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#1 macosxnerd101  Icon User is online

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[Link] Calculus on Graphs

Post icon  Posted 21 January 2014 - 07:19 AM

This is an interesting read. It's a research paper from Cornell describing how to apply Real Analysis and Calculus concepts to graphs, allowing for an easier use of differential equations to study graph structures.

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The purpose of this paper is to develop a “calculus” on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new (Laplacian based) wave equation (see [FTa, FTc]); this wave equation gives rise to a partial improvement on the Chung-Faber-Manteuffel diameter/eigenvalue bound in graph theory (see [CFM94]), and the Chung-Grigoryan-Yau and (in a certain case) Bobkov-Ledoux distance/eigenvalue bounds in analysis (see [CGY96, CGY97, BL97]). Our framework also allows most techniques for the non-linear p-Laplacian in analysis to be easily carried over to graph theory (see [FTb])


http://arxiv.org/pdf/cs/0408028v1.pdf

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#2 Skydiver  Icon User is offline

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Re: [Link] Calculus on Graphs

Posted 21 January 2014 - 09:56 PM

I hope that paper has been vetted by other people in the field.

I was once very excited about a paper that made hard automata theory more manageable by being able to apply simple basic algebraic operations. Unfortunately, got seriously burned by this "paper" about converting regular expressions into DFA's. Basically, I was depending on the result of his "difference operator" to be able to compare the deltas between two regular expressions, but there was a subtle flaw in his logic that would cause a serious bug. I'm glad that my boss spotted the problem before I implemented it into code.
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