PPT-Nearly-Linear Time Algorithms for Markov Chains and New Spectral Primitives for Directed

Richard Peng Georgia Tech In collaboration with Michael B Cohen Jon Kelner John Peebles Aaron Sidford Adrian Vladu Anup B Rao Rasmus Kyng Outline Graphs and Lx b G . e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations We call the tail of the head of and uv the ends of If there is an edge with tail and head then we let uv denote such an edge and we say that this edge is directed from to Loops Parallel Edges and Simple Digraphs An edge uv in a digraph is a Nimantha . Thushan. Baranasuriya. Girisha. . Durrel. De Silva. Rahul . Singhal. Karthik. . Yadati. Ziling. . Zhou. Outline. Random Walks. Markov Chains. Applications. 2SAT. 3SAT. Card Shuffling. . Character Positioning. Christine Talbot. Character Positioning. Discovery News – Avatar: Motion Capture Mirrors Emotions . http. ://. news.discovery.com. /videos/avatar-making-the-movie/. MindMakers. E. Tognoli, . october. 9. th. , 2008, HBBL meeting. Peaks~floor. floor. peak. Interim question 1: why are there more peaks . in structured behavioral tasks? . Steady-State paradigms and structured behavioral tasks. 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. 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. . (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 . Random Walks. Consider a particle moving along a line where it can move one unit to the right with probability p and it can move one unit to the left with probability q, where . p q. =1, then the particle is executing a random walk.. Quarter: Summer 2017. CSE 373: Data Structures and Algorithms. Lecture . 14: Introduction to Graphs. Today. Overview of Midterm. Introduce Graphs. Mathematical representation. Undirected & Directed Graphs. Announcements. A5 Heaps Due October 27. Prelim 2 in ~3 weeks: Thursday Nov 15. A4 being graded right now. Mid-Semester College Transitions Survey on Piazza. 2. These aren't the graphs we're looking for. Announcements. A5 Heaps Due October 27. Prelim 2 in ~3 weeks: Thursday Nov 15. A4 being graded right now. Mid-Semester College Transitions Survey on Piazza. 2. These aren't the graphs we're looking for. JFK. BOS. MIA. ORD. LAX. DFW. SFO. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Directed Graphs. 2. Digraphs. A . digraph.