Related papers: Intermittency and Localization
We attempt to provide a comprehensive model of evolution of science across millennia taking into account the contributions of other intellectual traditions, cultural value system and increasing in sophistication of humans in their study of…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices…
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational…
Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…
This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time,…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential…
Nature's many varied complex systems (including galaxies, stars, planets, life, and society) are islands of order within the increasingly disordered universe. All organized systems are subject to physical, biological or cultural evolution,…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…