Biological parameters and population structure of Psammobatis extenta in Ubatuba region, north coast of the State of São Paulo, Brazil

Specimens of the zipper sand skate Psammobatis extenta were collected in the region of Ubatuba off the northern coast of the State of São Paulo, Brazil, monthly for once year (January - December 2000), at 25- to 40-m isobaths. A total of 123 individuals were caught. The total length (TL) of females averaged 224.6 mm, and of males 217 mm. The overall sex ratio was 1:1. Analysis of the length-weight relationship indicated the existence of positive allometry in females, and isometry in males. The length at onset of sexual maturity was determined for both sexes; females reached sexual maturity at smaller sizes than males (TL50 = 230.7 and TL50 = 237.7 mm respectively). Females showed functional parity of both ovaries and uteri. Females that were pregnant or were carrying vitellogenic oocytes were observed during nine of 12 months of the survey, indicating a continuous reproductive cycle. Psammobatis extenta was most abundant from January to April, and again from June to October. Most individuals were collected at the 40-m isobath. Both adults and neonates were collected in the study area. However, adolescent skates were scarce, which either indicates differential occupation of the area, or suggests that the shallow waters of the continental shelf are used as breeding grounds.

Relative growth and morphological sexual maturity of Chasmagnathus granulatus (Crustacea, Varunidae) from a mangrove area in southeastern Brazilian coast

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

Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

Bioecology of the uçá-crab, Ucides cordatus (Linnaeus, 1763), in Vitória Bay, Espírito Santo State, Brazil

A biologia de Ucides cordatus na Baía de Vitória (ES) foi avaliada como subsídio ao manejo populacional. As amostragens ocorreram mensalmente durante um ano (outubro/1998 a setembro/1999), com análise biométrica (LC = largura da carapaça; PE = peso total úmido) e de fatores abióticos em quatro transectos, com quatro faixas cada (margem à região supratidal). A densidade foi de 3,7±1,5 caranguejos.m-2, com incremento em direção à região supratidal, sendo a profundidade das galerias de 1,1±0,3 m. A salinidade da água intersticial diferiu entre as faixas, sendo mais elevada na região supratidal. Houve correlação significativa entre a abundância de exemplares e alguns fatores ambientais, o mesmo ocorrendo quanto as tocas abertas e fechadas. A razão sexual evidenciou um predomínio de fêmeas (1,0M:1,6F), particularmente entre 50 e 75 mm LC. A maior incidência de tocas fechadas ocorreu em agosto e setembro, enquanto as fêmeas ovígeras foram registradas de janeiro a abril. A relação PE/LC mostrou isometria para os machos (PE=0,425.10-3 LC3,0014; R²=0,99) e fêmeas (P=0,439.10-3 LC2,97; R²=0,99). Para o total da população a média de tamanho (LC) e peso (PE) foi de 54,6±11,8 mm e de 77,5±42,4 g, respectivamente. Os dados evidenciam que a população encontra-se sobrexplotada, requerendo manejo adequado para a viabilidade da atividade extrativa na área estudada.

Relating propelinear and binary G-linear codes

In this paper we establish the connections between two different extensions of Z(4)-linearity for binary Hamming spaces, We present both notions - propelinearity and G-linearity - in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and translation-invariant propelinear codes are G-linear codes. (C) 2002 Elsevier B.V. B.V. All rights reserved.

RELATIVE GROWTH OF THE SPECKLED SWIMMING CRAB ARENAEUS-CRIBRARIUS (LAMARCK, 1818) (BRACHYURA, PORTUNIDAE), NEAR UBATUBA, STATE OF SAO-PAULO, BRAZIL

Arenaeus cribrarius is a mainly tropical crab that occurs in the Western Atlantic Ocean, Brazil being its type-locality. The species ranges from Vinevard Sound, Massachusetts, USA to La Paloma, Uruguay. Information about this species is scarce. The relative growth of A. cribrarius was analyzed, based on some morphometric relations, where the carapace width, excluding lateral spines (CW), was used as an independent variable. A total of 403 specimens (189 males and 214 females), was collected in Ubatuba, State of São Paulo, Brazil, with otter-trawls. The animals were sexed and sorted to maturation phase (juvenile or adult). Some measurements were made: carapace (length and width excluding lateral spines), abdomen (greatest width of the fifth somite in females and the sixth in males) and major chela (greatest length, width and height, dactylus length). This study was made by the application of the power function (y=a.x(b)) which was fitted to the data and the pattern of growth established for each parameter by the ''b''-value (constant of allometry), as positive allometry (b>1), negative allometry (b<1) or isometry (b=1). The morphometric relations of the carapace showed a tendency to isometry. In females, the abdominal width grew in positive allometry, higher in juveniles (b=1.33) than in adults (b=1.18). In this case, an overlap and discontinuity was noticed between the phases over a carapace width range of 55 to 70 mm, where the puberty molt occurs. The majority of relationships showed that the major chela of the males grew in positive allometry, however, the greatest allometric difference between the phases was observed towards the propodus length with 1.09 as juvenile and 1.26 as adult ''b''values. In the males, this variable showed an inflection between the CW range of 45' to 55 mm, where the transition to the maturation phase occurs. The relative growth of this species is similar to those of previously studied species. This indicates, that the propodus length and the abdominal width are the morphometric variables most appropriate to estimate the size of the beginning of the sexual maturity for males and females of this species, respectively.

