PPT-Full counting statistics of Markov chains applied to the kinetics of molecular motors

Intermediate presentation at the group seminar July 18th 2012 Maximilian Thaller 1 Contents Molecular Motors Connection between rates and cumulants Simulation Discussion of a special case. 1 Introduction Most of our study of probability has dealt with independent trials processes These processes are the basis of classical probability theory and much of statistics We have discussed two of the principal theorems The fundamental condition required is that for each pair of states ij the longrun rate at which the chain makes a transition from state to state equals the longrun rate at which the chain makes a transition from state to state ij ji 11 Twosided stat Sc in Applied Statistics MT2004 Robust Statistics 19922004 B D Ripley The classical books on this subject are Hampel et al 1986 Huber 1981 with somewhat simpler but partial introductions by Rousseeuw Ler We will also see that we can 64257nd by merely solving a set of linear equations 11 Communication classes and irreducibility for Markov chains For a Markov chain with state space consider a pair of states ij We say that is reachable from denoted Nimantha . Thushan. Baranasuriya. Girisha. . Durrel. De Silva. Rahul . Singhal. Karthik. . Yadati. Ziling. . Zhou. Outline. Random Walks. Markov Chains. Applications. 2SAT. 3SAT. Card Shuffling. Part 4. The Story so far …. Def:. Markov Chain: collection of states together with a matrix of probabilities called transition matrix (. p. ij. ) where . p. ij. indicates the probability of switching from state S. A Preliminary . Investigation. By Andres Calderon Jaramillo. Mentor - Larry Lucas, Ph.D.. University of Central Oklahoma. Presentation Outline. Project description and literature review.. Musical background.. Markov Models. A. AAA. : 10%. A. AAC. : 15%. A. AAG. : 40%. A. AAT. : 35%. AAA. AAC. AAG. AAT. ACA. . . .. TTG. TTT. Training. Set. Building the model. How to find foreign genes?. Markov Models. . Salehi. Marc D. Riedel. Keshab. K. Parhi. University of Minnesota, USA. . Markov Chain Computations. using . Molecular Reactions. 1. Introduction. Modeling of Molecular Systems. Mass-action Law. Stochastic . (part 2). 1. Haim Kaplan and Uri Zwick. Algorithms in Action. Tel Aviv University. Last updated: April . 18. . 2016. Reversible Markov chain. 2. A . distribution . is reversible . for a Markov chain if. (part 1). 1. Haim Kaplan and Uri Zwick. Algorithms in Action. Tel Aviv University. Last updated: April . 15 . 2016. (Finite, Discrete time) Markov chain. 2. A sequence . of random variables.  . Each . regular Or Ergodic?. Absorbing state: A state in a . Markov . chain . that . you . cannot . leave, . i.e. . p. ii. = 1. . Absorbing . Markov chain. : . if it has at least one absorbing state and it is possible to reach that absorbing state from any other state. . . CS6800. Markov Chain :. a process with a finite number of states (or outcomes, or events) in which the probability of being in a particular state at step n + 1 depends only on the state occupied at step n.. 1. Probability and Time: Markov Models. Computer Science cpsc322, Lecture 31. (Textbook . Chpt. . 6.5.1). Nov, 22, 2013. CPSC 322, Lecture 30. Slide . 2. Lecture Overview. Recap . Temporal Probabilistic Models.