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Graphs/Networks are common in real-world applications where data have rich content and complex relationships. The increasing popularity also motivates many network learning algorithms, such as community detection, clustering, classification, and embedding learning, etc.. In reality, the large network volumes often hider a direct use of learning algorithms to the graphs. As a result, it is desirable to have the flexibility to condense a network to an arbitrary size, with well-preserved network topology and node content information. In this paper, we propose a graph compression network (GEN) to achieve network compression and embedding at the same time. Our theme is to leverage the network topology to find node mappings, such that densely connected nodes, including their node content, are compressed as a new node, with a latent vector (i.e. embedding) being learned to represent the compressed node. In addition to compression learning, we also develop a novel encoding-decoding framework, using feature diffusion process, to "decompress" the condensed network. Different from traditional graph convolution which uses direct-neighbor message passing, our decompression advocates high-order message passing within compressed nodes to learning feature representation for all nodes in the network. A unique strength of GEN is that it leverages the graph neural network principle to learn mapping automatically, so one can compress a network to an arbitrary size, and also decompress it to the original node space with minimum information loss. Experiments and comparisons confirm that GEN can automatically find clusters and communities, and compress them as new nodes. Results also show that GEN achieves improved performance for numerous tasks, including graph classification and node clustering. 

Individuals infected by human immunodeficiency virus (HIV) are under oxidative stress due to the imbalance between reactive oxygen species (ROS) production and elimination. This paper presents a mathematical model with the cytotoxic T lymphocytes (CTL) immune response to examine the role of ROS in the dynamics of HIV infection. We classify the equilibria of the model and study the stability of these equilibria. Numerical simulations show that incorporating ROS and CTL immune response into the model leads to very rich dynamics, including bistable phenomena and periodic solutions. Although the current antiretroviral therapy can suppress viral load to the undetectable level, it cannot eradicate the virus. A high level of ROS may be a factor for HIV persistence in patients despite suppressive therapy. These results suggest that oxidative damage and anti-oxidant therapy should be considered in the study of HIV infection and treatment. 

Constrained learning, a weakly supervised learning task, aims to incorporate domain constraints to learn models without requiring labels for each instance. Because weak supervision knowledge is useful and easy to obtain, constrained learning outperforms unsupervised learning in performance and is preferable than supervised learning in terms of labeling costs. To date, constrained learning, especially constrained clustering, has been extensively studied, but was primarily focused on data in the Euclidean space. In this paper, we propose a weak supervision network embedding (WSNE) for constrained learning of graphs. Because no label is available for individual nodes, we propose a new loss function to quantify the constraint-based loss, and integrate this loss in a graph convolutional neural network (GCN) and variational graph auto-encoder (VGAE) combined framework to jointly model graph structures and node attributes. The joint optimization allows WSNE to learn embedding not only preserving network topology and content, but also satisfying the constraints. Experiments show that WSNE outperforms baselines for constrained graph learning tasks, including constrained graph clustering and constrained graph classification. 

In this paper, we propose a discriminative variational autoencoder (DVAE) to assist deep learning from data with imbalanced class distributions. DVAE is designed to alleviate the class imbalance by explicitly learning class boundaries between training samples, and uses learned class boundaries to guide the feature learning and sample generation. To learn class boundaries, DVAE learns a latent two-component mixture distributor, conditioned by the class labels, so the latent features can help differentiate minority class vs. majority class samples. In order to balance the training data for deep learning to emphasize on the minority class, we combine DVAE and generative adversarial networks (GAN) to form a unified model, DVAAN, which generates synthetic instances close to the class boundaries as training data to learn latent features and update the model. Experiments and comparisons confirm that DVAAN significantly alleviates the class imbalance and delivers accurate models for deep learning from imbalanced data. 

We have designed and synthesized a series of deep‐blue light‐emitting polyfluorenes, PF‐27SOs and PF‐36SOs, by introducing electron‐deficient 9,9‐dimethyl‐9H‐thioxanthene 10,10‐dioxide isomers (27SO and 36SO) into the poly(9,9‐dioctylfluorene) (PFO) backbone. Compared with PFO, the resulting polymers exhibit an equivalent thermal decomposition temperature (>415 °C), an enhanced glass transition temperature (>99 °C), a decreased lowest unoccupied molecular orbital energy level (E_LUMO) below −2.32 eV, a blue‐shifted photoluminescence spectra in solid film with a maximum emission at ~422 nm, and a shoulder peak at ~445 nm. The resulting polymers also show blue‐shifted and narrowed electroluminescence spectra with deep‐blue Commission Internationale de L'Eclairage (CIE) coordinates of (0.16, 0.07) for PF‐27SO20 and (0.16, 0.06) for PF‐36SO30, compared with (0.17, 0.13) for PFO. Moreover, simple device based on PF‐36SO30 achieves a superior device performance with a maximum external quantum efficiency (EQE_max= 3.62%) compared with PFO (EQE_max= 0.47%). The results show that nonconjugated 9,9‐dimethyl‐9H‐thioxanthene 10,10‐dioxide isomers can effectively perturb the conjugation length of polymers, significantly weaken the charge‐transfer effect in donor–acceptor systems, substantially improve electroluminescence device efficiency, and achieve deep‐blue light emission.