Yield mapping, soil fertility and tree gaps in an orange orchard

The current high competition on Citrus industry demands from growers new management technologies for superior efficiency and sustainability. In this context, precision agriculture (PA) has developed techniques based on yield mapping and management systems that recognize field spatial variability, which contribute to increase profitability of commercial crops. Because spatial variability is often not perceived the orange orchards are still managed as uniform and adoption of PA technology on citrus farms is low. Thus, the objective of the present study was to characterize the spatial variability of three factors: fruit yield, soil fertility and occurrence of plant gaps caused by either citrus blight or huanglongbing (HLB) in a commercial Valencia orchard in Brotas, São Paulo State, Brazil. Data from volume, geographic coordinates and representative area of the bags used on harvest were recorded to generate yield points that were then interpolated to produce the yield map. Soil chemical characteristics were studied by analyzing samples collected along planting rows and inter-rows in 24 points distributed in the field. A map of density of tree gaps was produced by georeferencing individual gaps and later by counting the number of gaps within 500 m² cells. Data were submitted to statistical and geostatistical analyses. A t test was used to compare means of soil chemical characteristics between sampling regions. High variation on yield and density of tree gaps was observed from the maps. It was also demonstrated overlapping regions of high density of plant absence and low fruit yield. Soil fertility varied depending on the sampling region in the orchard. The spatial variability found on yield, soil fertility and on disease occurrence demonstrated the importance to adopt site specific nutrient management and disease control as tools to guarantee efficiency of fruit production.

Spatial variability of soil fertility and its relationship with seed physiological potential in a soybean production area

The correlation of soil fertility x seed physiological potential is very important in the area of seed technology but results published with that theme are contradictory. For this reason, this study to evaluate the correlations between soil chemical properties and physiological potential of soybean seeds. On georeferenced points, both soil and seeds were sampled for analysis of soil fertility and seed physiological potential. Data were assessed by the following analyses: descriptive statistics; Pearson's linear correlation; and geostatistics. The adjusted parameters of the semivariograms were used to produce maps of spatial distribution for each variable. Organic matter content, Mn and Cu showed significant effects on seed germination. Most variables studied presented moderate to high spatial dependence. Germination and accelerated aging of seeds, and P, Ca, Mg, Mn, Cu and Zn showed a better fit to spherical semivariogram: organic matter, pH and K had a better fit to Gaussian model; and V% and Fe showed a better fit to the linear model. The values for range of spatial dependence varied from 89.9 m for P until 651.4 m for Fe. These values should be considered when new samples are collected for assessing soil fertility in this production area.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Female fertility in a Guzerat dairy subpopulation: Heterogeneity of variance components for calving intervals

The objectives of the present study were to determine if variance components of calving intervals varied with age at calving and if considering calving intervals as a longitudinal trait would be a useful approach for fertility analysis of Zebu dairy herds. With these purposes, calving records from females born from 1940 to 2006 in a Guzerat dairy subpopulation in Brazil were analyzed. The fixed effects of contemporary groups, formed by year and farm at birth or at calving, and the regressions of age at calving, equivalent inbreeding coefficient and day of the year on the studied traits were considered in the statistical models. In one approach, calving intervals (Cl) were analyzed as a single trait, by fitting a statistical model on which both animal and permanent environment effects were adjusted for the effect of age at calving by random regression. In a second approach, a four-trait analysis was conducted, including age at first calving (AFC) and three different female categories for the calving intervals: first calving females; young females (less than 80 months old, but not first calving); or mature females (80 months old or more). Finally, a two-trait analysis was performed, also including AFC and Cl, but calving intervals were regarded as a single trait in a repeatability model. Additionally, the ranking of sires was compared among approaches. Calving intervals decreased with age until females were about 80 months old, remaining nearly constant after that age. A quasi-linear increase of 11.5 days on the calving intervals was observed for each 10% increase in the female's equivalent inbreeding coefficient. The heritability of AFC was 0.37. For Cl. the genetic-phenotypic variance ratios ranged from 0.064 to 0.141, depending on the approach and on ages at calving. Differences among genetic variance components for calving intervals were observed along the animal's lifetime. Those differences confirmed the longitudinal aspect of that trait, indicating the importance of such consideration when accessing fertility of Zebu dairy females, especially in situations where the available information relies on their calving intervals. Spearman rank correlations among approaches ranged from 0.90 to 0.95, and changes observed in the ranking of sires suggested that the genetic progress of the population could be affected by the approach chosen for the analysis of calving intervals. (C) 2012 Elsevier ay. All rights reserved.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

Abundant and Stable Char Residues in Soils: Implications for Soil Fertility and Carbon Sequestration

Large-scale soil application of biochar may enhance soil fertility, increasing crop production for the growing human population, while also sequestering atmospheric carbon. But reaching these beneficial outcomes requires an understanding of the relationships among biochar's structure, stability, and contribution to soil fertility. Using quantitative C-13 nuclear magnetic resonance (NMR) spectroscopy, we show that Terra Preta soils (fertile anthropogenic dark earths in Amazonia that were enriched with char >800 years ago) consist predominantly of char residues composed of similar to 6 fused aromatic rings substituted by COO- groups that significantly increase the soils' cation-exchange capacity and thus the retention of plant nutrients. We also show that highly productive, grassland-derived soils in the U.S, (Mollisols) contain char (generated by presettlement fires) that is structurally comparable to char in the Terra Preta soils and much more abundant than previously thought (similar to 40-50% of organic C). Our findings indicate that these oxidized char residues represent a particularly stable, abundant, and fertility-enhancing form of soil organic matter.

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

Fertility in Curitiba, Brazil: levels, trends and differentials

Objectives: To identify levels, tendency and recent differentials in fertility in Curitiba, Brazil. Methods: It is a quantitative and temporal series study, in which the birth rates, general and total fertility indicators, for the period of 1995-2007, were calculated and analyzed in Curitiba, Brazil, as well as the proportion of women with high fertility in 2005-2007, compared to the state of Parana. In order to evaluate inner regional differences in the city of Curitiba the same rates were calculated for each one of the administrative districts in the capital. Results: It was noticed a tendency of decline in fertility rates in Curitiba. The total fertility rate in 2007 was 1.49 children per woman and 1.66 in Parana state. The proportion of women with high fertility in the interior of Parana was 1.8 times higher than in the capital. The analysis of fertility rates by districts in Curitiba pointed out important differences: only 10 out of 75 districts had total fertility rates higher than 2.1 children per woman, and 9 districts concentrated 59.6% of women with high fertility. Conclusions: Curitiba showed a quick and sharp reduction in fertility rates. However, the inner regional differences in the city suggests the need to devise actions of reproductive health and social measures, directed to specific groups of population.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

COMPARISON MEASURES OF MAPS GENERATED BY GEOSTATISTICAL METHODS

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.