Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

More documents

Recommendations

Info

7 Bibliography[52] S. Kirkpatrick, C. D. G. Jr., and M. P. Vecchi.: Optimization by Simulated Annealing., Science220, 671 (1983).[53] A. Nolte and R. Schrader: A note on the finite time behaviour of simulated annealing, Mathematicsof Operations Research 347, 476 (2000).[54] P. J. M. van Laarhoven and e. E. H. L. Aarts: Simulated Annealing: Theory and Applications(Springer, Kluwer Academic Publishers, Norwell, MA, USA, June 30, 1987, 1987).[55] B. Hajek: Cooling schedules for optimal annealing, Mathematics of Operations Research,(13) (1988).[56] M. Schöngen: Rasterkraftmikroskopie und Fluoreszenzspektroskopie zur nichtinvasiven undhochaufgelösten Untersuchung von Nanostrukturen, Diplomarbeit, Institut für Optik undAtomare Physik, Technische Universität Berlin (2008).[57] J. L. E. Dreyer: Tycho Brahe. A picture of scientific life and work in the sixteenth century,Edinburgh, 1890.[58] V. Westphal and S. W. Hell: Nanoscale Resolution in the Focal Plane of an Optical Microscope,Phys. Rev. Lett. 94, 143903 (2005).[59] S. W. Hell: Far-Field Optical Nanoscopy, Science 316, 1153 (2007), URL http://www.sciencemag.org/cgi/content/abstract/316/5828/1153.[60] H. Nyquist: Thermal Agitation of Electric Charge in Conductors, Phys. Rev. 32, 110 (1928).[61] H. B. Callen and T. A. Welton: Irreversibility and Generalized Noise, Phys. Rev. 83, 34(1951).[62] R. Kubo: Statistical-Mechanical Theory of Irreversible Processes. I: General Theory andSimple Applications to Magnetic and Conduction Problems, Journal of the Physical Societyof Japan 12, 570 (1957), URL http://jpsj.ipap.jp/link?JPSJ/12/570/.96
Index11-cis retinal isomer, 87TM serpentine receptor, 7Balance equations, 19Baum-Welch algorithm, 21, 25, 37Bayes theorem, 12Brownian Motion, 28, 30, 32, 36, 38, 48, 56,66, 85Brownian Particle, 32, 33cGMP, 8Chapman-Kolmogorov equation, 16, 18Cones, 6Diffusion, 28, 42Diffusion coefficient, 34, 37Diffusion process, 38Drift coefficient, 37Einstein-Smoluchowski relation, 34Equipartition theorem, 34Evolutionary Algorithms (EA), 57Expectation-Maximization algorithm, 24Expectation-Maximization Algorithm (EM),24Fluctuation-Dissipation-Theorem, 34, 109Fokker-Planck equation, 36, 42, 115, 118Forward problem, 12Forward-Backward variables, 25, 41G-Proteins, 7GDP, 8Generator matrix, 19Genetic Algorithm (GA), 57GTP, 8Harmonic potentials, 38, 39Hidden Markov Models, 19, 37, 38, 43, 46,54, 56, 73, 88, 89Inverse Problems, 12Itó SDE, 36Kolmogorov equation, 36Kramers-Moyal coefficients, 115Kramers-Moyal Expansion, 36, 113Langevin equation, 32, 35, 38, 115Likelihhod function, 21, 24Likelihood, 13, 40, 51, 52, 54, 89Likelihood function, 40, 43, 44, 57, 60Likelihood landscape, 54Log-Likelihood, 22Markov chain, 13Markov chains, 14, 19, 40, 89Markov jump process, 38Markov model, 20, 25Markov process, 13, 14, 19Markov property, 13Maximum Likelihood Principle, 21Maximum Likelihood Problem, 21mean square displacement, 34Optimization, 23Optimization Algorithm, 23Optimization Problem, 23Optimization, -Global, 23, 57Optimization, -Local, 23Parameter estimation, 40, 43, 46, 73, 75–77,79, 87Phosphodiesterase (PDE), 8Probability current, 37Random Variable, 13, 14, 32, 35, 38, 39, 88Retina, 6Rhodopsin, 7, 38Rhodopsin-Transducin-system, 8, 38, 101Rods, 697
Page 1:
Diploma ThesisDepartment for Theore
Page 5 and 6:
AbstractAnomalous diffusion is a ub
Page 7 and 8:
Zusammenfassung 1Anomale Diffusion
Page 9 and 10:
Contents1 Motivation 12 Visual Tran
Page 11 and 12:
List of Figures2.1 Anatomy of the e
Page 13 and 14:
1 Motivation„NEC FASCES, NEC OPES
Page 15 and 16:
Theoretically we profit from enormo
Page 17 and 18:
2 Visual Transduction”The eye owe
Page 19 and 20:
(a)(b)(c)Figure 2.3: (a) The anatom
Page 21 and 22:
effect of generating the photorecep
Page 23 and 24:
3 Theory”The theory is the net, t
Page 25 and 26:
3.2 Markov Chains, Markov Processes
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
3.3 Hidden Markov ModelsP[X(t + τ)
Page 33 and 34:
3.4 Maximum Likelihood Principlewit
Page 35 and 36:
3.5 Optimization3.5 OptimizationAcc
Page 37 and 38:
3.7 Baum-Welch-AlgorithmAlgorithm 3
Page 39 and 40:
3.8 Two Approaches on Stochastic Sy
Page 41 and 42:
3.9 DiffusionConsider a basin fille
Page 43 and 44:
3.9 Diffusion169].Rearranging (3.34
Page 45 and 46:
3.9 Diffusionwith τ = t −t ′ .
Page 47 and 48:
3.9 DiffusionD = 2k2 B T 2σ . (3.4
Page 49 and 50:
3.10 Hidden Markov Models with Stoc
Page 51 and 52:
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 and 106: 7 Bibliography[1] R. C. Aster, B. B
Page 107: [36] C. U. M. Smith: Elements of Mo
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,
show all

Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

Create successful ePaper yourself

Delete template?

Save as template?