Related papers: Cluster Scaling and Critical Points: A Cautionary …

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…

Several recent observational studies have shown that the clustering of young stars in local star-forming regions, and of Cepheids in the LMC, can be described by a power law two-point correlation function. We show by numerical simulations…

The concept of universality proposes that dynamical systems with the same power law behaviors are equivalent at large scales. We test this hypothesis on the Earth's crust and the epileptic brain, and discover that power laws also govern the…

Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in…

In this work, we report the preliminary analysis of the electrophysiological behavior of in vitro neuronal networks to identify when the networks are in a critical state based on the size distribution of network-wide avalanches of activity.…

In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…

A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies. A stochastic model is proposed for…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…

This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…

Experimental evaluation is a major research methodology for investigating clustering algorithms and many other machine learning algorithms. For this purpose, a number of benchmark datasets have been widely used in the literature and their…

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to…

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…

We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each…

We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…

We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…

Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…

The concept of the brain as a critical system is very attractive because systems close to criticality are thought to maximise their dynamic range of information processing and communication. To date, there have been two key experimental…