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This paper is concerned with a blood flow problem coupled with a slow plaque growth at the artery wall. In the model, the micro (fast) system is the Navier-Stokes equation with a periodically applied force and the macro (slow) system is a fractional reaction equation, which is used to describe the plaque growth with memory effect. We construct an auxiliary temporal periodic problem and an effective time-average equation to approximate the original problem and analyze the approximation error of the corresponding linearized PDE (Stokes) system, where the simple front-tracking technique is used to update the slow moving boundary. An effective multiscale method is then designed based on the approximate problem and the front tracking framework. We also present a temporal finite difference scheme with a spatial continuous finite element method and analyze its temporal discrete error. Furthermore, a fast iterative procedure is designed to find the initial value of the temporal periodic problem and its convergence is analyzed as well. Our designed front-tracking framework and the iterative procedure for solving the temporal periodic problem make it easy to implement the multiscale method on existing PDE solving software. The numerical method is implemented by a combination of the finite element platform COMSOL Multiphysics and the mainstream software MATLAB, which significantly reduce the programming effort and easily handle the fluid-structure interaction, especially moving boundaries with more complex geometries. We present some numerical examples of ODEs and 2-D Navier-Stokes system to demonstrate the effectiveness of the multiscale method. Finally, we have a numerical experiment on the plaque growth problem and discuss the physical implication of the fractional order parameter.

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers are broadly applicable, but rely on local search techniques to manage highly nonconvex objective functions. Recently, learning-based approaches have shown promise as a means to generate fast and accurate IK results; learned solvers can easily be integrated with other learning algorithms in end-to-end systems. However, learning-based methods have an Achilles' heel: each robot of interest requires a specialized model which must be trained from scratch. To address this key shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train the first learned generative graphical inverse kinematics (GGIK) solver that is, crucially, "robot-agnostic"-a single model is able to provide IK solutions for a variety of different robots. Additionally, the generative nature of GGIK allows the solver to produce a large number of diverse solutions in parallel with minimal additional computation time, making it appropriate for applications such as sampling-based motion planning. Finally, GGIK can complement local IK solvers by providing reliable initializations. These advantages, as well as the ability to use task-relevant priors and to continuously improve with new data, suggest that GGIK has the potential to be a key component of flexible, learning-based robotic manipulation systems.

In this paper, we propose a sequence-to-set method that can transform any sequence generative model based on maximum likelihood to a set generative model where we can evaluate the utility/probability of any set. An efficient importance sampling algorithm is devised to tackle the computational challenge of learning our sequence-to-set model. We present GRU2Set, which is an instance of our sequence-to-set method and employs the famous GRU model as the sequence generative model. To further obtain permutation invariant representation of sets, we devise the SetNN model which is also an instance of the sequence-to-set model. A direct application of our models is to learn an order/set distribution from a collection of e-commerce orders, which is an essential step in many important operational decisions such as inventory arrangement for fast delivery. Based on the intuition that small-sized sets are usually easier to learn than large sets, we propose a size-bias trick that can help learn better set distributions with respect to the $\ell_1$-distance evaluation metric. Two e-commerce order datasets, TMALL and HKTVMALL, are used to conduct extensive experiments to show the effectiveness of our models. The experimental results demonstrate that our models can learn better set/order distributions from order data than the baselines. Moreover, no matter what model we use, applying the size-bias trick can always improve the quality of the set distribution learned from data.

Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.

Imbalanced classification on graphs is ubiquitous yet challenging in many real-world applications, such as fraudulent node detection. Recently, graph neural networks (GNNs) have shown promising performance on many network analysis tasks. However, most existing GNNs have almost exclusively focused on the balanced networks, and would get unappealing performance on the imbalanced networks. To bridge this gap, in this paper, we present a generative adversarial graph network model, called ImGAGN to address the imbalanced classification problem on graphs. It introduces a novel generator for graph structure data, named GraphGenerator, which can simulate both the minority class nodes' attribute distribution and network topological structure distribution by generating a set of synthetic minority nodes such that the number of nodes in different classes can be balanced. Then a graph convolutional network (GCN) discriminator is trained to discriminate between real nodes and fake (i.e., generated) nodes, and also between minority nodes and majority nodes on the synthetic balanced network. To validate the effectiveness of the proposed method, extensive experiments are conducted on four real-world imbalanced network datasets. Experimental results demonstrate that the proposed method ImGAGN outperforms state-of-the-art algorithms for semi-supervised imbalanced node classification task.

Generative adversarial networks (GANs) have been extensively studied in the past few years. Arguably their most significant impact has been in the area of computer vision where great advances have been made in challenges such as plausible image generation, image-to-image translation, facial attribute manipulation and similar domains. Despite the significant successes achieved to date, applying GANs to real-world problems still poses significant challenges, three of which we focus on here. These are: (1) the generation of high quality images, (2) diversity of image generation, and (3) stable training. Focusing on the degree to which popular GAN technologies have made progress against these challenges, we provide a detailed review of the state of the art in GAN-related research in the published scientific literature. We further structure this review through a convenient taxonomy we have adopted based on variations in GAN architectures and loss functions. While several reviews for GANs have been presented to date, none have considered the status of this field based on their progress towards addressing practical challenges relevant to computer vision. Accordingly, we review and critically discuss the most popular architecture-variant, and loss-variant GANs, for tackling these challenges. Our objective is to provide an overview as well as a critical analysis of the status of GAN research in terms of relevant progress towards important computer vision application requirements. As we do this we also discuss the most compelling applications in computer vision in which GANs have demonstrated considerable success along with some suggestions for future research directions. Code related to GAN-variants studied in this work is summarized on //github.com/sheqi/GAN_Review.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.

Generating texts which express complex ideas spanning multiple sentences requires a structured representation of their content (document plan), but these representations are prohibitively expensive to manually produce. In this work, we address the problem of generating coherent multi-sentence texts from the output of an information extraction system, and in particular a knowledge graph. Graphical knowledge representations are ubiquitous in computing, but pose a significant challenge for text generation techniques due to their non-hierarchical nature, collapsing of long-distance dependencies, and structural variety. We introduce a novel graph transforming encoder which can leverage the relational structure of such knowledge graphs without imposing linearization or hierarchical constraints. Incorporated into an encoder-decoder setup, we provide an end-to-end trainable system for graph-to-text generation that we apply to the domain of scientific text. Automatic and human evaluations show that our technique produces more informative texts which exhibit better document structure than competitive encoder-decoder methods.

We present SlowFast networks for video recognition. Our model involves (i) a Slow pathway, operating at low frame rate, to capture spatial semantics, and (ii) a Fast pathway, operating at high frame rate, to capture motion at fine temporal resolution. The Fast pathway can be made very lightweight by reducing its channel capacity, yet can learn useful temporal information for video recognition. Our models achieve strong performance for both action classification and detection in video, and large improvements are pin-pointed as contributions by our SlowFast concept. We report 79.0% accuracy on the Kinetics dataset without using any pre-training, largely surpassing the previous best results of this kind. On AVA action detection we achieve a new state-of-the-art of 28.3 mAP. Code will be made publicly available.