相关论文: Non-Markovian recovery makes complex networks more…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…

Failures in optical network backbone can lead to major disruption of internet data traffic. Hence, minimizing such failures is of paramount importance for the network operators. Even better, if the network failures can be predicted and…

Memoryless (Markovian) system-bath interactions are of fundamental interest in physics. While typically, the absence of memory originates from the characteristics of the bath, here we demonstrate that it can result from the system becoming…

We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…

A networked system can fail when most of its components are unable to support flux through the nodes and edges. As studied earlier this scenario can be triggered by an external perturbation such as an intentional attack on nodes or for…

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…

Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…

We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…

We construct a continuous-time, positively divisible non-Markovian process with memory of the initial state that satisfies the differential Chapman--Kolmogorov equation. In the stationary state, the correlation function exhibits exponential…

A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…

Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system…

Non-Markovian stochastic processes are ubiquitous in biology. Nevertheless, we lack a general framework for quantifying historical dependencies. In this Letter, we propose an information-theoretic approach to decompose history dependence in…

Differential equations containing memory terms that depend nonlinearly on past states model a variety of non-Markovian processes. In this study, we present a Markovian embedding procedure for such equations with distributed delay by…

Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…

Non-Markovian dynamics are ubiquitous across physics, biology, and engineering. Yet our understanding of non-Markovian processes significantly lags that of simpler Markovian processes, due largely to a lack of tractable models. In this…

We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…

The existence of inter-dependence between multiple networks imparts an additional scale of complexity to such systems often referred to as `network of networks' (NON). We have investigated the robustness of NONs to random breakdown of their…

The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on…

Recent progress in network topology modeling [1], [2] has shown that it is possible to create smaller-scale replicas of large complex networks, like the Internet, while simultaneously preserving several important topological properties.…