-
1
-
-
0030560429
-
The law of the Euler scheme for stochastic differential equations: II. Convergence rate of the density
-
V. Bally and D. Talay, The law of the Euler scheme for stochastic differential equations: II. Convergence rate of the density, Probability Theory Rel. Fields, 104 (1996), pp. 43-60.
-
(1996)
Probability Theory Rel. Fields
, vol.104
, pp. 43-60
-
-
Bally, V.1
Talay, D.2
-
2
-
-
0000178531
-
Rates of convergence for everywhere-positive Markov chains
-
J. R. Baxter and J. S. Rosenthal, Rates of convergence for everywhere-positive Markov chains, Statist. Probab. Lett., 22 (1995), pp. 333-338.
-
(1995)
Statist. Probab. Lett.
, vol.22
, pp. 333-338
-
-
Baxter, J.R.1
Rosenthal, J.S.2
-
3
-
-
84942286187
-
Pseudo generators for under-resolved molecular dynamics
-
to appear
-
A. Bittracher, C. Hartmann, O. Junge, and P. Koltai, Pseudo generators for under-resolved molecular dynamics, EPJ-Special Topics, (2015), to appear.
-
(2015)
EPJ-Special Topics
-
-
Bittracher, A.1
Hartmann, C.2
Junge, O.3
Koltai, P.4
-
4
-
-
63449118443
-
Using generalized ensemble simulations and Markov state models to identify conformational states
-
G. R. Bowman, X. Huang, and V. S. Pande , Using generalized ensemble simulations and Markov state models to identify conformational states, Methods, 49 (2009), pp. 197-201.
-
(2009)
Methods
, vol.49
, pp. 197-201
-
-
Bowman, G.R.1
Huang, X.2
Pande, V.S.3
-
5
-
-
34247338100
-
Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics
-
J. D. Chodera, N. Singhal, V. S. Pande, K. A. Dill, and W. C. Swope, Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics, J. Chem. Phys., 126 (2007), 155101.
-
(2007)
J. Chem. Phys.
, vol.126
, pp. 155101
-
-
Chodera, J.D.1
Singhal, N.2
Pande, V.S.3
Dill, K.A.4
Swope, W.C.5
-
7
-
-
0005484783
-
The algorithms behind GAIO-Set oriented numerical methods for dynamical systems
-
Springer, Berlin, Heidelberg
-
M. Dellnitz, G. Froyland, and O. Junge, The algorithms behind GAIO-Set oriented numerical methods for dynamical systems, in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer, Berlin, Heidelberg, 2001, p p. 145-174.
-
(2001)
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
, pp. 145-174
-
-
Dellnitz, M.1
Froyland, G.2
Junge, O.3
-
8
-
-
0000371241
-
On the approximati on of complicated dynamical behavior
-
M. Dellnitz and O. Junge, On the approximati on of complicated dynamical behavior, SIAM J. Numer. Anal., 36 (1999), pp. 491-515.
-
(1999)
SIAM J. Numer. Anal.
, vol.36
, pp. 491-515
-
-
Dellnitz, M.1
Junge, O.2
-
9
-
-
0005055199
-
Computation of essential molecular dynamics by subdivision techniques
-
Springer, New York
-
P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte, Computation of essential molecular dynamics by subdivision techniques, in Computational Molecular Dynamics: Challenges, Methods, Ideas, Springer, New York, 1999, pp. 98-115.
-
(1999)
Computational Molecular Dynamics: Challenges, Methods, Ideas
, pp. 98-115
-
-
Deuflhard, P.1
Dellnitz, M.2
Junge, O.3
Schütte, C.4
-
10
-
-
0034370539
-
Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
-
P. Deuflhard, W. Huisinga, A. Fischer, and C. Schütte, Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains, Linear Algebra Appl., 315 (2000), pp. 39-59.
-
(2000)
Linear Algebra Appl.
, vol.315
, pp. 39-59
-
-
Deuflhard, P.1
Huisinga, W.2
Fischer, A.3
Schütte, C.4
-
11
-
-
13544256263
-
Robust Perron cluster analysis in conformation dynamics
-
P. Deuflhard and M. Weber, Robust Perron cluster analysis in conformation dynamics, Linear Algebra Appl., 398 (2005), pp. 161-184.
-
(2005)
Linear Algebra Appl.
, vol.398
, pp. 161-184
-
-
Deuflhard, P.1
Weber, M.2
-
12
-
-
0023140044
-
Multiple conformati onal states of proteins: A molecular dynamics analysis of myoglobin
-
R. Elber and M. Karplus, Multiple conformati onal states of proteins: A molecular dynamics analysis of myoglobin, Science, 235 (1987), pp. 318-321.
