Drawing cone spherical metrics via Strebel differentials

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. By using Strebel differentials as a bridge, we construct a new class of cone spherical metrics on compact Riemann surfaces by drawing on the surfaces some class of connected metric ribbon graphs.Comment: 25 pages, 8 figures. Version 2: minor typo corrections; revised according to referee's comments. We substantially revised the proof of the second theorem to make its exposition easier to understand. We added a new section, where we discuss on the Riemann sphere the consistence of metrics generated by Strebel differentials with the two angle conditions by Mondello-Panov and Eremenko, respectivel

Numerical simulation of clouds and precipitation depending on different relationships between aerosol and cloud droplet spectral dispersion

The aerosol effects on clouds and precipitation in deep convective cloud systems are investigated using the Weather Research and Forecast (WRF) model with the Morrison two-moment bulk microphysics scheme. Considering positive or negative relationships between the cloud droplet number concentration (Nc) and spectral dispersion (ɛ), a suite of sensitivity experiments are performed using an initial sounding data of the deep convective cloud system on 31 March 2005 in Beijing under either a maritime (‘clean’) or continental (‘polluted’) background. Numerical experiments in this study indicate that the sign of the surface precipitation response induced by aerosols is dependent on the ɛ−Nc relationships, which can influence the autoconversion processes from cloud droplets to rain drops. When the spectral dispersion ɛ is an increasing function of Nc, the domain-average cumulative precipitation increases with aerosol concentrations from maritime to continental background. That may be because the existence of large-sized rain drops can increase precipitation at high aerosol concentration. However, the surface precipitation is reduced with increasing concentrations of aerosol particles when ɛ is a decreasing function of Nc. For the ɛ−Nc negative relationships, smaller spectral dispersion suppresses the autoconversion processes, reduces the rain water content and eventually decreases the surface precipitation under polluted conditions. Although differences in the surface precipitation between polluted and clean backgrounds are small for all the ɛ−Nc relationships, additional simulations show that our findings are robust to small perturbations in the initial thermal conditions. Keywords: aerosol indirect effects, cloud droplet spectral dispersion, autoconversion parameterization, deep convective systems, two-moment bulk microphysics schem

Adversarial Spatio-Temporal Learning for Video Deblurring

Camera shake or target movement often leads to undesired blur effects in videos captured by a hand-held camera. Despite significant efforts having been devoted to video-deblur research, two major challenges remain: 1) how to model the spatio-temporal characteristics across both the spatial domain (i.e., image plane) and temporal domain (i.e., neighboring frames), and 2) how to restore sharp image details w.r.t. the conventionally adopted metric of pixel-wise errors. In this paper, to address the first challenge, we propose a DeBLuRring Network (DBLRNet) for spatial-temporal learning by applying a modified 3D convolution to both spatial and temporal domains. Our DBLRNet is able to capture jointly spatial and temporal information encoded in neighboring frames, which directly contributes to improved video deblur performance. To tackle the second challenge, we leverage the developed DBLRNet as a generator in the GAN (generative adversarial network) architecture, and employ a content loss in addition to an adversarial loss for efficient adversarial training. The developed network, which we name as DeBLuRring Generative Adversarial Network (DBLRGAN), is tested on two standard benchmarks and achieves the state-of-the-art performance.Comment: To appear in IEEE Transactions on Image Processing (TIP