Topological mirror symmetry for rank two character varieties of surface groups

The moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.

Multi-Channel Pooling Graph Neural Networks

Graph pooling is a critical operation to downsample a graph in graph neural networks. Existing coarsening pooling methods (e.g. DiffPool) mostly focus on capturing the global topology structure by assigning the nodes into several coarse clusters, while dropping pooling methods (e.g. SAGPool) try to preserve the local topology structure by selecting the top-k representative nodes. However, there lacks an effective method to integrate the two types of methods so that both the local and the global topology structure of a graph can be well captured. To address this issue, we propose a Multi-channel Graph Pooling method named MuchPool, which captures the local structure, the global structure, and node feature simultaneously in graph pooling. Specifically, we use two channels to conduct dropping pooling based on the local topology and node features respectively, and one channel to conduct coarsening pooling. Then a cross-channel convolution operation is designed to refine the graph representations of different channels. Finally, the pooling results are aggregated as the final pooled graph. Extensive experiments on six benchmark datasets present the superior performance of MuchPool. The code of this work is publicly available at Github.

An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection

In the past few decades, vibration-based structural damage detection (SDD) has attracted widespread attention. Using the response data of engineering structures, the researchers have developed many methods for damage localization and quantification. Adopting meta-heuristic algorithms, in which particle swarm optimization (PSO) is the most widely used, is a popular approach. Various PSO variants have also been proposed for improving its performance in SDD, and they are generally based on the Global topology. However, in addition to the Global topology, other topologies are also developed in the related literature to enhance the performance of the PSO algorithm. The effects of PSO topologies depend significantly on the studied problems. Therefore, in this article, we conduct a performance investigation of eight PSO topologies in SDD. The success rate and mean iterations that are obtained from the numerical simulations are considered as the evaluation indexes. Furthermore, the average rank and Bonferroni-Dunn’s test are further utilized to perform the statistic analysis. From these analysis results, the Four Clusters are shown to be the more favorable PSO topologies in SDD.

Informational Cost and Networks Navigability

Understanding how information navigates through nodes of a complex network has become an increasingly pressing problem across scientific disciplines. Several approaches have been proposed on the basis of shortest paths or diffusive navigation. However, no existing approaches have tackled the challenges of efficient communication in networks without full knowledge of their global topology under external noise. Here, we develop a first principles approach and mathematical formalism to determine the informational cost of navigating a network under different levels of external noise. Using this approach we discover the existence of a trade-off between the ways in which networks route information through shortest paths, their entropies and stability, which define three classes of real-world networks. This approach reveals that environmental pressure has shaped the ways in which information is transferred in bacterial metabolic net-works and allowed us to determine the levels of noise at which a protein-protein interaction network seems to work in normal conditions in a cell.

Evaluating on Topology Survivability Based on Largest Number of Node-Disjoint Paths

<p>On the point of view of Largest Number of Node-Disjoint Path (LNNDP for short) between a node pair in a network, this article states the importance of LNNDP to global survivability of topology at first, then proposes an algorithm to compute maximal number of node-disjoint paths between node pairs. A new topology survivability metric based on LNNDP is put forward to evaluate the global survivability of network topology. It can be used to evaluate the survivability of topology provided. This metric can express accurately global topology survivability.</p>

Fully Distributed Event-Triggered Containment Control of Uncertain Multiagent Systems

This paper investigates the event-triggered containment control problem of a class of uncertain nonlinear multiagent systems (MASs). By employing the local relative information, we design an adaptive event-triggered containment algorithm. The proposed containment algorithm can cope with the unavailability of global topology information and uncertain dynamics of follower agents. Therefore, the presented containment algorithm is free of global topology information, i.e., the designed algorithm is fully distributed. In addition, it is proved that Zeno behavior will not occur. At last, a numerical example is given to verify our event-triggered containment algorithm.