# Forschungstage **Need Title by May 26** -> Siehe appendix A https://hedge.leafbla.de/rsqCLH79Ti6-bCRVPZkENw ## Preliminaries - Motivation, bissle Stochastik rechnen, bis manuelles Rechnen ohne Matrizen zu aufwändig wird - Motivation für Markow-Ketten - Definition, bissle Framework, libraries - Welche Sprache? (jupyter, javascript, ...) - Task Forces 0-0'' sind introductory examples, die man auch ohne MKs lösen könnte. - Task Forces 1+ sind more involved und sollten mittels MKs modelliert werden ## TF 0: Simple Elevator Model - Elevator has three floors - Behaviour - Never goes 2→0 or 0→2 - Never goes i→i - goes down with θ, up with 1-θ - Starting at P(0) = <1,0,0>, P(2k+1) = <0,1,0> and P(2k) = <θ, 0, 1-θ> ## TF 0': Snakes and Ladders - Does not have to be S&L, but some motivaOdictional example that promotes the use of markov chains ## TF 0'': Simulating arbitrary Dice Given a coin, how can you simulate an arbitrary, fair die? - For a fixed *n*, draw a graph (an almost-tree) that expresses your idea - For any *n*, how can you generate the associated graph? - Markov Chains can model this problem elegantly ## TF 1: Language Model - I have this `harrypotter.txt` that can generate funny sentences like "You are broomstick, Potter!" - Always very entertaining, we can draw some parallels to ChaptGPT ## TF 3: Radioactive Decay - Data from https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html - Here, take this 1kg of U-238. How long until you receive 100g of Pb-206? - A sample of U-238 is left to age for 500 years. Which are the most common isotopes currently left? - Carbon dating für rumrechnen mit halbwertszeiten https://en.wikipedia.org/wiki/Radioactive_decay ## TF 4: Random walkers Simulate, or motivate n-dimensional random walkers, that choose directions with 1/2d probability - A drunk man always finds home - And hence, a drunk line-man as well. - A drunk bird may get lost forever ## Ditched Ideas ### Statistical Sampling - https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm - In here for # Appendix A: Title finding Cool Ideas by Holger - Some random notes on Markov Chains - Die Kunst des Gedächtnisverslustes - The Art of losing memory - Auch: The art of losing memory and the art of losing memory and [...] - Gedächtnisverlust für Anfänger und Fortgeschrittene - Ein diskreter Blick in [..?]