14,931 research outputs found
Nonparametric Stochastic Contextual Bandits
We analyze the -armed bandit problem where the reward for each arm is a
noisy realization based on an observed context under mild nonparametric
assumptions. We attain tight results for top-arm identification and a sublinear
regret of , where is the
context dimension, for a modified UCB algorithm that is simple to implement
(NN-UCB). We then give global intrinsic dimension dependent and ambient
dimension independent regret bounds. We also discuss recovering topological
structures within the context space based on expected bandit performance and
provide an extension to infinite-armed contextual bandits. Finally, we
experimentally show the improvement of our algorithm over existing multi-armed
bandit approaches for both simulated tasks and MNIST image classification.Comment: AAAI 201
Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction
Quantum criticality of strongly attractive Fermi gas with symmetry in
one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The
phase transitions driven by the chemical potential , effective magnetic
field , (chemical potential biases) are analyzed at the quantum
criticality. The phase diagram and critical fields are analytically determined
by the thermodynamic Bethe ansatz equations in zero temperature limit. High
accurate equations of state, scaling functions are also obtained analytically
for the strong interacting gases. The dynamic exponent and correlation
length exponent read off the universal scaling form. It turns out
that the quantum criticality of the three-component gases involves a sudden
change of density of states of one cluster state, two or three cluster states.
In general, this method can be adapted to deal with the quantum criticality of
multi-component Fermi gases with symmetry.Comment: 20 pages, 5 figures, submitted to J.Phys.A, revised versio
Unusually stable helical coil allotrope of phosphorus
We have identified an unusually stable helical coil allotrope of phosphorus.
Our ab initio Density Functional Theory calculations indicate that the
uncoiled, isolated straight 1D chain is equally stable as a monolayer of black
phosphorus dubbed phosphorene. The coiling tendency and the attraction between
adjacent coil segments add an extra stabilization energy of about 12 meV/atom
to the coil allotrope, similar in value to the approximately 16 meV/atom
inter-layer attraction in bulk black phosphorus. Thus, the helical coil
structure is essentially as stable as black phosphorus, the most stable
phosphorus allotrope known to date. With an optimum radius of 2.4 nm, the
helical coil of phosphorus may fit well and even form inside wide carbon
nanotubes.Comment: The paper has been accepted by Nano. Lett. (2016
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