Related papers: Slow dynamics of the contact process on complex ne…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
The Griffiths phase in systems with quenched disorder occurs below the ordering transition of the pure system down to the ordering transition of the actual disordered system. While it does not exhibit long-range order, large fluctuations in…
Balanced neural networks -- in which excitatory and inhibitory inputs compensate each other on average -- give rise to a dynamical phase dominated by fluctuations called asynchronous state, crucial for brain functioning. However, structural…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
The effect of strong disorder on the one-dimensional Kondo necklace model is studied using a perturbative real-space renormalization group approach which becomes asymptotically exact in the low energy limit. The phase diagram of the model…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that…
We study the effects of quenched disorder in a class of quantum chains with (p+1)-multispin interactions exhibiting a free fermionic spectrum, paying special attention to the case p=2. Depending if disorder couples to (i) all the couplings…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the…
I provide numerical evidence for the robustness of the Griffiths phase (GP) reported previously in dynamical threshold model simulations on a large human brain network with N=836733 connected nodes. The model, with equalized network…
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase". It is known that, in one dimension, these rare regions can cause the d.c.…
Criticality has been conjectured as an integral part of neuronal network dynamics. Operating at a critical threshold requires precise parameter tuning and a corresponding mechanism remains an open question. Recent studies have suggested…
We investigate heterogeneous coupling delays in complex networks of excitable elements described by the FitzHugh-Nagumo model. The effects of discrete as well as of uni- and bimodal continuous distributions are studied with a focus on…