{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T14:59:05Z","timestamp":1777733945652,"version":"3.51.4"},"reference-count":80,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T00:00:00Z","timestamp":1507766400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CRC 1114"],"award-info":[{"award-number":["CRC 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006188","name":"Einstein Stiftung Berlin","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006188","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s00332-017-9415-0","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T13:59:22Z","timestamp":1507816762000},"page":"471-512","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["Transition Manifolds of Complex Metastable Systems"],"prefix":"10.1007","volume":"28","author":[{"given":"Andreas","family":"Bittracher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P\u00e9ter","family":"Koltai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Klus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralf","family":"Banisch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Dellnitz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Sch\u00fctte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"issue":"4","key":"9415_CR1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0167-7152(94)00085-M","volume":"22","author":"JR Baxter","year":"1995","unstructured":"Baxter, J.R., Rosenthal, J.S.: Rates of convergence for everywhere-positive Markov chains. Stat. Probab. Lett. 22(4), 333\u2013338 (1995)","journal-title":"Stat. Probab. Lett."},{"issue":"17","key":"9415_CR2","doi-asserted-by":"crossref","first-page":"174118","DOI":"10.1063\/1.4704810","volume":"136","author":"NB Becker","year":"2012","unstructured":"Becker, N.B., Allen, R.J., ten Wolde, P.R.: Non-stationary forward flux sampling. J. Chem. Phys. 136(17), 174118 (2012)","journal-title":"J. Chem. Phys."},{"issue":"3","key":"9415_CR3","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1073\/pnas.0910390107","volume":"107","author":"RB Best","year":"2010","unstructured":"Best, R.B., Hummer, G.: Coordinate-dependent diffusion in protein folding. Proc. Natl. Acad. Sci. 107(3), 1088\u20131093 (2010)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"3","key":"9415_CR4","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1137\/14099872X","volume":"14","author":"A Bittracher","year":"2015","unstructured":"Bittracher, A., Koltai, P., Junge, O.: Pseudogenerators of spatial transfer operators. SIAM J. Appl. Dyn. Syst. 14(3), 1478\u20131517 (2015)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9415_CR5","doi-asserted-by":"crossref","first-page":"69","DOI":"10.4171\/jems\/22","volume":"7","author":"A Bovier","year":"2002","unstructured":"Bovier, A., Gayrard, V., Klein, M.: Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues. J. Eur. Math. Soc. 7, 69\u201399 (2002)","journal-title":"J. Eur. Math. Soc."},{"key":"9415_CR6","doi-asserted-by":"crossref","unstructured":"Bowman, G.R., Pande, V.S., No\u00e9, F. (eds): An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation, volume 797 of Advances in Experimental Medicine and Biology. Springer, Berlin (2014)","DOI":"10.1007\/978-94-007-7606-7"},{"issue":"13","key":"9415_CR7","doi-asserted-by":"crossref","first-page":"6369","DOI":"10.1073\/pnas.90.13.6369","volume":"90","author":"CJ Camacho","year":"1993","unstructured":"Camacho, C.J., Thirumalai, D.: Kinetics and thermodynamics of folding in model proteins. Proc. Natl. Acad. Sci. 90(13), 6369\u20136372 (1993)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9415_CR8","doi-asserted-by":"crossref","unstructured":"Chiavazzo, E., Coifman, R.R., Covino, R., Gear, C.W., Georgiou, A.S., Hummer, G., Kevrekidis, I.G.: iMapD: intrinsic map dynamics exploration for uncharted effective free energy landscapes. arXiv preprint arXiv:1701.01513 (2016)","DOI":"10.1073\/pnas.1621481114"},{"key":"9415_CR9","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.sbi.2014.04.002","volume":"25","author":"JD Chodera","year":"2014","unstructured":"Chodera, J.D., No\u00e9, F.: Markov state models of biomolecular conformational dynamics. Curr. Opin. Struct. Biol. 25, 135\u2013144 (2014)","journal-title":"Curr. Opin. Struct. Biol."