{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T02:13:56Z","timestamp":1769825636893,"version":"3.49.0"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032014351","type":"print"},{"value":"9783032014368","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"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\/978-3-032-01436-8_1","type":"book-chapter","created":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T03:24:30Z","timestamp":1755487470000},"page":"3-22","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computation of\u00a0Immediate Neighbours of\u00a0Monotone Boolean Functions"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7740-8539","authenticated-orcid":false,"given":"Jos\u00e9 E. R.","family":"Cury","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5904-2154","authenticated-orcid":false,"given":"Patr\u00edcia","family":"Tenera Roxo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4205-2189","authenticated-orcid":false,"given":"Vasco","family":"Manquinho","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2350-0756","authenticated-orcid":false,"given":"Claudine","family":"Chaouiya","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7934-5495","authenticated-orcid":false,"given":"Pedro T.","family":"Monteiro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"1_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2019.01.008","author":"W Abou-Jaoud\u00e9","year":"2019","unstructured":"Abou-Jaoud\u00e9, W., Monteiro, P.T.: On logical bifurcation diagrams. J. Theor. Biol. (2019). https:\/\/doi.org\/10.1016\/j.jtbi.2019.01.008","journal-title":"J. Theor. Biol."},{"key":"1_CR2","doi-asserted-by":"publisher","unstructured":"Abou-Jaoud\u00e9, W., et al.: Logical modeling and dynamical analysis of cellular networks. Front. Genet. 7, 94 (2016). https:\/\/doi.org\/10.3389\/fgene.2016.00094","DOI":"10.3389\/fgene.2016.00094"},{"key":"1_CR3","doi-asserted-by":"publisher","unstructured":"Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster. J. Theoret. Biol. 223, 1\u201318 (2003). https:\/\/doi.org\/10.1016\/S0022-5193(03)00035-3","DOI":"10.1016\/S0022-5193(03)00035-3"},{"key":"1_CR4","doi-asserted-by":"publisher","unstructured":"Aracena, J., Demongeot, J., Goles, E.: On limit cycles of monotone functions with symmetric connection graph. Theoret. Comput. Sci. 322(2), 237\u2013244 (2004). https:\/\/doi.org\/10.1016\/j.tcs.2004.03.010","DOI":"10.1016\/j.tcs.2004.03.010"},{"issue":"3","key":"1_CR5","doi-asserted-by":"publisher","first-page":"1702","DOI":"10.1137\/16M1060868","volume":"31","author":"J Aracena","year":"2017","unstructured":"Aracena, J., Richard, A., Salinas, L.: Number of fixed points and disjoint cycles in monotone Boolean networks. SIAM J. Discret. Math. 31(3), 1702\u20131725 (2017). https:\/\/doi.org\/10.1137\/16M1060868","journal-title":"SIAM J. Discret. Math."},{"key":"1_CR6","doi-asserted-by":"publisher","unstructured":"Bornholdt, S.: Boolean network models of cellular regulation: prospects and limitations. J. R. Soc. Interface 5(suppl_1), S85\u201394 (2008). https:\/\/doi.org\/10.1098\/rsif.2008.0132.focus","DOI":"10.1098\/rsif.2008.0132.focus"},{"key":"1_CR7","doi-asserted-by":"publisher","unstructured":"Caspard, N., Leclerc, B., Monjardet, B.: Finite ordered sets: concepts, results and uses. In: No.\u00a0144 in Encyclopedia of Mathematics and its Applications, Cambridge University Press (2012). https:\/\/doi.org\/10.1017\/CBO9781139005135","DOI":"10.1017\/CBO9781139005135"},{"key":"1_CR8","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1004571","volume":"11","author":"DPA Cohen","year":"2015","unstructured":"Cohen, D.P.A., Martignetti, L., Robine, S., Barillot, E., Zinovyev, A., Calzone, L.: Mathematical modelling of molecular pathways enabling tumour cell invasion and migration. PLoS Comput. Biol. 11, e1004571 (2015). https:\/\/doi.org\/10.1371\/journal.pcbi.1004571","journal-title":"PLoS Comput. Biol."