اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEfficient algorithm to study interconnected networks
53
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these questions is the percolation model, where the resilience of the system is quantified by the dependence of the size of the largest cluster on the number of failures. Numerically, the major challenge is the identification of this cluster and the calculation of its size. Here, we propose an efficient algorithm to tackle this problem. We show that the algorithm scales as O(N log N), where N is the number of nodes in the network, a significant improvement compared to O(N^2) for a greedy algorithm, what permits studying much larger networks. Our new strategy can be applied to any network topology and distribution of interdependencies, as well as any sequence of failures.
قيم البحث
اقرأ أيضاً
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on general graphs.
We show applications of our algorithm in graphical models, specifically on estimating free energy of spin glasses defined on various of graphs, where our method largely outperforms existing algorithms including the mean-field methods and the recently proposed neural-network-based methods. We further apply our method to the simulation of random quantum circuits, and demonstrate that, with a trade off of negligible truncation errors, our method is able to simulate large quantum circuits that are out of reach of the state-of-the-art simulation methods.
Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own i
ntention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics. The model is useful in understanding the formation and evolution of online social networks.
Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven t
hat the multiplexity has broad impact on the systems structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.
Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascadi
ng overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failures than ErdH{o}s-Renyi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works which neglect the effect of fluctuations of loads.
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the percolation phenomen
a of these systems, different mathematical frameworks have been proposed including generating functions, eigenvalues among some others. These different frameworks approach the phase transition behaviors from different angles, and have been very successful in shaping the different quantities of interest including critical threshold, size of the giant component, order of phase transition and the dynamics of cascading. These methods also vary in their mathematical complexity in dealing with interdependent networks that have additional complexity in terms of the correlation among different layers of networks or links. In this work, we review a particular approach of simple self-consistent probability equations, and illustrate that it can greatly simplify the mathematical analysis for systems ranging from single layer network to various different interdependent networks. We give an overview on the detailed framework to study the nature of the critical phase transition, value of the critical threshold and size of the giant component for these different systems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