},{"issue":"9","key":"9415_CR10","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.1002\/cphc.200400669","volume":"6","author":"G Ciccotti","year":"2005","unstructured":"Ciccotti, G., Kapral, R., Vanden-Eijnden, E.: Blue moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics. ChemPhysChem 6(9), 1809\u20131814 (2005)","journal-title":"ChemPhysChem"},{"issue":"1","key":"9415_CR11","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.acha.2006.04.006","volume":"21","author":"RR Coifman","year":"2006","unstructured":"Coifman, R.R., Lafon, S.: Diffusion maps. Appl. Comput. Harmon. Anal. 21(1), 5\u201330 (2006)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"2","key":"9415_CR12","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1137\/070696325","volume":"7","author":"RR Coifman","year":"2008","unstructured":"Coifman, R.R., Kevrekidis, I.G., Lafon, S., Maggioni, M., Nadler, B.: Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul. 7(2), 842\u2013864 (2008)","journal-title":"Multiscale Model. Simul."},{"issue":"1","key":"9415_CR13","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1137\/140970951","volume":"15","author":"M Crosskey","year":"2017","unstructured":"Crosskey, M., Maggioni, M.: ATLAS: a geometric approach to learning high-dimensional stochastic systems near manifolds. Multiscale Model. Simul. 15(1), 110\u2013156 (2017)","journal-title":"Multiscale Model. Simul."},{"issue":"14","key":"9415_CR14","doi-asserted-by":"crossref","first-page":"144120","DOI":"10.1063\/1.2829861","volume":"128","author":"E Darve","year":"2008","unstructured":"Darve, E., Rodr\u00edguez-G\u00f3mez, D., Pohorille, A.: Adaptive biasing force method for scalar and vector free energy calculations. J. Chem. Phys. 128(14), 144120 (2008)","journal-title":"J. Chem. Phys."},{"key":"9415_CR15","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/978-3-540-87706-6_3","volume-title":"Advanced Computer Simulation Approaches for Soft Matter Sciences III","author":"C Dellago","year":"2009","unstructured":"Dellago, C., Bolhuis, P.G.: Transition path sampling and other advanced simulation techniques for rare events. In: Holm, C., Kremer, K. (eds.) Advanced Computer Simulation Approaches for Soft Matter Sciences III, pp. 167\u2013233. Springer, Berlin (2009)"},{"issue":"3","key":"9415_CR16","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s002110050240","volume":"75","author":"M Dellnitz","year":"1997","unstructured":"Dellnitz, M., Hohmann, A.: A subdivision algorithm for the computation of unstable manifolds and global attractors. Numer. Math. 75(3), 293\u2013317 (1997)","journal-title":"Numer. Math."},{"issue":"2","key":"9415_CR17","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1137\/S0036142996313002","volume":"36","author":"M Dellnitz","year":"1999","unstructured":"Dellnitz, M., Junge, O.: On the approximation of complicated dynamical behavior. SIAM J. Numer. Anal. 36(2), 491\u2013515 (1999)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9415_CR18","first-page":"93","volume":"3","author":"M Dellnitz","year":"2016","unstructured":"Dellnitz, M., von Molo, M.H., Ziessler, A.: On the computation of attractors for delay differential equations. J. Comput. Dyn. 3(1), 93\u2013112 (2016)","journal-title":"J. Comput. Dyn."},{"issue":"1","key":"9415_CR19","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1137\/100798910","volume":"10","author":"N Djurdjevac","year":"2012","unstructured":"Djurdjevac, N., Sarich, M., Sch\u00fctte, C.: Estimating the eigenvalue error of Markov state models. Multiscale Model. Simul. 10(1), 61\u201381 (2012)","journal-title":"Multiscale Model. Simul."