},{"key":"1_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511852008","volume-title":"Boolean Functions: Theory, Algorithms, and Applications","author":"Y Crama","year":"2011","unstructured":"Crama, Y., Hammer, P.L.: Boolean Functions: Theory, Algorithms, and Applications. Cambridge University Press, Cambridge (2011)"},{"key":"1_CR10","unstructured":"Cury, J.E.R., Monteiro, P.T., Chaouiya, C.: Partial order on the set of Boolean regulatory functions. CoRR abs\/1901.07623 (2019). http:\/\/arxiv.org\/abs\/1901.07623"},{"key":"1_CR11","unstructured":"Cury, J.E.R., Roxo, P.T., Manquinho, V., Chaouiya, C., Monteiro, P.T.: Computation of immediate neighbours of monotone Boolean functions. CoRR abs\/2407.01337 (2025). http:\/\/arxiv.org\/abs\/2407.01337"},{"issue":"1","key":"1_CR12","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.jtbi.2010.09.017","volume":"270","author":"G Didier","year":"2011","unstructured":"Didier, G., Remy, E., Chaouiya, C.: Mapping multivalued onto Boolean dynamics. J. Theor. Biol. 270(1), 177\u2013184 (2011). https:\/\/doi.org\/10.1016\/j.jtbi.2010.09.017","journal-title":"J. Theor. Biol."},{"key":"1_CR13","doi-asserted-by":"publisher","first-page":"P1","DOI":"10.1186\/1471-2105-8-S8-P1","volume":"8","author":"A Faur\u00e9","year":"2007","unstructured":"Faur\u00e9, A., Chaouiya, C., Ciliberto, A., Thieffry, D.: Logical modelling and analysis of the budding yeast cell cycle. BMC Bioinform. 8, P1 (2007). https:\/\/doi.org\/10.1186\/1471-2105-8-S8-P1","journal-title":"BMC Bioinform."},{"issue":"12","key":"1_CR14","doi-asserted-by":"publisher","first-page":"i101","DOI":"10.1093\/bioinformatics\/btp214","volume":"25","author":"A Garg","year":"2009","unstructured":"Garg, A., Mohanram, K., Di Cara, A., De Micheli, G., Xenarios, I.: Modeling stochasticity and robustness in gene regulatory networks. Bioinformatics 25(12), i101\u2013i109 (2009). https:\/\/doi.org\/10.1093\/bioinformatics\/btp214","journal-title":"Bioinformatics"},{"key":"1_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2024.109225","volume":"374","author":"T Gedeon","year":"2024","unstructured":"Gedeon, T.: Lattice structures that parameterize regulatory network dynamics. Math. Biosci. 374, 109225 (2024). https:\/\/doi.org\/10.1016\/j.mbs.2024.109225","journal-title":"Math. Biosci."},{"key":"1_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/978-3-030-60327-4_18","volume-title":"Computational Methods in Systems Biology","author":"F Gouveia","year":"2020","unstructured":"Gouveia, F., Lynce, I., Monteiro, P.T.: ModRev - model revision tool for Boolean logical models of biological regulatory networks. In: Abate, A., Petrov, T., Wolf, V. (eds.) CMSB 2020. LNCS, vol. 12314, pp. 339\u2013348. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-60327-4_18"},{"key":"1_CR17","unstructured":"Hirtum, L.V., et al.: A computation of d(9) using FPGA supercomputing. CoRR abs\/2304.03039 (2023). http:\/\/arxiv.org\/abs\/2304.03039"},{"key":"1_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jaca.2023.100006","volume":"6\u20137","author":"C J\u00e4kel","year":"2023","unstructured":"J\u00e4kel, C.: A computation of the ninth Dedekind number. J. Comput. Algebra 6\u20137, 100006 (2023). https:\/\/doi.org\/10.1016\/j.jaca.2023.100006","journal-title":"J. Comput. Algebra"},{"issue":"3","key":"1_CR19","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","volume":"22","author":"SA Kauffman","year":"1969","unstructured":"Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437\u2013467 (1969). https:\/\/doi.org\/10.1016\/0022-5193(69)90015-0","journal-title":"J. Theor. Biol."},{"issue":"5","key":"1_CR20","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1070\/RM2003v058n05ABEH000667","volume":"58","author":"AD Korshunov","year":"2003","unstructured":"Korshunov, A.D.: Monotone Boolean functions. Russ. Math. Surv. 58(5), 929 (2003). https:\/\/doi.org\/10.1070\/RM2003v058n05ABEH000667","journal-title":"Russ. Math. Surv."},{"issue":"3","key":"1_CR21","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1038\/nrg3885","volume":"16","author":"N Le Nov\u00e8re","year":"2015","unstructured":"Le Nov\u00e8re, N.: Quantitative and logic modelling of molecular and gene networks. Nat. Rev. Genet. 