24,920 research outputs found

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

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    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 Uq(gln+1)U_q(gl_{n+1}).Comment: 17 pages, 1 figur

    Decomposition of the Symmetric Powers

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    A decomposition of any symmetric power of C2βŠ—C2βŠ—C2\Bbb C^2\otimes\Bbb C^2\otimes\Bbb C^2 into irreducible sl2(C)βŠ•sl2(C)βŠ•sl2(C)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'

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    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

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    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

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    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 33\frac{\sqrt{3}}{3} and 3\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

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    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

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    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

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    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

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    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

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    Let GG be a connected reductive algebraic group GG over an algebraically closed field kk of prime characteristic pp, and \ggg=\Lie(G). In this paper, we study modular representations of the reductive Lie algebra ⋙\ggg with pp-character χ\chi of standard Levi-form associated with an index subset II of simple roots. With aid of support variety theory we prove a theorem that a Uχ(⋙)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 G1TG_1T-modules, we construct so-called Andersen-Kaneda filtrations associated with each projective ⋙\ggg-module of pp-character χ\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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