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.

A PHASE TRANSITION FOR COMPETITION INTERFACES

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle theta of the cone: for theta >= 180 degrees, the direction is deterministic, while for theta < 180 degrees, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.

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.

Status of chemical elements in Atlantic Forest tree species near an industrial complex

Environmental quality assessment studies have been conducted with tree species largely distributed in the Atlantic Forest. Leaf and soil samples were collected in the conservation unit Parque Estadual da Serra do Mar (PESM) nearby the industrial complex of Cubatao, Sao Paulo State, Brazil, and analyzed for chemical elements by instrumental neutron activation analysis. Results were compared to background values obtained in the Parque Estadual Carlos Botelho (PECB). The higher As, Fe, Hg and Zn mass fractions in the tree leaves of PESM indicated anthropogenic influence on this conservation unit.

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.

Macronutrients in Marandu Palisade Grass as Influenced by Lime, Slag, and Nitrogen Fertilization

Soil acidity is one of the main limiting factors for the growth of pasture grasses in Brazilian soils. In addition to lime, slag can be used to correct soil acidity and help plants to absorb nutrients in adequate amounts. The objective of this experiment was to evaluate, under greenhouse conditions, the effects of slag and lime plus nitrogen (N) on marandu palisade grass plants` nutritional status as well as the absorption of macronutrients submitted to two cuts. The treatments consisted of two corrective materials (slag and lime), three corrective material rates (0.81, 1.61, and 3.22 g dm-3 of ECaCO3), three N rates (75, 150, and 300 mg dm-3) plus a control treatment, with four replications. Macronutrient contents in the forage plants were found to be present in adequate levels. The mean value of N accumulated in the shoot was 40.1 mg per plant, phosphorus (P) was 4.6 mg per plant, potassium (K) was 38.6 mg per plant, calcium (Ca) was 7.3 mg per plant, magnesium (Mg) was 6.7 mg per plant, and sulfur (S) was 3.5 mg per plant at the first cut. At the second cut, the nutrient accumulations values were N 50.8 mg per plant, P 6.3 mg per plant, K 20.7 mg per plant, Ca 21.6 mg per plant, Mg 24.0 mg per plant, and S 4.7 mg per plant. Macronutrients accumulation in the shoot of grass increased with the addition of both the correctives as well as the N rates.

A classification methodology for the risk of weed infestation using fuzzy logic

Despite modern weed control practices, weeds continue to be a threat to agricultural production. Considering the variability of weeds, a classification methodology for the risk of infestation in agricultural zones using fuzzy logic is proposed. The inputs for the classification are attributes extracted from estimated maps for weed seed production and weed coverage using kriging and map analysis and from the percentage of surface infested by grass weeds, in order to account for the presence of weed species with a high rate of development and proliferation. The output for the classification predicts the risk of infestation of regions of the field for the next crop. The risk classification methodology described in this paper integrates analysis techniques which may help to reduce costs and improve weed control practices. Results for the risk classification of the infestation in a maize crop field are presented. To illustrate the effectiveness of the proposed system, the risk of infestation over the entire field is checked against the yield loss map estimated by kriging and also with the average yield loss estimated from a hyperbolic model.

Tropical woods: influence of density in hardness parallel and normal to the grain for some Brazilian tropical tree species

The aim of this work is to verify the possibility to correlating specific gravity and wood hardness parallel and perpendicular to the grain. The purpose is to offer one more tool to help in the decision about wood species choice for use in floors and sleepers. To reach this intent, we considered the results of standard tests (NBR 7190:1997, Timber Structures Design, Annex B, Brazilian Association of Technical Standards) to determine hardness parallel and normal to the grain in fourteen tropical high density wood species (over 850 kg/m(3), at 12% moisture content). For each species twelve determinations were made, based on the material obtained at Sao Carlos and its regional wood market. Statistical analysis led to some expressions to describe the cited properties relationships, with a determination coefficient about 0.8.

Conceptual Design of Monocolumn Production and Storage With Dry Tree Capability

A new concept and a preliminary study for a monocolumn floating unit are introduced, aimed at exploring and producing oil in ultradeep waters. This platform, which combines two relevant features-great oil storage capacity and dry tree production capability-comprises two bodies with relatively independent heave motions between them. A parametric model is used to define the main design characteristics of the floating units. A set of design alternatives is generated using this procedure. These solutions are evaluated in terms of stability requirements and dynamic response. A mathematical model is developed to estimate the first order heave and pitch motions of the platform. Experimental tests are carried out in order to calibrate this model. The response of each body alone is estimated numerically using the WAMIT (R) code. This paper also includes a preliminary study on the platform mooring system and appendages. The study of the heave plates presents the gain, in terms of decreasing the motions, achieved by the introduction of the appropriate appendages to the platform. [DOI: 10.1115/1.4001429]

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

Spatio-temporal variability behavior of land surface soil water content in shrub- and grass-land

