相关论文: Re-inventing Willis

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…

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…

The Yule--Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is…

A multi-parametric family of stretch exponential distributions with various power law tails is introduced and is shown to describe adequately the empirical distributions of scientific citation of individual authors. The four-parametric…

Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…

Wheeler proposed that repeated acts of observation give rise to the reality that we observe, but offered no detailed mechanism for this. Here this creative process is accounted for on the basis of the idea that nature has a deep…

The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72} (2005) 036108, predicting the particle distribution function $p(E)= \exp_{\kappa}…

Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…

This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…

Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…

Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period of time…

We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin [2019] in the context of a preferential attachment algorithm with fading memory. By making the link to a…

This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely…

Systems with long-range interactions often exhibit power-law distributions and can by described by the non-extensive statistical mechanics framework proposed by Tsallis. In this contribution we consider a simple model reproducing continuous…

Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…

We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…

Studies on distribution, abundance and diversity of species revealed fascinating universalities in macroecology. Many of these patterns, like the species-area and range-abundance relationship or the year-to-year fluctuations in population…

Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…

The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…

The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…