An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

Estimation of the thickness and the optical parameters of several stacked thin films using optimization

The reverse engineering problem addressed in the present research consists of estimating the thicknesses and the optical constants of two thin films deposited on a transparent substrate using only transmittance data through the whole stack. No functional dispersion relation assumptions are made on the complex refractive index. Instead, minimal physical constraints are employed, as in previous works of some of the authors where only one film was considered in the retrieval algorithm. To our knowledge this is the first report on the retrieval of the optical constants and the thickness of multiple film structures using only transmittance data that does not make use of dispersion relations. The same methodology may be used if the available data correspond to normal reflectance. The software used in this work is freely available through the PUMA Project web page (http://www.ime.usp.br/similar to egbirgin/puma/). (C) 2008 Optical Society of America

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

Eddy Formation in the Tropical Atlantic Induced by Abrupt Changes in the Meridional Overturning Circulation

The variability of the meridional overturning circulation (MOC) in the upper tropical Atlantic basin is investigated using a reduced-gravity model in a simplified domain. Four sets of idealized numerical experiments are performed: (i) switch-on of the MOC until a fixed value when a constant northward flow is applied along the western boundary; (ii) MOC with a variable flow; (iii) MOC in a quasi-steady flow; and (iv) shutdown of the MOC in the Northern Hemisphere. Results from experiments (i) show that eddies are generated at the equatorial region by shear instability and detached northward; eddies are responsible for an enhancement of the mean flow and the variability of the MOC. Results from experiments (ii) show a transitional behavior of the MOC related to the eddy generation in interannual-decadal time scales as the Reynolds number varies due to the variations in the MOC. In experiments (iii), a critical Reynolds number Re(c) around 30 is found, above which eddies are generated. Experiments (iv) demonstrate that even after the collapse of MOC in the Northern Hemisphere, eddies can still be generated and carry energy across the equator into the Northern Hemisphere; these eddies act to attenuate the impact of the MOC shutdown on short time scales. The results described here may be particularly pertinent to ocean general circulation models in which the Reynolds number lies close to the bifurcation point separating the laminar and turbulent regimes.

INTERANNUAL VARIABILITY IN TROPICAL ESTUARINE COPEPOD ASSEMBLAGES OFF NORTHEASTERN BRAZIL

We studied copepod assemblage variability among years, seasons, and tidal states in the Mucuri River estuary (Bahia State, Brazil). Zooplankton samples were collected seasonally through five years (2002-2006) at three sampling stations, one of which was sampled over a complete tidal cycle (two ebb and two flood tides). Temperature, salinity, river flux, and rainfall data were collected. Winter and summer represented dry and wet seasons, respectively. Copepod abundances ranged from 40 to 63% of the total zooplankton assemblage and comprised 46 taxa, among which, common estuarine species such as Temora turbinata (first record for the studied area), Parvocalanus crassirostris, Acartia lilljeborgi, Oithona hebes were the most abundant (euryhaline species). Interannual and seasonal variations were most marked in stenohaline species, e.g.. Notodiaptomus sp. and Thermocyclops minutus; density variations of euryhaline species, which made up the majority of the abundant taxa, were most closely related to tides. Diversity and richness also followed an intertidal pattern of variation.

Stability of biomass-derived black carbon in soils

Black carbon (BC) may play ail important role in the global C budget, due to its potential to act as a significant sink of atmospheric CO(2). In order to fully evaluate the influence of BC oil the global C cycle, in understanding of the stability of BC is required. The biochemical stability of BC was assessed in a chronosequence of high-BC-containing Anthrosols from the central Amazon, Brazil, using a range of spectroscopic and biological methods. Results revealed that the Anthrosols had 61-80% lower (P < 0.05) CO(2) evolution per unit C over 532 days compared to their respective adjacent soils with low BC contents. No significant (P > 0.05) difference in CO(2) respiration per unit C was observed between Anthrosols with contrasting ages of BC (600-8700 years BP) Lind soil textures (0.3-36% clay). Similarly, the molecular composition of the core regions of micrometer-sized BC particles quantified by synchrotron-based Near-Edge X-ray Fine Structure (NEXAFS) spectroscopy coupled to Scanning Transmission X-ray Microscopy (STXM) remained similar regardless of their ages and closely resembled the spectral characteristics or fresh BC. BC decomposed extremely slowly to ail extent that it was not possible to detect chemical changes between Youngest and oldest samples, as also confirmed by X-ray Photoelectron Spectroscopy (XPS). Deconvolution of NEXAFS spectra revealed greater oxidation oil the surfaces of BC particles with little penetration into the core of the particles. The similar C mineralization between different BC-rich soils regardless of soil texture underpins the importance of chemical recalcitrance for the stability of BC, in contrast to adjacent soils which showed the highest mineralization in the sandiest soil. However, the BC-rich Anthrosols had higher proportions (72-90%) of C in the more stable organo-mineral fraction than BC-poor adjacent soils (2-70%), Suggesting some degree of physical stabilization. (c) 2008 Elsevier Ltd. All rights reserved.

