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 . 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 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. . Tensor Decomposition and Planted Sparse Vectors. Sam Hopkins. Cornell. Jonathan Shi. Cornell. Tselil. Schramm. UC Berkeley. David . Steurer. Cornell. Competing Themes in Algorithms. Polynomial time. via . Bases . of . Perfect Matchings. STOC 2013. Marek Cygan, Stefan Kratsch, . Jesper Nederlof. Hamiltonicity (aka Hamiltonian cycle). Held&Karp (‘61. ), Bellman (‘62): .                time and space (Dynamic Programming).. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Tensor Decomposition and Planted Sparse Vectors. Sam Hopkins. Cornell. Jonathan Shi. Cornell. Tselil. Schramm. UC Berkeley. David . Steurer. Cornell. Competing Themes in Algorithms. Polynomial time. 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. . 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.. 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.