},{"issue":"3","key":"9415_CR20","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1137\/151004896","volume":"15","author":"CJ Dsilva","year":"2016","unstructured":"Dsilva, C.J., Talmon, R., Gear, C.W., Coifman, R.R., Kevrekidis, I.G.: Data-driven reduction for a class of multiscale fast\u2013slow stochastic dynamical systems. SIAM J. Appl. Dyn. Syst. 15(3), 1327\u20131351 (2016)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"1","key":"9415_CR21","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1063\/1.475393","volume":"108","author":"R Du","year":"1998","unstructured":"Du, R., Pande, V.S., Grosberg, A.Y., Tanaka, T., Shakhnovich, E.S.: On the transition coordinate for protein folding. J. Chem. Phys. 108(1), 334\u2013350 (1998)","journal-title":"J. Chem. Phys."},{"key":"9415_CR22","unstructured":"E, W., Engquist, B.: The heterogenous multiscale method. Commun. Math. Sci. 1(1), 87\u2013132 (2003)"},{"key":"9415_CR23","unstructured":"E, W., Vanden-Eijnden, E.: Towards a theory of transition paths. J. Stat. Phys 123(3), 503\u2013523 (2006)"},{"key":"9415_CR24","unstructured":"E, W., Vanden-Eijnden, E.: Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem 61(1), 391\u2013420 (2010)"},{"key":"9415_CR25","doi-asserted-by":"crossref","unstructured":"E, W., Ren, W., Vanden-Eijnden, E.: String method for the study of rare events. Phys. Rev. B 66(5), 052301 (2002)","DOI":"10.1103\/PhysRevB.66.052301"},{"key":"9415_CR26","doi-asserted-by":"crossref","first-page":"10880","DOI":"10.1063\/1.1738640","volume":"120","author":"AK Faradjian","year":"2004","unstructured":"Faradjian, A.K., Elber, R.: Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120, 10880\u201310889 (2004)","journal-title":"J. Chem. Phys."},{"key":"9415_CR27","volume-title":"Geometric Measure Theory","author":"H Federer","year":"1969","unstructured":"Federer, H.: Geometric Measure Theory, vol. 1996. Springer, New York (1969)"},{"key":"9415_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0611-8","volume-title":"Random Perturbations of Dynamical Systems","author":"M Freidlin","year":"1998","unstructured":"Freidlin, M., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer, New York (1998)"},{"issue":"4","key":"9415_CR29","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1137\/130943637","volume":"13","author":"G Froyland","year":"2014","unstructured":"Froyland, G., Gottwald, G., Hammerlindl, A.: A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM J. Appl. Dyn. Syst. 13(4), 1816\u20131846 (2014)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9415_CR30","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.physd.2016.04.010","volume":"328","author":"G Froyland","year":"2016","unstructured":"Froyland, G., Gottwald, G.A., Hammerlindl, A.: A trajectory-free framework for analysing multiscale systems. Phys. D Nonlinear Phenom. 328, 34\u201343 (2016)","journal-title":"Phys. D Nonlinear Phenom."},{"issue":"1","key":"9415_CR31","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1214\/aoap\/1075828057","volume":"14","author":"W Huisinga","year":"2004","unstructured":"Huisinga, W., Meyn, S., Sch\u00fctte, C.: Phase transitions and metastability in Markovian and molecular systems. Ann. Appl. Probab. 14(1), 419\u2013458 (2004)","journal-title":"Ann. Appl. Probab."},{"issue":"5","key":"9415_CR32","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1088\/0951-7715\/12\/5\/303","volume":"12","author":"B Hunt","year":"1999","unstructured":"Hunt, B., Kaloshin, V.: Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces. Nonlinearity 12(5), 1263\u20131275 (1999)","journal-title":"Nonlinearity"},{"issue":"5","key":"9415_CR33","doi-asserted-by":"crossref","first-page":"3464","DOI":"10.1137\/080716864","volume":"47","author":"O Junge","year":"2009","unstructured":"Junge, O., Koltai, P.: Discretization of the Frobenius\u2013Perron operator using a sparse Haar tensor basis: the sparse Ulam method. SIAM J. Numer. Anal. 47(5), 3464\u20133485 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9415_CR34","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1146\/annurev.physchem.59.032607.093610","volume":"60","author":"IG Kevrekidis","year":"2009","unstructured":"Kevrekidis, I.G., Samaey, G.: Equation-free multiscale computation: algorithms and applications. Annu. Rev. Phys. Chem. 60(1), 321\u2013344 (2009)","journal-title":"Annu. Rev. Phys. Chem."