The knowledge of the relationship between spatial variability of the surface soil water content (theta) and its mean across a spatial domain (theta(m)) is crucial for hydrological modeling and understanding soil water dynamics at different scales. With the aim to compare the soil moisture dynamics and variability between the two land uses and to explore the relationship between the spatial variability of theta and theta(m), this study analyzed sets of surface theta measurements performed with an impedance soil moisture probe, collected 136 times during a period of one year in two transects covering different land uses, i.e., korshinsk peashrub transect (KPT) and bunge needlegrass transect (BNT), in a watershed of the Loess Plateau, China. Results showed that the temporal pattern of theta behaved similarly for the two land uses, with both relative wetter soils during wet period and relative drier soils during dry period recognized in BNT. Soil moisture tended to be temporally stable among different dates, and more stable patterns could be observed for dates with more similar soil water conditions. The magnitude of the spatial variation of theta in KPT was greater than that in ENT. For both land uses, the standard deviation (SD) of theta in general increased as theta(m) increased, a behavior that could be well described with a natural logarithmic function. Convex relationship of CV and theta(m) and the maximum CV for both land uses (43.5% in KPT and 41.0% in BNT) can, therefore, be ascertained. Geostatistical analysis showed that the range in KPT (9.1 m) was shorter than that in BNT (15.1 m). The nugget effects, the structured variability, hence the total variability increased as theta(m) increased. For both land uses, the spatial dependency in general increased with increasing theta(m). 2011 Elsevier B.V. All rights reserved.

Native tree seedling growth when fertilized with different amounts of dry sewage sludge and mineral fertilizer

The increasing volume of urban sewage nowadays generates considerable amount of sludge to be disposed of. One environmentally adequate destination could be the application of treated and stabilized sludge (biosolids) to forest plantations as fertilizer and soil conditioner. The purpose of this study was to analyze the feasibility of applying sewage sludge, evaluating its effects on native tree seedlings. The species evaluated were aroeira-pimenteira (Schinus terebinthifolia Raddi), cabreuva-vermelha (Myroxy-Ion peruiferum L. f.), pau-de-viola (Cytarexyllum myrianthum Cham), unha-de-vaca (Bauhinia forficata Link), which are usually planted in forest restoration. Seedlings were cultivated in pots, containing a volume of 4 dm(3) of soil, within a greenhouse. The study was developed in the proximity of Campinas, SP, Brazil, and installed in November, 2003. The design was entirely randomized including seven treatments: control; mineral fertilization; and different doses of sewage sludge (biosolids) complemented with potassium, due to the low concentration of this element in the sludge produced by the wastewater treatment plant of Barueri (Metropolitan region of Sao Paulo city). The results showed that the application of different dosages of biosolids promoted different responses in stem height and biomass production. The treatment with 20 g/dm(3) of dry sewage sludge promoted both the highest growth and the highest seedling biomass production, compared to the control treatment. All native tree species treated with the highest dosage of sewage sludge showed a growth similar to that of mineral fertilization. The seedlings of aroeira-pimenteira, pau-de-viola, and unha-de-vaca, all typical species of the initial succession in natural forest ecosystems, grew and produced more biomass than cabreuva-vermelha, a typical species of the final forest succession.

Characterization of tree-rings of Pinus caribaea var. hondurensis Barr. et Golf. trees by X ray densitometry

This work aimed to determining the anatomical structure of wood, through methodology of histology and X-ray densitometry, of resin-tapped and not resin-tapped Pinus caribaea var. hondurensis trees samples, of three diameter classes. Pine trees, in forest plantation established in 1969, in the Ecological Experimental Station of Itirapina, from the Forestry Institute of Sao Paulo State, were measured and stratified into three classes of trunk diameter. The pine trees were resin-tapped since 2004, with the opening of two simultaneous and opposing panels. Sixty samples of pine wood trees were extracted from the tree trunk through a non-destructive method and in the laboratory. Tree rings were determined in the laboratory and wood apparent density by X-ray densitometry. The test results showed that: (i) false tree rings occur in the early wood and late wood of the tree rings due to climate change; (ii) the X-ray densitometry allowed the demarcation of the tree rings limits; (iii) the wood apparent density average was significantly different between the trees in high class diameter and in the medium-low class; (iv) the wood characteristics from the resin-tapped and non resin-tapped faces did not show significant differences.

Tree-ring characterization of Araucaria columnaris Hook and its applicability as a lead indicator in environmental monitoring

Tree-rings have frequently been used for dating of trees and to determine annual growth increments and forest dynamics, but little is known in tropical conditions about their utilization for environmental monitoring. This paper presents the results of Araucaria columnaris tree-ring characterization by wood anatomy and X-ray densitometric analysis and the determination of Pb concentration. Core samples from twelve araucaria trees were extracted from two sites exposed to air pollution due to intense traffic of vehicles and industrial activities. The tree-rings distinctly presented radial variation in early-latewood thickness and density, and characteristics of juvenile and mature wood. Anatomical and X-ray densitometric analysis were useful to delimit the tree-ring boundaries and to date the tree-rings, as well as to prove the annual formation. The lead concentration in annual araucaria tree-rings, analyzed with graphite furnace atomic absorption spectrometry, indicated the seasonal presence of the heavy metal in the environment during the 30 years studied, although the Pb did not affect tree growth. (c) 2008 Elsevier GmbH. All rights reserved.