Growing complex network of citations of scientific papers -- measurements and modeling

To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such verification is performed by measuring citation dynamics of Physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including non-stationary citation distributions, diverging citation trajectory of similar papers, runaways or "immortal papers" with infinite citation lifetime etc. Thus, our most important finding is nonlinearity in complex network growth. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.Comment: 26 pages, 24 figure

Spontaneous Scaling Emergence in Generic Stochastic Systems

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range ($\alpha < -2.$) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents $\alpha > -2$ there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos and bursts/intermitency.Comment: latex, 11 page

Variations in the total electron content of the ionosphere at mid-latitudes during quiet sun conditions

Faraday rotation effect on satellite signals used to determine ionospheric electron content at midlatitudes during quiet sun condition

Some aspects of core formation in Mercury

An evaluation of existing theories on the existence of the planet's metallic core is presented. Topics considered are: (1) magnetic fields; (2) surface geology; (3) cosmochemical models

Ramsey-type theorems for lines in 3-space

We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space. Among other things, we prove that: (1) The intersection graph of n lines in R^3 has a clique or independent set of size Omega(n^{1/3}). (2) Every set of n lines in R^3 has a subset of n^{1/2} lines that are all stabbed by one line, or a subset of Omega((n/log n)^{1/5}) such that no 6-subset is stabbed by one line. (3) Every set of n lines in general position in R^3 has a subset of Omega(n^{2/3}) lines that all lie on a regulus, or a subset of Omega(n^{1/3}) lines such that no 4-subset is contained in a regulus. The proofs of these statements all follow from geometric incidence bounds -- such as the Guth-Katz bound on point-line incidences in R^3 -- combined with Tur\'an-type results on independent sets in sparse graphs and hypergraphs. Although similar Ramsey-type statements can be proved using existing generic algebraic frameworks, the lower bounds we get are much larger than what can be obtained with these methods. The proofs directly yield polynomial-time algorithms for finding subsets of the claimed size.Comment: 18 pages including appendi

An economic assessment of STOL aircraft potential including terminal area environmental considerations, volume 1

The results of an economic and environmental study of short haul airline systems using short takeoff and landing (STOL) aircraft are presented. The STOL system characteristics were optimized for maximum patronage at a specified return on investment, while maintaining noise impact compatibility with the terminal area. Supporting studies of aircraft air pollution and hub airport congestion relief were also performed. The STOL concept specified for this study was an Augmentor Wing turbofan aircraft having a field length capability of 2,000 ft. and an effective perceived noise level of 95 EPNdB at 500 ft. sideline distance. An economic and environmental assessment of the defined STOL system and a summary of the methodology, STOL system characteristics and arena characteristics are provided