},{"issue":"1","key":"9415_CR35","first-page":"51","volume":"3","author":"S Klus","year":"2016","unstructured":"Klus, S., Koltai, P., Sch\u00fctte, C.: On the numerical approximation of the Perron\u2013Frobenius and Koopman operator. J. Comput. Dyn. 3(1), 51\u201379 (2016)","journal-title":"J. Comput. Dyn."},{"key":"9415_CR36","doi-asserted-by":"crossref","unstructured":"Klus, S., N\u00fcske, F., Koltai, P., Wu, H., Kevrekidis, I., Sch\u00fctte, C., No\u00e9, F.: Data-driven model reduction and transfer operator approximation. ArXiv e-prints (2017)","DOI":"10.1007\/s00332-017-9437-7"},{"issue":"1","key":"9415_CR37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02289565","volume":"29","author":"JB Kruskal","year":"1964","unstructured":"Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29(1), 1\u201327 (1964a)","journal-title":"Psychometrika"},{"issue":"2","key":"9415_CR38","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02289694","volume":"29","author":"JB Kruskal","year":"1964","unstructured":"Kruskal, J.B.: Nonmetric multidimensional scaling: a numerical method. Psychometrika 29(2), 115\u2013129 (1964b)","journal-title":"Psychometrika"},{"issue":"8","key":"9415_CR39","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1002\/jcc.540130812","volume":"13","author":"S Kumar","year":"1992","unstructured":"Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., Kollman, P.A.: The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comput. Chem. 13(8), 1011\u20131021 (1992)","journal-title":"J. Comput. Chem."},{"issue":"12","key":"9415_CR40","doi-asserted-by":"crossref","first-page":"126601","DOI":"10.1088\/0034-4885\/71\/12\/126601","volume":"71","author":"A Laio","year":"2008","unstructured":"Laio, A., Gervasio, F.L.: Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys. 71(12), 126601 (2008)","journal-title":"Rep. Prog. Phys."},{"issue":"20","key":"9415_CR41","doi-asserted-by":"crossref","first-page":"12562","DOI":"10.1073\/pnas.202427399","volume":"99","author":"A Laio","year":"2002","unstructured":"Laio, A., Parrinello, M.: Escaping free-energy minima. Proc. Natl. Acad. Sci. 99(20), 12562\u201312566 (2002)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"9","key":"9415_CR42","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1088\/0951-7715\/23\/9\/006","volume":"23","author":"F Legoll","year":"2010","unstructured":"Legoll, F., Leli\u00e8vre, T.: Effective dynamics using conditional expectations. Nonlinearity 23(9), 2131 (2010)","journal-title":"Nonlinearity"},{"issue":"10\u201311","key":"9415_CR43","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1080\/08927022.2014.907898","volume":"40","author":"W Li","year":"2014","unstructured":"Li, W., Ma, A.: Recent developments in methods for identifying reaction coordinates. Mol. Simul. 40(10\u201311), 784\u2013793 (2014)","journal-title":"Mol. Simul."},{"issue":"4","key":"9415_CR44","first-page":"07B619_1","volume":"141","author":"J Lu","year":"2014","unstructured":"Lu, J., Vanden-Eijnden, E.: Exact dynamical coarse-graining without time-scale separation. J. Chem. Phys. 141(4), 07B619_1 (2014)","journal-title":"J. Chem. Phys."},{"key":"9415_CR45","doi-asserted-by":"crossref","first-page":"6769","DOI":"10.1021\/jp045546c","volume":"109","author":"A Ma","year":"2005","unstructured":"Ma, A., Dinner, A.R.: Automatic method for identifying reaction coordinates in complex systems. J. Phys. Chem. B 109, 6769\u20136779 (2005)","journal-title":"J. Phys. Chem. B"},{"issue":"1","key":"9415_CR46","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.cplett.2006.05.062","volume":"426","author":"L Maragliano","year":"2006","unstructured":"Maragliano, L., Vanden-Eijnden, E.: A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chem. Phys. Lett. 426(1), 168\u2013175 (2006)","journal-title":"Chem. Phys. Lett."