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We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the…
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed…
We aim at assessing the states of the nodes in a network by means of end-to-end monitoring paths. The contribution of this paper is twofold. First, we consider a static failure scenario. In this context, we aim at minimizing the number of…
Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…
Protein subcellular localization is an important factor in normal cellular processes and disease. While many protein localization resources treat it as static, protein localization is dynamic and heavily influenced by biological context.…
Quantum walks on networks are a paradigmatic model in quantum information theory. Quantum-walk algorithms have been developed for various applications, including spatial-search problems, element-distinctness problems, and node centrality…
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions…
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We report on a data-driven investigation aimed at understanding the dynamics of message spreading in a real-world dynamical network of human proximity. We use data collected by means of a proximity-sensing network of wearable sensors that…
Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e. involving one connection at a time, or as complex contagion, in which multiple…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…