Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

High precision Mg isotope measurements of meteoritic samples by secondary ion mass spectrometry

The possibility of establishing an accurate relative chronology of the early solar system events based on the decay of short-lived Al-26 to Mg-26 (half-life of 0.72 Myr) depends on the level of homogeneity (or heterogeneity) of Al-26 and Mg isotopes. However, this level is difficult. to constrain precisely because of the very high precision needed for the determination of isotopic ratios, typically of +/- 5 ppm. In this study, we report for the first time a detailed analytical protocol developed for high precision in situ Mg isotopic measurements ((25)mg/(24)mg and (26)mg/Mg-24 ratios, as well as Mg-26 excess) by MC-SIMS. As the data reduction process is critical for both accuracy and precision of the final isotopic results, factors such as the Faraday cup (FC) background drift and matrix effects on instrumental fractionation have been investigated. Indeed these instrumental effects impacting the measured Mg-isotope ratios can be as large or larger than the variations we are looking for to constrain the initial distribution of Al-26 and Mg isotopes in the early solar system. Our results show that they definitely are limiting factors regarding the precision of Mg isotopic compositions, and that an under- or over-correction of both FC background instabilities and instrumental isotopic fractionation leads to important bias on delta Mg-25, delta(26)mg and Delta Mg-26 values (for example, olivines not corrected for FC background drifts display Delta Mg-26 values that can differ by as much as 10 ppm from the truly corrected value). The new data reduction process described here can then be applied to meteoritic samples (components of chondritic meteorites for instance) to accurately establish their relative chronology of formation.

Off-site impacts of agricultural composting: role of terrestrially derived organic matter in structuring aquatic microbial communities and their metabolic potential

While considered as sustainable and low-cost agricultural amendments, the impacts of organic fertilizers on downstream aquatic microbial communities remain poorly documented. We investigated the quantity and quality of the dissolved organic matter leaching from agricultural soil amended with compost, vermicompost or biochar and assessed their effects on lake microbial communities, in terms of viral and bacterial abundances, community structure and metabolic potential. The addition of compost and vermicompost significantly increased the amount of dissolved organic carbon in the leachate compared with soil alone. Leachates from these additions, either with or without biochar, were highly bioavailable to aquatic microbial communities, although reducing the metabolic potential of the community and harbouring more specific communities. Although not affecting bacterial richness or taxonomic distributions, the specific addition of biochar affected the original lake bacterial communities, resulting in a strongly different community. This could be partly explained by viral burst and converging bacterial abundances throughout the samples. These results underline the necessity to include off-site impacts of agricultural amendments when considering their cascading effect on downstream aquatic ecosystems.

Impact of compost, vermicompost and biochar on soil fertility, maize yield and soil erosion in Northern Vietnam: A three year mesocosm experiment

Compost, vermicompost and biochar amendments are thought to improve soil quality and plant yield. However, little is known about their long-term impact on crop yield and the environment in tropical agro-ecosystems. In this study we investigated the effect of organic amendments (buffalo manure, compost and verrnicompost) and biochar (applied alone or with vermicompost) on plant yield, soil fertility, soil erosion and water dynamics in a degraded Acrisol in Vietnam. Maize growth and yield, as well as weed growth, were examined for three years in terrestrial mesocosms under natural rainfall. Maize yield and growth showed high inter-annual variability depending on the organic amendment. Vermicompost improved maize growth and yield but its effect was rather small and was only significant when water availability was limited (year 2). This suggests that vermicompost could be a promising substrate for improving the resistance of agrosystems to water stress. When the vermicompost biochar mixture was applied, further growth and yield improvements were recorded in some cases. When applied alone, biochar had a positive influence on maize yield and growth, thus confirming its interest for improving long-term soil productivity. All organic amendments reduced water runoff, soil detachment and NH4+ and NO3- transfer to water. These effects were more significant with vermicompost than with buffalo manure and compost, highlighting that the beneficial influence of vermicompost is not limited to its influence on plant yield. In addition, this study showed for the first time that the combination of vermicompost and biochar may not only improve plant productivity but also reduce the negative impact of agriculture on water quality. (C) 2015 Elsevier B.V. All rights reserved.

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.