-
(1987)
Science
, vol.235
, pp. 318-321
-
-
Elber, R.1
Karplus, M.2
-
13
-
-
0033695467
-
Energy landscape and fluctuations in proteins
-
H. Frauenfelder and B. H. McMahon, Energy landscape and fluctuations in proteins, Ann. Phys., 9 (2000), pp. 655-667.
-
(2000)
Ann. Phys.
, vol.9
, pp. 655-667
-
-
Frauenfelder, H.1
McMahon, B.H.2
-
14
-
-
78149337348
-
Mean field approximation in conformation dynamics
-
G. Friesecke, O. Junge, and P. Koltai, Mean field approximation in conformation dynamics, Multi-scale Model. Simul., 8 (2009), pp. 254-268.
-
(2009)
Multi-scale Model. Simul.
, vol.8
, pp. 254-268
-
-
Friesecke, G.1
Junge, O.2
Koltai, P.3
-
15
-
-
84876146361
-
Estimating long-term behavior of flows without trajectory integration: The infinitesimal generator approach
-
G. Froyland, O. Junge, and P. Koltai, Estimating long-term behavior of flows without trajectory integration: The infinitesimal generator approach, SIAM J. Numer. Anal., 51 (2013), pp. 223-247.
-
(2013)
SIAM J. Numer. Anal.
, vol.51
, pp. 223-247
-
-
Froyland, G.1
Junge, O.2
Koltai, P.3
-
16
-
-
0000603710
-
Time reversal of diffusions
-
U. G. Haussmann and E. Pardoux, Time reversal of diffusions, Ann. Probab., 14 (1986), pp. 1188- 1205.
-
(1986)
Ann. Probab.
, vol.14
, pp. 1188-1205
-
-
Haussmann, U.G.1
Pardoux, E.2
-
17
-
-
15244346736
-
Hypoelliptic second order differential equations
-
L. Hörmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), pp. 147-171.
-
(1967)
Acta Math.
, vol.119
, pp. 147-171
-
-
Hörmander, L.1
-
18
-
-
84873038722
-
-
World Scientific, River Edge, NJ
-
X. Huang, Y. Yao, G. R. Bowman, J. Sun, L. J. Guibas, G. E. Carlsson, and V. S. Pande, Constructing multi-resolution Markov state m odels (MSMs) to elucidate RNA hairpin folding mechanisms, in Pacific Symposium on Biocomputing, Vol. 15, World Scientific, River Edge, NJ, 2010, pp. 228-239.
-
(2010)
Constructing Multi-resolution Markov State M Odels (MSMs) to Elucidate RNA Hairpin Folding Mechanisms in Pacific Symposium on Biocomputing
, vol.15
, pp. 228-239
-
-
Huang, X.1
Yao, Y.2
Bowman, G.R.3
Sun, J.4
Guibas, L.J.5
Carlsson, G.E.6
Pande, V.S.7
-
20
-
-
12844274920
-
Phase transitions and metastability in Markovian and molecular systems
-
W. Huisinga, S. Meyn, and C. Schütte, Phase transitions and metastability in Markovian and molecular systems, Ann. Appl. Probab., 14 (2004), pp. 419-458.
-
(2004)
Ann. Appl. Probab.
, vol.14
, pp. 419-458
-
-
Huisinga, W.1
Meyn, S.2
Schütte, C.3
-
21
-
-
83255166989
-
Metastability and dominant eigenvalues of transfer operators, in New Algorithms for Macromolecular Simulation
-
B. Leimkuhler C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schütte, and R. Skeel, eds. Springer, Berlin, Heidelberg
-
W. Huisinga and B. Schmidt, Metastability and dominant eigenvalues of transfer operators, in New Algorithms for Macromolecular Simulation, B. Leimkuhler, C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schütte, and R. Skeel, eds., Lecture Notes Comput. Sci. Engrg. 49, Springer, Berlin, Heidelberg, 2006, pp. 167-182.
-
(2006)
Lecture Notes Comput. Sci. Engrg.
, vol.49
, pp. 167-182
-
-
Huisinga, W.1
Schmidt, B.2
-
22
-
-
77958604145
-
Discretization of the Frobenius-Perron operator using a sparse Haar tensor basis: The sparse Ulam method
-
O. Junge and P. Koltai, Discretization of the Frobenius-Perron operator using a sparse Haar tensor basis: The sparse Ulam method, SIAM J. Num er. Anal., 47 (2009), pp. 3464-3485.
