Related papers: Topology and higher-order global synchronization o…
Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces.…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as…
Generalized synchronization (GS) describes a state in which two coupled dynamical systems exhibit a functional relationship between their variables. GS can be achieved by appropriately designing the coupling to constrain the dynamics onto…
We consider a network of identical, first-order linear systems, and investigate how replacing a subset of the systems composing the network with higher-order ones, either taken to be generic or specifically designed, may affect its…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…
Music is inherently complex, with structures and interactions that unfold across multiple layers. Complex networks have emerged as powerful structures for the quantitative analysis of Western classical music, revealing significant features…
For the two-layer shallow water equations, a high-order compact gas-kinetic scheme (GKS) on triangular mesh is proposed. The two-layer shallow water equations have complex source terms in comparison with the single layer equations. The main…
Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons…
A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system…
Controlling complex networked systems to a desired state is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic…
Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
Localization transitions represent a fundamental class of continuous phase transitions, yet they occur without any accompanying symmetry breaking. We resolve this by introducing the concept of dynamical translational symmetry (DTS), which…