Multiscale Fractal Descriptors and Polynomial Classifier for Partial Pixels Identification in Regions of Interest of Mammographic Images

Computer systems are used to support breast cancer diagnosis, with decisions taken from measurements carried out in regions of interest (ROIs). We show that support decisions obtained from square or rectangular ROIs can to include background regions with different behavior of healthy or diseased tissues. In this study, the background regions were identified as Partial Pixels (PP), obtained with a multilevel method of segmentation based on maximum entropy. The behaviors of healthy, diseased and partial tissues were quantified by fractal dimension and multiscale lacunarity, calculated through signatures of textures. The separability of groups was achieved using a polynomial classifier. The polynomials have powerful approximation properties as classifiers to treat characteristics linearly separable or not. This proposed method allowed quantifying the ROIs investigated and demonstrated that different behaviors are obtained, with distinctions of 90% for images obtained in the Cranio-caudal (CC) and Mediolateral Oblique (MLO) views.

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the periodic orbits and the integrability of the regularized Hill lunar problem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Plethysms and interacting boson models

A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms. (C) 2003 American Institute of Physics.

Laguerre moments and generalized functions

Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.

Spin-2 Fields and Helicity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hydrothermal rare earth elements mineralization in the Barra do Itapirapua carbonatite, southern Brazil: behaviour of selected trace elements and stable isotopes (C, O)

The Bura do Itapira pua carbonatite is located in southern Brazil and belongs to the Cretaceous Ponta Grossa alkaline-carbonatitic province related to the opening of the South Atlantic. The carbonatite complex is emplaced in Proterozoic granites and is mainly composed of plutonic magnesio- to ferrocarbonatite, with smaller amounts of subvolcanic magnesiocarbonatite. Hydrothermal alteration of the carbonatite has led to the formation of quartz, apatite, fluorite, rue earth fluorocarbonates, barite and sulfides in variable proportions. Trace element data, delta(13)C and delta(18)O are presented here, with the aim of better understanding the geochemical nature of hydrothermal alteration related to rare earth elements (REE) mineralization. The non-overprinted plutonic carbonatite shows the lowest REE contents, and its primitive carbon and oxygen stable isotopic composition places it in the field of primary igneous carbonatites. Two types of hydrothermally overprinted plutonic carbonatites can be distinguished based on secondary minerals and geochemical composition. Type I contains mainly quartz, rare earth fluorocarbonates and apatite as hydrothermal secondary minerals, and has steep chondrite normalized REE patterns, with Sigma(REE+Y) of up to 3 wt.% (i.e., two orders of magnitude higher than in fresh plutonic samples). In contrast, the Type II overprint contains apatite, fluorite and barite as dominant hydrothermal minerals, and is characterized by heavy REE enrichment relative to the fresh samples, with flat chondrite normalized REE patterns. Carbon and oxygen stable isotope ratios of Types I and II are elevated (delta(18)O + 8 to + 12 parts per thousand; delta(13)C - 6 to - 2 parts per thousand) relative to the fresh samples. Hydrothermally overprinted carbonatites exposed to weathering show even higher delta(18)O values (delta(18)O 13 to 25 parts per thousand) but no additional REE enrichment. The subvolcanic carbonatite has anomalously high delta(13)C of up to + 1 parts per thousand, which suggests crustal contamination through interaction with carbonate-bearing metasediments. (C) 1999 Elsevier B.V. B.V. All rights reserved.

The effect of hydrothermal alteration on the Sr and Nd isotopic signatures of the Barra do Itapirapua Carbonatite, Southern Brazil

The Cretaceous Barra do Itapirapua carbonatite in southern Brazil experienced extensive postmagmatic hydrothermal alteration. In this article, Sr and Nd isotope ratios of coexisting samples of hydrothermally overprinted and of preserved, nonoverprinted carbonatite are presented. Hydrothermal alteration caused strong REE enrichment, leading to the formation of minerals of the bastnaesite group. In the overprinted carbonatite, Nd contents reach 4000 ppm, two orders of magnitude higher than in the fresh carbonatite, but epsilon(Nd) varies only within a range of 3.4 units. In contrast, Sr was leached from the carbonatite during the postmagmatic alteration; hence values of around 10,000 ppm in the fresh carbonatite drop to about 1000 ppm in the overprinted samples. Leaching is accompanied by a variation of Sr isotopic composition toward more radiogenic values, resulting in an increase of 15 units in epsilon(Sr). Variation of Sr isotopic composition is related to postmagmatic alteration and is decoupled from the variation of Nd isotopic composition, ruling out heterogeneities in the mantle source as the main cause of isotopic variability in the data set. Furthermore, this cannot be explained by bulk crustal contamination. A two-step model is proposed in which (1) a REE-rich, carbonatite-derived hydrothermal fluid overprinted the pristine carbonatite, causing REE-enrichment with a relative small change of isotopic composition; and (2) crust-derived hydrothermal fluids percolated the cooling carbonatite, leaching the original Sr from the carbonatite and introducing a more radiogenic Sr isotopic signature. The amounts of carbonatite-derived Nd with primitive, carbonatite-like Nd isotope ratios introduced during the first stage of hydrothermal alteration are high enough to buffer the effect of crust-derived Nd on the Nd isotopic composition of the overprinted carbonatite.

Rational approximations of the Arrhenius integral using Jacobi fractions and gaussian quadrature

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimation of (co)variance components and genetic parameters for weights of red-winged tinamou using random regression models

Com este trabalho objetivou-se determinar parâmetros genéticos para peso corporal de perdizes em cativeiro. Foram utilizados modelos de regressão aleatória na análise dos dados considerando os efeitos genéticos aditivos diretos (AD) e de ambiente permanente de animal (AP) como aleatórios. As variâncias residuais foram modeladas utilizando-se funções de variância de ordem 5. A curva média da população foi ajustada por polinômios ortogonais de Legendre de ordem 6. Os efeitos genéticos aditivos diretos e de ambiente permanente de animal foram modelados utilizando-se polinômios de Legendre de segunda a nona ordem. Os melhores resultados foram obtidos pelos modelos de ordem 6 de ajuste para os efeitos genéticos aditivos diretos e de ordem 3 para os de ambiente permanente pelo Critério de Informação de Akaike e ordem 3 para ambos os efeitos pelos Critério de Informação Bayesiano de Schwartz e Teste de Razão de Verossimilhança. As herdabilidades estimadas variaram de 0,02 a 0,57. O primeiro autovalor respondeu por 94 e 90% da variação decorrente de efeitos aditivos diretos e de ambiente permanente, respectivamente. A seleção de perdizes para peso corporal é mais efetiva a partir de 112 dias de idade.