相关论文: Degree product rule tempers explosive percolation …

$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…

Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

In a recent study [arXiv:1011.3254] the contact process with a modified creation rate at a single site was shown to exhibit a non-universal scaling behavior with exponents varying with the creation rate at the special site. In the present…

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…

We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…

A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…

In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…

Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…

The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…

For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical…

We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the…

We investigate variations of the well-known Achlioptas percolation problem, which uses the method of probing sites when building up a lattice system, or probing links when building a network, ultimately resulting in the delay of the…

A new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid. The inertia strength is controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model…

Continual learning aims to learn on non-stationary data streams without catastrophically forgetting previous knowledge. Prevalent replay-based methods address this challenge by rehearsing on a small buffer holding the seen data, for which a…

This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified…

Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…

We introduce Policy Gradient Guidance (PGG), a simple extension of classifier-free guidance from diffusion models to classical policy gradient methods. PGG augments the policy gradient with an unconditional branch and interpolates…

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…

We consider the constrained-degree percolation (CDP) model on the hypercubic lattice. This is a continuous-time percolation model defined by a sequence $(U_e)_{e\in\mathcal{E}^d}$ of i.i.d. uniform random variables and a positive integer…