메뉴 건너뛰기




Volumn 6, Issue 2, 2007, Pages 396-416

Stable computation of probability densities for metastable dynamical systems

Author keywords

Aggregation disaggregation; Cluster analysis; Domain decomposition; Dynamical systems; Metastability; Molecular conformations; Sampling

Indexed keywords

BOOLEAN FUNCTIONS; DYNAMICAL SYSTEMS; ELECTRIC NETWORK ANALYSIS; FARM BUILDINGS; LEARNING ALGORITHMS; PROBABILITY; SCHRODINGER EQUATION; TREES (MATHEMATICS);

EID: 43949112186     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/060675423     Document Type: Article
Times cited : (11)

References (41)
  • 1
    • 0035932735 scopus 로고    scopus 로고
    • Smart darting Monte Carlo
    • ANDRICIOAEI, J. STRAUB, AND A. VOTER, Smart darting Monte Carlo, J. Chem. Phys., 114 (2001), pp. 6994-7000.
    • (2001) J. Chem. Phys , vol.114 , pp. 6994-7000
    • ANDRICIOAEI1    STRAUB, J.2    VOTER, A.3
  • 2
    • 0036533049 scopus 로고    scopus 로고
    • A parallel solver for large scale Markov chains
    • M. BENZI AND M. TŮMA, A parallel solver for large scale Markov chains, Appl. Numer. Math., 41 (2002), pp. 135-153.
    • (2002) Appl. Numer. Math , vol.41 , pp. 135-153
    • BENZI, M.1    TŮMA, M.2
  • 3
    • 0030904524 scopus 로고    scopus 로고
    • Novel methods of sampling phase space in the simulation of biological systems
    • B. BERNE AND J. STRAUB, Novel methods of sampling phase space in the simulation of biological systems, Curr. Opin. Struct. Biol., 7 (1997), pp. 181-189.
    • (1997) Curr. Opin. Struct. Biol , vol.7 , pp. 181-189
    • BERNE, B.1    STRAUB, J.2
  • 4
    • 0022093129 scopus 로고    scopus 로고
    • W.-L. CAO AND W. J. STEWART, Iterative aggregation/ disaggregation techniques for nearly uncoupled Markov chains, J. Assoc. Comput. Mach., 32 (1985), pp. 702-719.
    • W.-L. CAO AND W. J. STEWART, Iterative aggregation/ disaggregation techniques for nearly uncoupled Markov chains, J. Assoc. Comput. Mach., 32 (1985), pp. 702-719.
  • 6
    • 0005616050 scopus 로고    scopus 로고
    • Permuting Markov Chains to Nearly Completely Decomposable Form
    • Technical report BU-CEIS-9808, Department of Computer Science and Engineering, Bilkent University, Ankara, Turkey
    • T. DAYAR, Permuting Markov Chains to Nearly Completely Decomposable Form, Technical report BU-CEIS-9808, Department of Computer Science and Engineering, Bilkent University, Ankara, Turkey, 1998, bttp://citeseer.ist.psu.edu/70412.html.
    • (1998)
    • DAYAR, T.1
  • 7
    • 0033709988 scopus 로고    scopus 로고
    • Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains
    • T. DAYAR AND W. J. STEWART, Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains, SIAM J. Sci. Comput., 21 (2000), pp. 1691-1705.
    • (2000) SIAM J. Sci. Comput , vol.21 , pp. 1691-1705
    • DAYAR, T.1    STEWART, W.J.2
  • 8
    • 3042829984 scopus 로고    scopus 로고
    • From molecular dynamics to conformational dynamics in drug design
    • M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds, Springer, Berlin
    • P. DEUFLHAAD, From molecular dynamics to conformational dynamics in drug design, in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds., Springer, Berlin, 2003, pp. 269-287.
    • (2003) Trends in Nonlinear Analysis , pp. 269-287
    • DEUFLHAAD, P.1
  • 9
    • 84862381097 scopus 로고    scopus 로고
    • Molecular conformation dynamics and computational drug design
    • J. M. Hill and R. Moore, eds, SIAM, Philadelphia
