A quartic system and a quintic system with fine focus of order 18

AbstractBy using an effective complex algorithm to calculate the Lyapunov constants of polynomial systems En: z˙=iz+Rn(z,z¯), where Rn is a homogeneous polynomial of degree n, in this note we construct two concrete examples, E4 and E5, such that in both cases, the corresponding orders of fine focus can be as high as 18. The systems are given, respectively, by the following ordinary differential equations:E4:z˙=iz+2iz4+izz¯3+5227820723eiθz¯4, where θ∉{kπ±π6,kπ+π2,k∈Z}, andE5:z˙=iz+3z5+20(c+3)9c2−15z4z¯+zz¯4+20(c+3)c29c2−15z¯5, where c is the root between (−3,−5/3) of the equation4155c6−10716c5−63285c4−18070c3+168075c2+205450c+60375=0

A Facile Synthesis and Optical Properties of Bundle-Shaped TbPO 4

Bundle-shaped TbPO4·H2O nanorods have been prepared by a facile hydrothermal technique and characterized by XRD, SEM, TEM, UV-Vis diffuse reflectance spectrum (DRS), photoluminescence (PL) spectrum, and lifetime. The results indicate that the obtained sample has hexagonal structure of TbPO4·H2O and is composed of nanorods bundles which is assembled from many single crystalline nanorods with the diameter of around 45 nm and the length of 2.3 μm. The growth of the single crystalline nanorod is along the (001) plane direction. Under the UV light irradiation, TbPO4·H2O nanorods bundles exhibit bright green emission corresponding to the D54→F7J (J=6,5,4,3) transitions of the Tb3+ ions, and the lifetime is determined to be about 0.24 ms

Unique normal forms for Hopf-zero vector fields

We consider normal forms of Hopf-zero vector fields in R-3. Unique normal forms under conjugacy and orbital equivalence for the generic case are given.MathematicsSCI(E)4ARTICLE4345-34833

Discovery and Identification of Pyrazolopyramidine Analogs as Novel Potent Androgen Receptor Antagonists

Androgen receptor (AR), an important target in the current androgen derivation therapy, plays a critical role in the development and progress of prostate cancer (PCa). Nonsteroidal antiandrogens, such as enzalutamide and bicalutamide, are commonly used in clinic to treat PCa. Though they are very effective at the beginning, drug resistance problem appears after about 18 months. One of the reasons is that these antiandrogens share similar structure skeleton. Therefore, it is urgent to discover novel antiandrogens with different skeletons for resistance problem. Herein, we combined structure- and ligand-based methodologies for virtual screening chemical databases to identify potent AR antagonists. Then the cytotoxic activities of the screened hit samples were evaluated by using LNCaP prostate cancer cells. Virtual screening and biological evaluation assay results suggest that several chemicals with novel pyrazolopyrimidine skeleton can inhibit the proliferation of prostate cancer cells with similar, or even higher, bioactivities to bicalutamide. AR reporter gene assay experiments proved that Compound III showed potential antagonistic effects. In addition, molecular dynamics simulations results proved that Compound III can properly bind to AR and prevent helix 12 (H12) from closing to distort the formation of activation function 2 (AF2) site, resulting in the invalid transcription. Hence, pyrazolopyrimidine was discovered as a novel, potent and promising antiandrogen skeleton deserved to be further studied

A Survey on Label-efficient Deep Image Segmentation: Bridging the Gap between Weak Supervision and Dense Prediction

The rapid development of deep learning has made a great progress in image segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level annotations, which are often expensive, tedious, and laborious. To alleviate this burden, the past years have witnessed an increasing attention in building label-efficient, deep-learning-based image segmentation algorithms. This paper offers a comprehensive review on label-efficient image segmentation methods. To this end, we first develop a taxonomy to organize these methods according to the supervision provided by different types of weak labels (including no supervision, inexact supervision, incomplete supervision and inaccurate supervision) and supplemented by the types of segmentation problems (including semantic segmentation, instance segmentation and panoptic segmentation). Next, we summarize the existing label-efficient image segmentation methods from a unified perspective that discusses an important question: how to bridge the gap between weak supervision and dense prediction -- the current methods are mostly based on heuristic priors, such as cross-pixel similarity, cross-label constraint, cross-view consistency, and cross-image relation. Finally, we share our opinions about the future research directions for label-efficient deep image segmentation.Comment: Accepted to IEEE TPAM

Calibrating the absorption imaging of cold atoms under high magnetic fields

We develop a theoretical model for calibrating the absorption imaging of cold atoms under high magnetic fields. Comparing to zero or low magnetic fields, the efficiency of the absorption imaging becomes lower while it requires an additional correction factor to obtain the absolute atom number under the Beer-Lambert law. Our model is based on the rate equations and can account many experimental imperfections such as Zeeman level crossing, failures of hyperfine structures, off-resonant couplings, and low repumping efficiency, etc. Based on this method, we can precisely calculate the correction factor for atom number measurement without any empirical or fitting parameters. Meanwhile, we use a cold-atom apparatus of rubidium-85 to experimentally verify our model. Besides these, we find our work can also serve as a benchmark to measure the polarization impurity of a circular-polarized laser beam with high sensitivities. We believe this work will bring convenience for most of cold-atom experiments using absorption imaging.Comment: 9 pages, 5 figure