Revealing spatiotemporal evolution regularity in the spatial diffusion of
epidemics is helpful for preventing and controlling the spread of epidemics.
Based on the real-time COVID-19 datasets by prefecture-level cities and date,
this paper is aimed at exploring the multifractal scaling in spatial diffusion
pattern of COVID-19 pandemic and its evolution characteristics in Chinese
mainland. The ArcGIS technology and box-counting method are employed to extract
spatial data and the least square calculation is used to calculate fractal
parameters. The results show multifractal distribution of COVID-19 pandemic in
China. The generalized correlation dimension spectrums are inverse S-shaped
curves, but the fractal dimension values significantly exceeds the Euclidean
dimension of embedding space when moment order q<<0. The local singularity
spectrums are asymmetric unimodal curves, which slant to right. The fractal
dimension growth curves are shown as quasi S-shaped curves. From these
spectrums and growth curves, the main conclusions can be drawn as follows.
First, self-similar patterns developed in the process of Covid-19 pandemic,
which seem be dominated by multi-scaling law. Second, the spatial pattern of
COVID-19 across China can be characterized by global clustering with local
disordered diffusion. Third, the spatial diffusion process of COVID-19 in China
experienced four stages, i.e., initial stage, the rapid diffusion stage, the
hierarchical diffusion stage, and finally the contraction stage. This study
suggests that multifractal theory can be utilized to characterize
spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be
instructive for further exploring natural laws of spatial diffusion.

通过中国境内实时 COVID-19 数据集，采用 ArcGIS 技术和盒计数方法，本文探索了 COVID-19 大流行在中国的空间扩散模式中的多重分形缩放及其演化特征，发现 COVID-19 在中国呈多分形分布，其空间扩散过程经历了四个阶段，即初始阶段、快速扩散阶段、分级扩散阶段和最终的收缩阶段；结果提示多重分形理论有望用于表征 COVID-19 大流行的时空扩散，推测对其他疾病的研究也有指导意义。

新冠疫情在中国内地的空间扩散模式的多重分形尺度分析

Multifractal scaling analyses of the spatial diffusion pattern of  COVID-19 pandemic in Chinese mainland

We propose a method for lossy image compression based on recurrent,
convolutional neural networks that outperforms BPG (4:2:0 ), WebP, JPEG2000,
and JPEG as measured by MS-SSIM. We introduce three improvements over previous
research that lead to this state-of-the-art result. First, we show that
training with a pixel-wise loss weighted by SSIM increases reconstruction
quality according to several metrics. Second, we modify the recurrent
architecture to improve spatial diffusion, which allows the network to more
effectively capture and propagate image information through the network's
hidden state. Finally, in addition to lossless entropy coding, we use a
spatially adaptive bit allocation algorithm to more efficiently use the limited
number of bits to encode visually complex image regions. We evaluate our method
on the Kodak and Tecnick image sets and compare against standard codecs as well
recently published methods based on deep neural networks.

本论文提出了一种基于循环卷积神经网络的有损图像压缩方法，通过像素权重损失、改进循环神经网络的结构以及自适应位分配算法，成功取得了多项实验成果优于 BPG、WebP、JPEG2000 和 JPEG 等标准方式。