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Extensive research has focused on studying the robustness of interdependent non-directed networks and the design of mitigation strategies aimed at reducing disruptions caused by cascading failures. However, real systems such as power and…
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially…
Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier…
The latest financial crisis has painfully revealed the dangers arising from a globally interconnected financial system. Conventional approaches based on the notion of the existence of equilibrium and those which rely on statistical…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
An epidemic spreading in a network calls for a decision on the part of the network members: They should decide whether to protect themselves or not. Their decision depends on the trade-off between their perceived risk of being infected and…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…
Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate…
Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to…
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
Earthquake faults occur in networks that have dynamical modes not displayed by single isolated faults. Using simulations of the network of strike-slip faults in southern California, we find that the physics depends critically on both the…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
We address a fundamental problem that is systematically encountered when modeling complex systems: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information…
We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or…