1.0Microsoft Researchhttps://www.microsoft.com/en-us/researchJeff Runninghttps://www.microsoft.com/en-us/research/people/jeffrunn/Fixed-Energy Harmonic Functions - Microsoft Researchrich600338<blockquote class="wp-embedded-content" data-secret="2J4o5XmjIt"><a href="https://www.microsoft.com/en-us/research/video/fixed-energy-harmonic-functions/">Fixed-Energy Harmonic Functions</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/video/fixed-energy-harmonic-functions/embed/#?secret=2J4o5XmjIt" width="600" height="338" title="“Fixed-Energy Harmonic Functions” — Microsoft Research" data-secret="2J4o5XmjIt" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe><script type="text/javascript">
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https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/fixed-energy-harmonic-functions-1.jpg640480We study the map from conductances to edge energies for harmonic functions on graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of conductances such that the associated harmonic function realizes those orientations and energies. For planar graphs there is a harmonic […]