829 research outputs found
Bandit Online Optimization Over the Permutahedron
The permutahedron is the convex polytope with vertex set consisting of the
vectors for all permutations (bijections) over
. We study a bandit game in which, at each step , an
adversary chooses a hidden weight weight vector , a player chooses a
vertex of the permutahedron and suffers an observed loss of
.
A previous algorithm CombBand of Cesa-Bianchi et al (2009) guarantees a
regret of for a time horizon of . Unfortunately,
CombBand requires at each step an -by- matrix permanent approximation to
within improved accuracy as grows, resulting in a total running time that
is super linear in , making it impractical for large time horizons.
We provide an algorithm of regret with total time
complexity . The ideas are a combination of CombBand and a recent
algorithm by Ailon (2013) for online optimization over the permutahedron in the
full information setting. The technical core is a bound on the variance of the
Plackett-Luce noisy sorting process's "pseudo loss". The bound is obtained by
establishing positive semi-definiteness of a family of 3-by-3 matrices
generated from rational functions of exponentials of 3 parameters
Unusual Low-Temperature Phase in VO Nanoparticles
We present a systematic investigation of the crystal and electronic structure
and the magnetic properties above and below the metal-insulator transition of
ball-milled VO nanoparticles and VO microparticles. For this research,
we performed a Rietveld analysis of synchrotron radiation x-ray diffraction
data, O x-ray absorption spectroscopy, V resonant inelastic x-ray
scattering, and magnetic susceptibility measurements. This study reveals an
unusual low-temperature phase that involves the formation of an elongated and
less-tilted V-V pair, a narrowed energy gap, and an induced paramagnetic
contribution from the nanoparticles. We show that the change in the crystal
structure is consistent with the change in the electronic states around the
Fermi level, which leads us to suggest that the Peierls mechanism contributes
to the energy splitting of the state. Furthermore, we find that the
high-temperature rutile structure of the nanoparticles is almost identical to
that of the microparticles.Comment: 7 pages, 8 figures, 2 table
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