{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T18:36:23Z","timestamp":1770921383612,"version":"3.50.1"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032178008","type":"print"},{"value":"9783032178015","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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\/978-3-032-17801-5_5","type":"book-chapter","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:52:54Z","timestamp":1770918774000},"page":"61-74","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithms and\u00a0Complexity Results for\u00a0K-Theoretic Persistent Homology"],"prefix":"10.1007","author":[{"given":"Yoshihiro","family":"Maruyama","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"5_CR1","unstructured":"Atiyah, M.F.: K-Theory. Benjamin (1967)"},{"issue":"2","key":"5_CR2","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1090\/S0273-0979-09-01249-X","volume":"46","author":"G Carlsson","year":"2009","unstructured":"Carlsson, G.: Topology and data. Bull. Am. Math. Soc. 46(2), 255\u2013308 (2009)","journal-title":"Bull. Am. Math. Soc."},{"key":"5_CR3","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)"},{"issue":"05","key":"5_CR4","doi-asserted-by":"publisher","first-page":"1550066","DOI":"10.1142\/S0219498815500668","volume":"14","author":"W Crawley-Boevey","year":"2015","unstructured":"Crawley-Boevey, W.: Decomposition of pointwise finite-dimensional persistence modules. J. Algebra Appl. 14(05), 1550066 (2015)","journal-title":"J. Algebra Appl."},{"key":"5_CR5","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society (2010)","DOI":"10.1090\/mbk\/069"},{"issue":"4","key":"5_CR6","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28(4), 511\u2013533 (2002)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"5_CR7","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1090\/S0273-0979-07-01191-3","volume":"45","author":"R Ghrist","year":"2008","unstructured":"Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61\u201375 (2008)","journal-title":"Bull. Am. Math. Soc."},{"issue":"44","key":"5_CR8","doi-asserted-by":"publisher","first-page":"13455","DOI":"10.1073\/pnas.1506407112","volume":"112","author":"C Giusti","year":"2015","unstructured":"Giusti, C., Pastalkova, E., Curto, C., Itskov, V.: Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Natl. Acad. Sci. 112(44), 13455\u201313460 (2015)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"5_CR9","doi-asserted-by":"crossref","unstructured":"Horak, D., Maleti\u0107, S., Rajkovi\u0107, M.: Persistent homology of complex networks. J. Stat. Mech. Theory Exp. P03034 (2009)","DOI":"10.1088\/1742-5468\/2009\/03\/P03034"},{"key":"5_CR10","unstructured":"Knuth, D.E.: The Art of Computer Programming. Addison\u2013Wesley (2011)"},{"key":"5_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/978-3-030-67220-1_11","volume-title":"Software Engineering and Formal Methods. SEFM 2020 Collocated Workshops","author":"Y Maruyama","year":"2021","unstructured":"Maruyama, Y.: Symbolic and statistical theories of cognition: towards integrated artificial intelligence. In: Cleophas, L., Massink, M. (eds.) SEFM 2020. LNCS, vol. 12524, pp. 129\u2013146. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-67220-1_11"},{"key":"5_CR12","doi-asserted-by":"crossref","unstructured":"Maruyama, Y.: Algorithm for Interpretable Graph Features via Motivic Persistent Cohomology. Springer (2026)","DOI":"10.1007\/978-3-032-15621-1_8"},{"key":"5_CR13","unstructured":"Maruyama, Y.: Reverse Mathematics for Neural Networks. Springer (2026)"},{"key":"5_CR14","doi-asserted-by":"publisher","unstructured":"Maruyama, Y.: Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-032-15621-1_7 (2026)","DOI":"10.1007\/978-3-032-15621-1_7"},{"key":"5_CR15","unstructured":"Maruyama, Y., Yasuda, A.: Homological Representation Learning for Molecular Graphs. In: Proceedings of Machine Learning Research (2025)"},{"key":"5_CR16","unstructured":"Maruyama, Y., Yasuda, A.: K-theoretic persistent cohomology. In: Proceedings of Machine Learning Research (2025)"},{"key":"5_CR17","unstructured":"Maruyama, Y.: Categorical Equivariant Deep Learning (2025). https:\/\/doi.org\/10.48550\/arXiv.2511.18417"},{"key":"5_CR18","unstructured":"Maruyama, Y.: Learning with Category-Equivariant Architectures for Human Activity Recognition. arXiv:2511.01139 (2025)"},{"key":"5_CR19","unstructured":"Maruyama, Y.: Learning with Category-Equivariant Representations for Human Activity Recognition. arXiv:2511.00900 (2025)"},{"issue":"6","key":"5_CR20","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0066506","volume":"8","author":"G Petri","year":"2013","unstructured":"Petri, G., Scolamiero, M., Donato, I., Vaccarino, F.: Topological strata of weighted complex networks. PLOS One 8(6), e66506 (2013)","journal-title":"PLOS One"},{"issue":"2","key":"5_CR21","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s00454-004-1146-y","volume":"33","author":"A Zomorodian","year":"2005","unstructured":"Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33(2), 249\u2013274 (2005)","journal-title":"Discrete Comput. Geom."}],"container-title":["Lecture Notes in Computer Science","SOFSEM 2026: Theory and Practice of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-17801-5_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:52:58Z","timestamp":1770918778000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-17801-5_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032178008","9783032178015"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-17801-5_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"13 February 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SOFSEM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Current Trends in Theory and Practice of Computer Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Krakow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 February 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 February 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"51","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sofsem2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sofsem.uj.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}