    • P. DEUFLHARD AND C. SCHÜTTE, Molecular conformation dynamics and computational drug design, in:, Applied Mathemetics Entering the 21st Century, J. M. Hill and R. Moore, eds., SIAM, Philadelphia, 2004, pp. 91-119.
    • (2004) Applied Mathemetics Entering the 21st Century , pp. 91-119
    • DEUFLHARD, P.1    SCHÜTTE, C.2
  • 10
    • 13544256263 scopus 로고    scopus 로고
    • 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
  • 14
    • 47949121217 scopus 로고    scopus 로고
    • Understanding Molecular Simulation: From Algorithms to Applications
    • Academic Press, San Diego, London
    • D. FRENKEL AND B. SMIT, Understanding Molecular Simulation: From Algorithms to Applications, Comput. Sci. Ser. 1, Academic Press, San Diego, London, 2002.
    • (2002) Comput. Sci. Ser , pp. 1
    • FRENKEL, D.1    SMIT, B.2
  • 15
    • 0000736067 scopus 로고    scopus 로고
    • Simulating normalizing constants: From importance sampling to bridge sampling to path sampling
    • A. GELMAN AND X. MENG, Simulating normalizing constants: From importance sampling to bridge sampling to path sampling, Statist. Sci., 13 (1998), pp. 163-185.
    • (1998) Statist. Sci , vol.13 , pp. 163-185
    • GELMAN, A.1    MENG, X.2
  • 16
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed, The Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • GOLUB, G.H.1    VAN LOAN, C.F.2
  • 17
    • 84893482610 scopus 로고
    • A solution for the best rotation to relate two sets of vectors
    • W. KABSCH, A solution for the best rotation to relate two sets of vectors, Acta Cryst. Sect. A, 32 (1976), pp. 922-923.
    • (1976) Acta Cryst. Sect. A , vol.32 , pp. 922-923
    • KABSCH, W.1
  • 18
    • 12944249776 scopus 로고
    • A discussion of the solution for the best rotation to relate two sets of vectors
    • W. KABSCH, A discussion of the solution for the best rotation to relate two sets of vectors, Acta Cryst. Sect. A, 34 (1978), pp. 827 828.
    • (1978) Acta Cryst. Sect. A , vol.34 , pp. 827-828
    • KABSCH, W.1
  • 20
    • 0000556573 scopus 로고
    • Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains
    • J. R. KOURY, D. F. MCALLISTER, AND W. J. STEWART, Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains, SIAM J. Algebraic Discrete Methods, 5 (1984), pp. 164-186.
    • (1984) SIAM J. Algebraic Discrete Methods , vol.5 , pp. 164-186
    • KOURY, J.R.1    MCALLISTER, D.F.2    STEWART, W.J.3
  • 21
    • 45849120304 scopus 로고    scopus 로고
    • THEMATHWORKS INC. GERMANY, MATLAB 6.5.0, 1994-2005.
    • THEMATHWORKS INC. GERMANY, MATLAB 6.5.0, 1994-2005.
  • 22
    • 21444451325 scopus 로고    scopus 로고
    • X.-L. MENG AND W. H. WONG, Simulating ratios of normalizing constants via a simple identity: A theoretical exploration, Statist. Sinica, 6 (1996), pp. 831-860.
    • X.-L. MENG AND W. H. WONG, Simulating ratios of normalizing constants via a simple identity: A theoretical exploration, Statist. Sinica, 6 (1996), pp. 831-860.
  • 23
    • 0024680811 scopus 로고
    • Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems
    • C. D. MEYER, Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems, SIAM Rev., 31 (1989), pp. 240-272.
    • (1989) SIAM Rev , vol.31 , pp. 240-272
    • MEYER, C.D.1
  • 24
    • 0043256056 scopus 로고
    • Sensitivity of the stationary distribution of a Markov chain
    • C. D. MEYER, Sensitivity of the stationary distribution of a Markov chain, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 715-728.
