Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations

Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector $\boldsymbol x = (x_1,\dots,x_d)$ such that for each node $v$ in a social network, $v$ could be activated as a seed of diffusion with probability $h_v(\boldsymbol x)$, where $h_v$ is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix $\boldsymbol x$ with constraint $\sum_i x_i \le k$ where $k$ is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as $g(\boldsymbol x)$, is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix $\boldsymbol x$ has a cost $c(\boldsymbol x)$ where $c$ is a convex cost function, we want to maximize the balanced sum $g(\boldsymbol x) + \lambda(k - c(\boldsymbol x))$ where $\lambda$ is a balance parameter, subject to the constraint of $c(\boldsymbol x) \le k$. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves $\left(\frac{1}{2}-\varepsilon\right)$-approximation, and for the case of independent strategy activations, we present an algorithm that achieves $\left(1-\frac{1}{e}-\varepsilon\right)$ approximation.Comment: To appear in AAAI-20, 43 page

A STM study of the self-assembly phenomenon and mechanism of cobalt-C60_{60} clusters on Au(111) surfaces

In 2013, Self-assembled Au-C$_{60}$ magic number clusters on Au (111) surfaces were successfully manufactured by the NPRL laboratory of the University of Birmingham. This work has important significance for the surface self-assembly of carbon nanostructures. However, this work has two key issues that can’t be solved: the Au cluster is too stable to be characterized and can’t expect further structure evolution. So, in the further work, the similar cobalt-C$_{60}$ clusters were attempted to be prepared. However, the C$_{60}$ on Au (111) substrate show the phase separation although the interaction between cobalt and C60 is much stronger than gold and C$_{60}$. In this thesis, a reasonable explanation for the formation mechanism of Cobalt-C$_{60}$ clusters is given based on the STM technique. Due to the 14% lattice mismatch between cobalt and gold, the cobalt clusters on Au (111) are irregular and rugged. Therefore, although the cobalt atoms have a good affinity for C$_{60}$, the cobalt clusters on the gold surface cannot form Cobalt-C$_{60}$ clusters, due to inefficient contact with C$_{60}$. Only at high temperature, the thermal motion of cobalt atoms is enhanced. Cobalt atoms refine themselves to be in complete contact with C$_{60}$ molecules, thus adsorbing C$_{60}$ to form Cobalt-C$_{60}$ clusters. As cobalt clusters at high temperature will gradually sink into the gold surface, if the order of annealing and C$_{60}$ deposition is exchanged, the pre-annealed cobalt clusters will partially sink into the gold surface resulting in a lack of C$_{60}$ adsorption sites. So, the Cobalt-C$_{60}$ clusters will not be able to form. In a common heating treatment for both, cobalt cluster will be wrapped by C$_{60}$ molecules in advance to prevent it from sinking. Further experimental evidences suggest that the opening of the carbon cage and the formation of the cobalt-carbon bond may also have occurred at higher temperatures

Learning Graph Convolutional Network for Skeleton-based Human Action Recognition by Neural Searching

Human action recognition from skeleton data, fueled by the Graph Convolutional Network (GCN), has attracted lots of attention, due to its powerful capability of modeling non-Euclidean structure data. However, many existing GCN methods provide a pre-defined graph and fix it through the entire network, which can loss implicit joint correlations. Besides, the mainstream spectral GCN is approximated by one-order hop, thus higher-order connections are not well involved. Therefore, huge efforts are required to explore a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for skeleton-based action recognition. Specifically, we enrich the search space by providing multiple dynamic graph modules after fully exploring the spatial-temporal correlations between nodes. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a sampling- and memory-efficient evolution strategy is proposed to search an optimal architecture for this task. The resulted architecture proves the effectiveness of the higher-order approximation and the dynamic graph modeling mechanism with temporal interactions, which is barely discussed before. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scaled datasets and the results show that our model gets the state-of-the-art results.Comment: Accepted by AAAI202