The Classical Limit of the Quantum Kepler Problem

The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.

Criticality, adaptability and early-warning signals in time series in a discrete quasispecies model

Complex systems from different fields of knowledge often do not allow a mathematical description or modeling, because of their intricate structure composed of numerous interacting components. As an alternative approach, it is possible to study the way in which observables associated with the system fluctuate in time. These time series may provide valuable information about the underlying dynamics. It has been suggested that complex dynamic systems, ranging from ecosystems to financial markets and the climate, produce generic early-warning signals at the ＂tipping points,＂ where they announce a sudden shift toward a different dynamical regime, such as a population extinction, a systemic market crash, or abrupt shifts in the weather. On the other hand, the framework of Self- Organized Criticality （SOC）, suggests that some complex systems, such as life itself, may spontaneously converge toward a critical point. As a particular example, the quasispecies model suggests that RNA viruses self-organize their mutation rate near the error-catastrophe threshold, where robustness and evolvability are balanced in such a way that survival is optimized. In this paper, we study the time series associated to a classical discrete quasispecies model for different mutation rates, and identify early-warning signals for critical mutation rates near the error-catastrophe threshold, such as irregularities in the kurtosis and a significant increase in the autocorrelation range, reminiscent of 1/f noise. In the present context, we find that the early-warning signals, rather than broadcasting the collapse of the system, are the fingerprint of survival optimization.

Data Mining of Historic Hydrogeological and Socioeconomic Data Bases of the Toluca Valley, Mexico

In this paper we used several data mining techniques to analyze the coevolution of hydrogeological and socioeconomical data for the Toluca Valley in Mexico. We found non trivial relations between two historic data bases that make clear that groundwater and economy may be much more linked than it was thought before. In particular, we found that hydrogeological data trends change during economical crisis and election years in Mexico. This shows that different macroeconomical policies implemented by several administrations have a direct impact in the way groundwater is used. We also found that hydrogoelogical data evolve in the direction of population transformation from rural to urban, which could represent a whole paradigm shift in groundwater management with profound repercussions in policy making.