PPT-The New World of Infinite Random Geometric Graphs

Anthony Bonato Ryerson University East Coast Combinatorics Conference coauthor talk postdoc Into the infinite R Infinite random geometric graphs 111 110 101 011 100 010 001 000 Some properties. Proof A geometric random variable has the memoryless property if for all nonnegative integers and or equivalently The probability mass function for a geometric random variab le is 1 0 The probability that is greater than or equal to is 1 Anthony Bonato. Ryerson University. CanaDAM. 2011. Cop number of a graph. the . cop number of a graph. , written . c(G). , is an elusive graph parameter. few connections to other graph parameters. hard to compute. 1. Distinguishing Infinite Graphs. Anthony Bonato. Ryerson University. . Discrete Mathematics Days 2009. May 23, . 2009. Distinguishing Infinite Graphs Anthony Bonato. 2. Dedicated to the memory of . Network Science: Random Graphs . 2012. Prof. Albert-László Barabási. Dr. Baruch Barzel, Dr. Mauro Martino. RANDOM NETWORK MODEL. Network Science: Random Graphs . 2012. Erdös-Rényi model (1960). Laurent . Massouli. é & . Fabien Mathieu. laurent.massoulie@inria.fr. & . fabien.mathieu@inria.fr. . The . “Code Red. ” Internet Worm. Epid. e. mics. . & rumours. Propagate fast. Power law . graphs. Small world graphs. Preferential attachment. Barabási. and Albert showed that when large networks are formed. by the rules of . preferential attachment . , the resulting graph shows. Angelika Steger. (j. oint. . work. . with. . Konstantinos . Panagiotou. , SODA‘11. ) . . TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. Random Graphs . Series. Find sums of infinite geometric series.. Use mathematical induction to prove statements.. Objectives. infinite geometric series. converge. limit. diverge. mathematical induction. Vocabulary. In Lesson 12-4, you found partial sums of geometric series. You can also find the sums of some infinite geometric series. An . TJTSD66: Advanced Topics in Social Media. (Social . Media . Mining). Dr. WANG, Shuaiqiang @ CS & IS, JYU. Email: . shuaiqiang.wang@jyu.fi. Homepage: . http://users.jyu.fi/~swang/. Why should I use network models?. Objectives: You should be able to. …. Formulas. The goal in this section is to find the sum of an infinite geometric series. However, this objective is very closely connected to the limit of an infinite sequence. . infinite random geometric . g. raphs. Anthony Bonato. Ryerson University. Random Geometric Graphs . and . Their Applications to Complex . Networks. BIRS. R. Infinite random geometric graphs. 111. 110. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. The purpose of this section is to discuss sums that contain infinitely many terms. Author: M.E.J. Newman. Presenter: Guoliang Liu. Date:5/4/2012. Outline. Networks in the real world. Properties of networks. Random graphs. Exponential random graphs and Markov graphs. The small-world model. Anthony Bonato. Ryerson University. CRM-ISM Colloquium. Université. Laval. Complex networks in the era of . Big Data. web graph, social networks, biological networks, internet networks. , …. Infinite random geometric graphs - Anthony Bonato.