Related papers: A record-driven growth process
Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial…
We consider a robust asymptotic growth problem under model uncertainty in the presence of stochastic factors. We fix two inputs representing the instantaneous covariance for the asset price process $X$, which depends on an additional…
The \b{eta} index is one of important measurements reflecting development level of traffic networks. However, how to explain and predict the \b{eta} index growth for a geographical region is a pending problem. With the help of mathematical…
We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…
We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes…
We consider models of evolving networks $\{\mathcal{G}_n:n\geq 0\}$ modulated by two parameters: an attachment function $f:\mathbb{N}_0\to\mathbb{R}_+$ and a (possibly random) attachment sequence $\{m_i:i\geq 1\}$. Starting with a single…
The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…
In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, additional…
Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function,…
World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a record sheds light on the underlying…
In graph theory and network analysis, node degree is defined as a simple but powerful centrality to measure the local influence of node in a complex network. Preferential attachment based on node degree has been widely adopted for modeling…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
We study a way to set the natural frequency of a newly added oscillator in a growing network to enhance synchronization. Population growth is one of the typical features of many oscillator systems for which synchronization is required to…
Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition…