Moving particles that rest along their trajectory lead to time-fractional diffusion equations for the scaling limit distributions. For power law waiting times with infinite mean, the equation contains a fractional time derivative of order between 0 and 1. For finite mean waiting times, the most...

Recently it has been found that composite Brownian walk searches are more efficient than any Lévy walk when searching is non-destructive and when the Lévy walks are not responsive to conditions found in the search. Here a new class of adaptive Lévy walk searches is presented that encompasses...

We show that within classical statistical mechanics it is possible to naturally derive power-law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system energy, which is reasonable for any sensible...

This paper discusses non-exponential growth patterns of macroeconomic models. More specifically, the paper discusses asymptotic growth patterns of the numbers of clusters and of components of partition vectors, that is, the number of clusters of specific sizes, of one- and two-parameter Poisson-...

The natural sciences have established a general scaling law that relates metabolism and body size of animals. Recently this association - known as Kleiber's law - has received deep theoretical foundation by network theory and has been fruitfully applied to explain various biological phenomena,...

Using a simple stochastic growth model, this paper demonstrates that the coefficient of variation of aggregate output or GDP does not necessarily go to zero even if the number of sectors or economic agents goes to infinity. This phenomenon known as non-self-averaging implies that even if the...

A large market economy has a huge number of degrees of freedom with weak microlevel coordination. The 'implicit microfoundations' approach assumes this property of micro-level interactions more strongly conditions macro-level outcomes compared to the precise details of individual choice...

A large market economy has a huge number of degrees of freedom with weak microlevel coordination. The 'implicit microfoundations' approach considers this property of micro-level interactions to more strongly determine macro-level outcomes compared to the precise details of individual choice...

The last 10 years witnessed an exponential growth of the Internet. According to Hobbes' Internet Timeline, the Internet hosts are about 93 million, while in 1989 they were 100,000. The same happens for second level domain names. In July 1989 the registered domains were about 3,900 while they...

This paper extends the work in Elder and Serletis [Long memory in energy futures prices, Rev. Financial Econ., forthcoming, 2007] and Serletis et al. [Detrended fluctuation analysis of the US stock market, Int. J. Bifurcation Chaos, forthcoming, 2007] by re-examining the empirical evidence for...