Related papers: Higher-order Connection Laplacians for Directed Si…

Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…

Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and…

In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…

Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…

The work done in this paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the…

Traditional graph signal processing (GSP) methods applied to brain networks focus on signals defined on the nodes. Thus, they are unable to capture potentially important dynamics occurring on the edges. In this work, we adopt an…

Our goal in this paper is to leverage the potential of the topological signal processing (TSP) framework for analyzing brain networks. Representing brain data as signals over simplicial complexes allows us to capture higher-order…

We study the effect of adding to a directed chain of interconnected systems a directed feedback from the last element in the chain to the first. The problem is closely related to the fundamental question of how a change in network topology…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

Network controllability is a powerful tool to study causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable…

Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…

Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its…

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…

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it…

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

Complex systems often involve higher-order interactions which require us to go beyond their description in terms of pairwise networks. Triadic interactions are a fundamental type of higher-order interaction that occurs when one node…

The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links…