    • (1994) SIAM J. Matrix Anal. Appl , vol.15 , pp. 715-728
    • MEYER, C.D.1
  • 25
    • 21144460955 scopus 로고
    • Entrywise perturbation theory and error analysis for Markov chains
    • C. A. O'CINNEIDE, Entrywise perturbation theory and error analysis for Markov chains, Numer. Math., 65 (1993), pp. 109-120.
    • (1993) Numer. Math , vol.65 , pp. 109-120
    • O'CINNEIDE, C.A.1
  • 26
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • E. PARZEN, On estimation of a probability density function and mode, Ann. Math. Statist., 33 (1962), pp. 1065-1076.
    • (1962) Ann. Math. Statist , vol.33 , pp. 1065-1076
    • PARZEN, E.1
  • 27
    • 0008441139 scopus 로고
    • Numerical methods in Markov chain modeling
    • B. PHILIPPE, Y. SAAD, AND W. J. STEWART, Numerical methods in Markov chain modeling, Oper. Res., 40 (1992), pp. 1156-1179.
    • (1992) Oper. Res , vol.40 , pp. 1156-1179
    • PHILIPPE, B.1    SAAD, Y.2    STEWART, W.J.3
  • 28
    • 45849126984 scopus 로고    scopus 로고
    • Master's thesis, Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
    • A. RIEMER, Accuracy, Stability, Convergence of Rigorous Thermodynamic Sampling Methods, Master's thesis, Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany, 2006, http://www.zib.de/bib/dipl/RiemerDiplom.pdf.
    • (2006) Accuracy, Stability, Convergence of Rigorous Thermodynamic Sampling Methods
    • RIEMER, A.1
  • 29
    • 0001509947 scopus 로고    scopus 로고
    • Using randomization to break the curse of dimensionality
    • J. RUST, Using randomization to break the curse of dimensionality, Econometrica, 65 (1997), pp. 487-516.
    • (1997) Econometrica , vol.65 , pp. 487-516
    • RUST, J.1
  • 30
    • 45849151823 scopus 로고    scopus 로고
    • CH. SCHÜTTE, Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules, Habilitation thesis, Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany, 1999, http://www.zib.de/bib/habil/index.de.html.
    • CH. SCHÜTTE, Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules, Habilitation thesis, Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany, 1999, http://www.zib.de/bib/habil/index.de.html.
  • 31
    • 13544266845 scopus 로고    scopus 로고
    • Biomolecular conformations can be identified as metastable sets of molecular dynamics
    • X, P. G. Ciarlet and C. Le Bris, eds, North-Holland, Amsterdam
    • CH. SCHÜTTE AND W. HUISINGA, Biomolecular conformations can be identified as metastable sets of molecular dynamics, in Handbook of Numerical Analysis, Vol. X, P. G. Ciarlet and C. Le Bris, eds., North-Holland, Amsterdam, 2003, pp. 699-744.
    • (2003) Handbook of Numerical Analysis , pp. 699-744
    • SCHÜTTE, C.H.1    HUISINGA, W.2
  • 32
    • 0000167458 scopus 로고
    • A smart Monte Carlo technique for free energy simulations of multiconformational molecules. Direct calculations of the conformational populations of organic molecules
    • H. SENDEROWITZ, F. GUARNIERI, AND W. C. STILL, A smart Monte Carlo technique for free energy simulations of multiconformational molecules. Direct calculations of the conformational populations of organic molecules, J. Am. Chem. Soc., 117 (1995), pp. 8211-8219.
    • (1995) J. Am. Chem. Soc , vol.117 , pp. 8211-8219
    • SENDEROWITZ, H.1    GUARNIERI, F.2    STILL, W.C.3
  • 33
    • 0012333020 scopus 로고    scopus 로고
    • Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules
    • H. SENDEROWITZ AND W. C. STILL, Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules, J. Comput. Chem., 19 (1998), pp. 1736-1745.
