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

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1 Motivation4
2 Visual Transduction”The eye owes its existence the light.From indifferent animal auxiliary organsthe light arouses for itself an organ,that shall become its own kind,and so constitutes the eye ajar the light for the light,there<strong>with</strong> the inner light shall counter the outer light.”(Johann Wolfgang Goethe) 1Figure 2.1: Anatomy of the eye. Light is propagating through the lens which focuses the light onthe retina.1 German translation: ”Das Auge hat sein Dasein dem Licht zu danken. Aus gleichgültigen tierischen Hilfsorganenruft sich das Licht ein Organ hervor, das seinesgleichen werde, und so bildet sich das Auge am Lichte fürs Licht,damit das innere Licht dem äusseren entgegentrete” (Johann Wolfgang von Goethe, Goethes NaturwissenschaftlicheSchriften (Kürschner) „Entwurf einer Farbenlehre“, Bd. 3, S. 88).5
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: Theoretically we profit from enormo
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 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 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 67 and 68:
3.12 Artificial Test Examples for H
Page 69 and 70:
3.13 Global Optimization Methods3.1
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3.13 Global Optimization MethodsEve
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4 Fluorescence Tracking Experiments
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4.2 Fluorescence SpectroscopyAfter
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4.3 Single Molecule Tracking via Wi
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4.4 Total Internal Reflection Fluor
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4.4 Total Internal Reflection Fluor
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4.6 The expected range for the Tran
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5 Modeling of the Experiment”The
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5.1 Experimental Data(a)(b)(c)(d)Fi
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5.2 Model Ansatz and Estimation of
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5.2 Model Ansatz and Estimation of
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5.3 Testing the Modelalgorithm was
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5.5 Estimation of the Noise Intensi
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5.6 Estimation on the Basis of Diff
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Page 101 and 102:
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6 Conclusion and OutlookThe main as
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7 Bibliography[1] R. C. Aster, B. B
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[36] C. U. M. Smith: Elements of Mo
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Index11-cis retinal isomer, 87TM se
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A AppendixA.1 From Copernicus to Ne
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A.2 Important Papers on the Rhodops
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A.3 Probability TheoryDefinition A.
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A.4 Definitions for OptimizationDef
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A.4 Definitions for OptimizationDef
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A.7 The Fluctuation-Dissipation-The
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A.7 The Fluctuation-Dissipation-The
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A.8 Kramers-Moyal Forward Expansion
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A.9 Deriving the Fokker-Planck Equa
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A.9 Deriving the Fokker-Planck Equa
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DanksagungenIch möchte folgenden M
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AffirmationHereby I, Arash Azhand,
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