{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T17:57:55Z","timestamp":1790791075562,"version":"4.1.0"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2011,4,1]]},"abstract":"<jats:p>In many fields of physics, chemistry, and biology, the characterization of rates and pathways between certain states or species is of fundamental interest. The central mathematical object in such situations is the committor probability\u2014a generalized reaction coordinate that measures the progress of the process as the probability of proceeding to the target state rather than relapsing to the source state. Here, we conduct a numerical analysis of the committor. First, it is shown that committors can be expressed by the stationary eigenfunctions of a modified dynamical operator, thus relating the committors to the dominant eigenfunctions of the original operator. Based on this reformulation, committors can be efficiently computed for systems with large state spaces. Moreover, a sensitivity analysis of the committor is conducted, which allows its statistical uncertainty from estimation to be quantified within a Bayesian framework. The methods are illustrated on two examples of diffusive dynamics: a two-dimensional model potential with three minima, and a three-dimensional model representing protein-ligand binding.<\/jats:p>","DOI":"10.1137\/100789191","type":"journal-article","created":{"date-parts":[[2011,6,25]],"date-time":"2011-06-25T17:45:35Z","timestamp":1309023935000},"page":"545-567","source":"Crossref","is-referenced-by-count":35,"title":["Efficient Computation, Sensitivity, and Error Analysis of Committor Probabilities for Complex Dynamical Processes"],"prefix":"10.1137","volume":"9","author":[{"given":"Jan-Hendrik","family":"Prinz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Held","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeremy C.","family":"Smith","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frank","family":"No\u00e9","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,6,24]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1802674"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0408098102"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.physchem.53.082301.113146"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.030902"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1002\/0471231509.ch1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1063\/1.475393"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2005.07.084"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1021\/ja048285t"},{"key":"R9","unstructured":"G. H. Golub and C. F. vanLoan,\n                      Matrix Computation\n                      , 3rd ed., Johns Hopkins University Press, Baltimore, MD,  1996."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/080715962"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/060670535"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1063\/1.1630572"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1063\/1.1667470"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1021\/jp045546c"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1063\/1.2212942"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.07.032"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/070699500"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.33.423"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1063\/1.2916718"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/j.sbi.2008.01.008"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0905466106"},{"key":"R22","unstructured":"J. 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Zwanzig,\n                      Nonequilibrium Statistical Mechanics\n                      , Oxford University Press, London,  2001.","DOI":"10.1093\/oso\/9780195140187.001.0001"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100789191","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:06:32Z","timestamp":1787227592000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100789191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,1]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,4,1]]}},"alternative-id":["10.1137\/100789191"],"URL":"https:\/\/doi.org\/10.1137\/100789191","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4,1]]}}}