18,420 research outputs found

    Optoelectromechanical transducer: reversible conversion between microwave and optical photons

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    Quantum states encoded in microwave photons or qubits can be effectively manipulated, whereas optical photons can be coherently transferred via optical fibre and waveguide. The reversible conversion of quantum states between microwave and optical photons will hence enable the distribution of quantum information over long distance and significantly improve the scalability of hybrid quantum systems. Owning to technological advances, mechanical resonators couple to quantum devices in distinctly different spectral range with tunable coupling, and can serve as a powerful interface to connect those devices. In this review, we summarize recent theory and experimental progress in the coherent conversion between microwave and optical fields via optoelectromechanical transducers. The challenges and perspectives in achieving single-photon-level quantum state conversion will also be discussed.Comment: Review article, to appear in Annalen der Physik; 7 figure

    The high-level error bound for shifted surface spline interpolation

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    Radial function interpolation of scattered data is a frequently used method for multivariate data fitting. One of the most frequently used radial functions is called shifted surface spline, introduced by Dyn, Levin and Rippa in \cite{Dy1} for R2R^{2}. Then it's extended to RnR^{n} for nβ‰₯1n\geq 1. Many articles have studied its properties, as can be seen in \cite{Bu,Du,Dy2,Po,Ri,Yo1,Yo2,Yo3,Yo4}. When dealing with this function, the most commonly used error bounds are the one raised by Wu and Schaback in \cite{WS}, and the one raised by Madych and Nelson in \cite{MN2}. Both are O(dl)O(d^{l}) as dβ†’0d\to 0, where ll is a positive integer and dd is the fill-distance. In this paper we present an improved error bound which is O(Ο‰1/d)O(\omega^{1/d}) as dβ†’0d\to 0, where 0<Ο‰<10<\omega <1 is a constant which can be accurately calculated.Comment: 14 pages, radial basis functions, approximation theory. arXiv admin note: text overlap with arXiv:math/060115

    The Mystery of the Shape Parameter II

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    In this paper we present criteria for the choice of the shape parameter c contained in the famous radial function multiquadric. It may be of interest to RBF people and all people using radial basis functions to do approximation.Comment: 15 figure

    The Mystery of the Shape Parameter IV

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    In this paper we present a set of criteria for the choice of the shape parameter c contained in multiquadrics.Comment: 12 pages, 15 figure

    A Smooth and Compactly Supported Radial Function

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    In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its computational properties will be very good since it's compactly supported. Second, its error bound will converge very fast since it's infinitely differentiable. However there is hitherto no such functions which can be expressed in a simple form. This is a famous question. The purpose of this paper is to answer this question.Comment: 4 pages, radial basis functions, approximation theor

    On the High-Level Error Bound for Gaussian Interpolation

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    It's well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It's of the form(Cd)cdβˆ₯fβˆ₯h% | f(x)-s(x)| \leq (Cd)^{\frac{c}{d}}\left\Vert f\right\Vert_{h} where C,cC,c are constants, hh is the Gaussian function, % s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as dβ†’0d\to 0. The constants CC and cc are very sensitive. A slight change of them will result in a huge change of the error bound. The number cc can be calculated as shown in [9]. However, CC cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.Comment: approximation theory,radial basis function

    The Mystery of the Shape Parameter III

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    In this paper we present a set of criteria for the choice of the shape parameter c contained in multiquadrics.Comment: 12 pages, 15 figures, experiment adde

    The Shape Parameter in the Gaussian Function

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    In this paper we explore the influence of the shape parameter in the gaussian function on error estimates and present a set of criteria for its optimal choice.Comment: 15 pages, 20 figure

    Archimedean Non-vanishing, Cohomological Test Vectors, and Standard LL-functions of GL2n\mathrm{GL}_{2n}: Complex Case

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    The purpose of this paper is to study the local zeta integrals of Friedberg-Jacquet at complex place and to establish similar results to our recent work in the reall case joint with C. Cheng and D. Jiang. In this paper, we will (1) give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation Ο€\pi of GL2n(C)\mathrm{GL}_{2n}(\mathbb{C}) with a non-zero Shalika model; (2) construct a new twisted linear period Ξ›s,Ο‡\Lambda_{s,\chi}; (3) give a necessary and sufficient condition on the character Ο‡\chi such that there exists a uniform cohomological test vector v∈VΟ€v\in V_\pi (which we construct explicitly) for Ξ›s,Ο‡\Lambda_{s,\chi}. As a consequence, we obtain the non-vanishing of local Friedberg-Jacquet integral at complex place. All of the above are essential preparations for attacking a global period relation problem.Comment: 42 pages. Section 2 is now reorganized for better readability; add one subsection in Section 3 to explain the strategy of the construction of cohomological test vector; revise minor inaccuracie

    Beamforming Design for Large-Scale Antenna Arrays Using Deep Learning

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    Beamforming (BF) design for large-scale antenna arrays with limited radio frequency chains and the phase-shifter-based analog BF architecture, has been recognized as a key issue in millimeter wave communication systems. It becomes more challenging with imperfect channel state information (CSI). In this letter, we propose a deep learning based BF design approach and develop a BF neural network (BFNN) which can be trained to learn how to optimize the beamformer for maximizing the spectral efficiency with hardware limitation and imperfect CSI. Simulation results show that the proposed BFNN achieves significant performance improvement and strong robustness to imperfect CSI over the conventional BF algorithms.Comment: The codes are available in https://github.com/TianLin0509/BF-design-with-D
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