Cycles and sorting index for matchings and restricted permutations

We prove that the Mahonian-Stirling pairs of permutation statistics (\sor, \cyc) and (\inv, \mathrm{rlmin}) are equidistributed on the set of permutations that correspond to arrangements of $n$ non-atacking rooks on a Ferrers board with $n$ rows and $n$ columns. The proofs are combinatorial and use bijections between matchings and Dyck paths and a new statistic, sorting index for matchings, that we define. We also prove a refinement of this equidistribution result which describes the minimal elements in the permutation cycles and the right-to-left minimum letters. Moreover, we define a sorting index for bicolored matchings and use it to show analogous equidistribution results for restricted permutations of type $B_n$ and $D_n$.Comment: 23 page

Nutrient relations in coniferous forests

The environment controls physiological processes in plants and thus their growth. The question how forests will respond to global environmental changes is addressed with different approaches and using two coniferous tree species: Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) I have used the relationship (nitrogen productivity) between a plant's growth rate and the amount of nitrogen in the plant to analyse the growth response to temperature. Data on needle dry matter, production, and nitrogen content in needles from a wide range of climatic conditions were collected and needle nitrogen productivities were calculated. The result is that the nitrogen productivity (net carbon gain of a canopy) of conifers is not sensitive to temperature. Growth responses to temperature in conifers are therefore mediated by changes in nitrogen availability. I have used three Swedish forest experiments to study the long-term fate of N addition. The fertilisation increased tree biomass, more strongly for spruce than pine. Once fertilisation had ceased, the growth rates in all treatments in pine and spruce stands at Lisselbo and Stråsan converged towards similar levels. Chronic fertilisation with complete nutrient solution in pine stands at Jädraås resulted in long-term increase in production. Nitrogen budgets established 12 years (pine) and 7 years (spruce) after the last N addition show that the increases in N stocks in the pine stands were mainly in the soil. In contrast, in the spruce ecosystem trees accumulated most of the added N and the increase in the soil was restricted to the humus layer. In the pine ecosystem, large losses of added N (between 254 and 738 kg ha-1 out of 1040 kg ha-1 added as fertilizer) occurred, whereas in the spruce ecosystem more N was recovered than could be accounted for by inputs (between 250 and 591 kg ha-1). I have used humus and needle nutrients and site characteristic from 37 pine and 50 spruce stands from all over Sweden to analyze forest nutrient relations. Biologically controlled nutrients (C, N, P, S) are less variable and more correlated, but the biological control is not limited to only the covalently bound elements. Stoichiometric relations are not entirely rigid but are more constrained in needles than in humus. The use of nitrogen as a basis in stoichiometric relations may give stronger relations than the use of carbon

A New role of ontologies and advanced scientific visualization in big data analytics

Accessing and contextual semantic searching structured, semi-structured and unstructured information resources and their ontology based analysis in a uniform way across text-free Big Data query implementation is a main feature of approach under discussion. To increase the semantic power of query results’ analysis the ontology based implementation of multiplatform adaptive tools of scientific visualization are demonstrated. The ontologies are used not for integration of heterogeneous resources in traditional way but for parallel analysis of recourses and its related ontologies to achieve the effect of a virtual integration

A discourse-based approach to verb placement in early West-Germanic

The paper presents a novel approach to explaining word order variation in the early Germanic languages. Initial observations about verb placement as a device marking types of rhetorical relations made on data from Old High German (cf. Hinterhölzl & Petrova 2005) are now reconsidered on a larger scale and compared with evidence from other early Germanic languages. The paper claims that the identification of information-structural domains in a sentence is best achieved by taking into account the interaction between the pragmatic features of discourse referents and properties of discourse organization