    • (1998) J. Comput. Chem , vol.19 , pp. 1736-1745
    • SENDEROWITZ, H.1    STILL, W.C.2
  • 34
    • 0001633546 scopus 로고
    • Aggregation of variables in dynamical systems
    • H. A. SIMON AND A. ANDO, Aggregation of variables in dynamical systems, Econometrica, 29 (1961), pp. 111-138.
    • (1961) Econometrica , vol.29 , pp. 111-138
    • SIMON, H.A.1    ANDO, A.2
  • 35
    • 0346922977 scopus 로고    scopus 로고
    • Numerical methods for computing stationary distributions of finite irreducible Markov chains
    • W. Grassmann, ed, Kluwer Academic Publishers, Dordrecht, The Netherlands
    • W. J. STEWART, Numerical methods for computing stationary distributions of finite irreducible Markov chains, in Computational Probability, W. Grassmann, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997, pp. 81-112.
    • (1997) Computational Probability , pp. 81-112
    • STEWART, W.J.1
  • 36
    • 0026880073 scopus 로고
    • Numerical experiments with iteration and aggregation for Markov chains
    • W. J. STEWART AND W. WU, Numerical experiments with iteration and aggregation for Markov chains, ORSA J. Comput., 4 (1992), pp. 336-350.
    • (1992) ORSA J. Comput , vol.4 , pp. 336-350
    • STEWART, W.J.1    WU, W.2
  • 37
    • 36749113356 scopus 로고
    • Monte Carlo study of a phase-separating liquid mixture by umbrella sampling
    • G. M. TORRIE AND J. P. VALLEAU, Monte Carlo study of a phase-separating liquid mixture by umbrella sampling, J. Chem. Phys., 66 (1977), pp. 1402-1408.
    • (1977) J. Chem. Phys , vol.66 , pp. 1402-1408
    • TORRIE, G.M.1    VALLEAU, J.P.2
  • 38
    • 45849097703 scopus 로고    scopus 로고
    • ConfJump: A Fast Biomolecular Sampling Method Which Drills Tunnels through High Mountains
    • 06-26, Zuse Institute Berlin, Berlin, Germany
    • L. WALTER AND M. WEBER, ConfJump: A Fast Biomolecular Sampling Method Which Drills Tunnels through High Mountains, ZIB-Report 06-26, Zuse Institute Berlin, Berlin, Germany, 2006, http:/ /www.zib.de/bib/pub/pw/.
    • (2006) ZIB-Report
    • WALTER, L.1    WEBER, M.2
  • 39
    • 45849139859 scopus 로고    scopus 로고
    • Verlag Dr. Hut, München, Germany, also available online from
    • M. WEBER, Meshless Methods in Conformation Dynamics, Verlag Dr. Hut, München, Germany, 2006; also available online from http://www.zib.de/bib/diss/index.de.html.
    • (2006) Meshless Methods in Conformation Dynamics
    • WEBER, M.1
  • 40
    • 3042789465 scopus 로고    scopus 로고
    • Characterization of Transition States in Conformational Dynamics Using Fuzzy Sets
    • 02-12, Zuse Institute Berlin, Berlin, Germany
    • M. WEBER AND T. GALLIAT, Characterization of Transition States in Conformational Dynamics Using Fuzzy Sets, ZIB-Report 02-12, Zuse Institute Berlin, Berlin, Germany, 2002, http://www.zib.de /bib/pub/pw/.
    • (2002) ZIB-Report
    • WEBER, M.1    GALLIAT, T.2
  • 41
    • 45849115586 scopus 로고    scopus 로고
    • ZIBgridfree - Adaptive Conformation Analysis with Qualified Support of Transition States and Thermodynamic Weights
    • 05-17, Zuse Institute Berlin, Berlin, Germany
    • M. WEBER AND H. MEYER, ZIBgridfree - Adaptive Conformation Analysis with Qualified Support of Transition States and Thermodynamic Weights, ZIB-Report 05-17, Zuse Institute Berlin, Berlin, Germany, 2005, http://www.zib.de/bib/pub/pw/.
    • (2005) ZIB-Report
    • WEBER, M.1    MEYER, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.