On Sparsification for Computing Treewidth

We investigate whether an n-vertex instance (G,k) of Treewidth, asking whether the graph G has treewidth at most k, can efficiently be made sparse without changing its answer. By giving a special form of OR-cross-composition, we prove that this is unlikely: if there is an e > 0 and a polynomial-time algorithm that reduces n-vertex Treewidth instances to equivalent instances, of an arbitrary problem, with O(n^{2-e}) bits, then NP is in coNP/poly and the polynomial hierarchy collapses to its third level. Our sparsification lower bound has implications for structural parameterizations of Treewidth: parameterizations by measures that do not exceed the vertex count, cannot have kernels with O(k^{2-e}) bits for any e > 0, unless NP is in coNP/poly. Motivated by the question of determining the optimal kernel size for Treewidth parameterized by vertex cover, we improve the O(k^3)-vertex kernel from Bodlaender et al. (STACS 2011) to a kernel with O(k^2) vertices. Our improved kernel is based on a novel form of treewidth-invariant set. We use the q-expansion lemma of Fomin et al. (STACS 2011) to find such sets efficiently in graphs whose vertex count is superquadratic in their vertex cover number.Comment: 21 pages. Full version of the extended abstract presented at IPEC 201

The uptake of selenium by perennial ryegrass in soils of different organic matter contents receiving sheep excreta

Background and aims The intake of selenium, an essential element for animals and humans, in ruminants is largely determined by selenium concentration in ingested forages, which take up selenium mainly from soil. Ruminant excreta is a common source of organic fertilizer, which provides both nutrients and organic matter. This study aims to unentangle the unclear effect of applying different types of ruminant excreta in soils of different organic matter contents on selenium uptake by forage. Methods Perennial ryegrass (Lolium perenne) was grown in soils of different organic matter contents. Urine and/or feces collected from sheep fed with organic or inorganic mineral supplements, including selenium, were applied to the soils. The selenium in the collected samples were analyzed using ICP-MS. The associated biogeochemical reactions were scrutinized by wet chemistry. Results The application of urine and/or feces resulted in either the same or lower selenium concentrations in perennial ryegrass. The excreta type did not affect total selenium accumulation in grass grown in low organic matter soil, whereas in high organic matter soil, feces resulted in significantly lower total selenium accumulation than urine, which was attributed to a possible interaction of selenium sorption in soil and microbial reduction of Se. Conclusion This one-time excreta application did not increase, but further decrease in some treatments, selenium concentration and accumulation in the perennial ryegrass. Consequently, to increase ruminant selenium intake, supplementing selenium directly to animals is more recommended than applying animal manure to soil, which might drive selenium reduction and decrease selenium uptake by grass

Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter

An important result in the study of polynomial-time preprocessing shows that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the terminology of parameterized complexity we say that k-Vertex Cover has a kernel with 2k vertices. There is complexity-theoretic evidence that both 2k vertices and Theta(k^2) edges are optimal for the kernel size. In this paper we consider the Vertex Cover problem with a different parameter, the size fvs(G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number vc(G) since fvs(G) <= vc(G) and the difference can be arbitrarily large. We give a kernel for Vertex Cover with a number of vertices that is cubic in fvs(G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that |V(G')| <= 2k and |V(G')| <= O(|X'|^3). A similar result holds when the feedback vertex set X is not given along with the input. In sharp contrast we show that the Weighted Vertex Cover problem does not have a polynomial kernel when parameterized by the cardinality of a given vertex cover of the graph unless NP is in coNP/poly and the polynomial hierarchy collapses to the third level.Comment: Published in "Theory of Computing Systems" as an Open Access publicatio

Influence of atmospheric deposits and secondary minerals on Li isotopes budget in a highly weathered catchment, Guadeloupe (Lesser Antilles)

To better constrain Li dynamics in the tropics, we sampled critical zone compartments of a small forested andesitic catchment in Guadeloupe (soils, parent rock, atmospheric dust, plants, soil solutions, stream and rain waters). The aims of this study are to identify the origin of Li in the different compartments and to better characterize the behavior of Li and its isotopes during water–rock interaction in a highly cation-depleted soil. The Li isotope signature (δ7Li) of throughfall samples varies between + 11.2‰ and + 26.4‰. As this is lower than the seawater signature (31‰) and vegetation does not fractionate Li isotopes, our data indicate that Saharan dust (− 0.7‰) significantly contributes to the throughfall signature. Li isotope composition measured in a 12.5 m deep soil profile varies from + 3.9‰ near the surface to − 13.5‰ at 11 m depth. Compared to unweathered andesite (+ 5‰), the deep soil signature is in agreement with preferential incorporation of light Li into secondary minerals. In the top soil however, our results also emphasized that atmospheric deposition (wet and dry) is a main source of Li to the soil. The decreasing δ7Li with increasing depth is consistent with a vertical gradient of incorporation of heavy atmospheric Li, this input being maximal near the surface. At the catchment scale, throughfall and total atmospheric inputs (sea salts + Saharan dust) provide 12.1 and 23.9 g Li yr− 1 respectively to the Quiock Creek catchment. These fluxes represent 34% and 67%, respectively, of Li exported at the outlet indicating that atmospheric deposition is one of the main Li inputs to the critical zone. Li concentration and isotopic mass balance at the catchment scale indicate that in addition to atmospheric deposition, secondary mineral phase dissolution is a major solute source and that andesite no longer participates in significant production of Li

Movement of micro- and macronutrients from sheep excreta to grass and leachate via soil

This dataset originates from an experiment designed to determine the fate of micro- and macronutrients from sheep excreta after application to soils seeded with grass. The experiment was conducted as a pot experiment in a controlled environment growing room over a period of approximately 7 weeks. Two soils were used, chosen because they were of the same soil type but with different organic matter contents. Sheep excreta (urine and faeces) originated from a feeding trial where sheep were given feed supplements where micronutrients were in either an organic or inorganic form, and full information on this feeding trial and the characterisation of the excreta are given in a linked dataset (https://doi.org/10.23637/rothamsted.98883). For the organic-supplemented sheep excreta and the inorganic-supplemented sheep excreta separately, excreta were applied to the soil as either urine only, faeces only, or a combination of faeces and urine, plus there was an untreated control. Measurements include leachate volume; grass yield; soil pH from before, during and after the experimental period; and macro- and micro-nutrient concentrations of soil prior to the experiment (total and available concentrations), grass (total concentrations) and leachate (total concentrations) and soil total carbon and nitrogen after the experiment. Grass was cut on 4 occasions and leachate collected 3 times