Critical theories of phase transition between symmetry protected topological states and their relation to the gapless boundary theories

Symmetry protected topological states (SPTs) have the same symmetry and the phase transition between them are beyond Landau's symmetry breaking formalism. In this paper we study (1) the critical theory of phase transition between trivial and non-trivial SPTs, and (2) the relation between such critical theory and the gapless boundary theory of SPTs. Based on examples of SO(3) and SU(2) SPTs, we propose that under appropriate boundary condition the critical theory contains the delocalized version of the boundary excitations. In addition, we prove that the boundary theory is the critical theory spatially confined between two SPTs. We expect these conclusions to hold in general and, in particular, for discrete symmetry groups as well.Comment: 16 pages, 7 figure

Robust Cooperative Strategy for Contour Matching Using Epipolar Geometry

Feature matching in images plays an important role in computer vision such as for 3D reconstruction, motion analysis, object recognition, target tracking and dynamic scene analysis. In this paper, we present a robust cooperative strategy to establish the correspondence of the contours between two uncalibrated images based on the recovered epipolar geometry. We take into account two representations of contours in image as contour points and contour chains. The method proposed in the paper is composed of the following two consecutive steps: (1) The first step uses the LMedS method to estimate the fundamental matrix based on Hartley’s 8-point algorithm, (2) The second step uses a new robust cooperative strategy to match contours. The presented approach has been tested with various real images and experimental results show that our method can produce more accurate contour correspondences.Singapore-MIT Alliance (SMA

Population Genetic Structure of Monimopetalum chinense (Celastraceae), an Endangered Endemic Species of Eastern China

• Background and Aims Monimopetalum chinense (Celastraceae) standing for the monotypic genus is endemic to eastern China. Its conservation status is vulnerable as most populations are small and isolated. Monimopetalum chinense is capable of reproducing both sexually and asexually. The aim of this study was to understand the genetic structure of M. chinense and to suggest conservation strategies. • Methods One hundred and ninety individuals from ten populations sampled from the entire distribution area of M. chinense were investigated by using inter-simple sequence repeats (ISSR). • Key Results A total of 110 different ISSR bands were generated using ten primers. Low levels of genetic variation were revealed both at the species level (Isp = 0·183) and at the population level (Ipop = 0·083). High clonal diversity (D = 0·997) was found, and strong genetic differentiation among populations was detected (49·06 %). • Conclusions Small population size, possible inbreeding, limited gene flow due to short distances of seed dispersal, fragmentation of the once continuous range and subsequent genetic drift, may have contributed to shaping the population genetic structure of the specie

Silicon nitride metalenses for unpolarized high-NA visible imaging

As one of nanoscale planar structures, metasurface has shown excellent superiorities on manipulating light intensity, phase and/or polarization with specially designed nanoposts pattern. It allows to miniature a bulky optical lens into the chip-size metalens with wavelength-order thickness, playing an unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and telephoto). However, a CMOS-compatible metalens has yet to be achieved in the visible region due to the limitation on material properties such as transmission and compatibility. Here, we experimentally demonstrate a divergent metalens based on silicon nitride platform with large numerical aperture (NA~0.98) and high transmission (~0.8) for unpolarized visible light, fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual focus spots are achieved within the visible region. Such metalens enables to shrink objects into a micro-scale size field of view as small as a single-mode fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also realized including over half billion nanoposts, showing a potential application of wide viewing-angle functionality. Thanks to the high-transmission and CMOS-compatibility of silicon nitride, our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, smart phones, aerial cameras, beam shaping, and other integrated on-chip devices.Comment: 16 pages, 7 figure

Finite-Key Analysis for Coherent-One-Way Quantum Key Distribution

Coherent-one-way (COW) quantum key distribution (QKD) is a significant communication protocol that has been implemented experimentally and deployed in practical products due to its simple equipment requirements. However, existing security analyses of COW-QKD either provide a short transmission distance or lack immunity against coherent attacks in the finite-key regime. In this study, we present a tight finite-key security analysis within the universally composable framework for a new variant of COW-QKD, which has been proven to extend the secure transmission distance in the asymptotic case. We combine the Quantum Leftover Hash Lemma and entropic uncertainty relation to derive the key rate formula. When estimating statistical parameters, we use the recently proposed Kato's inequality to ensure security against coherent attacks and achieve a higher key rate. Our work confirms the security and feasibility of COW-QKD for practical application and lays the foundation for further theoretical study and experimental implementation.Comment: 12 pages, 5 figure

Stabilizing a three-center single-electron metal–metal bond in a fullerene cage

Trimetallic carbide clusterfullerenes (TCCFs) encapsulating a quinary M3C2 cluster represent a special family of endohedral fullerenes with an open-shell electronic configuration. Herein, a novel TCCF based on a medium-sized rare earth metal, dysprosium (Dy), is synthesized for the first time. The molecular structure of Dy3C2@Ih(7)-C80 determined by single crystal X-ray diffraction shows that the encapsulated Dy3C2 cluster adopts a bat ray configuration, in which the acetylide unit C2 is elevated above the Dy3 plane by ∼1.66 Å, while Dy–Dy distances are ∼3.4 Å. DFT computational analysis of the electronic structure reveals that the endohedral cluster has an unusual formal charge distribution of (Dy3)8+(C2)2−@C806− and features an unprecedented three-center single-electron Dy–Dy–Dy bond, which has never been reported for lanthanide compounds. Moreover, this electronic structure is different from that of the analogous Sc3C2@Ih(7)-C80 with a (Sc3)9+(C2)3−@C806− charge distribution and no metal–metal bonding