16(3), 146\u2013158 (2015). https:\/\/doi.org\/10.1038\/nrg3885","journal-title":"Nat. Rev. Genet."},{"issue":"14","key":"1_CR22","doi-asserted-by":"publisher","first-page":"4781","DOI":"10.1073\/pnas.0305937101","volume":"101","author":"F Li","year":"2004","unstructured":"Li, F., Long, T., Lu, Y., Ouyang, Q., Tang, C.: The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. 101(14), 4781\u20134786 (2004). https:\/\/doi.org\/10.1073\/pnas.0305937101","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"1","key":"1_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1742-4682-3-13","volume":"3","author":"L Mendoza","year":"2006","unstructured":"Mendoza, L., Xenarios, I.: A method for the generation of standardized qualitative dynamical systems of regulatory networks. Theor. Biol. Med. Model. 3(1), 1\u201318 (2006). https:\/\/doi.org\/10.1186\/1742-4682-3-13","journal-title":"Theor. Biol. Med. Model."},{"issue":"10","key":"1_CR24","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1093\/bioinformatics\/btq124","volume":"26","author":"C M\u00fcssel","year":"2010","unstructured":"M\u00fcssel, C., Hopfensitz, M., Kestler, H.A.: BoolNet-an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 26(10), 1378\u20131380 (2010). https:\/\/doi.org\/10.1093\/bioinformatics\/btq124","journal-title":"Bioinformatics"},{"key":"1_CR25","doi-asserted-by":"publisher","first-page":"1000912","DOI":"10.1371\/journal.pcbi.1000912","volume":"6","author":"A Naldi","year":"2010","unstructured":"Naldi, A., Carneiro, J., Chaouiya, C., Thieffry, D.: Diversity and plasticity of Th cell types predicted from regulatory network modelling. PLoS Comput. Biol. 6, 1000912 (2010). https:\/\/doi.org\/10.1371\/journal.pcbi.1000912","journal-title":"PLoS Comput. Biol."},{"key":"1_CR26","doi-asserted-by":"publisher","first-page":"646","DOI":"10.3389\/fphys.2018.00646","volume":"9","author":"A Naldi","year":"2018","unstructured":"Naldi, A., Hernandez, C., Abou-Jaoud\u00e9, W., Monteiro, P.T., Chaouiya, C., Thieffry, D.: Logical modeling and analysis of cellular regulatory networks with GINsim 3.0. Front. Physiol. 9, 646 (2018). https:\/\/doi.org\/10.3389\/fphys.2018.00646","journal-title":"Front. Physiol."},{"key":"1_CR27","doi-asserted-by":"publisher","first-page":"680","DOI":"10.3389\/fphys.2018.00680","volume":"9","author":"A Naldi","year":"2018","unstructured":"Naldi, A., et al.: The colomoto interactive notebook: accessible and reproducible computational analyses for qualitative biological networks. Front. Physiol. 9, 680 (2018). https:\/\/doi.org\/10.3389\/fphys.2018.00680","journal-title":"Front. Physiol."},{"key":"1_CR28","doi-asserted-by":"publisher","first-page":"4256","DOI":"10.1038\/s41467-020-18112-5","volume":"11","author":"L Paulev\u00e9","year":"2020","unstructured":"Paulev\u00e9, L., Kol\u010d\u00e1k, J., Chatain, T., Haar, S.: Reconciling qualitative, abstract, and scalable modeling of biological networks. Nat. Commun. 11, 4256 (2020). https:\/\/doi.org\/10.1038\/s41467-020-18112-5","journal-title":"Nat. Commun."},{"key":"1_CR29","doi-asserted-by":"publisher","unstructured":"Paulev\u00e9, L., Sen\u00e9, S.: Non-deterministic updates of Boolean networks. In: International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021), vol.\u00a090. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, June 2021. https:\/\/doi.org\/10.4230\/OASIcs.AUTOMATA.2021.10","DOI":"10.4230\/OASIcs.AUTOMATA.2021.10"},{"key":"1_CR30","doi-asserted-by":"publisher","unstructured":"\u00c9lisabeth Remy, Ruet, P., Thieffry, D.: Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Adv. Appl. Math. 41(3), 335\u2013350 (2008). https:\/\/doi.org\/10.1016\/j.aam.2007.11.003","DOI":"10.1016\/j.aam.2007.11.003"},{"key":"1_CR31","doi-asserted-by":"publisher","first-page":"2407","DOI":"10.1158\/0008-5472.CAN-19-3147","volume":"80","author":"G Selvaggio","year":"2020","unstructured":"Selvaggio, G., et al.: Hybrid epithelial-mesenchymal phenotypes are controlled by microenvironmental factors. Cancer Res. 80, 2407\u20132420 (2020). https:\/\/doi.org\/10.1158\/0008-5472.CAN-19-3147","journal-title":"Cancer Res."},{"issue":"2","key":"1_CR32","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1093\/bioinformatics\/18.2.261","volume":"18","author":"I Shmulevich","year":"2002","unstructured":"Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.: Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261\u2013274 (2002). https:\/\/doi.org\/10.1093\/bioinformatics\/18.2.261","journal-title":"Bioinformatics"},{"key":"1_CR33","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.dam.2013.11.015","volume":"167","author":"T Stephen","year":"2014","unstructured":"Stephen, T., Yusun, T.: Counting inequivalent monotone Boolean functions. Discret. Appl. Math. 167, 15\u201324 (2014). https:\/\/doi.org\/10.1016\/j.dam.2013.11.015","journal-title":"Discret. Appl. Math."},{"key":"1_CR34","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1387\/ijdb.072439ls","volume":"52","author":"L S\u00e1nchez","year":"2008","unstructured":"S\u00e1nchez, L., Chaouiya, C., Thieffry, D.: Segmenting the fly embryo: logical analysis of the role of the segment polarity cross-regulatory module. Int. J. Dev. Biol. 52, 1059\u20131075 (2008). https:\/\/doi.org\/10.1387\/ijdb.072439ls","journal-title":"Int. J. Dev. Biol."},{"key":"1_CR35","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1006\/jtbi.2001.2335","volume":"211","author":"L S\u00e1nchez","year":"2001","unstructured":"S\u00e1nchez, L., Thieffry, D.: A logical analysis of the drosophila gap-gene system. J. Theoret. Biol. 211, 115\u2013141 (2001). https:\/\/doi.org\/10.1006\/jtbi.2001.2335","journal-title":"J. Theoret. Biol."},{"issue":"1","key":"1_CR36","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/S0303-2647(98)00087-2","volume":"50","author":"D Thieffry","year":"1999","unstructured":"Thieffry, D., Romero, D.: The modularity of biological regulatory networks. Biosystems 50(1), 49\u201359 (1999). https:\/\/doi.org\/10.1016\/S0303-2647(98)00087-2","journal-title":"Biosystems"},{"issue":"3","key":"1_CR37","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/0022-5193(73)90247-6","volume":"42","author":"R Thomas","year":"1973","unstructured":"Thomas, R.: Boolean formalization of genetic control circuits. J. Theor. Biol. 42(3), 563\u2013585 (1973). https:\/\/doi.org\/10.1016\/0022-5193(73)90247-6","journal-title":"J. Theor. Biol."},{"issue":"1","key":"1_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0022-5193(05)80350-9","volume":"153","author":"R Thomas","year":"1991","unstructured":"Thomas, R.: Regulatory networks seen as asynchronous automata: a logical description. J. Theor. Biol. 153(1), 1\u201323 (1991). https:\/\/doi.org\/10.1016\/S0022-5193(05)80350-9","journal-title":"J. Theor. Biol."},{"key":"1_CR39","doi-asserted-by":"publisher","unstructured":"Za\u00f1udo, J.G.T., Albert, R.: An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos: Interdiscipl. J. Nonlinear Sci. 23(2), 025111 (2013). https:\/\/doi.org\/10.1063\/1.4809777","DOI":"10.1063\/1.4809777"}],"container-title":["Lecture Notes in Computer Science","Computational Methods in Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-01436-8_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T04:27:35Z","timestamp":1757392055000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-01436-8_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"ISBN":["9783032014351","9783032014368"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-01436-8_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]},"assertion":[{"value":"19 August 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that\u00a0are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"CMSB","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Methods in Systems Biology","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lyon","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":"10 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cmsb2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/cmsb2025.sciencesconf.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}