},{"issue":"2","key":"9415_CR47","first-page":"199","volume":"8","author":"JC Mattingly","year":"2002","unstructured":"Mattingly, J.C., Stuart, A.M.: Geometric ergodicity of some hypo-elliptic diffusions for particle motions. Markov Process. Relat. Fields 8(2), 199\u2013214 (2002)","journal-title":"Markov Process. Relat. Fields"},{"issue":"2","key":"9415_CR48","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0304-4149(02)00150-3","volume":"101","author":"JC Mattingly","year":"2002","unstructured":"Mattingly, J.C., Stuart, A.M., Higham, D.J.: Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Stoch. Process. Appl. 101(2), 185\u2013232 (2002)","journal-title":"Stoch. Process. Appl."},{"issue":"4","key":"9415_CR49","doi-asserted-by":"crossref","first-page":"044109","DOI":"10.1063\/1.4974306","volume":"146","author":"RT McGibbon","year":"2017","unstructured":"McGibbon, R.T., Husic, B.E., Pande, V.S.: Identification of simple reaction coordinates from complex dynamics. J. Chem. Phys. 146(4), 044109 (2017)","journal-title":"J. Chem. Phys."},{"issue":"3","key":"9415_CR50","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1137\/070699500","volume":"7","author":"P Metzner","year":"2009","unstructured":"Metzner, P., Sch\u00fctte, C., Vanden-Eijnden, E.: Transition path theory for Markov jump processes. Multiscale Model. Simul. 7(3), 1192\u20131219 (2009)","journal-title":"Multiscale Model. Simul."},{"issue":"1","key":"9415_CR51","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.physa.2004.04.033","volume":"340","author":"D Moroni","year":"2004","unstructured":"Moroni, D., van Erp, T.S., Bolhuis, P.G.: Investigating rare events by transition interface sampling. Phys. A Stat. Mech. Appl. 340(1), 395\u2013401 (2004)","journal-title":"Phys. A Stat. Mech. Appl."},{"issue":"1","key":"9415_CR52","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.acha.2005.07.004","volume":"21","author":"B Nadler","year":"2006","unstructured":"Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Appl. Comput. Harmon. Anal. 21(1), 113\u2013127 (2006)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"2","key":"9415_CR53","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1137\/110858616","volume":"11","author":"F No\u00e9","year":"2013","unstructured":"No\u00e9, F., N\u00fcske, F.: A variational approach to modeling slow processes in stochastic dynamical systems. Multiscale Model. Simul. 11(2), 635\u2013655 (2013)","journal-title":"Multiscale Model. Simul."},{"key":"9415_CR54","doi-asserted-by":"crossref","first-page":"19011","DOI":"10.1073\/pnas.0905466106","volume":"106","author":"F No\u00e9","year":"2009","unstructured":"No\u00e9, F., Sch\u00fctte, C., Vanden-Eijnden, E., Reich, L., Weikl, T.R.: Constructing the full ensemble of folding pathways from short off-equilibrium simulations. Proc. Natl. Acad. Sci. 106, 19011\u201319016 (2009)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"1","key":"9415_CR55","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.ymeth.2010.06.002","volume":"52","author":"VS Pande","year":"2010","unstructured":"Pande, V.S., Beauchamp, K., Bowman, G.R.: Everything you wanted to know about Markov state models but were afraid to ask. Methods 52(1), 99\u2013105 (2010)","journal-title":"Methods"},{"key":"9415_CR56","volume-title":"Multiscale Methods: Averaging and Homogenization","author":"G Pavliotis","year":"2008","unstructured":"Pavliotis, G., Stuart, A.: Multiscale Methods: Averaging and Homogenization. Springer, Berlin (2008)"},{"issue":"1","key":"9415_CR57","doi-asserted-by":"crossref","first-page":"015102","DOI":"10.1063\/1.4811489","volume":"139","author":"G P\u00e9rez-Hern\u00e1ndez","year":"2013","unstructured":"P\u00e9rez-Hern\u00e1ndez, G., Paul, F., Giorgino, T., De Fabritiis, G., No\u00e9, F.: Identification of slow molecular order parameters for Markov model construction. J. Chem. Phys. 139(1), 015102 (2013)","journal-title":"J. Chem. Phys."