Diplomarbeit Torsten Lüdge

Theory

Inverse Problems and Bayes Ansatz

FRET Trajectory estimation: Window method, Optimal Random Walk

Forward-Backward and Expectation-Maximization Algorithm

Markov chains, Markov property

Hidden Markov Models (Discrete hidden state, discrete output)

Hidden Markov Models with Gauss Output

Hidden Markov Models with SDE Output

FRET Experimentals

Physical Principle (FRET)

Experimental Setup (Single Molecules, Fluorescence Microscrope, Beamsplitter, Photodetectors)

Measurement Errors (X-Talk, Background Noise, Gamma factor)

Trajectory Estimation (from photons to E(t) and r(t))

Comparison of Window and Optimal Random Walk on artificial Trajectories

Comparison of Window and Optimal Random Walk on experimental Trajectories

Hidden Markov Models (Get transition matrix and distribution of E(t) or r(t) in each state)

Application of HMM-Gauss and HMM-SDE to artificial Trajectories

Application of HMM-Gauss and HMM-SDE to experimental Trajectories

Variation of Window length, Central limit theorm ,..

Properties of T (transition matrix): Lifetimes of states.

Suggestion of new experiments.

Conclusions

Comments

Zeitplan