Related papers: Cluster Scaling and Critical Points: A Cautionary …
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a…
A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…
As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
Speech is a distinctive complex feature of human capabilities. In order to understand the physics underlying speech production, in this work we empirically analyse the statistics of large human speech datasets ranging several languages. We…
We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the…
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a…
Crackling noise is observed in many disordered non-equilibrium systems in response to slowly changing external conditions. Examples range from Barkhausen noise in magnets to acoustic emission in martensites to earthquakes. Using the…
An explosive percolation transition is the abrupt emergence of a giant cluster at a threshold caused by a suppression of the growth of large clusters. In this paper, we consider the information entropy of the cluster size distribution,…
Power laws in nature are considered to be signatures of complexity. The theory of self-organized criticality (SOC) was proposed to explain their origins. A longstanding principle of SOC is the \emph{separation of timescales} axiom. It…
The global energy fluctuations of a low density gas granular gas in the homogeneous cooling state near its clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…
The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent…
Earthquake network is known to be of the small-world type. The values of the network characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of…
We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three…