Molecular and morphological characterization of Amathia distans Busk and Amathia brasiliensis Busk (Bryozoa: Ctenostomata) from the tropical and subtropical Western Atlantic

Morphological and molecular analyses have proven to be complementary tools of taxonomic information for the redescription of the ctenostome bryozoans Amathia brasiliensis Busk, 1886 and Amathia distans Busk, 1886. The two species, originally described from material collected by the `Challenger` expedition but synonymized by later authors, now have their status fixed by means of the selection of lectotypes, morphological observations and analyses of DNA sequences described here. The morphological characters allowing the identification of living and/or preserved specimens are (1) A. brasiliensis: whitish-pale pigment spots in the frontal surface of stolons and zooids, and a wide stolon with biserial zooid clusters growing in clockwise and anti-clockwise spirals along it, the spirality direction being maintained from maternal to daughter stolons; and (2) A. distans: bright yellow pigment spots in stolonal and zooidal surfaces including lophophores, and a slender stolon, thickly cuticularized, with biserial zooid clusters growing in clockwise and anti-clockwise spirals along it and the spirality direction not maintained from maternal to daughter stolons. Pairwise comparisons of DNA sequences of the mitochondrial genes cytochrome c oxidase subunit I and large ribosomal RNA subunit revealed deep genetic divergence between A. brasiliensis and A. distans. Finally, analyses of those sequences within a Bayesian phylogenetic context recovered their genealogical species status.

Shallow-water species of Beania Johnston, 1840 (Bryozoa, Cheilostomata) from the tropical and subtropical Western Atlantic

This paper describes four new species of the bryozoan genus Beania from the Brazilian coast. Two of them have been previously recorded in the western Atlantic as Beania hirtissima (Heller, 1867) and Beania mirabilis Johnston, 1840, respectively; they are redescribed here as Beania americana n. sp. and Beania mirabilissima n. sp. Two reticulate species, Beania correiae n. sp. and Beania metrii n. sp., are newly described. Descriptions of four other species of Beania from the region are also included: Beania australis Busk, 1852, Beania cupulariensis Osburn, 1914, Beania klugei Cook, 1968 and Beania maxilladentata Ramalho, Muricy & Taylor, 2010.

Foraging by the omnivorous crab Pachygrapsus transversus affects the structure of assemblages on sub-tropical rocky shores

The roles of herbivory and predation in determining the structure and diversity of communities have been tested across most intertidal systems. In contrast, the importance of omnivorous consumers remains untested in many rocky shore communities. We tested the role of a small omnivorous crab in an intertidal food web on rocky shores of the sub-tropical southwest Atlantic. Exclusion of the grapsid crab Pachygrapsus transversus in the field resulted in significant changes in the abundance of functional groups in the sublittoral fringe of sheltered shores, where the dominant cover changed from a suite of macroalgae to an assemblage of filter-feeding animals (ascidians, sponges, mussels). In contrast, limpets, whelks, large crabs and fish did not significantly affect community composition of the assemblage. To examine the omnivorous feeding pattern of P. transversus, we did laboratory experiments to test its foraging behaviour among animal and algal groups. The crab showed selective behaviour, preferring invertebrate groups to macroalgae, and opportunistic behaviour among types of prey within those major groups. According to our results, the role of slow-moving and large fast-moving consumers is apparently negligible compared to the effect of an omnivorous consumer. P. transversus plays an important role in determining the intertidal community composition on these subtropical rocky shores, causing changes in the balance of functional groups and controlling invasive species.

Historical carbon emissions and uptake from the agricultural frontier of the Brazilian Amazon

