Related papers: Funnelling related phase transitions in networks
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…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…
Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a…
In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects…
GFlowNets is a novel flow-based method for learning a stochastic policy to generate objects via a sequence of actions and with probability proportional to a given positive reward. We contribute to relaxing hypotheses limiting the…
Network inference is the process of learning the properties of complex networks from data. Besides using information about known links in the network, node attributes and other forms of network metadata can help to solve network inference…
Multilayer networks describe well many real interconnected communication and transportation systems, ranging from computer networks to multimodal mobility infrastructures. Here, we introduce a model in which the nodes have a limited…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
We study the problem of explaining a rich class of behavioral properties of deep neural networks. Distinctively, our influence-directed explanations approach this problem by peering inside the network to identify neurons with high influence…
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…
An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
We derive novel analytic tools for the discrete Bass model, which models the diffusion of new products on networks. We prove that the probability that any two nodes adopt by time t, is greater than or equal to the product of the…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…