Related papers: Taylor's power law for the $N$-stars network evolu…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
We present a theory for the growth dynamics of the World Wide Web that takes into account the wide range of stochastic growth rates in the number of pages per site, as well as the fact that new sites are created at different times. This…
Power law distributions have been found in many natural and social phenomena, and more recently in the source code and run-time characteristics of Object-Oriented (OO) systems. A power law implies that small values are extremely common,…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted…
Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the…
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…
For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…
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…
Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by…
According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton-Watson process corresponding to the dynamics of a…
For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends…
A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are…
By using low-dimensional chaos maps, the power law relationship established between the sample mean and variance called Taylor's Law (TL) is studied. In particular, we aim to clarify the relationship between TL from the spatial ensemble…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…