We introduce a stochastic model which describes the information diffusion on the network of a popular web service, Twitter. Restricting our attention to the daily diffusion from a popular account, we model the information diffusion as a random multiplicative process. We justify our model by...

We explain a possible mechanism of an information spreading on a network which spreads extremely far from a seed node, namely the viral spreading. On the basis of a model of the information spreading in an online social network, in which the dynamics is expressed as a random multiplicative...

In this paper, we report an analysis of the protein sequence length distribution for 13 bacteria, four archaea and one eukaryote whose genomes have been completely sequenced. The frequency distribution of protein sequence length for all the 18 organisms are remarkably similar, independent of...

A random multiplicative process (RMP) is one of the basic models which can generate a power law distribution. Actually, the distribution generated by RMP has two parts, which are closely matched to the head of a log-normal distribution and the tail of a power law distribution. We investigated...

One class of universal mechanisms that generate power-law probability distributions is that of random multiplicative processes. In this paper, we consider a multiplicative Langevin equation driven by non-Gaussian colored multipliers. We analytically derive a formula that relates the power-law...