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Recent seminal work at the intersection of deep neural networks practice and random matrix theory has linked the convergence speed and robustness of these networks with the combination of random weight initialization and nonlinear…

We study the occurrence of frequency synchronised states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network,…

In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely…

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…

We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…

This paper presents an analytical framework to model fault-tolerance in unstructured peer-to-peer overlays, represented as complex networks. We define a distributed protocol peers execute for managing the overlay and reacting to node…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in coarse grained sense acts as an excellent order…

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…

We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

We study the occurrence of plateaux and jumps in the magnetization curves of a class of frustrated ladders for which the Hamiltonian can be written in terms of the total spin of a rung. We argue on the basis of exact diagonalization of…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…

Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies…

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms…

After a more than decade-long period of relatively little research activity in the area of recurrent neural networks, several new developments will be reviewed here that have allowed substantial progress both in understanding and in…