Adaptive Synchronization of Complex Dynamical Networks with State Predictor

This paper addresses the adaptive synchronization of complex dynamical networks with nonlinear dynamics. Based on the Lyapunov method, it is shown that the network can synchronize to the synchronous state by introducing local adaptive strategy to the coupling strengths. Moreover, it is also proved that the convergence speed of complex dynamical networks can be increased via designing a state predictor. Finally, some numerical simulations are worked out to illustrate the analytical results

Hierarchical Contrastive Learning Enhanced Heterogeneous Graph Neural Network

Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-view contrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, to further boost the performance of HeCo, two additional methods are designed to generate harder negative samples with high quality. Besides the invariant factors, view-specific factors complementally provide the diverse structure information between different nodes, which also should be contained into the final embeddings. Therefore, we need to further explore each view independently and propose a modified model, called HeCo++. Specifically, HeCo++ conducts hierarchical contrastive learning, including cross-view and intra-view contrasts, which aims to enhance the mining of respective structures.Comment: This paper has been accepted by TKDE as a regular paper. arXiv admin note: substantial text overlap with arXiv:2105.0911

Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains

Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. In this work, we uncover that the ``variational entanglement-enhancing'' field (VEEF) robustly induces a persistent ballistic spreading of entanglement in quantum spin chains. The VEEF is time dependent, and is optimally controlled to maximize the bipartite entanglement entropy (EE) of the final state. Such a linear growth persists till the EE reaches the genuine saturation $\tilde{S} = - \log_{2} 2^{-\frac{N}{2}}=\frac{N}{2}$ with $N$ the total number of spins. The EE satisfies $S(t) = v t$ for the time $t \leq \frac{N}{2v}$, with $v$ the velocity. These results are in sharp contrast with the behaviors without VEEF, where the EE generally approaches a sub-saturation known as the Page value $\tilde{S}_{P} =\tilde{S} - \frac{1}{2\ln{2}}$ in the long-time limit, and the entanglement growth deviates from being linear before the Page value is reached. The dependence between the velocity and interactions is explored, with $v \simeq 2.76$, $4.98$, and $5.75$ for the spin chains with Ising, XY, and Heisenberg interactions, respectively. We further show that the nonlinear growth of EE emerges with the presence of long-range interactions.Comment: 5 pages, 4 figure