Gluing simple-minded collections in triangulated categories

We provide a technique to glue simple-minded collections along a recollement of Hom-finite Krull-Schmidt triangulated categories over a field. This gluing technique for simple-minded collections is shown to be compatible with those for gluing bounded $t$-structures, silting objects, and co-$t$-structures in the literature. Furthermore, it also enjoys the properties of preserving partial order and commuting with the operation of mutation.Comment: 23 page

Joint Network Function Placement and Routing Optimization in Dynamic Software-defined Satellite-Terrestrial Integrated Networks

Software-defined satellite-terrestrial integrated networks (SDSTNs) are seen as a promising paradigm for achieving high resource flexibility and global communication coverage. However, low latency service provisioning is still challenging due to the fast variation of network topology and limited onboard resource at low earth orbit satellites. To address this issue, we study service provisioning in SDSTNs via joint optimization of virtual network function (VNF) placement and routing planning with network dynamics characterized by a time-evolving graph. Aiming at minimizing average service latency, the corresponding problem is formulated as an integer nonlinear programming under resource, VNF deployment, and time-slotted flow constraints. Since exhaustive search is intractable, we transform the primary problem into an integer linear programming by involving auxiliary variables and then propose a Benders decomposition based branch-and-cut (BDBC) algorithm. Towards practical use, a time expansion-based decoupled greedy (TEDG) algorithm is further designed with rigorous complexity analysis. Extensive experiments demonstrate the optimality of BDBC algorithm and the low complexity of TEDG algorithm. Meanwhile, it is indicated that they can improve the number of completed services within a configuration period by up to 58% and reduce the average service latency by up to 17% compared to baseline schemes.Comment: Accepted by IEEE Transactions on Wireless Communication

Succinct Representations in Collaborative Filtering: A Case Study using Wavelet Tree on 1,000 Cores

User-Item (U-I) matrix has been used as the dominant data infrastructure of Collaborative Filtering (CF). To reduce space consumption in runtime and storage, caused by data sparsity and growing need to accommodate side information in CF design, one needs to go beyond the UI Matrix. In this paper, we took a case study of Succinct Representations in Collaborative Filtering, rather than using a U-I Matrix. Our key insight is to introduce Succinct Data Structures as a new infrastructure of CF. Towards this, we implemented a User-based K-Nearest-Neighbor CF prototype via Wavelet Tree, by first designing a Accessible Compressed Documents (ACD) to compress U-I data in Wavelet Tree, which is efficient in both storage and runtime. Then, we showed that ACD can be applied to develop an efficient intersection algorithm without decompression, by taking advantage of ACD’s characteristics. We evaluated our design on 1,000 cores of Tianhe-II supercomputer, with one of the largest public data set ml-20m. The results showed that our prototype could achieve 3.7 minutes on average to deliver the results

Ada-NETS: Face Clustering via Adaptive Neighbour Discovery in the Structure Space

Face clustering has attracted rising research interest recently to take advantage of massive amounts of face images on the web. State-of-the-art performance has been achieved by Graph Convolutional Networks (GCN) due to their powerful representation capacity. However, existing GCN-based methods build face graphs mainly according to kNN relations in the feature space, which may lead to a lot of noise edges connecting two faces of different classes. The face features will be polluted when messages pass along these noise edges, thus degrading the performance of GCNs. In this paper, a novel algorithm named Ada-NETS is proposed to cluster faces by constructing clean graphs for GCNs. In Ada-NETS, each face is transformed to a new structure space, obtaining robust features by considering face features of the neighbour images. Then, an adaptive neighbour discovery strategy is proposed to determine a proper number of edges connecting to each face image. It significantly reduces the noise edges while maintaining the good ones to build a graph with clean yet rich edges for GCNs to cluster faces. Experiments on multiple public clustering datasets show that Ada-NETS significantly outperforms current state-of-the-art methods, proving its superiority and generalization. Code is available at https://github.com/damo-cv/Ada-NETS