Diplomarbeit Torsten Lüdge
Theory
Inverse Problems and Bayes Ansatz
FRET Trajectory estimation: Window method, Optimal Random Walk
(Probability to Observe Photon Type Y, given distance r: p(Y|r), p(Y|E)).
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)
and Corrections (in Terms of p(Y|r))
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
Zeitplan
| ToDo |
Juli(25) |
Aug(25) |
Sept(25) |
Okt(10) |
| LyX |
Alle SubSubtitles |
1.Vorversion |
1.Version |
Final |
| Data |
Korrektur Anwenden |
Alle Traces ausrechnen |
… |
… |
| Programm |
Correction/SDE generate |
Metamacs? |
Standalone? |
| Pictures |
unkorrigert/korrigier |
Traces |
| time window/FW BW |
Histograms |
| HMM Würfel Verweigungsmodell |
Diels Alderase (VMD) |
| time window/FW BW |
FRET-Potential |
| sonst |
Ressourcen Liste |
Schöll vorlegen |
Nienhaus&Schöll vorlegen |
Abgeben |