Estudo clínico e eletromiográfico da dinâmica do sistema mastigatório em pacientes adultos com paralisia cerebral

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Avaliação da biologia reprodutiva de Plagioscion squamosissimus (HECKEL, 1840) e Plagioscion surinamensis (BLEEKER, 1873) no terminal de Vila do Conde e área adjacente (Barcarena - PA)

O Porto de Vila do Conde, situado no município de Barcarena/PA, vêm sofrendo diversos desastres ambientais nos últimos anos o que pode eventualmente acarretar no desequilíbrio do uso que os recursos aquáticos fazem do ambiente e no ecossistema como um todo. A pesca artesanal nesta região é bastante relevante, destacando Plagioscion squamosissimus e P. surinamensis que são importantes como fontes de renda e de alimento para a população. O objetivo deste estudo foi descrever as áreas de concentração e a biologia reprodutiva de P. squamosissimus e P. surinamensis na área adjacente ao Porto de Vila do Conde, destacando a importância da utilização destes ambientes para reprodução. Para identificar a época e os pesqueiros de maior abundância foram realizados cálculos de CPUE (Kg/viagem) por meio de dados obtidos no período de junho de 2007 a maio de 2008. A determinação do uso da área para reprodução e a descrição da biologia reprodutiva foi efetuada através da coleta de 40 a 53 indivíduos de cada espécie por bimestre, obtidos pela pesca comercial. Em laboratório, foram obtidos valores de peso e comprimento e as gônadas foram retiradas para a determinação do estágio de maturidade. A abundância de P. squamosissimus é máxima entre setembro a fevereiro e P. surinamensis ocorreu principalmente entre março a maio. A relação peso-comprimento mostrou isometria para as fêmeas de P. squamosissimus e ambos os sexos de P. surinamensis. Apenas os machos da espécie P. squamosissimus apresentaram alometria positiva. A proporção sexual foi favorável aos machos de P. surinamensis (1,05macho: 1fêmea) e favorável às fêmeas (1,11fêmea: 1macho) para P. squamosissimus. O valor de L50 (Tamanho de primeira maturidade) para P. squamosissimus foi 16,14 cm para fêmeas e 21,43 cm para machos. P. surinamensis apresentou valor de L50 de 27,65 cm para fêmeas e 27,13 cm para os machos. O percentual de indivíduos em reprodução da P. squamisissimus é relevante. O pico da reprodução desta espécie (outubro/novembro e fevereiro/março) coincide com o pico de abundância, indicando que esta espécie está na área para reprodução. P. surinamensis apresentou maior porcentagem de indivíduos nos estádios imaturo e em maturação, indicando que a mesma utiliza esta área principalmente como área de criadouro. Os indivíduos que estavam reproduzindo foram mais numerosos entre agosto/setembro e outubro/novembro.

Uma abordagem de isometria em sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aprendendo isometria com mosaicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Allometric growth of two species of Ephemeroptera from Neotropical mountains streams

The present study evaluated the relative growth and allometry of Massartella brieni Lestage and Thraulodes sp. (Leptophlebiidae: Ephemeroptera). The morphometric analysis was based on 23 measurements and was conducted using a multivariate approach. Throughout postembryonic ontogeny, all of the head measurements, including those of the mouthparts, exhibited negative allometric growth. The mesothorax and wing pad exhibited positive allometric growth. The hind legs lengths in M. brieni and the fore and hind legs lengths in Thraulodes sp. exhibited positive allometry. The abdominal length in these two species exhibited positive allometric growth. Positive allometry was also observed along the abdomen width for M. brieni, and isometry was observed for Thraulodes sp. The relative strengthening of the thorax (in preparation for the winged stage) and the relative increase in the abdomen (which may be related to the development of the reproductive structures) during growth indicate that many of the structures that exhibit positive allometric growth are related to the transition from the aquatic to the adult stage of development.

Contribution to the biology and fishery of the deep-water red crab, Chaceon Affinis (A. Milne-Edwards & Bouvier, 1894) (Decapoda, Brachyura, Geryonidae) in deep waters of the Canary Islands (Central-East Atlantic)

[EN] This crab was captured in the whole range of depths sampled, although its highest abundance was found between 600 and 800 m, on muddy-rocky bottoms. Moreover, significant differences were observed in the average weight and length, according to depth of capture, island of origin, and date of survey. In general, the b parameter of length-weight relationship indicates a negative allometric growth pattern, although in some cases it was not statistically different from isometry, particularly in males. Males were heavier, larger, and more abundant in catches than females.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Morphometric measurements throughout ontogeny of selected planktic foraminiferal test species

Development plays an important part in shaping adult morphology and morphological disparity, yet its influence on evolutionary processes is seldom explored because of a lack of preservation of ontogenetic stages in the fossil record. By preserving their entire ontogenetic history within their test, and with the advent of high-resolution imaging techniques, planktic foraminifera allow us to investigate the influence of developmental constraints on disparity. Using Synchrotron radiation X-ray tomographic microscopy (SRXTM), we reconstruct the ontogenetic progression of seven species across several of the major morphotypic groups of planktic foraminifera, including morphotypes of a species exhibiting high phenotypic plasticity and closely related pseudo-cryptic sister-taxa. We show differences in growth patterns between the globigerinid species, which appear more tightly regulated within the framework of isometry from the neanic stage, and the globorotaliid species, whose adult stages present allometric trends. Morphological change through ontogeny results in a change in surface area to volume ratios. Different metabolic processes therefore dominate at different stages of ontogeny, changing the vulnerability of the organism to environmental influences over growth, from factors affecting diffusion rates in the juvenile to those affecting energy supply in the adult. These findings identify some of the parameters within which evolutionary mechanisms have to act.