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

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4 Fluorescence Tracking Experiments i cz ttn 2n 1i i rrn 1(a) i= cz t=90°tn 2n 1i i rrn 1(b) i czevanescence fieldn 2n 1i i rrn 1(c)Figure 4.5: Optical behavior of incident light radiance at the boundary surface between two mediawith different refraction indices n 1 ,n 2 (i: incident radiance, r: reflected radiance, t:transmitted radiance). (a) α i < α c : The transmitted radiance is refracted with an angleof α t > α i , (b) α i = α c : α t = 90 ◦ and the transmitted light rays are propagating alongthe boundary surface and (c) α i > α c : total internal reflection with the emergence ofan evanescence field over the boundary surface.68
4.4 Total Internal Reflection Fluorescence Microscopy (TIRFM)When α i is less than α c , then the transmitted light rays are refracted under an angle α t > α i (seeFigure 4.5 (a)). When α i = α c , then α t = 90 ◦ , the transmitted light rays are propagating alongthe boundary surface, and a part of the incident rays is reflected under the angle of reflection α r(see Figure 4.5 (b)). Finally, when it is α i > α c , one observes the above mentioned case of totalinternal reflection (see Figure 4.5 (c)). In this case the incident radiance is reflected completely atthe boundary surface, while a tiny part of the light energy propagates along the boundary surfaceas an evanescent electromagnetic wave, caused through diffraction at the boundary surface.In z−direction the intensity of this evanescent field decays exponentially with the depth of penetrationd p :(I(z) = I 0 exp − z ),d pwhile d p is given by that penetration depth at which the initial intensity I 0 of the evanescent waveis declined toI 0e .Theoretical research on and development of TIRFM was performed in the 1980s by Daniel Axelrodand colleagues (see in [43]). Two realizations of TIRFM can be differed from one another:Prism-TIRFM and Objective-TIRFM. Here we will focus on the latter.The principle of the objective-TIRFM is shown schematically in Figure 4.6.Figure 4.6: Schematic representation of objective-TIRFM. For description see text.In the objective-TIRFM method the excitation radiance is focused through the objective on the69
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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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3.2 Markov Chains, Markov Processes
Page 29 and 30: 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 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: 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 and 108: [36] C. U. M. Smith: Elements of Mo
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
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DanksagungenIch möchte folgenden M
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AffirmationHereby I, Arash Azhand,
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