arXiv subjects

Ran Yang

Publications and source records attributed to Ran Yang.

44 records · Page 3Linked to original sources

arXiv2019

Linear instability for periodic orbits of non-autonomous Lagrangian systems

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic solutions of a non-autonomous Lagrangian on a finite dimensional Riemannian manifold. We establish a general criterion for a priori detecting the linear instability of a periodic orbit on a Riemannian manifold for a (maybe not Legendre convex) non-autonomous Lagrangian simply by looking at the parity of the spectral index, which is the right substitute of the Morse index in the framework of strongly indefinite variational problems and defined in terms of the spectral flow of a path of Fredholm quadratic forms on a Hilbert bundle.

math.DS↗

arXiv2019

Narrow-band photonic quantum entanglement with counterpropagating domain engineering

Photonic entanglement is a crucial resource for quantum information technologies, including quantum information processing and long-distance communication. These applications call for narrow-band entanglement sources, being compatible with the photon-electron interfaces and relax the dispersion-induced entanglement-degradation in the network mediums. However, such Giga-hertz-level bandwidth is a challenge for the photonic entanglement based on conventional spontaneous parametric down-conversion. Here we introduce a state-of-art domain-engineering technology for the counterpropagating phase matching in the polarization-entanglement generation, which results in an inherent bandwidth of 7.1 GHz at telecom wavelength. This geometry also resolves the fundamental challenge for the deterministic separation of the entangled photon pairs at frequency degeneracy, so that efficient collinear interaction can be achieved in a periodically-poled KTP waveguide and results in a spectral brightness of 3.4*10^3(GHz*mW*s)^-1. The 155 ps base-to-base Hong-Ou-Mandel dip also confirms the source bandwidth, with and a high interference visibility of 97.1%. The entanglement is measured to violate the Bell inequality by up to 18.5 standard deviations, with Clauser-Horne-Shimony-Holt S-parameter of 2.720. The quantum state tomography further characterizes the entanglement, with fidelity F=95.71%. These unique features establish a cornerstone for the photonic entanglement sources development and warrant broad practical quantum information applications.

quant-ph↗

arXiv2019

Drone-based all-weather entanglement distribution

The quantum satellite is a cornerstone towards practical free-space quantum network and overcomes the photon loss over large distance. However, challenges still exist including real-time all-location coverage and multi-node construction, which may be complemented by the diversity of modern drones. Here we demonstrate the first drone-based entanglement distribution at all-weather conditions over 200 meters (test field limited), and the Clauser-Horne-Shimony-Holt S-parameter exceeds 2.49, within 35 kg take-off weight. With symmetric transmitter and receiver beam apertures and single-mode-fiber-coupling technology, such progress is ready for future quantum network with multi-node expansion. This network can be further integrated in picture-drone sizes for plug-and-play local-area coverage, or loaded onto high-altitude drones for wide-area coverage, which adds flexibility while connecting to the existing satellites and ground fiber-based quantum network.

quant-ph↗

arXiv2019

Instability of semi-Riemannian closed geodesics

A celebrated result due to Poincaré affirms that a closed non-degenerate minimizing geodesic $γ$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first main result is a general instability criterion for timelike and spacelike closed semi-Riemannian geodesics on a (non)oriented manifold. A key role is played by the spectral index, a new topological invariant that we define through the spectral flow (being the Morse index truly infinite) of a path of selfadjoint Fredholm operators. A major step in the proof of this result is a em new spectral flow formula. Bott's iteration formula, introduced by author in 1956, relates in a clear way the Morse index of an iterated closed Riemannian geodesic and the so-called $ω$-Morse indices. Our second result is a semi-Riemannian generalization of the famous Bott-type iteration formula in the case of closed (resp. timelike closed) Riemannian (resp. Lorentzian) geodesics. Our last result is a strong instability result obtained by controlling the Morse index of the geodesic and of all of its iterations.

math.DG↗

arXiv2019

Fast Single Image Dehazing via Multilevel Wavelet Transform based Optimization

The quality of images captured in outdoor environments can be affected by poor weather conditions such as fog, dust, and atmospheric scattering of other particles. This problem can bring extra challenges to high-level computer vision tasks like image segmentation and object detection. However, previous studies on image dehazing suffer from a huge computational workload and corruption of the original image, such as over-saturation and halos. In this paper, we present a novel image dehazing approach based on the optical model for haze images and regularized optimization. Specifically, we convert the non-convex, bilinear problem concerning the unknown haze-free image and light transmission distribution to a convex, linear optimization problem by estimating the atmosphere light constant. Our method is further accelerated by introducing a multilevel Haar wavelet transform. The optimization, instead, is applied to the low frequency sub-band decomposition of the original image. This dimension reduction significantly improves the processing speed of our method and exhibits the potential for real-time applications. Experimental results show that our approach outperforms state-of-the-art dehazing algorithms in terms of both image reconstruction quality and computational efficiency. For implementation details, source code can be publicly accessed via http://github.com/JiaxiHe/Image-and-Video-Dehazing.

cs.CV↗

arXiv2018

Density Deconvolution with Additive Measurement Errors using Quadratic Programming

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can achieve better estimation than kernel density deconvolution methods. The QP approach appears to have a more favorable regularization tradeoff between oversmoothing vs. oscillation, especially at the tails of the distribution. An additional advantage is that it is straightforward to incorporate a number of common density constraints such as nonnegativity, integration-to-one, unimodality, tail convexity, tail monotonicity, and support constraints. We demonstrate that the QP approach has outstanding estimation performance relative to existing methods. Its performance is superior when only the universally applicable nonnegativity and integration-to-one constraints are incorporated, and incorporating additional common constraints when applicable (e.g., nonnegative support, unimodality, tail monotonicity or convexity, etc.) can further substantially improve the estimation.

stat.ME↗

arXiv2018

Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit

In this paper, we prove Morse index theorem of Lagrangian system with any self-adjoint boundary conditions. Based on it, we give some nontrivial estimation on the difference of Morse indices. As an application, we get a new criterion for the stability problem of brake periodic orbit.

math.DS↗

arXiv2017

A dihedral Bott-type iteration formula and stability of symmetric periodic orbits

In 1956, Bott in his celebrated paper on closed geodesics and Sturm intersection theory, proved an Index Iteration Formula for closed geodesics on Riemannian manifolds. Some years later, Ekeland improved this formula in the case of convex Hamiltonians and, in 1999, Long generalized the Bott iteration formula by putting in its natural symplectic context and constructing a very effective Index Theory. The literature about this formula is quite broad and the dynamical implications in the Hamiltonian world (e.g. existence, multiplicity, linear stability etc.) are enormous. Motivated by the recent discoveries on the stability properties of symmetric periodic solutions of singular Lagrangian systems, we establish a Bott-type iteration formula for dihedrally equivariant Lagrangian and Hamiltonian systems. We finally apply our theory for computing the Morse indices of the celebrated Chenciner and Montgomery figure-eight orbit for the planar three body problem in different equivariant spaces. Our last dynamical consequence is an hyperbolicity criterion for reversible Lagrangian systems.

math.DS↗