},{"issue":"17","key":"9415_CR58","doi-asserted-by":"crossref","first-page":"174101","DOI":"10.1063\/1.4707167","volume":"136","author":"ZD Pozun","year":"2012","unstructured":"Pozun, Z.D., Hansen, K., Sheppard, D., Rupp, M., Mller, K.-R., Henkelman, G.: Optimizing transition states via kernel-based machine learning. J. Chem. Phys. 136(17), 174101 (2012)","journal-title":"J. Chem. Phys."},{"issue":"13","key":"9415_CR59","doi-asserted-by":"crossref","first-page":"134109","DOI":"10.1063\/1.2013256","volume":"123","author":"W Ren","year":"2005","unstructured":"Ren, W., Vanden-Eijnden, E., Maragakis, P., E, W.: Transition pathways in complex systems: application of the finite-temperature string method to the alanine dipeptide. J. Chem. Phys. 123(13), 134109 (2005)","journal-title":"J. Chem. Phys."},{"issue":"5","key":"9415_CR60","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1088\/0951-7715\/18\/5\/013","volume":"18","author":"JC Robinson","year":"2005","unstructured":"Robinson, J.C.: A topological delay embedding theorem for infinite-dimensional dynamical systems. Nonlinearity 18(5), 2135\u20132143 (2005)","journal-title":"Nonlinearity"},{"issue":"4","key":"9415_CR61","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1137\/090764049","volume":"8","author":"M Sarich","year":"2010","unstructured":"Sarich, M., No\u00e9, F., Sch\u00fctte, C.: On the approximation quality of Markov state models. Multiscale Model. Simul. 8(4), 1154\u20131177 (2010)","journal-title":"Multiscale Model. Simul."},{"issue":"3","key":"9415_CR62","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/BF01053745","volume":"65","author":"T Sauer","year":"1991","unstructured":"Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. J. Stat. Phys. 65(3), 579\u2013616 (1991)","journal-title":"J. Stat. Phys."},{"issue":"2","key":"9415_CR63","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/10618600.1992.10477008","volume":"1","author":"MJ Schervish","year":"1992","unstructured":"Schervish, M.J., Carlin, B.P.: On the convergence of successive substitution sampling. J. Comput. Graph. Stat. 1(2), 111\u2013127 (1992)","journal-title":"J. Comput. Graph. Stat."},{"key":"9415_CR64","doi-asserted-by":"crossref","unstructured":"Sch\u00fctte, C., Sarich, M.: Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis. Algorithmic Approaches. Courant Lecture Notes in Mathematics, vol. 24. American Mathematical Society (2013)","DOI":"10.1090\/cln\/024"},{"issue":"1","key":"9415_CR65","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1006\/jcph.1999.6231","volume":"151","author":"C Sch\u00fctte","year":"1999","unstructured":"Sch\u00fctte, C., Fischer, A., Huisinga, W., Deuflhard, P.: A direct approach to conformational dynamics based on hybrid Monte Carlo. J. Comput. Phys. 151(1), 146\u2013168 (1999)","journal-title":"J. Comput. Phys."},{"key":"9415_CR66","doi-asserted-by":"publisher","unstructured":"Sch\u00fctte, C., No\u00e9, F., Lu, J., Sarich, M., Vanden-Eijnden, E.: Markov state models based on milestoning. J. Chem. Phys. 134(20), 204105 (2011). doi: 10.1063\/1.3590108","DOI":"10.1063\/1.3590108"},{"issue":"38","key":"9415_CR67","doi-asserted-by":"crossref","first-page":"16090","DOI":"10.1073\/pnas.0905547106","volume":"106","author":"A Singer","year":"2009","unstructured":"Singer, A., Erban, R., Kevrekidis, I.G., Coifman, R.R.: Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proc. Natl. Acad. Sci. 106(38), 16090\u2013160955 (2009)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"15","key":"9415_CR68","doi-asserted-by":"crossref","first-page":"5860","DOI":"10.1063\/1.471317","volume":"104","author":"N Socci","year":"1996","unstructured":"Socci, N., Onuchic, J.N., Wolynes, P.G.: Diffusive dynamics of the reaction coordinate for protein folding funnels. J. Chem. Phys. 104(15), 5860\u20135868 (1996)","journal-title":"J. Chem. Phys."},{"key":"9415_CR69","doi-asserted-by":"crossref","unstructured":"Takens, F.: Detecting strange attractors in turbulence. In: Rand, D., Young, L.-S. (eds.) Springer Lecture Notes in Mathematics, vol. 898, pp. 366\u2013381. Springer, Berlin (1981)","DOI":"10.1007\/BFb0091924"},{"issue":"5500","key":"9415_CR70","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319\u20132323 (2000)","journal-title":"Science"},{"issue":"2","key":"9415_CR71","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0021-9991(77)90121-8","volume":"23","author":"GM Torrie","year":"1977","unstructured":"Torrie, G.M., Valleau, J.P.: Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23(2), 187\u2013199 (1977)","journal-title":"J. Comput. Phys."},{"key":"9415_CR72","doi-asserted-by":"crossref","DOI":"10.1515\/9780691213101","volume-title":"Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators","author":"LN Trefethen","year":"2005","unstructured":"Trefethen, L.N., Embree, M.: Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press, Princeton (2005)"},{"key":"9415_CR73","doi-asserted-by":"crossref","unstructured":"Vanden-Eijnden, E.: Transition path theory. In: Ferrario, M., Ciccotti, G., Binder, K. (eds.) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, vol. 1, pp. 453\u2013493 (2006)","DOI":"10.1007\/3-540-35273-2_13"},{"issue":"2","key":"9415_CR74","doi-asserted-by":"crossref","first-page":"495","DOI":"10.4310\/CMS.2007.v5.n2.a14","volume":"5","author":"E Vanden-Eijnden","year":"2007","unstructured":"Vanden-Eijnden, E.: On HMM-like integrators and projective integration methods for systems with multiple time scales. Commun. Math. Sci. 5(2), 495\u2013505 (2007)","journal-title":"Commun. Math. Sci."},{"key":"9415_CR75","unstructured":"Weber, M.: Meshless methods in conformation dynamics. Ph.D. thesis, FU Berlin (2006)"},{"key":"9415_CR76","unstructured":"Weber, M.: A subspace approach to molecular Markov state models via a new infinitesimal generator. Habilitation thesis (2012)"},{"key":"9415_CR77","doi-asserted-by":"crossref","first-page":"124133","DOI":"10.1063\/1.4978501","volume":"146","author":"M Weber","year":"2017","unstructured":"Weber, M., Fackeldey, K., Sch\u00fctte, C.: Set-free Markov state model building. J. Chem. Phys. 146, 124133 (2017)","journal-title":"J. Chem. Phys."},{"issue":"3","key":"9415_CR78","doi-asserted-by":"crossref","first-page":"645","DOI":"10.2307\/1968482","volume":"37","author":"H Whitney","year":"1936","unstructured":"Whitney, H.: Differentiable manifolds. Ann. Math. 37(3), 645\u2013680 (1936)","journal-title":"Ann. Math."},{"key":"9415_CR79","doi-asserted-by":"publisher","first-page":"367","DOI":"10.3390\/e19070367","volume":"19","author":"W Zhang","year":"2017","unstructured":"Zhang, W., Schuette, C.: Reliable approximation of long relaxation timescales in molecular dynamics. Entropy 19, 367 (2017). doi: 10.3390\/e19070367","journal-title":"Entropy"},{"key":"9415_CR80","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1039\/C6FD00147E","volume":"195","author":"W Zhang","year":"2016","unstructured":"Zhang, W., Hartmann, C., Sch\u00fctte, C.: Effective dynamics along given reaction coordinates, and reaction rate theory. Faraday Discuss. 195, 365\u2013394 (2016)","journal-title":"Faraday Discuss."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-017-9415-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9415-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9415-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T11:21:40Z","timestamp":1750936900000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-017-9415-0"}},"subtitle":["Theory and Data-Driven Computation of Effective Dynamics"],"short-title":[],"issued":{"date-parts":[[2017,10,12]]},"references-count":80,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["9415"],"URL":"https:\/\/doi.org\/10.1007\/s00332-017-9415-0","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,12]]}}}