In a low-research day, I saw two absolutely excellent seminars. The first was Alexander Rush (MIT, Columbia) talking about methods for finding the optimal parsing or syntactical structure for a natural-language sentence using lagrangian relaxation. The point is that the number of parsings is combinatorially large, so you have to do clever things to find good ones. He also looked at machine translation, which is a very related problem. At the end of his talk he discussed extraction of structured information from unstructured text, which might be applicable to the scientific literature.
Over lunch, Sergei Dubovsky (NYU) spoke about massive graviton theories and the recent BICEP2 results. He started by explaining that there are non-pathological gravity modifications in which the graviton is massive in its tensor effects, but doesn't get messed up in its scalar and vector effects. This means you have no change to the "force law" as it were (nor the black-hole solutions nor the cosmological world model) but you modify gravitational radiation. He then said two amazing things: The first is that the BICEP2 result, if it holds up, will put the strongest ever bound on the graviton mass, because it means that gravitational radiation propagated a significant fraction of a Hubble length. The second is that the BICEP2 data are better fit by a model with a tiny but nonzero graviton mass than by the standard massless theory. That's insane! But of course early days and much skepticism about the data, let alone the theory. Great talks today!
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