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7 Bibliography[16] I. Horenko, E. Dittmer, A. Fischer, and C. Schütte: Automated Model Reduction for ComplexSystems exhibiting Metastability, Mult. Mod. Sim., 5 (3). pp. 802-827. Official URL:http://dx.doi.org/10.1137/050623310 (2005).[17] I. Horenko, E. Dittmer, and C. Schütte: Reduced Stochastic Models for Complex MolecularSystems, Comp. Vis. Sci., 9 (2). pp. 89-102. Official URL: http://dx.doi.org/10.1007/s00791-006-0021-1 (2005).[18] C. S. I. Horenko, C. Hartmann and F. Noé: Data-Based Parameter Estimation of GeneralizedMultidimensional Langevin Processes, Phys. Rev. E, 76:016706 (2007).[19] M. Kahlert and K. P. Hofmann: Reaction Rate and Collisional Efficiency of the Rhodopsin-Transducin System in Intact Retinal Rods, Biophysical Journal 59, 375 (1991).[20] E. Fermi: Thermodynamics (Dover Publications, Inc. New York, 1937 and 1956), 2nd ed.[21] M. Fischbach: Methods for Modeling Metastable Conformational Dynamics from TrajectoryData, Diploma Thesis, Department of Mathematics and Computer Science Freie UniversitätBerlin, year = 2008,.[22] D. C. Lamb and C. Bäuchle: Dem Molekül auf der Spur - Mithilfe eines Weitfeld-Fluoreszenzmikroskops lässt sich der Weg einzelner Moleküle und Teilchen verfolgen, PhysikJournal 6 (2007) Nr. 12, S. 39-45 (2007).[23] T. D. Lamb: Gain and Kinetics of Activation in the G-Protein Cascade of Phototransduction,Proc. Natl. Acad. Sci. USA 93, 566 (1996).[24] E. Meerbach and C. Schütte: Sequential Change Point Detection in Molecular DynamicsTrajectories, Preprint submitted to Elsevier, to be published (2008).[25] R. Nelson: Probability, Stochastic Processes, and Queuing Theory - The Mathematics ofComputer Performance Modelling (Springer, 1995), 1st ed.[26] B. Oksendal: Stochastic Differential Equations (Springer, 2007), 6th ed.[27] L. Pachter and B. Sturmfels: Algebraic Statistics for Computational Biology (CambridgeUniversity Press, 2005).[28] I. Prigogine and I. Stengers: Dialog mit der Natur - Neue Wege naturwissenschaftlichenDenkens (Piper, Neuausgabe 1990), 6th ed.[29] L. R. Rabiner: A Tutorial on Hidden Markov Models and selected Applications in SpeechRecognition pp. 267–296 (1990).[30] H. Risken: The Fokker-Planck Equation (Springer, 1989), 2nd ed.[31] M. J. Saxton and J. C. Owicki: Concentration Effects on Reactions in Membranes:Rhodopsin and Transducin, Biochimica et Biophysica Acta 979, 27 (1989).[32] Scheibe and Erhard: Die Philosophie der Physiker, vol. 1 (C.H. Beck Verlag, 2006).[33] C. Schütte and I. Horenko: Likelihood-Based Estimation of Multidimensional Langevin Modelsand its Application to Biomolecular Dynamics, Multiscale Modelling and Simulation, toappear (2007).[34] F. Schwabl: Statistische Mechanik (Springer-Verlag, 2006), 3rd ed.[35] P. D. P. Schwille: Einblicke ins Leben - Mit den Methoden der Nanobiophotonik die kleinstenWerkstätten des Lebens entschlüsseln, Physik Journal 6 (2007) Nr. 12, S. 35-38 (2007).94
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Page 1:
Diploma ThesisDepartment for Theore
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AbstractAnomalous diffusion is a ub
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Zusammenfassung 1Anomale Diffusion
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Contents1 Motivation 12 Visual Tran
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List of Figures2.1 Anatomy of the e
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1 Motivation„NEC FASCES, NEC OPES
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Theoretically we profit from enormo
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2 Visual Transduction”The eye owe
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(a)(b)(c)Figure 2.3: (a) The anatom
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effect of generating the photorecep
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3 Theory”The theory is the net, t
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3.2 Markov Chains, Markov Processes
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3.3 Hidden Markov ModelsP[X(t + τ)
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3.4 Maximum Likelihood Principlewit
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3.5 Optimization3.5 OptimizationAcc
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3.7 Baum-Welch-AlgorithmAlgorithm 3
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3.8 Two Approaches on Stochastic Sy
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3.9 DiffusionConsider a basin fille
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3.9 Diffusion169].Rearranging (3.34
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3.9 Diffusionwith τ = t −t ′ .
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3.9 DiffusionD = 2k2 B T 2σ . (3.4
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3.10 Hidden Markov Models with Stoc
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Page 53 and 54:
Page 55 and 56: 3.11 Hidden Markov Model - Vector A
Page 57 and 58: 3.11 Hidden Markov Model - Vector A
Page 59 and 60: 3.12 Artificial Test Examples for H
Page 69 and 70: 3.13 Global Optimization Methods3.1
Page 71 and 72: 3.13 Global Optimization MethodsEve
Page 73 and 74: 4 Fluorescence Tracking Experiments
Page 75 and 76: 4.2 Fluorescence SpectroscopyAfter
Page 77 and 78: 4.3 Single Molecule Tracking via Wi
Page 79 and 80: 4.4 Total Internal Reflection Fluor
Page 81 and 82: 4.4 Total Internal Reflection Fluor
Page 83 and 84: 4.6 The expected range for the Tran
Page 85 and 86: 5 Modeling of the Experiment”The
Page 87 and 88: 5.1 Experimental Data(a)(b)(c)(d)Fi
Page 89 and 90: 5.2 Model Ansatz and Estimation of
Page 91 and 92: 5.2 Model Ansatz and Estimation of
Page 93 and 94: 5.3 Testing the Modelalgorithm was
Page 95 and 96: 5.5 Estimation of the Noise Intensi
Page 97 and 98: 5.6 Estimation on the Basis of Diff
Page 103 and 104: 6 Conclusion and OutlookThe main as
Page 105: 7 Bibliography[1] R. C. Aster, B. B
Page 109 and 110: Index11-cis retinal isomer, 87TM se
Page 111 and 112: A AppendixA.1 From Copernicus to Ne
Page 113 and 114: A.2 Important Papers on the Rhodops
Page 115 and 116: A.3 Probability TheoryDefinition A.
Page 117 and 118: A.4 Definitions for OptimizationDef
Page 119 and 120: A.4 Definitions for OptimizationDef
Page 121 and 122: A.7 The Fluctuation-Dissipation-The
Page 123 and 124: A.7 The Fluctuation-Dissipation-The
Page 125 and 126: A.8 Kramers-Moyal Forward Expansion
Page 127 and 128: A.9 Deriving the Fokker-Planck Equa
Page 129 and 130: A.9 Deriving the Fokker-Planck Equa
Page 131 and 132: DanksagungenIch möchte folgenden M
Page 133: AffirmationHereby I, Arash Azhand,
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