14,072 research outputs found
Online Local Learning via Semidefinite Programming
In many online learning problems we are interested in predicting local
information about some universe of items. For example, we may want to know
whether two items are in the same cluster rather than computing an assignment
of items to clusters; we may want to know which of two teams will win a game
rather than computing a ranking of teams. Although finding the optimal
clustering or ranking is typically intractable, it may be possible to predict
the relationships between items as well as if you could solve the global
optimization problem exactly.
Formally, we consider an online learning problem in which a learner
repeatedly guesses a pair of labels (l(x), l(y)) and receives an adversarial
payoff depending on those labels. The learner's goal is to receive a payoff
nearly as good as the best fixed labeling of the items. We show that a simple
algorithm based on semidefinite programming can obtain asymptotically optimal
regret in the case where the number of possible labels is O(1), resolving an
open problem posed by Hazan, Kale, and Shalev-Schwartz. Our main technical
contribution is a novel use and analysis of the log determinant regularizer,
exploiting the observation that log det(A + I) upper bounds the entropy of any
distribution with covariance matrix A.Comment: 10 page
Test of quantum chemistry in vibrationally-hot hydrogen molecules
Precision measurements are performed on highly excited vibrational quantum
states of molecular hydrogen. The rovibrational levels of H
(), lying only cm below the first dissociation
limit, were populated by photodissociation of HS and their level energies
were accurately determined by two-photon Doppler-free spectroscopy. A
comparison between the experimental results on level energies with the
best \textit{ab initio} calculations shows good agreement, where the present
experimental accuracy of cm is more precise than
theory, hence providing a gateway to further test theoretical advances in this
benchmark quantum system.Comment: 5 pages, 4 figures, and 2 table
The detection and interpretation of long-term changes in ozone from space
Long-term measurements of backscattered ultraviolet radiances, now being acquired by orbiting monochromators, will provide the basis for seeking trends in atmospheric ozone. The unambiguous detection of ozone trends on decadal time scales demands a data set that is essentially free of instrument drifts. Periodic flights of an ultraviolet monochromator on the space shuttle will provide an independent means of evaluating the long-term stability of identical instruments operating on free-flying satellites. A successful calibration of the free-flying sensors using the shuttle instrument places strict demands on calibration repeatability from one flight to the next. In addition, spatial and temporal variability in cloud cover could pose further complications in carrying out these in-flight calibrations
High-precision laser spectroscopy of the CO A - X (2,0), (3,0) and (4,0) bands
High-precision two-photon Doppler-free frequency measurements have been
performed on the CO A - X fourth-positive system (2,0),
(3,0), and (4,0) bands. Absolute frequencies of forty-three transitions, for
rotational quantum numbers up to , have been determined at an accuracy
of cm, using advanced techniques of two-color 2+1'
resonance-enhanced multi-photon ionization, Sagnac interferometry,
frequency-chirp analysis on the laser pulses, and correction for AC-Stark
shifts. The accurate transition frequencies of the CO A - X
system are of relevance for comparison with astronomical data in the search for
possible drifts of fundamental constants in the early universe. The present
accuracies in laboratory wavelengths of may be considered exact for the purpose of such comparisons.Comment: 13 pages, 6 figures, The Journal of Chemical Physics (2015) accepte
Unbalanced edge modes and topological phase transition in gated trilayer graphene
Gapless edge modes hosted by chirally-stacked trilayer graphene display
unique features when a bulk gap is opened by applying an interlayer potential
difference. We show that trilayer graphene with half-integer valley Hall
conductivity leads to unbalanced edge modes at opposite zigzag boundaries,
resulting in a natural valley current polarizer. This unusual characteristic is
preserved in the presence of Rashba spin-orbit coupling that turns a gated
trilayer graphene into a topological insulator with an odd number of
helical edge mode pairs.Comment: 5 pages, 4 figure
Quasi-particle random phase approximation with quasi-particle-vibration coupling: application to the Gamow-Teller response of the superfluid nucleus Sn
We propose a self-consistent quasi-particle random phase approximation (QRPA)
plus quasi-particle-vibration coupling (QPVC) model with Skyrme interactions to
describe the width and the line shape of giant resonances in open-shell nuclei,
in which the effect of superfluidity should be taken into account in both the
ground state and the excited states. We apply the new model to the Gamow-Teller
resonance in the superfluid nucleus Sn, including both the isoscalar
spin-triplet and the isovector spin-singlet pairing interactions. The strength
distribution in Sn is well reproduced and the underlying microscopic
mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in
detail.Comment: 32 pages, 11 figures, 4 table
Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes
The phase transition of Reissner-Nordstr\"om black holes in
-dimensional anti-de Sitter spacetime is studied in details using the
thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid
gas system. We first investigate critical phenomena of the RN-AdS black hole.
The critical exponents of relevant thermodynamical quantities are evaluated. We
find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas
system. This suggests a possible universality in the phase transitions of these
systems. We finally study the thermodynamic behavior using the equilibrium
thermodynamic state space geometry and find that the scalar curvature diverges
exactly at the van der Waals-like critical point where the heat capacity at
constant charge of the black hole diverges.Comment: 18 pages, 5 figure
Valley Dependent Optoelectronics from Inversion Symmetry Breaking
Inversion symmetry breaking allows contrasted circular dichroism in different
k-space regions, which takes the extreme form of optical selection rules for
interband transitions at high symmetry points. In materials where band-edges
occur at noncentral valleys, this enables valley dependent interplay of
electrons with light of different circular polarizations, in analogy to spin
dependent optical activities in semiconductors. This discovery is in perfect
harmony with the previous finding of valley contrasted Bloch band features of
orbital magnetic moment and Berry curvatures from inversion symmetry breaking
[Phys. Rev. Lett. 99, 236809 (2007)]. A universal connection is revealed
between the k-resolved optical oscillator strength of interband transitions,
the orbital magnetic moment and the Berry curvatures, which also provides a
principle for optical measurement of orbital magnetization and intrinsic
anomalous Hall conductivity in ferromagnetic systems. The general physics is
demonstrated in graphene where inversion symmetry breaking leads to valley
contrasted optical selection rule for interband transitions. We discuss
graphene based valley optoelectronics applications where light polarization
information can be interconverted with electronic information.Comment: Expanded version, to appear in Phys. Rev.
Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
We propose a gauge invariant expression for the side jump associated with
scattering between particular Bloch states. Our expression for the side jump
follows from the Born series expansion for the scattering T-matrix in powers of
the strength of the scattering potential. Given our gauge invariant side jump
expression, it is possible to construct a semiclassical Boltzmann theory of the
anomalous Hall effect which expresses all previously identified contributions
in terms of gauge invariant quantities and does not refer explicitly to
off-diagonal terms in the density-matrix response.Comment: 6 pages, 1 fugure. submitted to PR
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