"Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” <i>Transformation Groups</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00031-024-09873-0\">https://doi.org/10.1007/s00031-024-09873-0</a>.","ista":"Vernet T. 2026. Rational singularities for moment maps of totally negative quivers. Transformation Groups. 31, 1047–1083.","ieee":"T. Vernet, “Rational singularities for moment maps of totally negative quivers,” <i>Transformation Groups</i>, vol. 31. Springer Nature, pp. 1047–1083, 2026.","mla":"Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” <i>Transformation Groups</i>, vol. 31, Springer Nature, 2026, pp. 1047–83, doi:<a href=\"https://doi.org/10.1007/s00031-024-09873-0\">10.1007/s00031-024-09873-0</a>.","apa":"Vernet, T. (2026). Rational singularities for moment maps of totally negative quivers. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-024-09873-0\">https://doi.org/10.1007/s00031-024-09873-0</a>"},"doi":"10.1007/s00031-024-09873-0","researchdata_availability":"not applicable","date_updated":"2026-07-23T05:51:07Z","publication_identifier":{"issn":["1083-4362"],"eissn":["1531-586X"]},"das_tickbox":"1","abstract":[{"lang":"eng","text":"We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau categories, based on recent work of Davison. This has interesting arithmetic applications on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic behaviour of counts of jets of quiver moment maps over finite fields. Moreover, we interpret the limit of counts of jets on a given moduli space as its p-adic volume under a canonical measure analogous to the measure built by Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves."}],"ddc":["510"],"type":"journal_article","day":"01","publication_status":"published","language":[{"iso":"eng"}],"PlanS_conform":"1","page":"1047-1083","file_date_updated":"2026-07-23T05:50:09Z","_id":"17437","year":"2026","corr_author":"1","title":"Rational singularities for moment maps of totally negative quivers","publication":"Transformation Groups","volume":31,"ec_funded":1,"external_id":{"isi":["001287455300001"]},"publisher":"Springer Nature","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"scopus_import":"1","author":[{"id":"19f1e3bf-c59a-11ee-a1af-ed269948817b","full_name":"Vernet, Tanguy","last_name":"Vernet","first_name":"Tanguy"}],"acknowledgement":"I would like to warmly thank Dimitri Wyss for his guidance and supervision and Nero Budur for helpful discussions and answering all my questions on his previous works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart and Olivier Schiffmann for helpful remarks and discussions during the writing of this paper. Finally, I would like to thank the anonymous referees for their careful reading and suggesting improvements in the exposition.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This work was supported by the Swiss National Science Foundation [No. 196960]. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","fulldoi":"https://doi.org/10.1007/s00031-024-09873-0","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-03-01T00:00:00Z","oa":1,"file":[{"success":1,"date_updated":"2026-07-23T05:50:09Z","file_size":912029,"creator":"dernst","content_type":"application/pdf","file_name":"2026_TransformationGroups_Vernet.pdf","file_id":"22385","access_level":"open_access","date_created":"2026-07-23T05:50:09Z","relation":"main_file","checksum":"8985b4154b730284d3412ddc9e55d965"}],"date_created":"2024-08-18T22:01:04Z","supplementarymaterial":"no","article_processing_charge":"Yes (via OA deal)","isi":1,"department":[{"_id":"TaHa"}],"oa_version":"Published Version","OA_place":"publisher","quality_controlled":"1","OA_type":"hybrid","mathsc":["14B05","14D23","14G20","16G20"],"article_type":"original","month":"03","has_accepted_license":"1","dataavailabilitystatement":"Not applicable."}]