Individual level and exhaustive income data for Romania (Cluj county) is analysed for several consecutive years. The income distributions collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data. A dynamical model based on a master equation with growth and reset terms is successful in explaining the observed distribution in a self-consistent manner, i.e. the growth and reset rates are evaluated from the same individual level data. Income distribution derived for other countries are following similar trends. The collapse on the master-curve is not perfect however, suggesting that for a more realistic modelling specific socio-economic characteristics have to be taken also into account. Significance StatementAlthough income inequalities are in the constant focus of many studies in ecnomics, sociology, mathematical modelling and econo-physics, presently we do not have a satisfactory description for the entire income distribution function. Here we provide an analytically treatable model that describes in a unified manner income distribution for all income categories. It is found that the properly renormalized income distributions collapse on a master-curve, which is a described by a Beta Prime distribution. As a consequence, the much-debated Pareto-exponent and its universality for the tail of the distribution function should be reconsidered.

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Global cities are defined, on the one hand, as the major command and control centres of the world economy and, on the other hand, as the most significant sites of the production of innovation. As command and control centres, they are home to the headquarters of the most powerful MNCs of the global economy, while as sites for the production of innovation they are supposed to be the most important sites of corporate research and development (R&D) activities. In this paper, we conduct a bibliometric analysis of the data located in the Scopus and Forbes 2000 databases to reveal the correlation between the characteristics of the above global city definitions. We explore which cities are the major control points of the global corporate R&D (home city approach), and which cities are the most important sites of corporate R&D activities (host city approach). According to the home city approach we assign articles produced by companies to cities where the decision-making headquarters are located (i.e. to cities that control the companies' R&D activities), while according to the host city approach we assign articles to cities where the R&D activities are actually conducted. Given Sassen's global city concept, we expect global cities to be both the leading home cities and host cities.The results show that, in accordance with the global city concept, Tokyo, New York, London and Paris surpass other cities as command points of global corporate R&D (having 42 percent of companies' scientific articles). However, as sites of corporate R&D activities to be conducted, New York and Tokyo form a unique category (having 28 percent of the articles). The gap between San Jose and Boston, and the global cities has consistently narrowed because the formers are the leading centres of the fastest growing innovative industries (e.g. information technology and biotechnology) in the world economy, and important sites of international R&D activities within these industries. The emerging economies are singularly represented by Beijing; however, the position of Chinese capital (i.e. the number of its companies' scientific articles), has been strengthening rapidly.

Several empirical models aimed at describing human mobility have been proposed in the past. Most of them are based on an unjustified analogy, with a focus on gravity and physical vector or scalar fields. Recently, however, statistical physicists introduced a new category of models that are theoretically motivated by a few simple and reasonable socioeconomic assumptions. The Radiation Model (Simini et al. 2012) and the Radiation Model with Selection (Simini-Maritan-Néda 2013) are such successful approaches. Here, we introduce a new version of the radiation model, the Travel Cost Optimized Radiation Model, and test its applicability for describing the commuting patterns in Hungary. We compare critically the performance of this model with the results of the previous radiation type models.

The average travelling speed increases in a nontrivial manner with the travel distance. This leads to scaling-like relations on quite extended spatial scales, for all mobility modes taken together and also for a given mobility mode in part. We offer a wide range of experimental results, investigating and quantifying this universal effect and its measurable causes. The increasing travelling speed with the travel distance arises from the combined effects of: choosing the most appropriate travelling mode; the structure of the travel networks; the travel times lost in the main hubs, starting or target cities; and the speed limit of roads and vehicles.