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Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Graph Spectra / Sparsest Cuts in Minimum Time
Pages 40-43

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 40...
... Similarly, problems like designing a computer chip that runs efficiently, identifying communities within a social network, or creating a computer network that won't shut down if some of the computers go offline, all involve analyzing the spectra of networks, or what mathematicians call "graphs." To understand what a molecular spectrum is, think of a molecule as a collection of balls bound together with the aid of springs. The springs are always vibrating, and there are certain modes of vibration that, if left alone, will keep on going indefinitely.
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From page 41...
... For example, the users of Facebook form a social network with nearly 1 billion active users. An Intel Xeon chip is a network with 800 million transistors.
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From page 42...
... . 18 / The Ambassador Bridge connecting Detroit, Michigan, and Windsor, Ontario, is a very visible example of a "miminum cut." / Detroit-Windsor Tunnel Ambassador Bridge Port of Detroit FUELING innovation and discovery 42
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From page 43...
... In 2004, a method was devised for solving equations involving graph Laplacians that was significantly faster (in theory) than any previously known method.
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