24,920 research outputs found

### Crystal Structure on the Category of Modules over Colored Planar Rook Algebra

Colored planar rook algebra is a semigroup algebra in which the basis element
has a diagrammatic description. The category of finite dimensional modules over
this algebra is completely reducible and suitable functors are defined on this
category so that it admits a crystal structure in the sense of Kashiwara. We
show that the category and functors categorify the crystal bases for the
polynomial representations of quantized enveloping algebra $U_q(gl_{n+1})$.Comment: 17 pages, 1 figur

### Decomposition of the Symmetric Powers

A decomposition of any symmetric power of $\Bbb C^2\otimes\Bbb C^2\otimes\Bbb
C^2$ into irreducible $sl_2(\Bbb C)\oplus sl_2(\Bbb C)\oplus sl_2(\Bbb
C)$-submodules are presented. Namely, the multiplicities of irreducible
summands in the symmetric power are determined.Comment: 13 page

### Towards extremely high-resolution broad-band flat-field spectrometer in 'water window'

The optical design of a novel spectrometer is present, combining a
cylindrically convex pre-mirror with a cylindrically concave VLS grating (both
in meridional) to deliver a resolving power of 100,000-200,000 in 'water
window' (2-5nm). More remarkably, unlike a typical RIXS spectrometer to obtain
such high resolution by tight focusing or tiny confinement slit (<1{\mu}m),
here the resolution could be achieved for an effective meridional source size
of 50{\mu}m (r.m.s.). The overall optical aberrations of the system are well
analysed and compensated, providing an excellent flat field at the detector
domain throughout the whole spectral range. And a machine learning scheme - SVM
is introduced to explore and reconstruct the optimal system with pretty high
efficiency.Comment: 11 pages, 6 figure

### General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to arbitrarily high-dimensional systems. Based on this
generalization, we construct the general CHSH inequality for bipartite quantum
systems of arbitrarily high dimensionality, which takes the same simple form as
CHSH inequality for two-dimension. This inequality is optimal in the same sense
as the CHSH inequality for two dimensional systems, namely, the maximal amount
by which the inequality is violated consists with the maximal resistance to
noise. We also discuss the physical meaning and general definition of the
correlation functions. Furthermore, by giving another specific set of the
correlation functions with the same physical meaning, we realize the inequality
presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].Comment: 4 pages, accepted by Phys. Rev. Let

### Generation of maximally entangled mixed states of two atoms via on-resonance asymmetric atom-cavity couplings

A scheme for generating the maximally entangled mixed state of two atoms
on-resonance asymmetrically coupled to a single mode optical cavity field is
presented. The part frontier of both maximally entangled mixed states and
maximal Bell violating mixed states can be approximately reached by the
evolving reduced density matrix of two atoms if the ratio of coupling strengths
of two atoms is appropriately controlled. It is also shown that exchange
symmetry of global maximal concurrence is broken if and only if coupling
strength ratio lies between $\frac{\sqrt{3}}{3}$ and $\sqrt{3}$ for the case of
one-particle excitation and asymmetric coupling, while this partial
symmetry-breaking can not be verified by detecting maximal Bell violation.Comment: 5 pages, 5 figure

### Squeezing induced transition of long-time decay rate

We investigate the nonclassicality of several kinds of nonclassical optical
fields such as the pure or mixed single photon-added coherent states and the
cat states in the photon-loss or the dephasing channels by exploring the
entanglement potential as the measure. It is shown that the long-time decay of
entanglement potentials of these states in photon loss channel is dependent of
their initial quadrature squeezing properties. In the case of photon-loss,
transition of long-time decay rate emerges at the boundary between the
squeezing and non-squeezing initial non-gaussian states if log-negativity is
adopted as the measure of entanglement potential. However, the transition
behavior disappears if the concurrence is adopted as the measure of
entanglement potential. For the case of the dephasing, distinct decay behaviors
of the nonclassicality are also revealed.Comment: 7 pages, 7 figures, RevTex

### Dynamics of a single hole in the Heisenberg-Kitaev model: a self-consistent Born approximation study

The magnetic properties of 4d and 5d transition-metal insulating compounds
with the honeycomb structure are believed to be described by the
Heisenberg-Kitaev model, which contains both the isotropic Heisenberg
interaction J and anisotropic Kitaev interaction K. In this paper, to
investigate the charge dynamics in these materials, we study the single-hole
propagation of the t-J-K model in various magnetically ordered phases by the
self-consistent Born approximation. We find that there are low-energy coherent
quasiparticle (QP) excitations in all of these phases which appear firstly
around the K point in the Brillouin zone (BZ), but the band-widths of these QPs
are very small due to the hole-magnon coupling. Interestingly, in the zigzag
phase relevant to recent experiments, though the QP weights are largely
suppressed in the physical spectra in the first BZ, we find that they recover
in the extended BZs. Moreover, our results reveal that the low-energy QP
spectra are reduced with the increase of K.Comment: 9 pages, 5 figure

### General drawdown of general tax model in a time-homogeneous Markov framework

Drawdown/regret times feature prominently in optimal stopping problems, in
statistics (CUSUM procedure) and in mathematical finance (Russian options).
Recently it was discovered that a first passage theory with general drawdown
times, which generalize classic ruin times, may be explicitly developed for
spectrally negative L\'evy processes -- see Avram, Vu, Zhou(2017), Li, Vu,
Zhou(2017). In this paper, we further examine general drawdown related
quantities for taxed time-homogeneous Markov processes, using the pathwise
connection between general drawdown and tax

### Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing

Crowdsourcing has become an effective and popular tool for human-powered
computation to label large datasets. Since the workers can be unreliable, it is
common in crowdsourcing to assign multiple workers to one task, and to
aggregate the labels in order to obtain results of high quality. In this paper,
we provide finite-sample exponential bounds on the error rate (in probability
and in expectation) of general aggregation rules under the Dawid-Skene
crowdsourcing model. The bounds are derived for multi-class labeling, and can
be used to analyze many aggregation methods, including majority voting,
weighted majority voting and the oracle Maximum A Posteriori (MAP) rule. We
show that the oracle MAP rule approximately optimizes our upper bound on the
mean error rate of weighted majority voting in certain setting. We propose an
iterative weighted majority voting (IWMV) method that optimizes the error rate
bound and approximates the oracle MAP rule. Its one step version has a provable
theoretical guarantee on the error rate. The IWMV method is intuitive and
computationally simple. Experimental results on simulated and real data show
that IWMV performs at least on par with the state-of-the-art methods, and it
has a much lower computational cost (around one hundred times faster) than the
state-of-the-art methods.Comment: Journal Submissio

### Filtrations in Modular Representations of Reductive Lie Algebras

Let $G$ be a connected reductive algebraic group $G$ over an algebraically
closed field $k$ of prime characteristic $p$, and \ggg=\Lie(G). In this
paper, we study modular representations of the reductive Lie algebra $\ggg$
with $p$-character $\chi$ of standard Levi-form associated with an index subset
$I$ of simple roots. With aid of support variety theory we prove a theorem that
a $U_\chi(\ggg)$-module is projective if and only if it is a strong "tilting"
module, i.e. admitting both \cz_Q- and \cz^{w^I}_Q-filtrations (to see
Theorem \ref{THMFORINV}). Then by analogy of the arguments in \cite{AK} for
$G_1T$-modules, we construct so-called Andersen-Kaneda filtrations associated
with each projective $\ggg$-module of $p$-character $\chi$, and finally obtain
sum formulas from those filtrations.Comment: The current version of this paper will appear in Algebra Colloquiu

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