Path Integral Based Convolution and Pooling for Graph Neural Networks

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.Comment: 15 pages, 4 figures, 6 tables. arXiv admin note: text overlap with arXiv:1904.1099

Comparison of endostatin(endostar)and avastin's inhibition effect on mice choroidal neovascularization

AIM:To observe the inhibition effect of endostatin(endostar)on mice choroidal neovascularization model(CNV)and compare with the Avastin.<p>METHODS: Using 532nm laser photocoagulation to establish a mouse model of CNV. We observed the formation of CNV by histopathological examination after 2wk later. Forty successful models of mice were randomly divided into control group(group 1, 10 rats), normal saline group(group 2, 10 rats), endostatin group(group 3, 10 rats)and avastin group(group 4, 10 rats). The drugs were injected into the mice' vitreous after photocoagulation 2wk later. Then 1wk later, we took the mice eyeballs to perform the HE and immunohistochemical staining to observe. The statistical analysis of ANOVA was done by SPSS 16.0 and the LSD-<i>t</i> test was used for multiple samples, taking <i>P</i><0.05 as the test standards.<p>RESULTS: Two weeks later, HE histopathological examination was done, light microscope showed large amount of new vessels' formation, the positive rate for CNV was 72.8%. The blank control group compared with the normal saline group <i>P</i>>0.05, had no inhibitory effect on CNV; endostatin treated group compared with control group, <i>P</i><0.05, had a certain inhibitory effect; avastin group compared with the control group, <i>P</i><0.05, had an inhibitory effect on CNV; the LSD-<i>t</i> was performed on Avastin group and endostatin group, <i>P</i><0.05, which were statistically significant. We thought that the two drugs have different inhibitory effect on mice' CNV, because <i>(-overx)</i>_Avastin=26.90,<i>(-overx)</i>_endostatin=29.13,<i>(-overx)</i>_Avastin<<i>(-overx)</i>_endostatin, we can infer that endostar had lower inhibitory effect on mice CNV than Avastin.<p>CONCLUSION: Laser-induced CNV animal models of colored mice C57BL/6J is of short time and high rate establishment and it is an ideal model for CNV study. Endostar has certain inhibitory effect on CNV, and it is likely to become one of the important drugs for CNV-related diseases in the future

Internet Financial Credit Risk Assessment with Sliding Window and Attention Mechanism LSTM Model

With the accelerated pace of market-oriented reform, Internet finance has gained a broad and healthy development environment. Existing studies lack consideration of time trends in financial risk, and treating all features equally may lead to inaccurate predictions. To address the above problems, we propose an LSTM model based on sliding window and attention mechanism. The model uses sliding windows to enable the model to effectively exploit the contextual relevance of loan data. And we introduce the attention mechanism into the model, which enables the model to focus on important information. The result on the Lending Club public desensitization dataset shows that our model outperforms ARIMA, SVM, ANN, LSTM, and GRU models