PPT-Topological Summaries: Using Graphs for Chemical Searching

Graphs are a flexible amp unifying model Scalable similarity searches through novel index structure Mining of significant fragments in collections Classification of compounds based on significant fragments . Trees are a specific instance of a construct called a graph In general a graph is composed of edges and vertice s that link the nodes together A graph G is often denoted GVE where V is the set of vertices and E the set of edges Two types of graphs Chemical Incidents Create. Various Information Needs. California: 2012 Chevron Refinery Fire. Source: abcnews.com. Texas: 2013 Fertilizer Plant Explosion. Source: U.S. Chemical Safety Board. West Virginia: 2014 West Virginia Chemical Leak/Water Ban. Superconductors. Akira . Furusaki. 2012/2/8. 1. YIPQS Symposium. Condensed matter physics. Diversity of materials. Understand their properties. Find. new states of matter. Emergent behavior of electron systems at low energy. v 1 v 2 v 3 v 4 v 5 v 6 v 7 2 Directed Acyclic Graphs Def. A DAG is a directed graph that contains no directed cycles. Ex. Precedence constraints: edge (v i , v j ) means v i must precede v j . Node and Edge Searching . Spanning Tree . Problems. Sheng-Lung Peng. Department of Computer Science and Information Engineering. National Dong . Hwa. University, . Hualien. 974, Taiwan. Outline. Introduction. 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. Graphs.  . Graphs . capture . much more detail than numerical summaries, so very useful for learning about data and communicating its features.. At the same time, graphical interpretation isn’t standard in the way that numerical summaries are, and our eyes can fool us.. on Cops and Robbers. Anthony Bonato. Ryerson University. Genus. (Aigner, . Fromme. , 84) . planar graphs (genus . 0. ) have cop number . ≤ 3.. (Clarke, 02) . outerplanar. graphs have cop number . Eyal. Ackerman. University of Haifa and . Oranim. College. Drawing graphs in the plane. Consider drawings of graphs in the plane . s.t. .. No loops or parallel edges. Vertices .  distinct points. Anthony Bonato. Ryerson University. GRASCan’17. Grenfell Campus. Graphs on surfaces. ?. ?. S. 0. S. 1. Genus of a graph. a graph that can be embedded in an (orientable!) surface with . g. holes (and . 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. Hafezi. , S. Mittal, J. Fan, A. . Migdall. , J.M. Taylor, Nature Photonics, . (. 2013. ) . doi:10.1038/nphoton.2013.274. . Topology . -- the understanding of how things are connected -- remains abstract, even with the popular example of doughnuts and coffee cups. This concept, esoteric as it appears, is also neat because it is the basis for creating . 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.