In this paper, random walks with independent steps distributed according to a Q-power-law probability distribution function with Q=1/(1-q) are studied. In the case q>1, we show that (i) a stochastic representation of the location of the walk after n steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be establi...

Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cut algorithms still suffer from several limitations: first, they require the n...

Complex systems theory pays much attention to simple mechanisms producing nontrivial patterns, especially power laws. However, power laws with exponent τ ≈ 1 also result from complex mixtures of mechanisms that, in isolation, would not necessarily give this type of distribution. Probably, both paths to the power law are relevant in nature. The second gives a plausible explanation for some insta...

We present a model for random simple graphs with power law (i.e., heavy-tailed) degree distributions. To attain this behavior, the edge probabilities in the graph are constructed from Bertoin–Fujita–Roynette–Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the construction of power law models in several applications. Our construction readily extends to c...

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to ava...

Pathogenic bacteria such as Listeria and Yersinia gain initial entry by binding to host target cells and stimulating their internalization. Bacterial uptake entails successive, increasingly strong associations between receptors on the surface of bacteria and hosts. Even with genetically identical cells grown in the same environment, there are vast differences in the number of bacteria entering ...

Self-organized criticality has been proposed to explain complex dynamical systems near their critical points. This experiment examined a monodisperse conical bead pile and how the distribution of avalanches is affected by the pattern of beads glued on a base, by the size or shape of the base, and by the height at which each bead was dropped onto the pile. By measuring the number of avalanches f...

We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of inter-contact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the distribution decays exponentially. Up to ...

By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to β q , with β being the angle of the anvil rotation. The meaning of the p...