The Moebius geometry of Wintgen ideal submanifolds

Wintgen ideal submanifolds in space forms are those ones attaining equality pointwise in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the scalar normal curvature. They are Moebius invariant objects. The mean curvature sphere defines a conformal Gauss map into a Grassmann manifold. We show that any Wintgen ideal submanifold has a Riemannian submersion structure over a Riemann surface with the fibers being round spheres. Then the conformal Gauss map is shown to be a super-conformal and harmonic map from the underlying Riemann surface. Some of our previous results are surveyed in the final part.Comment: This is a survey of our recent work on the Moebius geometry of Wintgen ideal submanifolds, which also include two new important results. Submitted to the the conference "ICM 2014 Satellite Conference on Real and Complex Submanifolds

Adversarial Deep Structured Nets for Mass Segmentation from Mammograms

Mass segmentation provides effective morphological features which are important for mass diagnosis. In this work, we propose a novel end-to-end network for mammographic mass segmentation which employs a fully convolutional network (FCN) to model a potential function, followed by a CRF to perform structured learning. Because the mass distribution varies greatly with pixel position, the FCN is combined with a position priori. Further, we employ adversarial training to eliminate over-fitting due to the small sizes of mammogram datasets. Multi-scale FCN is employed to improve the segmentation performance. Experimental results on two public datasets, INbreast and DDSM-BCRP, demonstrate that our end-to-end network achieves better performance than state-of-the-art approaches. \footnote{https://github.com/wentaozhu/adversarial-deep-structural-networks.git}Comment: Accepted by ISBI2018. arXiv admin note: substantial text overlap with arXiv:1612.0597

Implication the observed ψ(3770)→ppˉπ0\psi(3770)\to p\bar{p}\pi^0 for studying the ppˉ→ψ(3770)π0p\bar{p}\to \psi(3770)\pi^0 process

We study the charmonium $p \bar{p} \to \psi(3770) \pi^0$ reaction using effective lagrangian approach where the contributions from well established $N^*$ states are considered, and all parameters are fixed in the process of $e^+e^- \to p \bar{p}\pi^0$ at center of mass energy $\sqrt{s} = 3.773$ GeV. The experimental data on the line shape of the mass distribution of the $e^+e^- \to p\bar{p}\pi^0$ can be well reproduced. Based on the studying of $e^+e^- \to p \bar{p}\pi^0$, the total and differential cross sections of the $p \bar{p} \to \psi(3770) \pi^0$ reaction are predicted. At the same time we evaluated also the cross sections of the $p \bar{p} \to \psi(3686) \pi^0$ reaction. It is shown that the contribution of nucleon pole to this reaction is largest close to the reaction threshold. However, the interference between nucleon pole and the other nucleon resonance can still change the angle distributions significantly. Those theoretical results may be test by the future experiments at \overline{\mbox{P}}ANDA.Comment: 8 pages, 10 figures, and 4 tables. More discussions added and typos corrected. Accepted by Eur. Phys. J.

Jet-dominated quiescent states in black hole X-ray binaries: the case of V404 Cyg

The dynamical and radiative properties of the quiescent state (X-ray luminosity $<10^{34}\ {\rm erg s^{-1} cm^{-2}}$) of black hole X-ray transients (BHXTs) remains unclear, mainly because of low-luminosity and poor data quantity. We demonstrate that, the simultaneous multi-wavelength (including radio, optical, ultraviolet and X-ray bands) spectrum of V404 Cyg in its bright quiescent state can be well described by the radiation from the companion star and more importantly, the compact jet. Neither the outer thin disc nor the inner hot accretion flow is important in the total spectrum. Together with several additional recent findings, i.e. the power-law X-ray spectrum and the constant X-ray spectral shape (or constant photon index) in contrast to the dramatic change in the X-ray luminosity, we argue the quiescent state spectrum of BHXTs is actually jet-dominated. Observational features consistent with this jet model are also discussed as supporting evidences.Comment: accepted for the publication in MNRAS Letters, 5 pages, 2 figure