The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Tooth Abnormalities of Number and Position in the Permanent Dentition of Patients With Complete Bilateral Cleft Lip and Palate

Objective: To radiographically evaluate the prevalence of tooth abnormalities of number and position in the permanent dentition of individuals with complete bilateral cleft lip and palate. Design: Cross-sectional retrospective. Setting: Hospital for Rehabilitation of Craniofacial Anomalies, University of Sao Paulo, Bauru, Brazil. Patients: Two hundred five individuals with complete bilateral cleft lip and palate. Interventions: Analysis of patient records and panoramic radiographs. Main outcome measures: Evaluation of hypodontia and supernumerary teeth and analysis of the position of the permanent maxillary lateral incisor in relation to the alveolar cleft. Results: Hypodontia was observed in 144 patients (70.2%), and the highest prevalence was observed for the maxillary lateral incisor. When both lateral incisors were present (43%), they were primarily located on the distal side of the cleft (25%). Supernumerary teeth were observed in 11.7% of individuals. Conclusion: Patients with cleft lip and palate presented high prevalence of hypodontia and supernumerary teeth. The prevailing characteristics of their location may suggest the presence of a similar genetic component for the occurrence of hypodontia and cleft.

Morphological properties of superclusters of galaxies

We studied superclusters of galaxies in a volume-limited sample extracted from the Sloan Digital Sky Survey Data Release 7 and from mock catalogues based on a semi-analytical model of galaxy evolution in the Millennium Simulation. A density field method was applied to a sample of galaxies brighter than M(r) = -21+5 log h(100) to identify superclusters, taking into account selection and boundary effects. In order to evaluate the influence of the threshold density, we have chosen two thresholds: the first maximizes the number of objects (D1) and the second constrains the maximum supercluster size to similar to 120 h(-1) Mpc (D2). We have performed a morphological analysis, using Minkowski Functionals, based on a parameter, which increases monotonically from filaments to pancakes. An anticorrelation was found between supercluster richness (and total luminosity or size) and the morphological parameter, indicating that filamentary structures tend to be richer, larger and more luminous than pancakes in both observed and mock catalogues. We have also used the mock samples to compare supercluster morphologies identified in position and velocity spaces, concluding that our morphological classification is not biased by the peculiar velocities. Monte Carlo simulations designed to investigate the reliability of our results with respect to random fluctuations show that these results are robust. Our analysis indicates that filaments and pancakes present different luminosity and size distributions.

The taxonomic position of the pelagic `staurozoan` Tessera gemmaria as a ceriantharian larva

Based on 16 specimens from the Southwestern Atlantic coast (Argentina and Brazil) we reinterpret the taxonomic position of Tessera gemmaria Goy, 1979, a stauromedusa considered as incertae sedis for a long time. Using external morphology, histological preparations and molecular data (16S and COI) we conclude that T. gemmaria is an early stage of a cerinula, the long-lived planktonic larval stage of the Ceriantharia (Anthozoa).

Croton laceratoglandulosus (Euphorbiaceae s.s.), a new glandular-stipulate species from Brazil and Bolivia, and its systematic position based on molecular analysis

Croton laceratoglandulosus, a new species from the dry forests of the Brazilian states of Piaui, Ceara, Bahia and Minas Gerais, and the Bolivian department of Santa Cruz, is described and illustrated here. Molecular sequence data demonstrate that it is most closely related to the taxa of Croton section Cascarilla, and not to sections Medea or Barhamia, which also have glandular calyces and laciniate stipules. (C) 2008 The Linnean Society of London, Botanical Journal of the Linnean Society, 2008, 158, 493-498.

Phylogenetic position of Dendropsophus gaucheri (Lescure and Marty 2000) highlights the need for an in-depth investigation of the phylogenetic relationships of Dendropsophus (Anura: Hylidae)

Dendropsophus gaucheri is a recently described species which inhabits open areas of the eastern part of the Guiana Shield and is currently assigned to the D. parviceps species group based on the presence of a subocular cream spot. Herein we investigate its phylogenetic position including material from the type locality and newly documented populations from Suriname and Brazil based on mtDNA sequences. The species, as well as D. riveroi which is assigned to the D. minimus species group, were recovered nested within the D. microcephalus species group which implies the paraphyly of the three Dendropsophus species groups. Such result, along with other evidences, highlights the need for a thorough revision of the genus. The genetic distances among D. gaucheri samples studied are low confirming their conspecificity and suggesting recent connections among populations from open areas currently isolated by rainforest in the lowlands of the Guiana Shield.

An interleukin-1 beta (IL-1 beta) single-nucleotide polymorphism at position 3954 and red complex periodontopathogens independently and additively modulate the levels of IL-1 beta in diseased periodontal tissues

Inflammatory cytokines such as interieukin-1 beta (IL-1 beta) are involved in the pathogenesis of periodontal diseases. A high individual variation in the levels of IL-10 mRNA has been verified, which is possibly determined by genetic polymorphisms and/or by the presence of periodontopathogens such as Porphyromonas gingivalis, Tannerella forsythia, Treponema denticola, and Aggregatibacter actinomycetemcomitans. In this study, we investigated the role of an IL-10 promoter single-nucleotide polymorphism at position 3954 [IL-1 beta(3954) SNP] and the presence of the periodontopathogens in the determination of the IL-1 beta levels in the periodontal tissues of nonsmoking chronic periodontitis (CP) patients (n = 117) and control (C) subjects in = 175) and the possible correlations with the clinical parameters of the disease. IL-1 beta(3954) SNP was investigated by restriction fragment length polymorphism, while the IL-1 beta levels and the presence of the periodontopathogens were determined by real-time PCR. Similar frequencies of IL-1 beta(3954) SNP were found in the C and CP groups, in spite of a trend toward a higher incidence of T alleles in the CP group. The IL-1 beta (3954) SNP CT and TT genotypes, as well as P. gingivalis, T. forsythia, and T. denticola, were associated with higher IL-1 beta levels and with higher values of the clinical parameters of disease severity. Concomitant analyses demonstrate that IL-1 beta(3954) and the red complex periodontopathogens were found to independently and additively modulate the levels of IL-1 beta in periodontal tissues. Similarly, the concurrent presence of both factors was associated with increased scores of disease severity. IL-1 beta(3954) genotypes and red complex periodontopathogens, individually and additively, modulate the levels of IL-1 beta in the diseased tissues of nonsmoking CP patients and, consequently, are potentially involved in the determination of the disease outcome.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

The position of the Amazonian Craton in supercontinents

This paper examines the extensive regions of Proterozoic accretionary belts that either formed most of the Amazonian Craton, or are marginal to its southeastern border. Their overall geodynamic significance is considered taking into account the paleogeographic reconstruction of Columbia, Rodinia and Gondwana. Amazonia would be part of Columbia together With Laurentia, North China and Baltica, forming a continuous, continental landmass linked by the Paleo- to Mesoproterozoic mobile belts that constitute large portions of it. The Rodinia supercontinent was formed in the Mesoproterozoic by the agglutination of the existing cratonic fragments, such as Laurentia and Amazonia, during contemporary continental collisions worldwide. The available paleomagnetic data suggest that Laurentia and Amazonia remained attached until at least 600 Ma. Since all other cratonic units Surrounding Laurentia have already rifted away by that time, the separation between Amazonia and Laurentia marks the final break-up of Rodinia with the opening of the lapetus ocean. (C) 2009 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.