相关论文: Random Birth-and-Death Networks

We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…

We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neural network (RNN) with identity…

The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…

We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…

The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…

We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…

Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node…

We provide the first classification of different types of Random Boolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define…

The polynomial birth-death distribution (abbr. as PBD) on $\ci=\{0,1,2, >...\}$ or $\ci=\{0,1,2, ..., m\}$ for some finite $m$ introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates…

We study the organization and dynamics of growing directed networks. These networks are built by adding nodes successively in such a way that each new node has $K$ directed links to the existing ones. The organization of a growing directed…

In this paper, we propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted…

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due…

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…

We present a probabilistic model for learning from dynamic relational data, wherein the observed interactions among networked nodes are modeled via the Bernoulli Poisson link function, and the underlying network structure are characterized…

Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs…

In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…

The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree…