{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:26:09Z","timestamp":1787232369137,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Scaling Cascades in Complex Systems, project A05","award":["CRC-1114"],"award-info":[{"award-number":["CRC-1114"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The aim of this paper is to investigate the rebinding effect, a phenomenon describing a \u201cshort-time memory\u201d which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov state model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors we are thus able to compute the minimal rebinding effect for nonreversible processes.<\/jats:p>","DOI":"10.1137\/20m1334966","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T12:00:51Z","timestamp":1615896051000},"page":"460-477","source":"Crossref","is-referenced-by-count":0,"title":["Computing the Minimal Rebinding Effect for NonReversible Processes"],"prefix":"10.1137","volume":"19","author":[{"given":"Susanne","family":"R\u00f6hl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcus","family":"Weber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4373-3672","authenticated-orcid":true,"given":"Konstantin","family":"Fackeldey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,3,16]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Gregory R. Bowman, Vijay S. Pande, and Frank No\u00e9,\n                      An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation\n                      , Springer Science & Business Media, New York, 2013.","DOI":"10.1007\/978-94-007-7606-7"},{"key":"atypb2","unstructured":"Susanne R\u00f6hl,\n                      Computing the Minimal Rebinding Effect for Nonreversible Processes\n                      , Master's thesis, Freie Universit\u00e4t Berlin, 2017."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/nla.274"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1186\/1752-0509-5-48"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.sbi.2014.04.002"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-02970-2_2"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.10.026"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1063\/1.5058128"},{"key":"atypb9","unstructured":"Konstantin Fackeldey and Marcus Weber,\n                      GenPCCA - Markov State Models for Non-Equilibrium Steady States\n                      , WIAS Report no. 29, 2017, WIAS."},{"key":"atypb10","unstructured":"Konstantin Fackeldey and Marcus Weber,\n                      Molecular Kinetics for Non-Reversible Chemical Processes\n                      , Manuscript, 2017."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/anie.201201114"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(95)80298-5"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"Douglas A. Lauffenburger and Jennifer Linderman,\n                      Receptors: Models for Binding, Trafficking, and Signaling\n                      , Oxford University Press, Oxford, UK, 1993.","DOI":"10.1093\/oso\/9780195064667.001.0001"},{"key":"atypb14","unstructured":"Axel Schild,\n                      Electron Fluxes During Chemical Processes in the Electronic Ground State\n                      , Ph.D. thesis, Freie Universit\u00e4t Berlin, 2013."},{"key":"atypb15","first-page":"191","author":"Sch\u00fctte Christof","year":"2001","journal-title":"Berlin"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/cbic.201100529"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1517\/17460441.2010.512037"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1002\/chem.201603098"},{"key":"atypb19","unstructured":"Marcus Weber,\n                      Meshless Methods in Conformation Dynamics\n                      , Ph. D. thesis, Freie Universit\u00e4t Berlin, 2006."},{"key":"atypb20","unstructured":"Marcus Weber,\n                      A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator\n                      , habilitation thesis, Freie Universit\u00e4t Berlin, 2011."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1063\/1.4739501"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/13091124X"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/120899959"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1063\/1.3590108"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1063\/1.5064530"},{"key":"atypb26","unstructured":"Axel Schild,\n                      Electron Fluxes During Chemical Processes in the Electronic Ground State\n                      , Ph.D. thesis, Freie Universit\u00e4t Berlin, 2013."}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1334966","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:42:08Z","timestamp":1787229728000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1334966"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1334966"],"URL":"https:\/\/doi.org\/10.1137\/20m1334966","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}