Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Climate variability and socio-environmental changes in the northern Aegean (NE Mediterranean) during the last 1500 years

We provide new evidence on sea surface temperature (SST) variations and paleoceanographic/paleoenvironmental changes over the past 1500 years for the north Aegean Sea (NE Mediterranean). The reconstructions are based on multiproxy analyses, obtained from the high resolution (decadal to multidecadal) marine record M2 retrieved from the Athos basin. Reconstructed SSTs show an increase from ca. 850 to 950 AD and from ca. 1100 to 1300 AD. A cooling phase of almost 1.5 �C is observed from ca. 1600 AD to 1700 AD. This seems to have been the starting point of a continuous SST warming trend until the end of the reconstructed period, interrupted by two prominent cooling events at 1832 ± 15 AD and 1995 ± 1 AD. Application of an adaptive Kernel smoothing suggests that the current warming in the reconstructed SSTs of the north Aegean might be unprecedented in the context of the past 1500 years. Internal variability in atmospheric/oceanic circulations systems as well as external forcing as solar radiation and volcanic activity could have affected temperature variations in the north Aegean Sea over the past 1500 years. The marked temperature drop of approximately ~2 �C at 1832 ± 15 yr AD could be related to the 1809 АD ‘unknown’ and the 1815 AD Tambora volcanic eruptions. Paleoenvironmental proxy-indices of the M2 record show enhanced riverine/continental inputs in the northern Aegean after ca. 1450 AD. The paleoclimatic evidence derived from the M2 record is combined with a socio-environmental study of the history of the north Aegean region. We show that the cultivation of temperature-sensitive crops, i.e. walnut, vine and olive, co-occurred with stable and warmer temperatures, while its end coincided with a significant episode of cooler temperatures. Periods of agricultural growth in Macedonia coincide with periods of warmer and more stable SSTs, but further exploration is required in order to identify the causal links behind the observed phenomena. The Black Death likely caused major changes in agricultural activity in the north Aegean region, as reflected in the pollen data from land sites of Macedonia and the M2 proxy-reconstructions. Finally, we conclude that the early modern peaks in mountain vegetation in the Rhodope and Macedonia highlands, visible also in the M2 record, were very likely climate-driven.

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Home range and habitat use by the roadside hawk, Rupornis magnirostris (Gmelin, 1788) (Aves: Falcaniformes) in southeastern Brazil

Although most raptor species are found mainly in the tropics, information on their home range and spatial requirements in the Neotropics is still scarce. In this study, we used radio telemetry to evaluate the home range and the habitat use and selection of five Roadside hawks, Rupornis magnirostris (Gmelin, 1788) in a heterogeneous landscape in southeastern Brazil. The average home range size calculated using the adaptive kernel method (95% isopleth) was 126.1ha (47.4-266.7ha), but using the minimum convex polygon method (95% isopleth) it was 143.54ha (32.6-382.3ha). The roadside hawk explored a wide variety of habitats, most of them opportunistically, as suggested in the literature. Despite this, habitat quality could influence home range size and promote habitat selection. The observation of habitat use as expected, as well as the relatively small home range size, could be related to the generalist/opportunistic behaviour of the roadside hawk.

Fungi, mycotoxins and phytoalexin in peanut varieties, during plant growth in the field

The aim of the present study was to analyze the mycobiota, occurrence of mycotoxins (aflatoxins and cyclopiazonic acid), and production of phytoalexin (trans-resveratrol) in two peanut varieties (Runner IAC 886 and Caiapo) during plant growth in the field. Climatic factors (rainfall, relative humidity and temperature) and water activity were also evaluated. The results showed a predominance of Fusarium spp. in kernels and pods, followed by Penicillium spp. and Aspergillus flavus. Aflatoxins were detected in 20% and 10% of samples of the IAC 886 and Caiapo varieties, respectively. Analysis showed that 65% of kernel samples of the IAC 886 variety and 25% of the Caiapo variety were contaminated with cyclopiazonic acid. trans-Resveratrol was detected in 6.7% of kernel samples of the IAC 886 variety and in 20% of the Caiapo variety. However, trans-resveratrol was found in 73.3% of leaf samples in the two varieties studied. (C) 2011 Published by Elsevier Ltd.

