Phase transitions in optimal strategies for betting

Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.Comment: 23 pages, 5 figure

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.Comment: 4 pages, 4 figure

Understanding exploratory use of ERP systems

One way for organizations to move from superficial to more comprehensive usage is to get users to go beyond the basic capabilities of the system and to uncover new ways of using it, either on their own or with the help of others, i.e., through exploratory use. This study focuses on ERP systems as an example of complex IT. Building on the Theory of Planned Behavior (TPB), sets of salient behavioral, normative, and control beliefs are identified as determinants of the intention to explore

Variability of Indoor Radon Level Accumulation: a Study in Portuguese Thermal Spas

The aim of this work was to measure the concentration of the indoor radon in 16 Portuguese thermal spas (38% of the thermal spas in Portugal) and assess its variability within each establishment as well as its contribution to the effective dose. The measurements were performed with CR-39 passive detectors placed at different workplaces within each thermal spa, for an average period of 42 days, in different seasons of the year. The indoor radon concentrations ranged from 68 to 4335 Bq/m3 with a geometric mean of 437 Bq/m3 and an arithmetic mean of 702 Bq/m3. Geological factors that can lead to such behaviour are discussed. The results showed that the EU reference level of 300 Bq/m3 (Directive 2013/59/EURATOM) was exceeded in several cases. No significant differences were observed among measurements taken during different seasons of the year, however, large differences of radon concentrations in different rooms of the same thermal establishment were noted as well as significant difference when comparing to other thermal establishments. The effective dose resulting from the inhalation of radon ranged between 2 and 32 mSv/y. In 43% of the thermal spas, the effective dose is likely to be higher than 6 mSv/y, which means that the exposure should be managed as a "planned exposure situation" according to the European Directive 2013/59/EURATOM. Also, in 19% of the cases, the annual effective dose exceeds 20 mSv/y, and in these cases, monitoring and radiological protection is required as laid down in the European Directive 2013/59/EURATOM. (c) RAD Conference Proceedings. All rights reserved