FRUIT MORPHOLOGY AND PRODUCTIVITY OF BABASSU PALMS IN NORTHERN MINAS GERAIS STATE, BRAZIL1

ABSTRACT The objectives of this study were to morphologically characterize fruits of the babassu palm tree (Attalea vitrivir) and to estimate their productivity in the north of Minas Gerais State, Brazil. Twenty mature fruits were collected from 10 plants in three different areas in Januária, Minas Gerais. Eighteen biometric parameters of the fruits were measured, the oil contents of the seeds was determined, the adherence to normal distribution was evaluated, distribution frequencies were evaluated and the effects of individuals and areas on the variables and the correlations between them were analyzed. The production of fruit bunches per plant and the number of fruits per bunch from 10 plants were quantified in three areas and the potential production under both natural harvesting and cultivation conditions were estimated. Significant differences were found among all of the biometric parameters examined between the different individuals and the different areas, which shows wide morphological variability in the fruits. The average oil content was 45.7%, but with significant differences among individuals. The observed variability favors the selection of productive individuals in genetic improvement programs. The potential productivity of endocarps and oil based on a density of 400/plants per hectare would be respectively 6.4 and 1.2 tons/ha, which indicates the possibility of using A. vitrivir for producing charcoal, bio fuels, and for carbon fixation.

Spatial variability of leaf nutrient contents in a drip irrigated citrus orchard

This study aimed to evaluate the spatial variability of leaf content of macro and micronutrients. The citrus plants orchard with 5 years of age, planted at regular intervals of 8 x 7 m, was managed under drip irrigation. Leaf samples were collected from each plant to be analyzed in the laboratory. Data were analyzed using the software R, version 2.5.1 Copyright (C) 2007, along with geostatistics package GeoR. All contents of macro and micronutrients studied were adjusted to normal distribution and showed spatial dependence.The best-fit models, based on the likelihood, for the macro and micronutrients were the spherical and matern. It is suggest for the macronutrients nitrogen, phosphorus, potassium, calcium, magnesium and sulfur the minimum distances between samples of 37; 58; 29; 63; 46 and 15 m respectively, while for the micronutrients boron, copper, iron, manganese and zinc, the distances suggests are 29; 9; 113; 35 and 14 m, respectively.

Monte Carlo Hypothesis Testing with The Sharpe Ratio

The purpose of this master thesis was to perform simulations that involve use of random number while testing hypotheses especially on two samples populations being compared weather by their means, variances or Sharpe ratios. Specifically, we simulated some well known distributions by Matlab and check out the accuracy of an hypothesis testing. Furthermore, we went deeper and check what could happen once the bootstrapping method as described by Effrons is applied on the simulated data. In addition to that, one well known RobustSharpe hypothesis testing stated in the paper of Ledoit and Wolf was applied to measure the statistical significance performance between two investment founds basing on testing weather there is a statistically significant difference between their Sharpe Ratios or not. We collected many literatures about our topic and perform by Matlab many simulated random numbers as possible to put out our purpose; As results we come out with a good understanding that testing are not always accurate; for instance while testing weather two normal distributed random vectors come from the same normal distribution. The Jacque-Berra test for normality showed that for the normal random vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal distribution in contrast 5,3% and 4,3% failed to shown the truth already known; but when we introduce the bootstrapping methods by Effrons while estimating pvalues where the hypothesis decision is based, the accuracy of the test was 100% successful. From the above results the reports showed that bootstrapping methods while testing or estimating some statistics should always considered because at most cases the outcome are accurate and errors are minimized in the computation. Also the RobustSharpe test which is known to use one of the bootstrapping methods, studentised one, were applied first on different simulated data including distribution of many kind and different shape secondly, on real data, Hedge and Mutual funds. The test performed quite well to agree with the existence of statistical significance difference between their Sharpe ratios as described in the paper of Ledoit andWolf.

