SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

Novel sources of witches` broom resistance (causal agent Moniliophthora perniciosa) from natural populations of Theobroma cacao from the Brazilian Amazon

Witches` broom is a severe disease of Theobroma cacao L. (cacao), caused by the basidiomycete Moniliophthora perniciosa. The use of resistant cultivars is the ultimate method of control, but there are limited sources of resistance. Further, resistance from the most widely used source (`Scavina 6`) has been overcome after a few years of deployment. New sources of resistance have been intensively searched for in the Amazon basin. Here, we evaluated for witches` broom resistance, cacao accessions from various natural cacao populations originally collected in the Brazilian Amazon. Resistance of 43 families was evaluated under nursery and/or field conditions by artificial or natural infection, respectively, based on disease incidence. Screening for resistance by artificial inoculation under nursery conditions appeared to be efficient in identifying these novel resistance sources, confirmed by natural field evaluation over a nine-year period. The increase in natural field infection of `Scavina 6` was clearly demonstrated. Among the evaluated families with the least witches` broom incidence, there were accessions originally collected from distinct river basins, including the Jamari river (`CAB 0371`; `CAB 0388`; `CAB 0392`; and `CAB 0410`); Acre (`CAB 0169`); Javari (`CAB 0352`); Solimes (`CAB 0270`); and from the Purus river basin, the two most outstanding resistant accessions, `CAB 0208` and `CAB 0214`. The large genetic diversity found in cacao populations occurring at river basins from Acre and Amazonas states, Brazil, increased the chance that the selected resistant accessions would be genetically more dissimilar, and represent distinct sources of resistance to M. perniciosa from `Scavina 6`.

Carbon and nitrogen cycling in a tropical Brazilian soil cropped with sugarcane and irrigated with wastewater

Carbon (C) and nitrogen (N) dynamics in agro-systems can be altered as a consequence of treated sewage effluent (TSE) irrigation. The present study evaluated the effects of TSE irrigation over 16 months on N concentrations in sugarcane (leaves, stalks and juice), total soil carbon (TC), total soil nitrogen (TN), NO(3)(-)-N in soil and nitrate (NO(3)(-)) and dissolved organic carbon (DOC) in soil solution. The soil was classified as an Oxisol and samplings were carried out during the first productive crop cycle, from February 2005 (before planting) to September 2006 (after sugarcane harvest and 16 months of TSE irrigation). The experiment was arranged in a complete block design with five treatments and four replicates. Irrigated plots received 50% of the recommended mineral N fertilization and 100% (T100), 125% (T125), 150% (T150) and 200% (T200) of crop water demand. No mineral N and irrigation were applied to the control plots. TSE irrigation enhanced sugarcane yield but resulted in total-N inputs(804-1622 kg N ha(-1)) greater than exported N (463-597 kg N ha(-1)). Hence, throughout the irrigation period, high NO(3)(-) concentrations (up to 388 mg L(-1) at T200) and DOC (up to 142 mg L(-1) at T100) were measured in soil solution below the root zone, indicating the potential of groundwater contamination. TSE irrigation did not change soil TC and TN. (C) 2009 Elsevier B.V. All rights reserved.