Time series forecasting has attracted significant interest across various fields in recent years. Notably, Transformers have been extensively investigated for long-term time series forecasting (LTSF) due to their remarkable ability on modeling sequential data. However, the point-wise calculation of its self-attention leads to a challenging task for accurately capturing real-world time series' local and global characteristics, especially with multiple seasonal periodic components and outliers. In this article, we leverage wavelet analysis to recognize different frequency patterns and design an effective attention mechanism for time series forecasting to address this issue. In detail, we employ the maximal overlap discrete wavelet transform (MODWT) to construct a novel wavelet attention (WA) mechanism and propose the wavelet transformer (Waveformer) prediction technique. This approach effectively extracts multiple periodic features, mitigates the influence of anomalies and improves the precision of time series prediction under seasonal-trend decomposition methods. Experimental evaluations on six real-world datasets from various application fields demonstrate that the multiple periodic decomposition strategy of Waveformer successfully captures time series seasonal patterns and improves forecasting performance in comparison with many state-of-art methods.

When Linton C. Freeman made his conceptual clarifications about centrality measures in social network analysis in 1979 he exclusively focused on unweighted, symmetric, and connected networks without the possibility of self-loops. Even though a lot of articles have been published in the last years discussing network measures for weighted, asymmetric or unconnected networks, the vast majority of researchers dealing with social network data simplify their networks based on Freeman's 1979 definitions before they calculate centrality measures. When dealing with weighted and/or asymmetric networks which can have self links and consist of multiple components, researchers are confronted with a lack of standardization. Different tools for social network analysis treat specific cases differently. In this article we describe and discuss the ways the software ORA (developed by CASOS at Carnegie Mellon University) handles the most important network measures in case of weighted, asymmetric, self-looped, and disconnected networks. In the center of our attention are the following measures, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and clustering coefficient.

In cooperative multi-agent reinforcement learning (MARL), value function factorization methods have been proposed to address the dimensionality explosion problem encountered in centralized training and decentralized execution (CTDE). The existing value function factorization methods lack a perspective from the global system when addressing credit assignment, failing to measure each agent’s contribution to the current system. A typical limitation is that these factorization approaches primarily rely on the proximity of local individual groups to assign credit. There are challenges such as the sensitivity of credit assignment weights to local information and instability in the learning process. In this study, we focus on redistributing agents’ features during the system evolution and suggest employing an enhanced attention mechanism with system entropy measure to factorize value function. Specifically, this method emphasizes each agent’s representation between their local and global contributions and then redesigns multi-head attention to optimize the credit assignment in value function factorization. To evaluate the effectiveness of our method, we conduct a series of cooperative multi-agent tasks on the StarCraft II platform and compare the results with several state-of-the-art techniques, including Qatten, QMIX, QTRAN, COMA, and VDN. The experimental results demonstrate that our method achieves faster overall convergence speed, higher stability, and robust performance across various scenarios.

Packet classification is a key function for software-defined networking switches. For example, OpenFlow Switch examines up to 15 required fields, against thousands of rules. With the proliferation of new header fields in a ruleset, it becomes a great challenge to design a high performance packet classification solution. In this paper, we present a scalable many-field packet classification algorithm and its prototype implementation on a graphics processing unit (GPU). By exploiting the sparsity of ruleset, our algorithm uses a few effective bits to divide a large ruleset into multiple subsets with low rule replication for economic memory usage at the offline stage. These effective bits are chosen based on our selection metrics: wildcard ratio, independence index, and diversity index. Using these effective bits, our algorithm can quickly filter out the majority rules which do not need to be full-matched to improve the online system performance. Moreover, the choice of effective bits is adjustable to meet the implementation requirements of varying environments for good performance scalability. Our prototype on a single NVIDIA K20C GPU achieves more than 160 MPPS throughput for 100K 15-field synthetic ruleset.

The link prediction problem in the network concerns to predict the existence of links between node pairs, which is a research hotspot in different scenarios with network applications. Methods of predicting links based on network topology and structures provide a number of measurements to reveal the underlying relationship between two nodes. In this paper, a motif-based similarity index for link prediction is proposed to calculate the similarity score of two nodes concerning their local environment, which takes advantage of existing similarity definitions and the motifs. This motif-based similarity can be generalized to more complicated cases by considering different motifs and keeps the same level of computational complexity with the existing indexes. Experimental results on 9 public benchmark datasets and 1 randomly generated dataset show the effectiveness of our proposed index, and accuracies on several datasets are significantly improved. The performance of motif-based similarity suggests that considering typical motifs on networks could improve the precisions of link prediction tasks, and exploring specific structure characteristics on networks will point out an important and effective direction for more research with network methods applied.

Percolation is one of the most widely studied models in which a unique giant cluster emerges after the phase transition. Recently, a new phenomenon, where multiple giant clusters are observed in the so called Bohman-Frieze-Wormald (BFW) model, has attracted much attention, and how multiple giant clusters could emerge in generic percolation processes on random networks will be discussed in this paper. By introducing the merging probability and inspecting the distinct mechanisms which contribute to the growth of largest clusters, a sufficient condition to generate multiple stable giant clusters is given. Based on the above results, the BFW model and a multi-Erdös-Rényi (ER) model given by us are analyzed, and the mechanism of multiple giant clusters of these two models is revealed. Furthermore, large fluctuations are observed in the size of multiple giant clusters in many models, but the sum size of all giant clusters exhibits self-averaging as that in the size of unique giant cluster in ordinary percolation. Besides, the growth modes of different giant clusters are discussed, and we find that the large fluctuations observed are mainly due to the stochastic behavior of the evolution in the critical window. For all the discussion above, numerical simulations on the BFW model and the multi-ER model are done, which strongly support our analysis. The investigation of merging probability and the growth mechanisms of largest clusters provides insight for the essence of multiple giant clusters in the percolation processes and can be instructive for modeling or analyzing real-world networks consisting of many large clusters.