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Data reconstruction is the most essential step in seismic data processing. Although the compressed sensing (CS) theory breaks through the Nyquist sampling theorem, we previously proved that the CS-based reconstruction of spatially irregular seismic data could not fully meet the theoretical requirements, resulting in low reconstruction accuracy. Although deep learning (DL) has great potential in mining features from data and accelerating the process, it faces challenges in earth science such as limited labels and poor generalizability. To improve the generalizability of deep neural network (DNN) in reconstructing seismic data in the actual situation of limited labeling, this paper proposes a method called CSDNN that combines model-driven CS and data-driven DNN to reconstruct the spatially irregular seismic data. By physically constraining neural networks, this method increases the generalizability of the network and improves the insufficient reconstruction caused by the inability to sample randomly in the whole data definition domain. Experiments on the synthetic and field seismic data show that the CSDNN reconstruction method achieves better performance compared with the conventional CS method and DNN method, including those with low sampling rates, which verifies the feasibility, effectiveness and generalizability of this approach. [ABSTRACT FROM AUTHOR]

Precipitation nowcasting has important implications for urban operation and flood prevention. Radar echo extrapolation is a common method in precipitation nowcasting. Using deep learning models to extrapolate radar echo data has great potential. The increase of lead time leads to a weaker correlation between the real rainfall evolution and the generated images. The evolution information is easily lost during extrapolation, which is reflected as echo attenuation. Existing models, including generative adversarial network (GAN)-based models, have difficulty curbing attenuation, resulting in insufficient accuracy in rainfall prediction. To solve this issue, a spatiotemporal process enhancement network (GAN-argcPredNet v2.0) based on GAN-argcPredNet v1.0 has been designed. GAN-argcPredNet v2.0 curbs attenuation by avoiding blurring or maintaining the intensity. A spatiotemporal image correlation (STIC) prediction network is designed as the generator. By suppressing the blurring effect of rain distribution and reducing the negative bias by STIC attention, the generator generates more accurate images. Furthermore, the discriminator is a channel–spatial (CS) convolution network. The discriminator enhances the discrimination of echo information and provides better guidance to the generator in image generation by CS attention. The experiments are based on the radar dataset of southern China. The results show that GAN-argcPredNet v2.0 performs better than other models. In heavy rainfall prediction, compared with the baseline, the probability of detection (POD), the critical success index (CSI), the Heidke skill score (HSS) and bias score increase by 18.8 %, 17.0 %, 17.2 % and 26.3 %, respectively. The false alarm ratio (FAR) decreases by 3.0 %. [ABSTRACT FROM AUTHOR]

A graph is called $k$ -critical if its chromatic number is $k$ but every proper subgraph has chromatic number less than $k$. An old and important problem in graph theory asks to determine the maximum number of edges in an $n$ -vertex $k$ -critical graph. This is widely open for every integer $k\geq 4$. Using a structural characterisation of Greenwell and Lovász and an extremal result of Simonovits, Stiebitz proved in 1987 that for $k\geq 4$ and sufficiently large $n$ , this maximum number is less than the number of edges in the $n$ -vertex balanced complete $(k-2)$ -partite graph. In this paper, we obtain the first improvement in the above result in the past 35 years. Our proofs combine arguments from extremal graph theory as well as some structural analysis. A key lemma we use indicates a partial structure in dense $k$ -critical graphs, which may be of independent interest. [ABSTRACT FROM AUTHOR]