46,193 research outputs found
Boundary expansions and convergence for complex Monge-Ampere equations
We study boundary expansions of solutions of complex Monge-Ampere equations
and discuss the convergence of such expansions. We prove a global conver- gence
result under that assumption that the entire boundary is analytic. If a portion
of the boundary is assumed to be analytic, the expansions may not converge
locally
On black hole spectroscopy via adiabatic invariance
In this paper, we obtain the black hole spectroscopy by combining the black
hole property of adiabaticity and the oscillating velocity of the black hole
horizon. This velocity is obtained in the tunneling framework. In particular,
we declare, if requiring canonical invariance, the adiabatic invariant quantity
should be of the covariant form . Using it,
the horizon area of a Schwarzschild black hole is quantized independent of the
choice of coordinates, with an equally spaced spectroscopy always given by
in the Schwarzschild and Painlev\'{e}
coordinates.Comment: 13 pages, some references added, to be published in Phys. Lett.
Dependency Grammar Induction with Neural Lexicalization and Big Training Data
We study the impact of big models (in terms of the degree of lexicalization)
and big data (in terms of the training corpus size) on dependency grammar
induction. We experimented with L-DMV, a lexicalized version of Dependency
Model with Valence and L-NDMV, our lexicalized extension of the Neural
Dependency Model with Valence. We find that L-DMV only benefits from very small
degrees of lexicalization and moderate sizes of training corpora. L-NDMV can
benefit from big training data and lexicalization of greater degrees,
especially when enhanced with good model initialization, and it achieves a
result that is competitive with the current state-of-the-art.Comment: EMNLP 201
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