Tropical ecosystems play a large and complex role in the global carbon cycle. Clearing of natural ecosystems for agriculture leads to large pulses of CO(2) to the atmosphere from terrestrial biomass. Concurrently, the remaining intact ecosystems, especially tropical forests, may be sequestering a large amount of carbon from the atmosphere in response to global environmental changes including climate changes and an increase in atmospheric CO(2). Here we use an approach that integrates census-based historical land use reconstructions, remote-sensing-based contemporary land use change analyses, and simulation modeling of terrestrial biogeochemistry to estimate the net carbon balance over the period 1901-2006 for the state of Mato Grosso, Brazil, which is one of the most rapidly changing agricultural frontiers in the world. By the end of this period, we estimate that of the state`s 925 225 km(2), 221 092 km(2) have been converted to pastures and 89 533 km(2) have been converted to croplands, with forest-to-pasture conversions being the dominant land use trajectory but with recent transitions to croplands increasing rapidly in the last decade. These conversions have led to a cumulative release of 4.8 Pg C to the atmosphere, with similar to 80% from forest clearing and 20% from the clearing of cerrado. Over the same period, we estimate that the residual undisturbed ecosystems accumulated 0.3 Pg C in response to CO2 fertilization. Therefore, the net emissions of carbon from Mato Grosso over this period were 4.5 Pg C. Net carbon emissions from Mato Grosso since 2000 averaged 146 Tg C/yr, on the order of Brazil`s fossil fuel emissions during this period. These emissions were associated with the expansion of croplands to grow soybeans. While alternative management regimes in croplands, including tillage, fertilization, and cropping patterns promote carbon storage in ecosystems, they remain a small portion of the net carbon balance for the region. This detailed accounting of a region`s carbon balance is the type of foundation analysis needed by the new United Nations Collaborative Programmme for Reducing Emissions from Deforestation and Forest Degradation (REDD).

The Amazon Frontier of Land-Use Change: Croplands and Consequences for Greenhouse Gas Emissions

The Brazilian Amazon is one of the most rapidly developing agricultural frontiers in the world. The authors assess changes in cropland area and the intensification of cropping in the Brazilian agricultural frontier state of Mato Grosso using remote sensing and develop a greenhouse gas emissions budget. The most common type of intensification in this region is a shift from single-to double-cropping patterns and associated changes in management, including increased fertilization. Using the enhanced vegetation index (EVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor, the authors created a green-leaf phenology for 2001-06 that was temporally smoothed with a wavelet filter. The wavelet-smoothed green-leaf phenology was analyzed to detect cropland areas and their cropping patterns. The authors document cropland extensification and double-cropping intensification validated with field data with 85% accuracy for detecting croplands and 64% and 89% accuracy for detecting single-and double-cropping patterns, respectively. The results show that croplands more than doubled from 2001 to 2006 to cover about 100 000 km(2) and that new double-cropping intensification occurred on over 20% of croplands. Variations are seen in the annual rates of extensification and double-cropping intensification. Greenhouse gas emissions are estimated for the period 2001-06 due to conversion of natural vegetation and pastures to row-crop agriculture in Mato Grosso averaged 179 Tg CO(2)-e yr(-1),over half the typical fossil fuel emissions for the country in recent years.

Soil carbon stocks under no-tillage mulch-based cropping systems in the Brazilian Cerrado: An on-farm synchronic assessment

No-tillage mulch-based (NTM) cropping systems have been widely adopted by farmers in the Brazilian savanna region (Cerrado biome). We hypothesized that this new type of management should have a profound impact on soil organic carbon (SOC) at regional scale and consequently on climate change mitigation. The objective of this study was thus to quantify the SOC storage potential of NTM in the oxisols of the Cerrado using a synchronic approach that is based on a chronosequence of fields of different years under NTM. The study consisted of three phases: (1) a farm/cropping system survey to identify the main types of NTM systems to be chosen for the chronosequence; (2) a field survey to identify a homogeneous set of situations for the chronosequence and (3) the characterization of the chronosequence to assess the SOC storage potential. The main NTM system practiced by farmers is an annual succession of soybean (Glycine max)or maize (Zea mays) with another cereal crop. This cropping system covers 54% of the total cultivated area in the region. At the regional level, soil organic C concentrations from NTM fields were closely correlated with clay + silt content of the soil (r(2) = 0.64). No significant correlation was observed (r(2) = 0.07), however, between these two variables when we only considered the fields with a clay + silt content in the 500-700 g kg(-1) range. The final chronosequence of NTM fields was therefore based on a subsample of eight fields, within this textural range. The SOC stocks in the 0-30 cm topsoil layer of these selected fields varied between 4.2 and 6.7 kg C m(-2) and increased on average (r(2) = 0.97) with 0.19 kg C m(-2) year(-1). After 12 years of NTM management, SOC stocks were no longer significantly different from the stocks under natural Cerrado vegetation (p < 0.05), whereas a 23-year-old conventionally tilled and cropped field showed SOC stocks that were about 30% below this level. Confirming our hypotheses, this study clearly illustrated the high potential of NTM systems in increasing SOC storage under tropical conditions, and how a synchronic approach may be used to assess efficiently such modification on farmers` fields, identifying and excluding non desirable sources of heterogeneity (management, soils and climate). (C) 2010 Elsevier B.V. All rights reserved.

