PPT-Topological Data Analysis

Applications I 2008 IK Darcy All rights reserved This work was partially supported by  the Joint DMSNIGMS Initiative to Support Research in the Area of Mathematical Biology NSF 0800285 Isabel K Darcy. “Topologically . Robust Transport of Photons in a Synthetic Gauge Field. ," S. Mittal, J. Fan, S. . Faez. , A. . Migdall. , J.M. Taylor, M. . Hafezi. , Phys. Rev. . Lett. ., 113, 087403 (2014. ). Topological transport of light is the photonic analog of topological electron flow in certain semiconductors. In the electron case, the current flows around the edge of the material but not through the bulk. It is “topological” in that even if electrons encounter impurities in the material the electrons will continue to flow without losing energy. Weisong. . Tu. Department of Physics and Astronomy. University of Tennessee. Instructor: Dr. . George . Siopsis. Introduction. Quantum Hall Effect. The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields. In the quantum hall effect, and the conductivity can be represented as. Lecture 23. a. acyclic with neg. weights (topological sort algorithm). 8/25/2009. 1. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. “The shortest-path algorithms are all . single-source algorithms. Michael Freedman. April 23, 2009. Parsa Bonderson. Adrian Feiguin. Matthew Fisher. Michael Freedman. Matthew Hastings. Ribhu Kaul. Scott Morrison. Chetan Nayak. Simon Trebst. Kevin Walker. Zhenghan Wang. Dimitrie Culcer. D. Culcer, PRB 84, 235411 (2011). . D. Culcer, . Physica. E 44, 860 (2012) – review on TI transport . Outline. Introduction to topological insulators. 组员：马润泽 金佳霖 孙晋茹 宋化鼎 罗巍 申攀攀 沈齐欣 生冀明 刘易. Outline. Introduction. Brief history of topological insulators. Band theory. Quantum Hall effect. Superconducting proximity effect. Guillaume Flandin. Wellcome. Trust Centre for Neuroimaging. University College London. SPM Course. London, . May 2014. Many thanks to Justin . Chumbley. , Tom Nichols and Gareth Barnes . for slides. . and. . Topological. . phases. . of. matter. b. y. Reichmann Alexander. Overview. Phase . transitions. Topology. Quantum Hall . effect. Superconductivity. Applications. Phase . transition. Different . Michael Freedman. April 23, 2009. Parsa Bonderson. Adrian Feiguin. Matthew Fisher. Michael Freedman. Matthew Hastings. Ribhu Kaul. Scott Morrison. Chetan Nayak. Simon Trebst. Kevin Walker. Zhenghan Wang. Graph Traversals. Spring 2015. Yanling He. Graphs. A Graph G = (V, E). Represents relationships among items. Can be directed or undirected. Complexity is O(|E|+|V|) is O(|V|^2). Graph Data Structure. Topological methods and cortical thickness. Chung et al., 2009 discovered differences in cortical thickness comparing individuals with autism to controls using topology. Work flow. Visualization of persistence plot. Girish S . Setlur. Department of Physics. IIT Guwahati. COPYRIGHT DISCLAIMER: . ALL ILLUSTRATIONS . AND SOME PASSAGES IN . THESE SLIDES HAVE BEEN DOWNLOADED FROM VARIOUS INTERNET SOURCES.. LISTING EACH SOURCE SEPARATELY WILL TAKE UP ALL MY TIME SO I SHALL DESIST FROM DOING SO.. Takehito. Yokoyama, Yukio Tanaka. *. , and Naoto . Nagaosa. Department of Applied Physics, University of . Tokyo, Japan. *. Department . of Applied Physics, Nagoya . University, . Japan. arXiv:0907.2810. Iris Cong. Dept. of Computer Science, UCLA. Jointly authored with Prof. . Zhenghan. Wang (advisor) and . Meng. Cheng. arXiv:1609.02037. Contents. Introduction. Part I: Hamiltonian Realization. Part II: Algebraic Theory.