-
(2009)
SIAM J. Num Er. Anal.
, vol.47
, pp. 3464-3485
-
-
Junge, O.1
Koltai, P.2
-
23
-
-
0003242243
-
Brownian Motion and Stochastic Calculus
-
Springer-Verlag, New York
-
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Grad. Texts Math. 113, Springer-Verlag, New York, 1991.
-
(1991)
Grad. Texts Math.
, vol.113
-
-
Karatzas, I.1
Shreve, S.E.2
-
24
-
-
84876135269
-
Efficient approximation methods for the global long-term behavior of dynamical systems: Theory
-
Ph.D. thesis, TU München, Munich, Germany
-
P. Koltai, Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems: Theory, Algorithms and Examples, Ph.D. thesis, TU München, Munich, Germany, 2010.
-
(2010)
Algorithms and Examples
-
-
Koltai, P.1
-
25
-
-
0002556345
-
Applications of the malliavin calculus, part II
-
S. Kusuoka and D. W. Stroock, Applications of the Malliavin calculus, Part II, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), pp. 1-76.
-
(1985)
J. Fac. Sci. Univ. Tokyo Sect. IA Math.
, vol.32
, pp. 1-76
-
-
Kusuoka, S.1
Stroock, D.W.2
-
26
-
-
0003228410
-
Chaos, fractals, and noise: Stochastic aspects of dynamics
-
Springer-Verlag, New York
-
A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer-Verlag, New York, 1994.
-
(1994)
Appl. Math. Sci.
, vol.97
-
-
Lasota, A.1
Mackey, M.C.2
-
27
-
-
19744380438
-
Geometric ergodicity of some hypo-elliptic diffusions for particle motions
-
J. C. Mattingly and A. M. Stuart, Geometric ergodicity of some hypo-elliptic diffusions for particle motions, Markov Process. Related Fields, 8 (2002), pp. 199-214.
-
(2002)
Markov Process. Related Fields
, vol.8
, pp. 199-214
-
-
Mattingly, J.C.1
Stuart, A.M.2
-
28
-
-
0036789329
-
Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise
-
J. C. Mattingly, A. M. Stuart, and D. J. Higham, Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise, Stochastic Process. Appl., 101 (2002), pp. 185-232.
-
(2002)
Stochastic Process. Appl.
, vol.101
, pp. 185-232
-
-
Mattingly, J.C.1
Stuart, A.M.2
Higham, D.J.3
-
30
-
-
33846184750
-
Transition networks for the comprehensive characterization of complex conformational change in proteins
-
F. Nóe, D. Krachtus, J. C. Smith, and S. Fischer, Transition networks for the comprehensive characterization of complex conformational change in proteins, J. Chem. Theory Comput., 2 (2006), pp. 840-857.
-
(2006)
J. Chem. Theory Comput.
, vol.2
, pp. 840-857
-
-
Nóe, F.1
Krachtus, D.2
Smith, J.C.3
Fischer, S.4
-
32
-
-
0034624691
-
Ligand binding and confor-mational motions in myoglobin
-
A. Ostermann, R. Waschipky, F. G. Parak, and G. Ulrich Nienhaus, Ligand binding and confor-mational motions in myoglobin, Nature, 404 (2000), pp. 205-208.
-
(2000)
Nature
, vol.404
, pp. 205-208
-
-
Ostermann, A.1
Waschipky, R.2
Parak, F.G.3
Ulrich Nienhaus, G.4
-
33
-
-
77956220940
-
Everything you wanted to know about Markov state models but were afraid to ask
-
V. S. Pande, K. Beauchamp, and G. R. Bowm an, Everything you wanted to know about Markov state models but were afraid to ask, Methods, 52 (2010), pp. 99-105.
-
(2010)
Methods
, vol.52
, pp. 99-105
-
-
Pande, V.S.1
Beauchamp, K.2
Bowman, G.R.3
-
34
-
-
77954205385
-
Multiscale methods: Averaging and homogenization
-
Springer, New York
-
G. A. Pavliotis and A. M. Stuart, Multiscale Methods: Averaging and Homogenization, Texts Appl. Math. 53, Springer, New York, 2008.
-
(2008)
Texts Appl. Math.
, vol.53
-
-
Pavliotis, G.A.1
Stuart, A.M.2
-
36
-
-
79957488000
-
Markov models of molecular kinetics: Generation and validation
-
J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J. D. Chodera, C. Schütte, and F. Nóe, Markov models of molecular kinetics: Generation and validation, J. Chem. Phys., 134 (2011), 174105.
