Related papers: Taylor's power law for the $N$-stars network evolu…

We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading…

What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…

Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…

Many biological phenomena or social events critically depend on how information evolves in complex networks. However, a general theory to characterize information evolution is yet absent. Consequently, numerous unknowns remain about the…

Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…

For most technical networks, the interplay of dynamics, traffic and topology is assumed crucial to their evolution. In this paper, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general…

Spreading on networks is influenced by a number of factors including different parts of the inter-event time distribution (IETD), the topology of the network and non-stationarity. In order to understand the role of these factors we study…

The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…

Evolutionary graph theory is the study of evolutionary dynamics in structured populations. A well-known problem in evolutionary graph theory is that the spread of mutation (measured by fixation probability) is impacted by the graph type…

With a simple model, we study the evolution of random networks under attack and reconstruction. We introduce a new quality, invulnerability I(s), to describe the stability of the system. We find that the network can evolve to a stationary…

This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…

We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…

In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…

Consider a network of M >> 1 nodes connected by N >> 1 links, in which the distribution of the number of links per node follows a power law with exponent 0<\alpha <1. The power law is naturally truncated due to the fact that N is finite. A…

Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…

We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent…