5,733 research outputs found
Non-perturbative positive Lyapunov exponent of Schr\"odinger equations and its applications to skew-shift
We first study the discrete Schr\"odinger equations with analytic potentials
given by a class of transformations. It is shown that if the coupling number is
large, then its logarithm equals approximately to the Lyapunov exponents. When
the transformation becomes the skew-shift, we prove that the Lyapunov exponent
is week H\"older continuous, and the spectrum satisfies Anderson Localization
and contains large intervals. Moreover, all of these conclusions are
non-perturbative
H\"older continuity of the integrated density of states for quasi-periodic Jacobi operators
We show H\"older continuity for the integrated density of states of a
quasi-periodic Jacobi operator with analytic coefficients, in the regime of
positive Lyapunov exponent and with a strong Diophantine condition on the
frequency. In particular, when the coefficients are trigonometric polynomials
we express the H\"older exponent in terms of the degrees of the coefficients.Comment: v.2: fixed some typo
Once for All: a Two-flow Convolutional Neural Network for Visual Tracking
One of the main challenges of visual object tracking comes from the arbitrary
appearance of objects. Most existing algorithms try to resolve this problem as
an object-specific task, i.e., the model is trained to regenerate or classify a
specific object. As a result, the model need to be initialized and retrained
for different objects. In this paper, we propose a more generic approach
utilizing a novel two-flow convolutional neural network (named YCNN). The YCNN
takes two inputs (one is object image patch, the other is search image patch),
then outputs a response map which predicts how likely the object appears in a
specific location. Unlike those object-specific approach, the YCNN is trained
to measure the similarity between two image patches. Thus it will not be
confined to any specific object. Furthermore the network can be end-to-end
trained to extract both shallow and deep convolutional features which are
dedicated for visual tracking. And once properly trained, the YCNN can be
applied to track all kinds of objects without further training and updating.
Benefiting from the once-for-all model, our algorithm is able to run at a very
high speed of 45 frames-per-second. The experiments on 51 sequences also show
that our algorithm achieves an outstanding performance
Direct optical detection of pure spin current in semiconductors
We suggest a new practical scheme for the direct detection of pure spin
current by using the two-color Faraday rotation of optical quantum interference
process (QUIP) in a semiconductor system. We demonstrate theoretically that the
Faraday rotation of QUIP depends sensitively on the spin orientation and wave
vector of the carriers, and can be tuned by the relative phase and the
polarization direction of the and laser beams. By adjusting
these parameters, the magnitude and direction of the spin current can be
detected.Comment: 4 pages, 3 figure
Payoff Control in the Iterated Prisoner's Dilemma
Repeated game has long been the touchstone model for agents' long-run
relationships. Previous results suggest that it is particularly difficult for a
repeated game player to exert an autocratic control on the payoffs since they
are jointly determined by all participants. This work discovers that the scale
of a player's capability to unilaterally influence the payoffs may have been
much underestimated. Under the conventional iterated prisoner's dilemma, we
develop a general framework for controlling the feasible region where the
players' payoff pairs lie. A control strategy player is able to confine the
payoff pairs in her objective region, as long as this region has feasible
linear boundaries. With this framework, many well-known existing strategies can
be categorized and various new strategies with nice properties can be further
identified. We show that the control strategies perform well either in a
tournament or against a human-like opponent
Nematic antiferromagnetic states in bulk FeSe
We revisit bulk FeSe through the systematic first-principles electronic
structure calculations. We find that there are a series of staggered -mer
antiferromagnetic (AFM) states with corresponding energies below that of the
collinear AFM state which is the ground state for the parent compounds of most
iron-based superconductors. Here the staggered -mer ( any integer )
means that a set of adjacent spins parallel on a line along -axis with
spins in antiparallel between -mers and along -axis. Among them, the
lowest energy states are quasi-degenerate staggered dimer and staggered trimer
AFM states as well as their any staggered combinations. Thus, to have the
largest entropy to minimize the free energy at low temperature, the most
favorable state is such a quasi-one-dimensional antiferromagnet in which along
-axis a variety of -mers, mostly dimers and trimers, are randomly
antiparallel aligned while along -axis spins are antiparallel aligned, i.e.
