The structure of real-world multilayer infrastructure systems usually exhibits anisotropy due to constraints of the embedding space. For example, geographical features like mountains, rivers and shores influence the architecture of critical infrastru
cture networks. Moreover, such spatial networks are often non-homogeneous but rather have a modular structure with dense connections within communities and sparse connections between neighboring communities. When the networks of the different layers are interdependent, local failures and attacks may propagate throughout the system. Here we study the robustness of spatial interdependent networks which are both anisotropic and heterogeneous. We also evaluate the effect of localized attacks having different geometrical shapes. We find that anisotropic networks are more robust against localized attacks and that anisotropic attacks, surprisingly, even on isotropic structures, are more effective than isotropic attacks.
In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian and econom
ic impact, it is important to develop models to estimate the probability of a worldwide pandemic. In this paper, we propose a model of disease spreading in a structural modular complex network (having communities) and study how the number of bridge nodes $n$ that connect communities affects disease spread. We find that our model can be described at a global scale as an infectious transmission process between communities with global infectious and recovery time distributions that depend on the internal structure of each community and $n$. We find that near the critical point as $n$ increases, the disease reaches most of the communities, but each community has only a small fraction of recovered nodes. In addition, we obtain that in the limit $n to infty$, the probability of a pandemic increases abruptly at the critical point. This scenario could make the decision on whether to launch a pandemic alert or not more difficult. Finally, we show that link percolation theory can be used at a global scale to estimate the probability of a pandemic since the global transmissibility between communities has a weak dependence on the global recovery time.
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of
growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characterise the screening effect observed in the structures by analysing the multifractal properties of the growth probability.
Interdependencies are ubiquitous throughout the world. Every real-world system interacts with and is dependent on other systems, and this interdependency affects their performance. In particular, interdependencies among networks make them vulnerable
to failure cascades, the effects of which are often catastrophic. Failure propagation fragments network components, disconnects them, and may cause complete systemic failure. We propose a strategy of avoiding or at least mitigating the complete destruction of a system of interdependent networks experiencing a failure cascade. Starting with a fraction $1-p$ of failing nodes in one network, we reconnect with a probability $gamma$ every isolated component to a functional giant component (GC), the largest connected cluster. We find that as $gamma$ increases the resilience of the system to cascading failure also increases. We also find that our strategy is more effective when it is applied in a network of low average degree. We solve the problem theoretically using percolation theory, and we find that the solution agrees with simulation results.
Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdandv{z}ic $et;al.$ [Nature Physics 10, 34
(2014)] proposed a model to study systems in which active nodes fail and recover spontaneously in a complex network and found that in the steady state the density of active nodes can exhibit an abrupt transition and hysteresis depending on the values of the parameters. Here we investigate a model of recovery-failure from a dynamical point of view. Using an effective degree approach we find that the systems can exhibit a temporal sharp decrease in the fraction of active nodes. Moreover we show that, depending on the values of the parameters, the fraction of active nodes has an oscillatory regime which we explain as a competition between different failure processes. We also find that in the non-oscillatory regime, the critical fraction of active nodes presents a discontinuous drop which can be related to a targeted k-core percolation process. Finally, using mean field equations we analyze the space of parameters at which hysteresis and oscillatory regimes can be found.
We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a technique, b
ased on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.
Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$ of nodes
in one network, exposes the system to cascade of failures and, as a consequence, to a full collapse of the overall system. Therefore it is important to develop efficient strategies to avoid the collapse by increasing the robustness of the individual networks against failures. Here, we provide an exact theoretical approach to study the evolution of the cascade of failures on interdependent networks when a fraction $alpha$ of the nodes with higher connectivity in each individual network are autonomous. With this pattern of interdependency we found, for pair of heterogeneous networks, two critical percolation thresholds that depend on $alpha$, separating three regimes with very different networks final sizes that converge into a triple point in the plane $p-alpha$. Our findings suggest that the heterogeneity of the networks represented by high degree nodes is the responsible of the rich phase diagrams found in this and other investigations.
We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure ca
n be partially adapted to the user load by activating just some of the service units, we aim at finding the configuration of active service units that achieves the best trade-off between maintenance (e.g. energetic) costs for the provider and user satisfaction. The core of our technique resides in the implementation of a belief-propagation (BP) algorithm to evaluate the cost configurations. Numerical results confirm the effectiveness of our approach.
The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection un
der a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing.
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical trajectories, which c
an be crucial for the understanding of the out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems.
