Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Effects of land cover on chemical characteristics of streams in the Cerrado region of Brazil

The Cerrado is the second largest Brazilian biome and contains the headwaters of three major hydrological basins in Brazil. In spite of the biological and ecological relevance of this biome, there is little information about how land use changes affect the chemistry of low-order streams in the Cerrado. To evaluate these effects streams that drain areas under natural, rural, and urban land cover were sampled near Brasilia, Brazil. Water samples were collected between September 2004 and December 2006. Chemical concentrations generally followed the pattern of Urban > Rural > Natural. Median conductivity of stream water of 21.6 (interquartile: 22.7) mu S/cm in urban streams was three and five-fold greater relative to rural and natural areas, respectively. In the wet season, despite of increasing discharge, concentration of many solutes were higher, particularly in rural and natural streams. Streams also presented higher total dissolved N (TDN) loads from natural to rural and urban although DIN:DON ratios did not differ significantly. In natural and urban streams TDN was 80 and 77% dissolved organic N, respectively. These results indicate that alterations in land cover from natural to rural and urban are changing stream water chemistry in the Cerrado with increasing solute concentrations, in addition to increased TDN output in areas under urban cover, with potential effects on ecosystem function.

Runoff sources and land cover change in the Amazon: an end-member mixing analysis from small watersheds

The flowpaths by which water moves from watersheds to streams has important consequences for the runoff dynamics and biogeochemistry of surface waters in the Amazon Basin. The clearing of Amazon forest to cattle pasture has the potential to change runoff sources to streams by shifting runoff to more surficial flow pathways. We applied end-member mixing analysis (EMMA) to 10 small watersheds throughout the Amazon in which solute composition of streamwater and groundwater, overland flow, soil solution, throughfall and rainwater were measured, largely as part of the Large-Scale Biosphere-Atmosphere Experiment in Amazonia. We found a range in the extent to which streamwater samples fell within the mixing space determined by potential flowpath end-members, suggesting that some water sources to streams were not sampled. The contribution of overland flow as a source of stream flow was greater in pasture watersheds than in forest watersheds of comparable size. Increases in overland flow contribution to pasture streams ranged in some cases from 0% in forest to 27-28% in pasture and were broadly consistent with results from hydrometric sampling of Amazon forest and pasture watersheds that indicate 17- to 18-fold increase in the overland flow contribution to stream flow in pastures. In forest, overland flow was an important contribution to stream flow (45-57%) in ephemeral streams where flows were dominated by stormflow. Overland flow contribution to stream flow decreased in importance with increasing watershed area, from 21 to 57% in forest and 60-89% in pasture watersheds of less than 10 ha to 0% in forest and 27-28% in pastures in watersheds greater than 100 ha. Soil solution contributions to stream flow were similar across watershed area and groundwater inputs generally increased in proportion to decreases in overland flow. Application of EMMA across multiple watersheds indicated patterns across gradients of stream size and land cover that were consistent with patterns determined by detailed hydrometric sampling.

Soil nitrous oxide emissions in long-term cover crops-based rotations under subtropical climate

It has been shown that cover crops can enhance soil nitrous oxide (N(2)O) emissions, but the magnitude of increase depends on the quantity and quality of the crop residues. Therefore, this study aimed to evaluate the effect of long-term (19 and 21 years) no-till maize crop rotations including grass [black oat (Avena strigosa Schreb)] and legume cover crops [vetch (Vigna sativa L), cowpea (Vigna unguiculata L. Walp), pigeon pea (Cajanus cajan L. Millsp.) and lablab (Dolichos lablab)] on annual soil N(2)O emissions in a subtropical Acrisol in Southern Brazil. Greater soil N(2)O emissions were observed in the first 45 days after the cover crop residue management in all crop rotations, varying from -20.2 +/- 1.9 to 163.9 +/- 24.3 mu g N m(-2) h(-1). Legume-based crop rotations had the largest cumulative emissions in this period, which were directly related to the quantity of N (r(2) = 0.60, p = 0.13)and inversely related to the lignin:N ratio(r(2) = 0.89,p = 0.01) of the cover crop residues. After this period, the mean fluxes were smaller and were closely related to the total soil N stocks (r(2) = 0.96, p = 0.002). The annual soil N(2)O emission represented 0.39-0.75% of the total N added by the legume cover crops. Management-control led soil variables such as mineral N (NO(3)(-) and NH(4)(+)) and dissolved organic C influenced more the N(2)O fluxes than environmental-related variables as water-filled pore space and air and soil temperature. Consequently, the synchronization between N mineralization and N uptake by plants seems to be the main challenge to reduce N(2)O emissions while maintaining the environmental and agronomic services provided by legume cover crops in agricultural systems. (C) 2009 Elsevier B.V. All rights reserved.

Host Status of Graminaceous Cover Crops for Pratylenchus brachyurus

Taking into account that information about the host status of cover crops for Pratylenchus brachyurus is scarce or contradictory, this study was undertaken to assess the host status of selected graminaceous cover crops by estimating nematode reproduction and their ability to decrease the nematode density in glasshouse conditions. Furthermore, the reproductive fitness of three P. brachyurus populations was assessed for Brachiaria grasses. Silage and forage sorghum proved to be good hosts for P. brachyurus; consequently, they should be avoided in fields infested with this lesion nematode, mainly before susceptible crop such as soybean, common bean, cowpea, and cotton. Dictyoneura grass, the pearl millet cv. ADR 300, and black oat were poor hosts for P. brachyurus but may increase densities of this nematode over time. Consequently, these cover crops might be used in infested fields for only short periods, because they could increase the P. brachyurus population density slowly but progressively.

Effects of roads, topography, and land use on forest cover dynamics in the Brazilian Atlantic Forest

Roads and topography can determine patterns of land use and distribution of forest cover, particularly in tropical regions. We evaluated how road density, land use, and topography affected forest fragmentation, deforestation and forest regrowth in a Brazilian Atlantic Forest region near the city of Sao Paulo. We mapped roads and land use/land cover for three years (1962, 1981 and 2000) from historical aerial photographs, and summarized the distribution of roads, land use/land cover and topography within a grid of 94 non-overlapping 100 ha squares. We used generalized least squares regression models for data analysis. Our models showed that forest fragmentation and deforestation depended on topography, land use and road density, whereas forest regrowth depended primarily on land use. However, the relationships between these variables and forest dynamics changed in the two studied periods; land use and slope were the strongest predictors from 1962 to 1981, and past (1962) road density and land use were the strongest predictors for the following period (1981-2000). Roads had the strongest relationship with deforestation and forest fragmentation when the expansions of agriculture and buildings were limited to already deforested areas, and when there was a rapid expansion of development, under influence of Sao Paulo city. Furthermore, the past(1962)road network was more important than the recent road network (1981) when explaining forest dynamics between 1981 and 2000, suggesting a long-term effect of roads. Roads are permanent scars on the landscape and facilitate deforestation and forest fragmentation due to increased accessibility and land valorization, which control land-use and land-cover dynamics. Topography directly affected deforestation, agriculture and road expansion, mainly between 1962 and 1981. Forest are thus in peril where there are more roads, and long-term conservation strategies should consider ways to mitigate roads as permanent landscape features and drivers facilitators of deforestation and forest fragmentation. (C) 2009 Elsevier B.V. All rights reserved.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.