Structure Diploma Thesis Arash

Introduction

Theory

Inverse Problems and Bayes Ansatz

Markov chains, Markov property

Forward-Backward and Expectation-Maximization Algorithm

Hidden Markov Models (Discrete hidden state, discrete output)

Diffusion, SDEs

From SDEs to Fokker-Planck

Hidden Markov Models with SDE Output

Case of Pure Diffusion

Fluorescence Tracking Experimentals

Physical Principle (Fluorescence)

Experimental Setup (Single Molecules, Fluorescence Microscrope, Photodetectors)

Modeling of the Experiment

Model Ansatz (Observe 2D-Projection of 3D-Diffusion; At least 3 hidden states: free diff., Diff in Membrane, Diff bound to Rhodopsin)

Artificial Example (Transducin diffuison in 3D, Membrane, Transition Probabilities between states, Diffusion constants)

Application to Experimental Data (Dark State). Diffusion constants? Transition Matrix? Analysis?

Goodness of Fit.

Application to Experimental Data (Active State). Diffusion constants? Transition Matrix? Analysis?

Goodness of Fit.

Conclusions

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