Related papers: Cluster Synchronization via Graph Laplacian Eigenv…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
Networks are often interconnected, with one system wielding greater influence over another. However, the effects of such asymmetry on self-organized phenomena (e.g., consensus and synchronization) are not well understood. Here, we study…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition…
We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the…
A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an…