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In this article, a deep probability model, called the discriminative mixture variational autoencoder (DMVAE), is developed for the feature extraction in semisupervised learning. The DMVAE consists of three parts 1) the encoding; 2) decoding; and 3) classification modules. In the encoding module, the encoder projects the observation to the latent space, and then the latent representation is fed to the decoding part, which depicts the generative process from the hidden variable to data. In particular, the decoding module in our DMVAE partitions the observed dataset into some clusters via multiple decoders whose number is automatically determined via the Dirichlet process (DP) and learns a probability distribution for each cluster. Compared to the standard variational autoencoder (VAE) describing all data with a single probability function, the DMVAE has the capacity to give a more accurate description for observations, thus improving the characterization ability of the extracted features, especially for the data with complex distribution. Moreover, to obtain a discriminative latent space, the class labels of labeled data are introduced to restrict the feature learning via a softmax classifier, with which the minimum entropy of the predicted labels for the features from unlabeled data can also be guaranteed. Finally, the joint optimization of the marginal likelihood, label, and entropy constraints makes the DMVAE have higher classification confidence for unlabeled data while accurately classifying the labeled data, ultimately leading to better performance. Experiments on several benchmark datasets and the measured radar echo dataset show the advantages of our DMVAE-based semisupervised classification over other related methods.In this article, we investigate the synchronization of complex networks with general time-varying delay, especially with nondifferentiable delay. selleck chemical In the literature, the time-varying delay is usually assumed to be differentiable. This assumption is strict and not easy to verify in engineering. Until now, the synchronization of networks with nondifferentiable delay through adaptive control remains a challenging problem. By analyzing the boundedness of the adaptive control gain and extending the well-known Halanay inequality, we solve this problem and establish several synchronization criteria for networks under the centralized adaptive control and networks under the decentralized adaptive control. Particularly, the boundedness of the centralized adaptive control gain is theoretically proved. Numerical simulations are provided to verify the theoretical results.Emerging evidence indicates that circular RNA (circRNA) has been an indispensable role in the pathogenesis of human complex diseases and many critical biological processes. Using circRNA as a molecular marker or therapeutic target opens up a new avenue for our treatment and detection of human complex diseases. The traditional biological experiments, however, are usually limited to small scale and are time consuming, so the development of an effective and feasible computational-based approach for predicting circRNA-disease associations is increasingly favored. In this study, we propose a new computational-based method, called IMS-CDA, to predict potential circRNA-disease associations based on multisource biological information. More specifically, IMS-CDA combines the information from the disease semantic similarity, the Jaccard and Gaussian interaction profile kernel similarity of disease and circRNA, and extracts the hidden features using the stacked autoencoder (SAE) algorithm of deep learning. After training in the rotation forest (RF) classifier, IMS-CDA achieves 88.08% area under the ROC curve with 88.36% accuracy at the sensitivity of 91.38% on the CIRCR2Disease dataset. Compared with the state-of-the-art support vector machine and K-nearest neighbor models and different descriptor models, IMS-CDA achieves the best overall performance. In the case studies, eight of the top 15 circRNA-disease associations with the highest prediction score were confirmed by recent literature. These results indicated that IMS-CDA has an outstanding ability to predict new circRNA-disease associations and can provide reliable candidates for biological experiments.Artificial neural networks inspired from the learning mechanism of the brain have achieved great successes in machine learning, especially those with deep layers. The commonly used neural networks follow the hierarchical multilayer architecture with no connections between nodes in the same layer. In this article, we propose a new group architectures for neural-network learning. In the new architecture, the neurons are assigned irregularly in a group and a neuron may connect to any neurons in the group. The connections are assigned automatically by optimizing a novel connecting structure learning probabilistic model which is established based on the principle that more relevant input and output nodes deserve a denser connection between them. In order to efficiently evolve the connections, we propose to directly model the architecture without involving weights and biases which significantly reduce the computational complexity of the objective function. The model is optimized via an improved particle swarm optimization algorithm. After the architecture is optimized, the connecting weights and biases are then determined and we find the architecture is robust to corruptions. From experiments, the proposed architecture significantly outperforms existing popular architectures on noise-corrupted images when trained only by pure images.The measurement algebraic connectivity plays an important role in many graph theory-based investigations, such as cooperative control of multiagent systems. In general, the measurement is considered to be centralized. In this article, a distributed model is proposed to estimate the algebraic connectivity (i.e., the second smallest eigenvalue of the corresponding Laplacian matrix) by the approach of distributed estimation via high-pass consensus filters. The global asymptotic convergence of the proposed model is theoretically guaranteed. Numerical examples are shown to verify the theoretical results and the superiority of the proposed distributed model.