actually a nematic paramagnet. This finding accounts well for the absence of
long-range magnetic order in bulk FeSe and meanwhile indicates the dominant
stripe spin fluctuation and the nematicity as spin-driven.Comment: 6 pages and 3 figures with Supplementary Material
SentiBERT: A Transferable Transformer-Based Architecture for Compositional Sentiment Semantics
We propose SentiBERT, a variant of BERT that effectively captures
compositional sentiment semantics. The model incorporates contextualized
representation with binary constituency parse tree to capture semantic
composition. Comprehensive experiments demonstrate that SentiBERT achieves
competitive performance on phrase-level sentiment classification. We further
demonstrate that the sentiment composition learned from the phrase-level
annotations on SST can be transferred to other sentiment analysis tasks as well
as related tasks, such as emotion classification tasks. Moreover, we conduct
ablation studies and design visualization methods to understand SentiBERT. We
show that SentiBERT is better than baseline approaches in capturing negation
and the contrastive relation and model the compositional sentiment semantics.Comment: ACL-202
Electronic structures of quasi-one-dimensional cuprate superconductors BaCuO
An intact CuO plane is widely believed to be a prerequisite for the
high- superconductivity in cuprate superconductors. However, an exception
may exist in the superconducting BaCuO materials where CuO
chains play a more important role. From first-principles density functional
theory calculations, we have studied the electronic and magnetic structures of
BaCuO. The stoichiometric BaCuO and BaCuO
contain quasi-one-dimensional CuO chains and intact two-dimensional CuO
planes, respectively. In comparison with the nonmagnetic metal BaCuO,
BaCuO is found to be an antiferromagnetic (AFM) Mott insulator. It
possesses a nearest-neighbor intra-chain antiferromagnetic (AFM) coupling and a
weak inter-chain interaction, and its lowest unoccupied band and highest
occupied band are contributed by Cu 3-orbital (or
-orbital if we denote the -plane as the -plane) and O
2-orbitals, respectively. Total energy calculations indicate that the oxygen
vacancies in BaCuO prefer to reside in the planar sites rather
than the apical oxygens in the CuO chains, in agreement with the experimental
observation. Furthermore, we find that the magnetic frustrations or spin
fluctuations can be effectively induced by moderate charge doping. This
suggests that the superconducting pairing in oxygen-enriched
BaCuO or oxygen-deficient BaCuO is likely to
be mainly driven by the AFM fluctuations within CuO chains.Comment: 7 pages, 7 figures, 3 table
H\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators
We consider the quasi-periodic Jacobi operator in
where
are analytic function on , is not identically
zero, and obeys some strong Diophantine condition.
We consider the corresponding unimodular cocycle. We prove that if the
Lyapunov exponent of the cocycle is positive for some , then
there exists , such
that for any . If
for all in some compact interval then is H\"{o}lder
continuous on with a H\"{o}lder exponent . In
our derivation we follow the refined version of the Goldstein-Schlag method
\cite{GS} developed by Bourgain and Jitomirskaya \cite{BJ}
Minkowski formulae and Alexandrov theorems in spacetime
The classical Minkowski formula is extended to spacelike codimension-two
submanifolds in spacetimes which admit "hidden symmetry" from conformal
Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem
for spacelike codimension-two submanifolds in a static spherically symmetric
spacetime: a codimension-two submanifold with constant normalized null
expansion (null mean curvature) must lie in a shear-free (umbilical) null
hypersurface. These results are generalized for higher order curvature
invariants. In particular, the notion of mixed higher order mean curvature is
introduced to highlight the special null geometry of the submanifold. Finally,
Alexandrov type theorems are established for spacelike submanifolds with
constant mixed higher order mean curvature, which are generalizations of
hypersurfaces of constant Weingarten curvature in the Euclidean space.Comment: 38 pages. To appear in J. Differential Geometr
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