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).

Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Beta-2 adrenergic receptor gene polymorphisms Gln27Glu, Arg16Gly in patients with heart failure

Background -: Beta-2 adrenergic receptor gene polymorphisms Gln27Glu, Arg16Gly and Thr164Ile were suggested to have an effect in heart failure. We evaluated these polymorphisms relative to clinical characteristics and prognosis of alarge cohort of patients with heart failure of different etiologies. Methods -: We studied 501 patients with heart failure of different etiologies. Mean age was 58 years (standard deviation 14.4 years), 298 (60%) were men. Polymorphisms were identified by polymerase chain reaction-restriction fragment length polymorphism. Results -: During the mean follow-up of 12.6 months (standard deviation 10.3 months), 188 (38%) patients died. Distribution of genotypes of polymorphism Arg16Gly was different relative to body mass index (chi(2) = 9.797; p = 0.04). Overall the probability of survival was not significantly predicted by genotypes of Gln27Glu, Arg16Gly, or Thr164Ile. Allele and haplotype analysis also did not disclose any significant difference regarding mortality. Exploratory analysis through classification trees pointed towards a potential association between the Gln27Glu polymorphism and mortality in older individuals. Conclusion -: In this study sample, we were not able to demonstrate an overall influence of polymorphisms Gln27Glu and Arg16Gly of beta-2 receptor gene on prognosis. Nevertheless, Gln27Glu polymorphism may have a potential predictive value in older individuals.

Solution structure of the human signaling protein RACK1

Background: The adaptor protein RACK1 (receptor of activated kinase 1) was originally identified as an anchoring protein for protein kinase C. RACK1 is a 36 kDa protein, and is composed of seven WD repeats which mediate its protein-protein interactions. RACK1 is ubiquitously expressed and has been implicated in diverse cellular processes involving: protein translation regulation, neuropathological processes, cellular stress, and tissue development. Results: In this study we performed a biophysical analysis of human RACK1 with the aim of obtaining low resolution structural information. Small angle X-ray scattering (SAXS) experiments demonstrated that human RACK1 is globular and monomeric in solution and its low resolution structure is strikingly similar to that of an homology model previously calculated by us and to the crystallographic structure of RACK1 isoform A from Arabidopsis thaliana. Both sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation techniques showed that RACK1 is predominantly a monomer of around 37 kDa in solution, but also presents small amounts of oligomeric species. Moreover, hydrodynamic data suggested that RACK1 has a slightly asymmetric shape. The interaction of RACK1 and Ki1/57 was tested by sedimentation equilibrium. The results suggested that the association between RACK1 and Ki-1/57(122-413) follows a stoichiometry of 1:1. The binding constant (KB) observed for RACK1-Ki-1/57(122-413) interaction was of around (1.5 +/- 0.2) x 10(6) M(-1) and resulted in a dissociation constant (KD) of (0.7 +/- 0.1) x 10(-6) M. Moreover, the fluorescence data also suggests that the interaction may occur in a cooperative fashion. Conclusion: Our SAXS and analytical ultracentrifugation experiments indicated that RACK1 is predominantly a monomer in solution. RACK1 and Ki-1/57(122-413) interact strongly under the tested conditions.

Nitrogen dynamics during ecosystem development in tropical forest restoration

We considered whether ecological restoration using high diversity of native tree species serves to restore nitrogen dynamics in the Brazilian Atlantic Forest. We measured delta(15)N and N content in green foliage and soil; vegetation N:P ratio; and soil N mineralization in a preserved natural forest and restored forests of ages 21 and 52 years. Green foliage delta(15)N values, N content, N:P ratio, inorganic N and net mineralization and nitrification rates were all higher, the older the forest. Our findings indicate that the recuperation of N cycling has not been achieved yet in the restored forests even after 52 years, but show that they are following a trajectory of development that is characterized by their N cycling intensity becoming similar to a natural mature forest of the same original forest formation. This study demonstrated that some young restored forests are more limited by N compared to mature natural forests. We document that the recuperation of N cycling in tropical forests can be achieved through ecological restoration actions. (C) 2011 Elsevier B.V. All rights reserved.

Do plant species influence soil CO(2) and N(2)O fluxes in a diverse tropical forest?

