Diffusion Processes with Hidden States from ... - FU Berlin, FB MI
Diffusion Processes with Hidden States from ... - FU Berlin, FB MI
Diffusion Processes with Hidden States from ... - FU Berlin, FB MI
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List of Figures2.1 Anatomy of the eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 The layers of the retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 The anatomy of the rod photoreceptor cell (<strong>from</strong> [7]) . . . . . . . . . . . . . . . 72.4 Scheme of the visual transduction process in the retinal rod discs (<strong>from</strong> [7]) . . . 82.5 Scheme of the 7TM serpentine receptor (<strong>from</strong> [36, p.170 , Fig. 8.3]) . . . . . . . 92.6 (A) 11-cis-retinal and (B) all-trans-retinal. C : Carbon, H : Hydrogen, O :Oxygen,N : Nitrogen. The numbers are atom positions. (<strong>from</strong> [36, p. 190, Fig. 8.23]) . . 103.1 Scheme of a Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Scheme of a Markov chain path (sequence) . . . . . . . . . . . . . . . . . . . . 163.3 Time-Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Scheme of a <strong>Hidden</strong> Markov Model (HMM) . . . . . . . . . . . . . . . . . . . . 203.5 Global and local optima of a two-dimensional function f (<strong>from</strong> [46]). This functionis plotted versus two elements X 1 and X 2 of the problem space X. . . . . . . 233.6 Schematic representation of the diffusion phenomenon . . . . . . . . . . . . . . 293.7 (a) Brownian Movement and (b) Stochastic Force (<strong>from</strong> [34, p. 418]) . . . . . . . 323.8 Stochastic Force Correlation (<strong>from</strong> [34, p. 419]) . . . . . . . . . . . . . . . . . . 333.9 Three-dimensional free diffusion <strong>with</strong> 100.000 time steps . . . . . . . . . . . . . 473.10 Three-dimensional free diffusion <strong>with</strong> 1000 time steps . . . . . . . . . . . . . . 473.11 Three-dimensional diffusion <strong>with</strong> potential and 1000 time steps . . . . . . . . . . 483.12 Random sequence of three states . . . . . . . . . . . . . . . . . . . . . . . . . . 493.13 2D free diffusion trajectory <strong>with</strong> 1000 time steps . . . . . . . . . . . . . . . . . 503.14 Likelihood convergence 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.15 Likelihood convergence 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.16 Likelihood landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.17 Energy minimization procedure via Simulated Annealing (SA) . . . . . . . . . . 604.1 Jablonski-Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2 Stokes-shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3 Wide-Field Fluorescence Spectroscopy (<strong>from</strong> [22]) . . . . . . . . . . . . . . . . 654.4 Different types of diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.5 Optical behavior of incident light radiance at the boundary surface between twomedia <strong>with</strong> different refraction indices . . . . . . . . . . . . . . . . . . . . . . . 684.6 Schematic representation of objective-TIRFM . . . . . . . . . . . . . . . . . . . 694.7 Experimental preparation of disc membranes . . . . . . . . . . . . . . . . . . . 715.1 Transducin trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.2 Several single transducin trajectories in one plot . . . . . . . . . . . . . . . . . . 755.3 Enlargement of the small areas, marked in Figure 5.2 . . . . . . . . . . . . . . . 76XI