The mainly used welfare criterion in the social network literature is Bentham ́s utilitarian concept. The shortcomings of this concept are well-known. We compare the outcomes of the utilitarian concept with the Nash social welfare function. By using a Taylor approximation we deduce a formula which allows the direct comparison of both concepts. The implications of welfare considerations of import...

Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks exhibit a power-law distribution: the number of nodes yi of a given degree i is proportional to i−β where β > 0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization...

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...

In this article, the authors investigate the multi-scale structure of the S&P500 minute-by-minute time series. The authors attempt to find the answer to the following question: Are upward and downward regimes in the S&P500 time series exhibit different long-range power-law correlations? To answer this question, the authors apply the discrete wavelet transform (DWT) to the original time series f...

– We monitor the stick-slip displacements of a very slowly driven moveable perforated top plate which interacts via shearing with a packing of identical glass beads confined in a tray. When driven at a constant stress rate, the distributions of large event displacements and energies triggered by the stick-slip instabilities exhibit power law responses reminiscent of the Gutenberg-Richter law fo...

after ordering the accused arrest on warrant, its implementation requires compliance with the conditions. in iran, enforcement the arrest on warrant by the court officers takes place in the judicial area of the prosecution or court of justice, but, in england, the entire territory of the country is in place that may catch the accused by policeman. iranian general officers in justice alone often...