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