Relative populations and toxin production by Aspergillus flavus and Fusarium verticillioides in artificially inoculated corn at various stages of development under field conditions

The presence, development and production of mycotoxins by Aspergillus flavus and Fusarium verticillioides were studied in corn ears under field conditions after artificial contamination of corn silks. The planted area was divided into five treatments: T1, inoculated with A.flavus solution containing 1 x 10(8) spores, ears covered; T2, inoculated with F. verticillioides solution containing 1 X 10(8) spores, ears covered; T3, inoculated with E verticillioides plus A. flavus solution containing 1 x 10(8) spores of each, ears covered; T4, sprayed with sterile phosphate-buffered saline, ears covered; TS, non-sprayed silks, uncovered ears. Soil and air samples were also collected and analysed for the occurrence of fungi. Water activity, relative air humidity, rainfall and temperature were determined to assess the correlation between abiotic factors and the presence of fungi in the samples. Contamination with the inoculated fungus predominated in T1 and T2. In the other treatments, F. verticillioides was the most frequently isolated contaminant irrespective of treatment. Considering the production of mycotoxins, a positive relation between the production of fumonisins B-1 and B-2 and the frequency of F. verticillioides was statistically verified in all treatments. (C) 2007 Society of Chemical Industry.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

New insights on the Lewis acidity of diorganolead(IV) compounds: Diphenyllead(IV) complexes with N,O,S-chelating ligands

The reactions of PbPh2(OAC)(2) with alkylglyoxylate thiosemicarbazones (HRGTSC, R = Et, Bu) afforded complexes of the type [PbPh2(GTSC)] center dot H2O, [PbPh2(RGTSC)(2)] and [PbPh2Cl(BUGTSC)]. The structures of HRGTSC (R = Me, Et, Bu), [PbPh2(OAc)(RGTSC)](R = Me, Et, Bu), [PbPh2Cl(BuGTSC)] and [PbPh2(GTSC)] center dot H2O have been studied by X-ray diffraction. [PbPh2(OAc)(RGTSC)] and [PbPh2(GTSC)] center dot H2O have [PbC2NO3S] kernels and the coordination sphere of the metal is pentagonal bipyramidal. [PbPh2Cl(BuGTSC)] has a [PbC2NOSCI] kernel and the coordination geometry around lead is pentagonal bipyramidal with one vacant site. Analysis of the bond distances in [PbPh2(GTSC)] center dot H2O suggests a significant affinity between diphenyllead(IV) and carboxylate donor groups, supporting a borderline acidic character for this organometallic cation. H-1 and C-13 NMR spectra in DMSO-d(6) suggest the partial dissociation of the acetate in [PbPh2(OAc)(RGTSC)] solutions and indicate some differences in the coordination mode of the two RGTSC(-) ligands in [PbPh2(RGTSC)(2)] complexes. (C) 2007 Elsevier Ltd. All rights reserved.

Xyloglucan nano-aggregates: Physico-chemical characterisation in buffer solution and potential application as a carrier for camptothecin, an anti-cancer drug

In this work, native xyloglucan was extracted from Tamarindus indica seeds (XGT), and its properties in phosphate buffer solution (PBS) were evaluated in comparison with a commercial tamarind kernel powder (TKP). The physico-chemical characteristics of the polysaccharides such as molar mass, critical concentration and intrinsic viscosity were determined. Furthermore, using spectroscopic and microscopy techniques, it was observed that the XGs tested can be considered macromolecules able to aggregate as nano-entities of 60-140 nm. The XGT tended to an ordered and compact spherical conformation determined by the Huggins constant, circular dichroism, atomic force microscopy and transmission electron microscopy. After the determination of the properties in PBS the XGs, at concentrations of 25% above their critical aggregation concentration, were used to encapsulate camptothecin, an anti-cancer drug. The XGT sample showed an encapsulation efficiency of 42% and first-order drug delivery kinetics. These results demonstrated the importance of knowledge of the physico-chemical properties of polysaccharides, for example, to better conduct their biotechnological applications as drug carriers. (C) 2010 Elsevier Ltd. All rights reserved.

Dually discrete spaces

A neighbourhood assignment in a space X is a family O = {O-x: x is an element of X} of open subsets of X such that X is an element of O-x for any x is an element of X. A set Y subset of X is a kernel of O if O(Y) = U{O-x: x is an element of Y} = X. We obtain some new results concerning dually discrete spaces, being those spaces for which every neighbourhood assignment has a discrete kernel. This is a strictly larger class than the class of D-spaces of [E.K. van Douwen, W.F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (2) (1979) 371-377]. (c) 2008 Elsevier B.V. All rights reserved.