Stability of the Bergman kernel on a tower of coverings

We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings on hyperbolic Riemann surfaces and on complete Kaehler manifolds satisfying certain potential conditions. As a consequence, stability of the Bergman kernel is established for any tower of coverings of Riemann surfaces when the top manifold is simply-connected.Comment: 22 page

Beyond Fermi pseudopotential: a modified GP equation

We present an effective potential and the corresponding modified Gross-Pitaevskii equation that account for the energy dependence of the two-body scattering amplitude through an effective-range expansion. For the ground state energy of a trapped condensate, the theory leads to what we call a shape-dependent confinement correction that improves agreements with diffusion Monte Carlo calculations. The theory illustrates, for relatively strong confinement and/or high density, how the shape dependence on atom-atom interaction can come into play in a many-atom quantum system.Comment: 8 pages, 5 figure

Efficient quantum entanglement distribution over an arbitrary collective-noise channel

We present an efficient quantum entanglement distribution over an arbitrary collective-noise channel. The basic idea in the present scheme is that two parties in quantum communication first transmit the entangled states in the frequency degree of freedom which suffers little from the noise in an optical fiber. After the two parties share the photon pairs, they add some operations and equipments to transfer the frequency entanglement of pairs into the polarization entanglement with the success probability of 100\%. Finally, they can get maximally entangled polarization states with polarization independent wavelength division multiplexers and quantum frequency up-conversion which can erase distinguishability for frequency. Compared with conventional entanglement purification protocols, the present scheme works in a deterministic way in principle. Surprisingly, the collective noise leads to an additional advantage.Comment: 6 pages, 2 figure

Proposal for a quantum delayed-choice experiment with a spin-mechanical setup

We describe an experimentally feasible protocol for performing a variant of the quantum delayed-choice experiment with massive objects. In this scheme, a single nitrogen-vacancy (NV) center in diamond driven by microwave fields is dispersively coupled to a massive mechanical resonator. A double-pulse Ramsey interferometer can be implemented with the spin-mechanical setup, where the second Ramsey microwave pulse drives the spin conditioned on the number states of the resonator. The probability for finding the NV center in definite spin states exhibits interference fringes when the mechanical resonator is prepared in a specific number state. On the other hand, the interference is destroyed if the mechanical resonator stays in some other number states. The wavelike and particlelike behavior of the NV spin can be superposed by preparing the mechanical resonator in a superposition of two distinct number states. Thus a quantum version of Wheeler's delayed-choice experiment could be implemented, allowing of fundamental tests of quantum mechanics on a macroscopic scale.Comment: To be published in Phys.Rev.

Image Super-Resolution Using TV Priori Guided Convolutional Network

We proposed a TV priori information guided deep learning method for single image super-resolution(SR). The new alogorithm up-sample method based on TV priori, new learning method and neural networks architecture are embraced in our TV guided priori Convolutional Neural Network which diretcly learns an end to end mapping between the low level to high level images.Comment: This paper is underviewring in Journal of Pattern Recognition Letter

Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement

Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocl, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve the efficiency of long-distance quantum communication exponentially. Meanwhile, it will be shown that this EPP can be used to complete nonlocal Bell-state analysis perfectly. We also discuss this EPP in a practical transmission.Comment: 8 pages, 2 figure

One-step deterministic polarization entanglement purification using spatial entanglement

We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol (Phys. Rev. Lett. 89, 257901 (2002)), this one-step protocol has some advantages. First, it can get a maximally entangled pair with only one step, not only improve the fidelity of less-entangled photon pairs by performing the protocol repeatedly. Second, it works in a deterministic way, not a probabilistic one, which will reduce a great deal of entanglement resources. Third, it does not require the polarization state be entangled, only spatial entanglement is needed. Moreover, it is feasible with current techniques (Nature 423, 417 (2003)). All these advantages will make this one-step protocol more convenient than others in the applications in quantum communication.Comment: 5 pages, 1 figures. A negligible error about the density matrix \rho"_p in Eq. (9) is correcte

Learning From Hidden Traits: Joint Factor Analysis and Latent Clustering

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations that are well-suited for the intended task is more appealing. This paper proposes a joint factor analysis and latent clustering framework, which aims at learning cluster-aware low-dimensional representations of matrix and tensor data. The proposed approach leverages matrix and tensor factorization models that produce essentially unique latent representations of the data to unravel latent cluster structure -- which is otherwise obscured because of the freedom to apply an oblique transformation in latent space. At the same time, latent cluster structure is used as prior information to enhance the performance of factorization. Specific contributions include several custom-built problem formulations, corresponding algorithms, and discussion of associated convergence properties. Besides extensive simulations, real-world datasets such as Reuters document data and MNIST image data are also employed to showcase the effectiveness of the proposed approaches

RaD-VIO: Rangefinder-aided Downward Visual-Inertial Odometry

State-of-the-art forward facing monocular visual-inertial odometry algorithms are often brittle in practice, especially whilst dealing with initialisation and motion in directions that render the state unobservable. In such cases having a reliable complementary odometry algorithm enables robust and resilient flight. Using the common local planarity assumption, we present a fast, dense, and direct frame-to-frame visual-inertial odometry algorithm for downward facing cameras that minimises a joint cost function involving a homography based photometric cost and an IMU regularisation term. Via extensive evaluation in a variety of scenarios we demonstrate superior performance than existing state-of-the-art downward facing odometry algorithms for Micro Aerial Vehicles (MAVs).Comment: Accepted by ICRA 201

Wavelet Video Coding Algorithm Based on Energy Weighted Significance Probability Balancing Tree

This work presents a 3-D wavelet video coding algorithm. By analyzing the contribution of each biorthogonal wavelet basis to reconstructed signal's energy, we weight each wavelet subband according to its basis energy. Based on distribution of weighted coefficients, we further discuss a 3-D wavelet tree structure named \textbf{significance probability balancing tree}, which places the coefficients with similar probabilities of being significant on the same layer. It is implemented by using hybrid spatial orientation tree and temporal-domain block tree. Subsequently, a novel 3-D wavelet video coding algorithm is proposed based on the energy-weighted significance probability balancing tree. Experimental results illustrate that our algorithm always achieves good reconstruction quality for different classes of video sequences. Compared with asymmetric 3-D orientation tree, the average peak signal-to-noise ratio (PSNR) gain of our algorithm are 1.24dB, 2.54dB and 2.57dB for luminance (Y) and chrominance (U,V) components, respectively. Compared with temporal-spatial orientation tree algorithm, our algorithm gains 0.38dB, 2.92dB and 2.39dB higher PSNR separately for Y, U, and V components. In addition, the proposed algorithm requires lower computation cost than those of the above two algorithms.Comment: 17 pages, 2 figures, submission to Multimedia Tools and Application