Related papers: A theoretical approach for Pareto-Zipf law
Individual participants in human society collectively exhibit aggregation behavior. In this study, we present a simple microscopic model of labor force migration based on the active Brownian particles framework. In particular, agent-based…
The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported…
Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP…
Populations of globally coupled identical maps subject to additive, independent noise are studied in the regimes of strong coupling. Contrary to each noisy population element, the mean field dynamics undergoes qualitative changes when the…
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than expected ones, in accordance with an existing extremum…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
We consider a self-similar fragmentation process in which the generic particle of size $x$ is replaced at probability rate $x^\alpha$, by its offspring made of smaller particles, where $\alpha$ is some positive parameter. The total of…
In the first part of this paper we propose a new theoretical model of city growth based on percolation. The second half oh the paper is devoted to a concrete application of the model, namely to the city of Montargis. It appears that the…
We explore the statistical laws behind the plurality voting system by investigating the election results for mayor held in Brazil in 2004. Our analysis indicate that the vote partition among mayor candidates of the same city tends to be…
This paper focuses on the challenge of interactively modeling street networks. In this work, we extend the simple fractal model, which is particularly useful for describing small cities or individual districts, by constructing random cities…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We describe the link between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in Ising as well as Potts models. From these results it is seen that Zipf's law can be a criterion of a phase transition, but it does…
We propose a quantitative method to classify cities according to their street pattern. We use the conditional probability distribution of shape factor of blocks with a given area, and define what could constitute the `fingerprint' of a…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central…
One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…
City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…