Related papers: Scaling and correlations in the dynamics of forest…
In tropical regions, fires propagate readily in grasslands but typically consume only edges of forest patches. Thus forest patches grow due to tree propagation and shrink by fires in surrounding grasslands. The interplay between these…
We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…
The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from…
We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We…
Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting…
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real…
Reaction-diffusion systems with reversible reactions generically display power-law relaxation towards chemical equilibrium. In this work we investigate through numerical simulations aging processes that characterize the non-equilibrium…
Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
We report here a series of detailed statistical analyses on the sea level variations in the Port of Trieste using one of the largest existing catalogues that covers more than a century of measurements. We show that the distribution of…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumours, or…
Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and…