Related papers: Synchronous and Asynchronous Recursive Random Scal…

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…

Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…

Real-world networks may exhibit detachment phenomenon determined by the cancelling of previously existing connections. We discuss a tractable extension of Yule model to account for this feature. Analytical results are derived and discussed…

We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…

Recurrent neural nets are widely used for predicting temporal data. Their inherent deep feedforward structure allows learning complex sequential patterns. It is believed that top-down feedback might be an important missing ingredient which…

It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed…

Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108, 3838 (2011)], using simulations, that scale-free networks with "onion structure" are very robust against targeted high degree attacks. The onion structure is a…

An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we…

We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may…

We present the distance matrix evolution for different types of networks: exponential, scale-free and classical random ones. Statistical properties of these matrices are discussed as well as topological features of the networks. Numerical…

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…

Synchronization problem for linear coupled networks is a hot topic in recent decade. However, until now, some confused concepts and results still puzzle people. To avoid further misleading researchers, it is necessary to point out these…

Extending previous results in the literature, random colored substitution networks and degree dimension are defined in this paper. The scale-freeness of these networks is proved by introducing a new definition for degree dimension that is…

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where…

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…

Originally, protocols were designed for multi-agent systems (MAS) using information about the network which might not be available. Recently, there has been a focus on scale-free synchronization where the protocol is designed without any…

Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…

Adaptive Computation Time for Recurrent Neural Networks (ACT) is one of the most promising architectures for variable computation. ACT adapts to the input sequence by being able to look at each sample more than once, and learn how many…