-
(2011)
J. Chem. Phys.
, vol.134
, pp. 174105
-
-
Prinz, J.-H.1
Wu, H.2
Sarich, M.3
Keller, B.4
Senne, M.5
Held, M.6
Chodera, J.D.7
Schütte, C.8
Nóe, F.9
-
37
-
-
84878874568
-
Fuzzy spectral clustering by PCCA+: Application to Markov state models and data classification
-
S. Röblitz and M. Weber, Fuzzy spectral clustering by PCCA+: Application to Markov state models and data classification, Adv. Data Anal. Classification, 7 (2013), pp. 147-179.
-
(2013)
Adv. Data Anal. Classification
, vol.7
, pp. 147-179
-
-
Röblitz, S.1
Weber, M.2
-
38
-
-
0003767327
-
-
ZIB-Report SC-99-18
-
C. Schütte, Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules, ZIB-Report SC-99-18, 1999.
-
(1999)
Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules
-
-
Schütte, C.1
-
39
-
-
2442600512
-
Transfer operator approach to conformational dynamics in biomolecular systems
-
B. Fiedler, ed. Springer Berlin, Heidelberg
-
C. Schütte, W. Huisinga, and P. Deuflhard, Transfer operator approach to conformational dynamics in biomolecular systems, in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, B. Fiedler, ed., Springer, Berlin, Heidelberg, 2001, pp. 191-223.
-
(2001)
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
, pp. 191-223
-
-
Schütte, C.1
Huisinga, W.2
Deuflhard, P.3
-
40
-
-
79958151345
-
Markov state models based on milestoning
-
C. Schütte, F. Nóe, J. Lu, M. Sarich, and E. Vanden-Eijnden, Markov state models based on milestoning, J. Chem. Phys., 134 (2011), 204105.
-
(2011)
J. Chem. Phys.
, vol.134
, pp. 204105
-
-
Schütte, C.1
Nóe, F.2
Lu, J.3
Sarich, M.4
Vanden-Eijnden, E.5
-
41
-
-
84884402408
-
Metastability and markov state models in molecular dynamics
-
New York
-
C. Schütte and M. Sarich, Metastability and Markov State Models in Molecular Dynamics, Courant Lect. Notes Math., New York, 2013.
-
(2013)
Courant Lect. Notes Math.
-
-
Schütte, C.1
Sarich, M.2
-
43
-
-
77951688892
-
Transition-path theory and path-finding algorithms for the study of rare events
-
E. Vanden-Eijnden, Transition-path theory and path-finding algorithms for the study of rare events, Ann. Rev. Phys. Chem., 61 (2010), pp. 391-420.
-
(2010)
Ann. Rev. Phys. Chem.
, vol.61
, pp. 391-420
-
-
Vanden-Eijnden, E.1
-
46
-
-
17044437988
-
Metastability, conformation dynamics, and transition pathways in complex systems
-
Springer, New York
-
E. Weinan and E. Vanden-Eijnden, Metastability, conformation dynamics, and transition pathways in complex systems, in Multiscale Modelling and Simulation, Springer, New York, 2004, pp. 35-68.
-
(2004)
Multiscale Modelling and Simulation
, pp. 35-68
-
-
Weinan, E.1
Vanden-Eijnden, E.2
-
47
-
-
33747589472
-
Towards a theory of transition paths
-
E. Weinan and E. Vanden-Eijnden, Towards a theory of transition paths, J. Statist. Phys., 123 (2006), pp. 503-523.
-
(2006)
J. Statist. Phys.
, vol.123
, pp. 503-523
-
-
Weinan, E.1
Vanden-Eijnden, E.2
-
48
-
-
0003687335
-
Applications to mathematical physics
-
Springer-Verlag, New York
-
E. Zeidler, Applied Functional Analysis, Applications to Mathematical Physics, Appl. Math. Sci. 108, Springer-Verlag, New York, 1995.
-
(1995)
Appl. Math. Sci.
, vol.108
-
-
Zeidler, E.1
-
49
-
-
0032482925
-
Conformation gating as a mechanism for enzyme specificity
-
H.-X. Zhou, S. T. Wlodek, and J. A. McCammon, Conformation gating as a mechanism for enzyme specificity, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 9280-9283.
-
(1998)
Proc. Natl. Acad. Sci. USA
, vol.95
, pp. 9280-9283
-
-
Zhou, H.-X.1
Wlodek, S.T.2
McCammon, J.A.3
|