A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto distributions. Urban infrastructures – like transportation (railways, roads, etc.) and distribution (gas, water, energy, etc.) systems – are peculiar networks st...

Passive scalar motion in a family of random Gaussian velocity fields with longrange correlations is shown to converge to persistent fractional Brownian motions in long times.

Abstract. We calculate correlation functions of the (charge) density of zeroes of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one and two point functions. The zeroes of a two dimensional Gaussian vector field model the di...

MOTIVATION High-throughput RNA sequencing (RNA-seq) is now the standard method to determine differential gene expression. Identifying differentially expressed genes crucially depends on estimates of read-count variability. These estimates are typically based on statistical models such as the negative binomial distribution, which is employed by the tools edgeR, DESeq and cuffdiff. Until now, the...

Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of selforganized criticality is not yet identified. The Gaussian probability distribution used widely for analysis and description of large data sets underestimat...

A multicanonical formalism is introduced to describe the statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs" with fluctuating "temperatures." The probability distribution of states at small scales is written as an appropriate averaging of the large-scale distribut...

Gas distribution models can provide comprehensive information about a large number of gas concentration measurements, highlighting, for example, areas of unusual gas accumulation. They can also help to locate gas sources and to plan where future measurements should be carried out. Current physical modeling methods, however, are computationally expensive and not applicable for real world scenari...

We study a statistical model consisting of N basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter l. We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a...

A new probability distribution, the xgamma distribution, is proposed and studied. The distribution is generated as a special finite mixture of exponential and gamma distributions and hence the name proposed. Various mathematical, structural, and survival properties of the xgamma distribution are derived, and it is found that in many cases the xgamma has more flexibility than the exponential dis...

All pairs of a large set of known vertebrate DNA sequences were searched by computer for most similar segments. Analysis of this data shows that the computed similarity scores are distributed proportionally to the logarithm of the product of the lengths of the sequences involved. This distribution is closely related to recent results of Erdos and others on the longest run of heads in coin tossi...