3,458 research outputs found
Homogenization of variational problems in manifold valued Sobolev spaces
Homogenization of integral functionals is studied under the constraint that
admissible maps have to take their values into a given smooth manifold. The
notion of tangential homogenization is defined by analogy with the tangential
quasiconvexity introduced by Dacorogna, Fonseca, Maly and Trivisa \cite{DFMT}.
For energies with superlinear or linear growth, a -convergence result
is established in Sobolev spaces, the homogenization problem in the space of
functions of bounded variation being the object of \cite{BM}.Comment: 22 page
Homogenization of variational problems in manifold valued BV-spaces
This paper extends the result of \cite{BM} on the homogenization of integral
functionals with linear growth defined for Sobolev maps taking values in a
given manifold. Through a -convergence analysis, we identify the
homogenized energy in the space of functions of bounded variation. It turns out
to be finite for -maps with values in the manifold. The bulk and Cantor
parts of the energy involve the tangential homogenized density introduced in
\cite{BM}, while the jump part involves an homogenized surface density given by
a geodesic type problem on the manifold.Comment: 32 page
Few Graphene layer/Carbon-Nanotube composite Grown at CMOS-compatible Temperature
We investigate the growth of the recently demonstrated composite material
composed of vertically aligned carbon nanotubes capped by few graphene layers.
We show that the carbon nanotubes grow epitaxially under the few graphene
layers. By using a catalyst and gaseous carbon precursor different from those
used originally we establish that such unconventional growth mode is not
specific to a precise choice of catalyst-precursor couple. Furthermore, the
composite can be grown using catalyst and temperatures compatible with CMOS
processing (T < 450\degree C).Comment: 4 pages, 4 figure
On overfitting and asymptotic bias in batch reinforcement learning with partial observability
This paper provides an analysis of the tradeoff between asymptotic bias
(suboptimality with unlimited data) and overfitting (additional suboptimality
due to limited data) in the context of reinforcement learning with partial
observability. Our theoretical analysis formally characterizes that while
potentially increasing the asymptotic bias, a smaller state representation
decreases the risk of overfitting. This analysis relies on expressing the
quality of a state representation by bounding L1 error terms of the associated
belief states. Theoretical results are empirically illustrated when the state
representation is a truncated history of observations, both on synthetic POMDPs
and on a large-scale POMDP in the context of smartgrids, with real-world data.
Finally, similarly to known results in the fully observable setting, we also
briefly discuss and empirically illustrate how using function approximators and
adapting the discount factor may enhance the tradeoff between asymptotic bias
and overfitting in the partially observable context.Comment: Accepted at the Journal of Artificial Intelligence Research (JAIR) -
31 page
Natural occupation numbers in two-electron quantum rings
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient
approximations. Here, we report the closed-form expression of the NOs of two-electron quantum
rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems. C 2016 AIP Publishing
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