Properties of on-line social systems

We study properties of five different social systems: (i) internet society of friends consisting of over 10⁶ people, (ii) social network consisting of 3 × 10⁴ individuals, who interact in a large virtual world of Massive Multiplayer Online Role Playing Games (MMORPGs), (iii) over 10⁶ users of music community website, (iv) over 5 × 10⁶ users of gamers community server and (v) over 0.25 × 10⁶ users of books admirer website. Individuals included in large social network form an Internet community and organize themselves in groups of different sizes. The destiny of those systems, as well as the method of creating of new connections, are different, however we found that the properties of these networks are very similar. We have found that the network components size distribution follow the power-law scaling form. In all five systems we have found interesting scaling laws concerning human dynamics. Our research has shown how long people are interested in a single task, how much time they devote to it and how fast they are making friends. It is surprising that the time evolution of an individual connectivity is very similar in each system.     

Random Sierpinski network with scale-free small-world and modular structure

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our network representation method could be applied to study the complexity of some real systems in biological and information fields.     

Silver fractal networks for surface-enhanced Raman scattering substrates

Based on diffusion-limited aggregation process, a convenient nanotechnique is demonstrated to obtain large silver fractal networks for a surface-enhanced Raman scattering (SERS)-active substrate. The silver fractal networks are of high SERS enhancement factor, large dynamical range. The observed SERS efficiency can be explained in terms of strongly localized plasmon modes relative to the single particle plasmon resonance.     

Large Relative Raman Shift for Molecules Adsorbed on Metallic Nano-particles

The enhancement of two order-of-magnitudes is observed in surface-enhanced Raman spectroscopy （SERS） of gases （CO, C2H2, C2H4, etc） adsorbed on nitric acid-roughened metal foil. In addition, some Raman lines of gases adsorbed on these active substrates show larger frequency shifts and linewidth broadening, compared with the Raman spectroscopy of free gases. Using the two-oscillator electromagnetic model, we explain this phenomenon. It is related to the large non-regular particles on the active substrate we prepared. It is found that the parameters of the surface-plasmon dispersion, the distance of molecules from the surface and the radius of particles play crucial roles on the relative large Raman shifts.     

Diagnosis of Multiple Gases Separated from Transformer Oil Using Cavity-Enhanced Raman Spectroscopy

The Raman signal of gas molecules is very weak due to its small scattering cross section. Here, a near-confocal cavity-enhanced Raman detection system is demonstrated. In the cavity, a high power light of 9W is achieved by using a cw 200mW 532nm laser, which greatly enhances the detection sensitivity of gas species. A photomultiplier tube connected to a spectrometer is used as the detection system. The Raman spectra of the mixed gases separated from transformer oil has been observed. The relationship of absolute Raman intensity and gas pressure is also obtained. To our knowledge, this is the first Raman system to detect the gases separated from transformer oil.     

Calculations of Photo-Ionization Cross Sections for Lithium Atoms

Photo-ionization cross sections for the ground and the ≤5 excited states of lithium atoms are calculated in the photoelectron energy ranging from threshold to 0.5 Rydberg. The wavefunctions for both the bound and continuum states are obtained by solving the SchrSdinger equation numerically in a symplectic scheme. Our results are in excellent agreement with the recent experimental measurements and in harmony with other theoretical calculations.     

Undercooling and Unidirectional Solidification of CuNi Alloy Melts

Cylinder-shaped CusoNi20 alloy melt is undercooled and solidified by the combination of the electromagnetic levitation technique and the flux treatment method. Nearly constant temperature gradient of 8-10 K/cm is realized for the cylindrical melts with differen~ undercooling levels at the bottom ends. The experimental results reveal that with the increase of the undercoo]ing of the melts from 35 to 220 K, the microstructures undergo transition from coarse dendrites to granular grains, unidirectional dendrites, and finally to equiaxed grains.     

The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are gS and gP, respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition gS=gP is the border between two distinctly different conditions: For gS<gP, the P events are attractors of the S events and for gS>gP they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or gP, depending on which is the parameter changed, thereby resulting in a discontinuous transition.     

Influence of different initial distributions on robust cooperation in scale-free networks: A comparative study

We study the evolutionary Prisoner's dilemma game on scale-free networks, focusing on the influence of different initial distributions for cooperators and defectors on the evolution of cooperation. To address this issue, we consider three types of initial distributions for defectors: uniform distribution at random, occupying the most connected nodes, and occupying the lowest-degree nodes, respectively. It is shown that initial configurations for defectors can crucially influence the cooperation level and the evolution speed of cooperation. Interestingly, the situation where defectors initially occupy the lowest-degree vertices can exhibit the most robust cooperation, compared with two other distributions. That is, the cooperation level is least affected by the initial percentage of defectors. Moreover, in this situation, the whole system evolves fastest to the prevalent cooperation. Besides, we obtain the critical values of initial frequency of defectors above which the extinction of cooperators occurs for the respective initial distributions. Our results might be helpful in explaining the maintenance of high cooperation in scale-free networks.     

Measuring distances between complex networks

A previously introduced concept of higher order neighborhoods in complex networks, [R.F.S. Andrade, J.G.V. Miranda, T.P. Lobão, Phys. Rev. E 73 (2006) 046101] is used to define a distance between networks with the same number of nodes. With such measure, expressed in terms of the matrix elements of the neighborhood matrices of each network, it is possible to compare, in a quantitative way, how far apart in the space of neighborhood matrices two networks are. The distance between these matrices depends on both the network topologies and the adopted node numberings. While the numbering of one network is fixed, a Monte Carlo algorithm is used to find the best numbering of the other network, in the sense that it minimizes the distance between the matrices. The minimal value found for the distance reflects differences in the neighborhood structures of the two networks that arise only from distinct topologies. This procedure ends up by providing a projection of the first network on the pattern of the second one. Examples are worked out allowing for a quantitative comparison for distances among distinct networks, as well as among distinct realizations of random networks.