Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds \Si with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of \Si at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on \Si. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.Comment: 38 page

Ecological thresholds and large carnivores conservation: Implications for the Amur tiger and leopard in China

The ecological threshold concept describes how changes in one or more factors at thresholds can result in a large shift in the state of an ecosystem. This concept focuses attention on limiting factors that affect the tolerance of systems or organisms and changes in them. Accumulating empirical evidence for the existence of ecological thresholds has created favorable conditions for practical application to wildlife conservation. Applying the concept has the potential to enhance conservation of two large carnivores, Amur tiger and leopard, and the knowledge gained could guide the construction of a proposed national park. In this review, ecological thresholds that result from considering a paradigm of bottom-up control were evaluated for their potential to contribute to the conservation of Amur tiger and leopard. Our review highlights that large carnivores, as top predators, are potentially affected by ecological thresholds arising from changes in climate (or weather), habitat, vegetation, prey, competitors, and anthropogenic disturbances. What's more, interactions between factors and context dependence need to be considered in threshold research and conservation practice, because they may amplify the response of ecosystems or organisms to changes in specific drivers. Application of the threshold concept leads to a more thorough evaluation of conservation needs, and could be used to guide future Amur tiger and leopard research and conservation in China. Such application may inform the conservation of other large carnivores worldwide

Generating EPR beams in a cavity optomechanical system

We propose a scheme to produce continuous variable entanglement between phase-quadrature amplitudes of two light modes in an optomechanical system. For proper driving power and detuning, the entanglement is insensitive with bath temperature and $Q$ of mechanical oscillator. Under realistic experimental conditions, we find that the entanglement could be very large even at room temperature.Comment: 4.1 pages, 4 figures, comments are welcome; to appear in PRA, published version with corrections of typo

A Survey of Positioning Systems Using Visible LED Lights

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.As Global Positioning System (GPS) cannot provide satisfying performance in indoor environments, indoor positioning technology, which utilizes indoor wireless signals instead of GPS signals, has grown rapidly in recent years. Meanwhile, visible light communication (VLC) using light devices such as light emitting diodes (LEDs) has been deemed to be a promising candidate in the heterogeneous wireless networks that may collaborate with radio frequencies (RF) wireless networks. In particular, light-fidelity has a great potential for deployment in future indoor environments because of its high throughput and security advantages. This paper provides a comprehensive study of a novel positioning technology based on visible white LED lights, which has attracted much attention from both academia and industry. The essential characteristics and principles of this system are deeply discussed, and relevant positioning algorithms and designs are classified and elaborated. This paper undertakes a thorough investigation into current LED-based indoor positioning systems and compares their performance through many aspects, such as test environment, accuracy, and cost. It presents indoor hybrid positioning systems among VLC and other systems (e.g., inertial sensors and RF systems). We also review and classify outdoor VLC positioning applications for the first time. Finally, this paper surveys major advances as well as open issues, challenges, and future research directions in VLC positioning systems.Peer reviewe

Doublet bands in 126^{126}Cs in the triaxial rotor model coupled with two quasiparticles

The positive parity doublet bands based on the $\pi h_{11/2}\otimes\nu h_{11/2}$ configuration in $^{126}$Cs have been investigated in the two quasi-particles coupled with a triaxial rotor model. The energy spectra $E(I)$, energy staggering parameter $S(I)=[E(I)-E(I-1)]/2I$, $B(M1)$ and $B(E2)$ values, intraband $B(M1)/B(E2)$ ratios, $B(M1)_{\textrm{in}}/B(M1)_{\textrm{out}}$ ratios, and orientation of the angular momentum for the rotor as well as the valence proton and neutron are calculated. After including the pairing correlation, good agreement has been obtained between the calculated results and the data available, which supports the interpretation of this positive parity doublet bands as chiral bands.Comment: Phys.Rev.C (accepted

Box Drawings for Learning with Imbalanced Data

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly imbalanced classification problems. The classifiers constructed by both methods are created as unions of parallel axis rectangles around the positive examples, and thus have the benefit of being interpretable. The first algorithm uses mixed integer programming to optimize a weighted balance between positive and negative class accuracies. Regularization is introduced to improve generalization performance. The second method uses an approximation in order to assist with scalability. Specifically, it follows a \textit{characterize then discriminate} approach, where the positive class is characterized first by boxes, and then each box boundary becomes a separate discriminative classifier. This method has the computational advantages that it can be easily parallelized, and considers only the relevant regions of feature space