Tropical cyclone (TC) motion has an important impact on both human lives and infrastructure. Predicting TC intensity is crucial, especially within the 24 h warning time. TC intensity change prediction can be regarded as a problem of both regression and classification. Statistical forecasting methods based on empirical relationships and traditional numerical prediction methods based on dynamical equations still have difficulty in accurately predicting TC intensity. In this study, a prediction algorithm for TC intensity changes based on deep learning is proposed by exploring the joint spatial features of three-dimensional (3D) environmental conditions that contain the basic variables of the atmosphere and ocean. These features can also be interpreted as fused characteristics of the distributions and interactions of these 3D environmental variables. We adopt a 3D convolutional neural network (3D-CNN) for learning the implicit correlations between the spatial distribution features and TC intensity changes. Image processing technology is also used to enhance the data from a small number of TC samples to generate the training set. Considering the instantaneous 3D status of a TC, we extract deep hybrid features from TC image patterns to predict 24 h intensity changes. Compared to previous studies, the experimental results show that the mean absolute error (MAE) of TC intensity change predictions and the accuracy of the classification as either intensifying or weakening are both significantly improved. The results of combining features of high and low spatial layers confirm that considering the distributions and interactions of 3D environmental variables is conducive to predicting TC intensity changes, thus providing insight into the process of TC evolution.

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The isomorphism problem involves judging whether two graphs are topologically the same and producing structure-preserving isomorphism mapping. It is widely used in various areas. Diverse algorithms have been proposed to solve this problem in polynomial time, with the help of quantum walks. Some of these algorithms, however, fail to find the isomorphism mapping. Moreover, most algorithms have very limited performance on regular graphs which are generally difficult to deal with due to their symmetry. We propose IsoMarking to discover an isomorphism mapping effectively, based on the quantum walk which is sensitive to topological structures. Firstly, IsoMarking marks vertices so that it can reduce the harmful influence of symmetry. Secondly, IsoMarking can ascertain whether the current candidate bijection is consistent with existing bijections and eventually obtains qualified mapping. Thirdly, our experiments on 1585 pairs of graphs demonstrate that our algorithm performs significantly better on both ordinary graphs and regular graphs.

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Graph isomorphism is to determine whether two graphs have the same topological structure. It plays a significant role in areas of image matching, biochemistry, and information retrieval. Quantum walk, as a novel quantum computation model, has been employed to isomorphic mapping detection to optimize the time complexity compared with a classical computation model. However, these quantum-inspired algorithms do not perform well-and even cease to work-for graphs with inherent symmetry, such as regular graphs. By analyzing the impacts of graphs symmetry on isomorphism detection, we proposed an effective graph isomorphism algorithm (MapEff) based on the discrete-time quantum walk (DTQW) to improve the accuracy of isomorphic mapping detection, especially for regular graphs. With the help of auxiliary edges, this algorithm can distinguish the symmetric nodes efficiently and, thus, deduct the qualified isomorphic mapping by rounds of selections. The experiments tested on 1585 pairs of graphs demonstrated that our algorithm has a better performance compared with other state-of-the-art algorithms.

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