Spectrum of stochastic adding machines and fibered Julia sets

Consider the basic algorithm to perform the transformation n--> n+1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through sucessive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enable us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains.Comment: 26pages, 2 figure

Local dynamics for fibered holomorphic transformations

Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case

The ECB's Controversial Securities Market Programme(SMP) and its role in relation to the modified EFSF andthe future ESM

The article analyzes how the role of the European Central Bank (ECB) has developed throughout the sovereign debt crisis. The author concludes that the ECB acted, so far, within the limits of its competences. However, he recognizes that this judgment is built on a rather "aggressive” interpretation of the TFEU and the statute of the ECB. The author is very sceptical that the existence of the modified EFSF and ESM will allow the ECB to stop buying sovereign bonds in secondary markets. He outlines the structure of a potential future Fiscal Union including Eurobond

Improving Parking Availability Maps using Information from Nearby Roads

Parking search traffic causes increased travel times and air pollution in many cities. Real-time parking availability maps are expected to help drivers to find a parking space faster and thus to reduce parking search traffic. A possibility to create such maps is the aggregation of parking availability information from crowdsourcing solutions like probe vehicles and mobile phone applications. Since these sources cannot sense the whole city at the same time, estimation methods are necessary to fill uncovered areas. This paper investigates the estimation of parking availability based on spatial methods using sensor data from San Francisco. First, spatial similarities in parking availability are evaluated for different aspects like time of day and number of parking spaces depending on the distance to reveal the parking characteristics. Then, interpolation methods are examined to estimate parking availability in unobserved road segments. Results show that relevant similarities mainly exist for short distances of less than hundred meters. Their similarity values are lower than the temporal similarity even for multiple hours of time gap. Nevertheless, spatial information is useful to interpolate parking availability. Investigated interpolation methods show significantly better results than random guess. Inverse distance weighting method outperforms a simple averaging by up to 5%.DFG/GRK/193

Cropping system to limit blast disease in upland rice

Cropping system is an essential aspect to take into account to manage blast disease (caused by the fungus Magnaporthe oryzae). In addition to the selection of resistant cultivars, studies report opportunities to limit blast incidence by managing mineral amendment (N, Si, P, etc.), cultivar mixtures or other cropping system adaptations. In Madagascar, rice is the staple crop and food. Farmers traditionally grow irrigated or rainfed lowland rice wherever possible. In the mid-1980s, CIRAD and FOFIFA launched a research program for the highlands to extend upland rice growing areas in high elevation areas of the tropics. This program was consolidated with research on cropping practices that ensure the sustainability of upland rice based cropping systems in this poor and fragile environment. New varieties where obtained, adapted for rainfed cropping up to 1800 m altitude (Dzido et al., 2004). However, farmers had to face attacks of blast disease. Due to the small genetic basis of these varieties, the fungus quickly overcame resistant or tolerant lines selected by breeders. The ways of management of blast disease are very limited in a country like Madagascar where efficient solutions are often not suitable for farmers. Observations of blast epidemics in different regions made us consider the soil as a key factor for rice susceptibility. In a first experiment, we measured the potential of our very susceptible varieties to tolerate blast when cropped in different soil conditions. During two years, we transported volcanic soil from a very fertile area close to the experimentation site and where blast pressure is much lower. We observed a decrease of blast symptoms on rice cropped on that soil compared to the soil of the experimental site, both on leaves and panicles. That decrease was bound to a significant yield increase, demonstrating the importance of plant nutrition on blast incidence. Such results confirm those obtained in 1981 by Seguy et al. Our aim was then to develop cropping systems that could influence blast incidence through an improvement of soil functions. Direct seeded mulch based (DSMB) cropping systems were first used in Madagascar to limit erosion in upland areas. During 4 years, we compared blast epidemics between a traditional cropping system with ploughing each year and a DSMB cropping system, on a midsusceptible variety specific of the highlands conditions. Two fertilisation levels were also tested in these systems: zebu manure only and manure plus additional mineral fertiliser. A significant difference between the two systems was observed, both at leaf and panicle stage. Blast incidence was reduced in DSMB cropping system and, on the contrary to the traditional cropping system, the mineral fertilisation had no effect on blast in DSMB. N fertilisation is known for a long time as an essential factor in blast management. The fact that DSMB cropping system reduced the effect of N-fertilisation made us consider N as the determinant factor of the interaction between cropping system and blast incidence. The determinants of this interaction must then be explained to enable new and durable cropping systems to be developed to manage blast epidemics, in addition to cultivar improvement. This is the objectives of the starting project GARP (ANR-Systerra) which is conducted in Bolivia, Brazil, France, and Madagascar. Its aim is to quantify the interactions between cropping system, N-nutrition and blast resistance in upland rice. Hypotheses and preliminary results of the project will be presented. (Texte intégral