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Some phase transition phenomena in graphical data analysis

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Some phase transition phenomena in graphical data analysis
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5
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CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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I'll present two problems where data naturally present a graphical structure: the analysis of champions in a tournament and the problem of matching. I'll present for each problem intuitive results in toy models and discuss various mathematical tools involved to prove them. I'll also present many open problems, hopefully convincing people to jump in this growing area.
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