To test whether plant species influence greenhouse gas production in diverse ecosystems, we measured wet season soil CO(2) and N(2)O fluxes close to similar to 300 large (>35 cm in diameter at breast height (DBH)) trees of 15 species at three clay-rich forest sites in central Amazonia. We found that soil CO(2) fluxes were 38% higher near large trees than at control sites >10 m away from any tree (P < 0.0001). After adjusting for large tree presence, a multiple linear regression of soil temperature, bulk density, and liana DBH explained 19% of remaining CO(2) flux variability. Soil N(2)O fluxes adjacent to Caryocar villosum, Lecythis lurida, Schefflera morototoni, and Manilkara huberi were 84%-196% greater than Erisma uncinatum and Vochysia maxima, both Vochysiaceae. Tree species identity was the most important explanatory factor for N(2)O fluxes, accounting for more than twice the N(2)O flux variability as all other factors combined. Two observations suggest a mechanism for this finding: (1) sugar addition increased N(2)O fluxes near C. villosum twice as much (P < 0.05) as near Vochysiaceae and (2) species mean N(2)O fluxes were strongly negatively correlated with tree growth rate (P = 0.002). These observations imply that through enhanced belowground carbon allocation liana and tree species can stimulate soil CO(2) and N(2)O fluxes (by enhancing denitrification when carbon limits microbial metabolism). Alternatively, low N(2)O fluxes potentially result from strong competition of tree species with microbes for nutrients. Species-specific patterns in CO(2) and N(2)O fluxes demonstrate that plant species can influence soil biogeochemical processes in a diverse tropical forest.

Forest structure and live aboveground biomass variation along an elevational gradient of tropical Atlantic moist forest (Brazil)

Live aboveground biomass (AGB) is an important source of uncertainty in the carbon balance from the tropical regions in part due scarcity of reliable estimates of live AGB and its variation across landscapes and forest types. Studies of forest structure and biomass stocks of Neotropical forests are biased toward Amazonian and Central American sites. In particular, standardized estimates of aboveground biomass stocks for the Brazilian Atlantic forest are rarely available. Notwithstanding the role of environmental variables that control the distribution and abundance of biomass in tropical lowland forests has been the subject of considerable research, the effect of short, steep elevational gradients on tropical forest structure and carbon dynamics is not well known. In order to evaluate forest structure and live AGB variation along an elevational gradient (0-1100 m a.s.l.) of coastal Atlantic Forest in SE Brazil, we carried out a standard census of woody stems >= 4.8 cm dbh in 13 1-ha permanent plots established on four different sites in 2006-2007. Live AGB ranged from 166.3 Mg ha(-1) (bootstrapped 95% CI: 1444,187.0) to 283.2 Mg ha(-1) (bootstrapped 95% CI: 253.0,325.2) and increased with elevation. We found that local-scale topographic variation associated with elevation influences the distribution of trees >50 cm dbh and total live AGB. Across all elevations, we found more stems (64-75%) with limited crown illumination but the largest proportion of the live AGB (68-85%) was stored in stems with highly illuminated or fully exposed crowns. Topography, disturbance and associated changes in light and nutrient supply probably control biomass distribution along this short but representative elevational gradient. Our findings also showed that intact Atlantic forest sites stored substantial amounts of carbon aboveground. The live tree AGB of the stands was found to be lower than Central Amazonian forests, but within the range of Neotropical forests, in particular when compared to Central American forests. Our comparative data suggests that differences in live tree AGB among Neotropical forests are probably related to the heterogeneous distribution of large and medium-sized diameter trees within forests and how the live biomass is partitioned among those size classes, in accordance with general trends found by previous studies. In addition, the elevational variation in live AGB stocks suggests a large spatial variability over coastal Atlantic forests in Brazil, clearly indicating that it is important to consider regional differences in biomass stocks for evaluating the role of this threatened tropical biome in the global carbon cycle. (C) 2010 Elsevier B.V. All rights reserved.

Nitrogen availability patterns in white-sand vegetations of Central Brazilian Amazon

Addressing spatial variability in nitrogen (N) availability in the Central Brazilian Amazon, we hypothesized that N availability varies among white-sand vegetation types (campina and campinarana) and lowland tropical forests (dense terra-firme forests) in the Central Brazilian Amazon, under the same climate conditions. Accordingly, we measured soil and foliar N concentration and N isotope ratios (delta(15)N) throughout the campina-campinarana transect and compared to published dense terra-firme forest results. There were no differences between white-sand vegetation types in regard to soil N concentration, C:N ratio and delta(15)N across the transect. Both white-sand vegetation types showed very low foliar N concentrations and elevated foliar C:N ratios, and no significant difference between site types was observed. Foliar delta(15)N was depleted, varying from -9.6 to 1.6aEuro degrees in the white-sand vegetations. The legume Aldina heterophylla had the highest average delta(15)N values (-1.5aEuro degrees) as well as the highest foliar N concentration (2.1%) while the non-legume species had more depleted delta(15)N values and the average foliar N concentrations varied from 0.9 to 1.5% among them. Despite the high variation in foliar delta(15)N among plants, a significant and gradual (15)N-enrichment in foliar isotopic signatures throughout the campina-campinarana transect was observed. Individual plants growing in the campinarana were significantly enriched in (15)N compared to those in campina. In the white-sand N-limited ecosystems, the differentiation of N use seems to be a major cause of variations observed in foliar delta(15)N values throughout the campina-campinarana transect.

