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.

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.

Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1.

On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.