Related papers: Griffiths phases in infinite-dimensional, non-hier…
Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this…
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge…
Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully…
We investigate the emergence of synchronization in a network of coupled chaotic macroeconomic systems. Each node represents an economy characterized by three key variables savings, gross domestic product (GDP), and foreign capital inflows.…
An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter…
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.…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
This paper investigates questions related to the modularity in discrete models of biological interaction networks. We develop a theoretical framework based on the analysis of their asymptotic dynamics. More precisely, we exhibit formal…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…
A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…