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We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
The processing of signals on simplicial and cellular complexes defined by nodes, edges, and higher-order cells has recently emerged as a principled extension of graph signal processing for signals supported on more general topological…
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
The influence of array geometry on synchronization properties of a 2-D oscillator array is investigated based on a comparison between a rectangular and a hexagonal grid. The Kuramoto model is solved for a nearest-neighbor case with periodic…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
In this paper, we investigate the factors that affect the synchronization of coupled oscillators on networks. By using the edge-intercrossing method, we keep the degree distribution unchanged to see other statistical properties' effects on…
We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the mean-square…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators…
Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
Cortical regions without direct neuronal connections have been observed to exhibit synchronized dynamics. A recent empirical study has further revealed that such regions that share more common neighbors are more likely to behave coherently.…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains,…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…