| Website in VV: | Lecture, Exercise (please register for both lecture and exercise!) |
| Lecture dates (2 SWS): | Wednesday 14:15 - 15:45, Seminar room 119, Arnimallee 3. |
| Exercise dates (2 SWS): | Tuesday 12:15 - 13:45, Seminar room 031, Arnimallee 7. |
| Lecture period: | 16.4.2025 - 16.07.2025 |
| Exercise period: | 22.4.2025 - 15.07.2025 |
| Final exam: | An oral exam at the end of the semester |
| Other prerequisite: | Active and regular participation in the exercises |
| Active participation: | You prove this by completing and submitting checklists |
| Regular participation: | You prove this by mandatory attendance in the exercise sessions |
| Date | Markov Processes... | Mathematics | Level | Material* |
| 16.4. | Model-Based | Discrete | Theory | Frobenius Theorem Eigenvalues |
| 23.4. | Model-Based | Discrete | Application | Generator Matrix Spectral Clustering SqRA |
| 30.4. | Model-Based | Continuous | Theory | (various operators...) |
| 7.5. | Model-Based | Continuous | Application | (Functional analysis, committor...) |
| 14.5. | Data-Based | Discrete | Theory | (Ulam, "Count"-Galerkin...) |
| 21.5. | Data-Based | Discrete | Application | (PCCA+ ...) |
| 28.5. | Data-Based | Continuous | Theory | (ISOKANN) |
| 4.6. | Data-Based | Continuous | Application | (ISOKANN) |
| 11.6. | Expert-Based | Logic | Theory | (Boole...) |
| 18.6. | Expert-Based | Logic | Application | (Gröbner basis ...) |
| 25.6. | Expert-Based | Coordination | Theory | (What is relevance? Ring homomorphism) |
| 2.7. | Expert-Based | Coordination | Application | (Coordination) |
| 9.7. | Special topic | Importance Sampling | Theo/App | (Optimal Control?) |
| 16.7. | Special topic | Reaction pathways | Theo/App | (Explainable A.I.?) |
16.4.: select one(!) of the following topics and to fill out the checklist according to your actions. Send it via eMail to me.
Topic1: Perron-Frobenius-Theorem. What does it say? How is it proven?
Topic2: Find a process which is not Markovian. (In your example the process itself has to be non-Markovian. Do not try to "hide away Markovianity" by an "inappropriate" modelling or by a clustering of states)
Topic3: If a transition probability matrix P is perturbed into a transition probability matrix P+E, what do we know about the changes of its eigenvalues?
Topic4: A doubly-stochastic matrix can be represented by a convex combination of permutation matrices. How does the Birkhoff-von Neumann method find this decomposition?