Related papers: Gutenberg-Richter Law for Internetquakes
A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…
We study an extension of Bernstein's theorem to the setting of quantum groups. For a d-tuple of free, identically distributed random variables we consider a problem of preservation of freeness under the action of a quantum subset of the…
Classical cybernetics is a successful meta-theory to model the regulation of complex systems from an abstract information-theoretic viewpoint, regardless of the properties of the system under scrutiny. Fundamental limits to the…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. The general solution of this equation for q=1 is a product of an…
A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the…
The evaluation of the $b$ value of the Gutenberg-Richter (GR) law, for a sample composed of $n$ earthquakes, presents a systematic positive bias $\delta b$ which is proportional to $1/n$, as already observed by Ogata \& Yamashina (1986). In…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…
We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal $-5/3$ scaling law in the turbulent energy spectrum is intimately connected…
We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…
The area-characteristic, maximum possible earthquake magnitude $T_M$ is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg-Richter law predicts that earthquake magnitudes…
Formulating a lattice gauge theory using only physical degrees of freedom generically leads to non-local interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace…
In their paper (Europhys. Lett., 71 (2005) 1036), Carbone, Sorriso-Valvo, Harabaglia and Guerra showed that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. (Phys. Rev. Lett., 88 (2002) 178501) is…
Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches,…
We critically discuss the measure of very short time intervals. By means of a "gedankenexperiment", we describe an ideal clock based on the occurrence of completely random events. We show that the minimum time interval Delta t that this…