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Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on…
The ability of humans and animals to quickly adapt to novel tasks is difficult to reconcile with the standard paradigm of learning by slow synaptic weight modification. Here we show that fixed-weight neural networks can learn to generate…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic…
Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution…
This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike…
Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account, by assuming that the relevant information to study…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
We study expansion and information diffusion in dynamic networks, that is in networks in which nodes and edges are continuously created and destroyed. We consider information diffusion by {\em flooding}, the process by which, once a node is…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly.…
Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in…
Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…