Erythrocyte phosphoglucomutase activity of bipolar I patients currently using lithium or carbamazepine

Lithium has been used for the last five decades to treat bipolar disorder, but the molecular basis of its therapeutic effect is unknown. Phosphoglucomutase is a key enzyme in the metabolism of glycogen. In yeast, rabbit and human HEK293 cells, it is inhibited by lithium in the therapeutic concentration range. We measured the phosphoglucomutase activity in erythrocytes and the inhibitor constant for lithium in a population of healthy subjects and compared them to those of bipolar patients treated with lithium or carbamazepine. The specific activity of phosphoglucomutase measured in vitro in erythrocytes from control subjects presented a normal distribution, with the difference between the lowest and the highest activity being approximately 2-fold (0.53-1.10 nmol mg Hb-1 min-1). Comparison of phosphoglucomutase activity in untreated bipolar patients and control subjects showed no significant difference, whereas comparison between bipolar patients treated with carbamazepine or lithium revealed significantly lower mean values in patients treated with carbamazepine (747.3 ± 27.6 vs 879.5 ± 35.9 pmol mg Hb-1 min-1, respectively). When we studied the concentration of lithium needed to inhibit phosphoglucomutase activity by 50%, a bimodal distribution among the population tested was obtained. The concentration of LiCl needed to inhibit phosphoglucomutase activity by 50% was 0.35 to 1.8 mM in one group of subjects and in the other it was 3 to 4 mM. These results suggest that phosphoglucomutase activity may be significant in patients with bipolar disorder treated with lithium and carbamazepine.

A morphometric study of the lumbar spinous process in the Chinese population

Our goal was to analyze the anatomical parameters of the lumbar spine spinous process for an interspinous stabilization device designed for the Chinese population and to offer an anatomical basis for its clinical application. The posterior lumbar spines (T12-S1) of 52 adult cadavers were used for measuring the following: distance between two adjacent spinous processes (DB), distance across two adjacent spinous processes (DA), thickness of the central spinous processes (TC), thickness of the superior margin of the spinous processes (TS), thickness of the inferior margin of the spinous processes (TI), and height of the spinous processes (H). Variance and correlation analyses were conducted for these data, and the data met the normal distribution and homogeneity of variance. DB decreased gradually from L1-2 to L5-S1. DA increased from T12-L1 to L2-3 and then decreased from L2-3 to L4-5. The largest H in males was noted at L3 (25.45±5.96 mm), whereas for females the largest H was noted at L4 (18.71±4.50 mm). Usually, TS of the adjacent spinous process was lower than TI. Based on the anatomical parameters of the lumbar spinous processes obtained in this study, an “H”-shaped coronal plane (posterior view) was proposed as an interspinous stabilization device for the Chinese population. This study reports morphometric data of the lumbar spinous processes in the Chinese population, which provides an anatomical basis for future clinical applications.

Educators' attitudes to philosophies of music education

This study used Q methodology to measure the extent to which individuals with five educational roles (student teacher, elementary music teacher, principal, high school music teacher, and music consultant) held five proposed philosophies of music education (hedonic, utilitarian, aesthetic cognitivism, aesthetic formalist, and praxial). Twenty-seven sUbjects participated in the Q study. These subjects were a convenience sample based on their educational role, accessibility, and willingness to participate. Participants completed a background sheet which indicated their background in music, and their responsibility for teaching music. The sUbjects in this Q study rank-ordered a set of 60 Q sort items (each item representing a proposed philosophical position) twice: Sort P to reflect current practice, and Sort I to reflect the ideal situation. The results of the sorting procedures were recorded by the participant on the response page which organized the rankings according to an approximated normal distribution as required by Q methodology. The analysis of the data suggested that the comparison across philosophical positions was significant and that the results of the interaction between philosophical position and educational role were significant, although educational role alone was not significant. Post-hoc analysis of the data was used to determine the significant differences between the levels of the, independent variables used in the model: philosophical position, educational role, and music background. A model of the association of the five philosophical positions was presented and discussed in relation to the Q study results. Further research could refine the Q sort items to better reflect each philosophical position.

The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Convex linear combination processes for compositions

Aitchison and Bacon-Shone (1999) considered convex linear combinations of compositions. In other words, they investigated compositions of compositions, where the mixing composition follows a logistic Normal distribution (or a perturbation process) and the compositions being mixed follow a logistic Normal distribution. In this paper, I investigate the extension to situations where the mixing composition varies with a number of dimensions. Examples would be where the mixing proportions vary with time or distance or a combination of the two. Practical situations include a river where the mixing proportions vary along the river, or across a lake and possibly with a time trend. This is illustrated with a dataset similar to that used in the Aitchison and Bacon-Shone paper, which looked at how pollution in a loch depended on the pollution in the three rivers that feed the loch. Here, I explicitly model the variation in the linear combination across the loch, assuming that the mean of the logistic Normal distribution depends on the river flows and relative distance from the source origins

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

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