The pore radius distribution in paper is known to be influenced by changes in the mean grammage and formation. Experimental data are presented that confirm the established result that the standard deviation of pore radii is proportional to the mean. The data show also that this proportionality is the same for changes in grammage and formation and that, contrary to results reported in the litera...

Scale free graphs have attracted attention by their non-uniform structure that can be used as a model for various social and physical networks. In this paper, we propose a natural and simple random model for generating scale free interval graphs. The model generates a set of intervals randomly under a certain distribution, which defines a random interval graph. The main advantage of the model i...

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving limit theorems resulting in non-Gaussian, scale-invariant diffusions. We apply the generalized characteristic functions in combination with a martingale const...

[This corrects the article DOI: 10.1186/s40064-016-2868-z.].

The capacity of a wireless network with fractal and hierarchical social communications is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution P (k), and we capture the direct social connection feature between two nodes with degree k1 and k2 by a joint probability distribution P (k1, k2). Firstly, f...

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features – such as degree distribution and clustering coefficient – provide measurements for comparing networks from different points of view, but a global and integrated distance metric is still miss-

Random matrix theory has successfully modeled many systems in physics and mathematics, and often analysis in one area guides development in the other. Hughes and Rudnick computed 1-level density statistics for low-lying zeros of the family of primitive Dirichlet L-functions of fixed prime conductor Q, as Q→∞, and verified the unitary symmetry predicted by random matrix theory. We compute 1and 2...

We briefly review and summarize the results in research of China High Technology Networks(CHTN), which can be composed by three levels. A weighted framework is put forward and can be used to study some similar networks. According to our idea and method, the CHTN is constructed. Then the CHTN’s topological properties are investigated, including degree distribution, shortest path length, clusteri...