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.

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.

Improving sample representativeness in environmental studies: a major component for the uncertainty budget

For environmental quality assessment, INAA has been applied for determining chemical elements in small (200 mg) and large (200 g) samples of leaves from 200 trees. By applying the Ingamells` constant, the expected percent standard deviation was estimated in 0.9-2.2% for 200 mg samples. Otherwise, for composite samples (200 g), expected standard deviation varied from 0.5 to 10% in spite of analytical uncertainties ranging from 2 to 30%. Results thereby suggested the expression of the degree of representativeness as a source of uncertainty, contributing for increasing of the reliability of environmental studies mainly in the case of composite samples.

Elemental composition changes in citrus affected by the CVC disease

The citrus variegated chlorosis (CVC) disease results in serious economical losses for the Brazilian citriculture. The influence of CVC disease on the elemental composition of citrus plants was investigated. Leaves of sweet orange varieties Hamlin, Pera Rio and Valencia were collected from healthy and CVC-affected trees for chemical characterization by instrumental neutron activation analysis (INAA). Significant differences between healthy and CVC-affected leaves were identified for Ca, Ce, Co, Eu, Fe, K, La, Na, Nd, Rb, Sc and Sm. Rare earth elements presented consistently higher mass fractions in the healthy leaves.

Characterization of unisexual flower development in the endangered mahogany tree Swietenia macrophylla King. (Meliaceae)

The selection of candidate plus trees of desirable phenotypes from tropical forest trees and the rapid devastation of the natural environments in which these trees are found have created the need for a more detailed knowledge of the floral and reproductive biology of tropical tree species. In this article, the organogenic processes related to unisexual flower development in tropical mahogany, Swietenia macrophylla, are described. Mahogany inflorescences at different developmental stages were evaluated using scanning electron microscopy or optical microscopy of histological sections. The unisexual flowers of S. macrophylla are usually formed in a thyrse, in which the positions of the female and male flowers are not random. Differences between male and female flowers arise late during development. Both female and male flowers can only be structurally distinguished after stage 9, where ovule primordia development is arrested in male flowers and microspore development is aborted in female flower anthers. After this stage, male and female flowers can be distinguished by the naked eye as a result of differences in the dimensions of the gynoecium. The floral characteristics of S. macrophylla (distribution of male and female flowers within the inflorescence, and the relative number of male to female flowers) have practical implications for conservation strategies of this endangered species. (c) 2008 The Linnean Society of London, Botanical Journal of the Linnean Society, 2008, 156, 529-535.

Influence of Post-Clearing Treatment on the Recovery of Herbaceous Plant Communities in Amazonian Secondary Forests

Secondary forests are an increasingly common feature in tropical landscapes worldwide and understanding their regeneration is necessary to design effective restoration strategies. It has previously been shown that the woody species community in secondary forests can follow different successional pathways according to the nature of past human activities in the area, yet little is known about patterns of herbaceous species diversity in secondary forests with different histories of land use. We compared the diversity and abundance of herbaceous plant communities in two types of Central Amazonian secondary forests-those regenerating on pastures created by felling and burning trees and those where trees were felled only. We also tested if plant density and species richness in secondary forests are related to proximity to primary forest. In comparison with primary forest sites, forests regenerating on non-burned habitats had lower herbaceous plant density and species richness than those on burned ones. However, species composition and abundance in non-burned stands were more similar to those of primary forest, whereas several secondary forest specialist species were found in burned stands. In both non-burned and burned forests, distance from the forest edge was not related to herbaceous density and species richness. Overall, our results suggest that the natural regeneration of herbaceous species in secondary tropical forests is dependent on a site`s post-clearing treatment. We recommend evaluating the land history of a site prior to developing and implementing a restoration strategy, as this will influence the biological template on which restoration efforts are overlaid.