Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

Ralstonia solanacearum is a pathogen that causes bacterial wilt producing severe damage in staple solanaceous crops. Traditional control has low efficacy and/or environmental impact. Recently, the bases of a new biotechnological method by lytic bacteriophages vRsoP-WF2, vRsoP-WM2 and vRsoP-WR2 with specific activity against R. solanacearum were established. However, some aspects remain unknown, such as the survival and maintenance of the lytic activity after submission to a preservation method as the lyophilization. To this end, viability and stability of lyophilized vRsoP-WF2, vRsoP-WM2 and vRsoP-WR2 and their capacity for bacterial wilt biocontrol have been determined against one pathogenic Spanish reference strain of R. solanacearum in susceptible tomato plants in different conditions and making use of various cryoprotectants. The assays carried out have shown satisfactory results with respect to the viability and stability of the bacteriophages after the lyophilization process, maintaining high titres throughout the experimental period, also with respect to the capacity of the bacteriophages for the biological control of bacterial wilt, controlling this disease in more than 50% of the plants. The results offer good prospects for the use of lyophilization as a conservation method for the lytic bacteriophages of R. solanacearum in view of their commercialization as biocontrol agents.

A new approach to the measurement with elastic lidar of depolarization produced by atmospheric aerosols is presented. The system uses two different telescopes: one for depolarization measurements and another for total-power measurements. The system architecture and principle of operation are described. The first experimental results are also presented, corresponding to a collection of atmospheric conditions over the city of Barcelona.