Related papers: Interlayer antisynchronization in degree-biased du…
We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our…
Future communication networks are expected to feature autonomic (or self-organizing) mechanisms to ease deployment (self-configuration), tune parameters automatically (self-optimization) and repair the network (self-healing).…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
The effects of nonlocal and reflecting connectivities have been previously investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. In this work we investigate the…
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail,…
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in such systems possesses a hierarchical structure, with different parts scaling with the…
We consider the problem of asymptotic synchronization of different spatial points coupled to each other in inhomogeneous spacetime and undergoing chaotic Mixmaster oscillations towards the singularity. We demonstrate that for couplings…
The way the topological structure goes from a decoupled state into a coupled one in multiplex networks has been widely studied by means of analytical and numerical studies, involving models of artificial networks. In general, these…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize…
The paper addresses the synchronization of multi-agent systems with continuous-time dynamics interacting through a very general class of monotonic continuous signal functions that covers estimation biases, approximation of discrete…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
Deep neural networks can achieve remarkable generalization performances while interpolating the training data perfectly. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent" -…
We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength $J_{\rm I}$) is ferromagnetically intercoupled (the strength $J$) to the Watts-Strogatz (WS)…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
In a predator-prey metapopulation, the two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a…
It is widely held that identical systems tend to behave similarly under comparable conditions. Yet, for systems that interact through a network, symmetry breaking can lead to scenarios in which this expectation does not hold. Prominent…
The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \;\mbox{mod}…