Understanding the Influences of Spatial Patterns on N Availability Within the Brazilian Amazon Forest

Nitrogen variations at different spatial scales and integrated across functional groups were addressed for lowland tropical forests in the Brazilian Amazon as follows: (1) how does N availability vary across the region over different spatial scales (regional x landscape scale); ( 2) how are these variations in N availability integrated across plant functional groups ( legume 9 non-legume trees). Leaf N, P, and Ca concentrations as well the leaf N isotope ratios (delta(15)N) from a large set of legume and non-legume tree species were measured. Legumes had higher foliar N/Ca ratios than non-legumes, consistent with the high energetic costs in plant growth associated with higher foliar P/Ca ratios found in legumes than in non-legumes. At the regional level, foliar delta(15)N decreased with increasing rainfall. At the landscape level, N availability was higher in the forests on clayey soils on the plateau than in forests on sandier soils. The isotope as well as the non-isotope data relationships here documented, explain to a large extent the variation in delta(15)N signatures across gradients of rainfall and soil. Although at the regional level, the precipitation regime is a major determinant of differences in N availability, at the landscape level, under the same precipitation regime, soil type seems to be a major factor influencing the availability of N in the Brazilian Amazon forest.

Spatio-temporal patterns of throughfall and solute deposition in an open tropical rain forest

The brief interaction of precipitation with a forest canopy can create a high spatial variability of both throughfall and solute deposition. We hypothesized that (i) the variability in natural forest systems is high but depends on system-inherent stability, (ii) the spatial variability of solute deposition shows seasonal dynamics depending on the increase in rainfall frequency, and (iii) spatial patterns persist only in the short-term. The study area in the north-western Brazilian state of Rondonia is subject to a climate with a distinct wet and dry season. We collected rain and throughfall on an event basis during the early wet season (n = 14) and peak of the wet season (n = 14) and analyzed the samples for pH and concentrations of NH4+, Na+, K+, Ca2+ Mg2+,, Cl-, NO3-, SO42- and DOC. The coefficient 3 4 cient of variation for throughfall based on both sampling intervals was 29%, which is at the lower end of values reported from other tropical forest sites, but which is higher than in most temperate forests. Coefficients of variation of solute deposition ranged from 29% to 52%. This heterogeneity of solute deposition is neither particularly high nor particularly tow compared with a range of tropical and temperate forest ecosystems. We observed an increase in solute deposition variability with the progressing wet season, which was explained by a negative correlation between heterogeneity of solute deposition and antecedent dry period. The temporal stability of throughfall. patterns was Low during the early wet season, but gained in stability as the wet season progressed. We suggest that rapid plant growth at the beginning of the rainy season is responsible for the lower stability, whereas less vegetative activity during the later rainy season might favor the higher persistence of ""hot"" and ""cold"" spots of throughfall. quantities. The relatively high stability of throughfall patterns during later stages of the wet season may influence processes at the forest floor and in the soil. Solute deposition patterns showed less clear trends but all patterns displayed a short-term stability only. The weak stability of those patterns is apt to impede the formation of solute deposition -induced biochemical microhabitats in the soil. (C) 2008 Elsevier B.V. All rights reserved.

Functional specialization of Eucalyptus fine roots: contrasting potential uptake rates for nitrogen, potassium and calcium tracers at varying soil depths

1. Little is known about the role of deep roots in the nutrition of forest trees and their ability to provide a safety-net service taking up nutrients leached from the topsoil. 2. To address this issue, we studied the potential uptake of N, K and Ca by Eucalyptus grandis trees (6 years of age - 25 m mean height), in Brazil, as a function of soil depth, texture and water content. We injected NO(3)(-)- (15)N, Rb(+) (analogue of K(+)) and Sr(2+) (analogue of Ca(2+)) tracers simultaneously in a solution through plastic tubes at 10, 50, 150 and 300 cm in depth in a sandy and a clayey Ferralsol soil. A complete randomized design was set up with three replicates of paired trees per injection depth and soil type. Recently expanded leaves were sampled at various times after tracer injection in the summer, and the experiment was repeated in the winter. Soil water contents were continuously monitored at the different depths in the two soils. 3. Determination of foliar Rb and Sr concentrations and (15)N atom % made it possible to estimate the relative uptake potential (RUP) of tracer injections from the four soil depths and the specific RUP (SRUP), defined as RUP, per unit of fine root length density in the corresponding soil layer. 4. The highest tracer uptake rates were found in the topsoil, but contrasting RUP distributions were observed for the three tracers. Whilst the RUP was higher for NO(3)(-)- (15)N than for Rb(+) and Sr(2+) in the upper 50 cm of soil, the highest SRUP values for Sr(2+) and Rb(+) were found at a depth of 300 cm in the sandy soil, as well as in the clayey soil when gravitational solutions reached that depth. 5. Our results suggest that the fine roots of E. grandis trees exhibit contrasting potential uptake rates with depth depending on the nutrient. This functional specialization of roots might contribute to the high growth rates of E. grandis trees, efficiently providing the large amounts of nutrients required throughout the development of these fast-growing plantations.