Blow-Up Phenomena for Porous Medium Equation with Nonlinear Flux on the Boundary

We investigate the blow-up phenomena for nonnegative solutions of porous medium equation with Neumann boundary conditions. We find that the absorption and the nonlinear flux on the boundary have some competitions in the blow-up phenomena

Global exponential convergence of delayed inertial Cohen–Grossberg neural networks

In this paper, the exponential convergence of delayed inertial Cohen–Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results

DGRec: Graph Neural Network for Recommendation with Diversified Embedding Generation

Graph Neural Network (GNN) based recommender systems have been attracting more and more attention in recent years due to their excellent performance in accuracy. Representing user-item interactions as a bipartite graph, a GNN model generates user and item representations by aggregating embeddings of their neighbors. However, such an aggregation procedure often accumulates information purely based on the graph structure, overlooking the redundancy of the aggregated neighbors and resulting in poor diversity of the recommended list. In this paper, we propose diversifying GNN-based recommender systems by directly improving the embedding generation procedure. Particularly, we utilize the following three modules: submodular neighbor selection to find a subset of diverse neighbors to aggregate for each GNN node, layer attention to assign attention weights for each layer, and loss reweighting to focus on the learning of items belonging to long-tail categories. Blending the three modules into GNN, we present DGRec(Diversified GNN-based Recommender System) for diversified recommendation. Experiments on real-world datasets demonstrate that the proposed method can achieve the best diversity while keeping the accuracy comparable to state-of-the-art GNN-based recommender systems.Comment: 9 pages, WSDM 202

Uncovering the role of superplasticizer in developing nano-engineered ultra-high-performance concrete

The effect of superplasticizer (SP) on the performance of ultra-high-performance concrete (UHPC) and ultra-high-performance fiber-reinforced concrete (UHPFRC) has been systematically investigated aiming to optimize the use of SP. The slump flow, and V-funnel time were employed to evaluate the impact of SP on the workability, while compressive strength had been used for mechanical property. Moreover, the packing density, as well as the water film thickness had been calculated to uncover the mechanism. The obtained results indicated that the addition of SP improved the workability of specimens with an ultimate-low water-to-binder (W/B) ratio, while it benefited the strength development of UHPC with a lower W/B ratio. This novel phenomenon (SP enhances the mechanical properties of UHPC) is due to the fact that SP reduced the water film thickness and enhanced the packing structure, therefore resulting in an increased compressive strength. For UHPFRC, similar trends can be witnessed regarding the flowability. However, the alternation of the fresh behavior of UHPFRC, attributed to the inclusion of SP, had an obvious impact on the fiber distribution, which altered the strength development of UHPFRC. This study revealed the significant effect of SP on the performance, especially on the strength development, of UHPC and UHPFRC

Graph-based Alignment and Uniformity for Recommendation

Collaborative filtering-based recommender systems (RecSys) rely on learning representations for users and items to predict preferences accurately. Representation learning on the hypersphere is a promising approach due to its desirable properties, such as alignment and uniformity. However, the sparsity issue arises when it encounters RecSys. To address this issue, we propose a novel approach, graph-based alignment and uniformity (GraphAU), that explicitly considers high-order connectivities in the user-item bipartite graph. GraphAU aligns the user/item embedding to the dense vector representations of high-order neighbors using a neighborhood aggregator, eliminating the need to compute the burdensome alignment to high-order neighborhoods individually. To address the discrepancy in alignment losses, GraphAU includes a layer-wise alignment pooling module to integrate alignment losses layer-wise. Experiments on four datasets show that GraphAU significantly alleviates the sparsity issue and achieves state-of-the-art performance. We open-source GraphAU at https://github.com/YangLiangwei/GraphAU.Comment: 4 page