On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

Coincidence theorems and its applications to equilibrium problems

Given two maps h : X x K -> R and g : X -> K such that, for all x is an element of X, h(x, g(x)) = 0, we consider the equilibrium problem of finding (x) over tilde is an element of X such that h((x) over tilde, g(x)) >= 0 for every x is an element of X. This question is related to a coincidence problem.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Geographical distribution of American cutaneous leishmaniasis and its phlebotomine vectors (Diptera: Psychodidae) in the state of Sao Paulo, Brazil

Background: American cutaneous leishmaniasis (ACL) is a re-emerging disease in the state of Sao Paulo, Brazil. It is important to understand both the vector and disease distribution to help design control strategies. As an initial step in applying geographic information systems (GIS) and remote sensing (RS) tools to map disease-risk, the objectives of the present work were to: (i) produce a single database of species distributions of the sand fly vectors in the state of Sao Paulo, (ii) create combined distributional maps of both the incidence of ACL and its sand fly vectors, and (iii) thereby provide individual municipalities with a source of reference material for work carried out in their area. Results: A database containing 910 individual records of sand fly occurrence in the state of Sao Paulo, from 37 different sources, was compiled. These records date from between 1943 to 2009, and describe the presence of at least one of the six incriminated or suspected sand fly vector species in 183/645 (28.4%) municipalities. For the remaining 462 (71.6%) municipalities, we were unable to locate records of any of the six incriminated or suspected sand fly vector species (Nyssomyia intermedia, N. neivai, N. whitmani, Pintomyia fischeri, P. pessoai and Migonemyia migonei). The distribution of each of the six incriminated or suspected vector species of ACL in the state of Sao Paulo were individually mapped and overlaid on the incidence of ACL for the period 1993 to 1995 and 1998 to 2007. Overall, the maps reveal that the six sand fly vector species analyzed have unique and heterogeneous, although often overlapping, distributions. Several sand fly species - Nyssomyia intermedia and N. neivai - are highly localized, while the other sand fly species - N. whitmani, M. migonei, P. fischeri and P. pessoai - are much more broadly distributed. ACL has been reported in 160/183 (87.4%) of the municipalities with records for at least one of the six incriminated or suspected sand fly vector species, while there are no records of any of these sand fly species in 318/478 (66.5%) municipalities with ACL. Conclusions: The maps produced in this work provide basic data on the distribution of the six incriminated or suspected sand fly vectors of ACL in the state of Sao Paulo, and highlight the complex and geographically heterogeneous pattern of ACL transmission in the region. Further studies are required to clarify the role of each of the six suspected sand fly vector species in different regions of the state of Sao Paulo, especially in the majority of municipalities where ACL is present but sand fly vectors have not yet been identified.

Clinical evaluation and COL2A1 gene analysis in 21 Brazilian families with Stickler syndrome: Identification of novel mutations, further genotype/phenotype correlation, and its implications for the diagnosis

We present clinical and molecular evaluation from a large cohort of patients with Stickler syndrome: 78 individuals from 21 unrelated Brazilian families. The patients were selected in a Hospital with a craniofacial dysmorphology assistance service and clinical diagnosis was based on the presence of cleft palate associated to facial and ocular anomalies of Stickler syndrome. Analysis of COL2A1 gene revealed 9 novel and 4 previously described pathogenic mutations. Except for the mutation c.556G>T (p.Gly186X), all the others were located in the triple helical domain. We did not find genotype/phenotype correlation in relation to type and position of the mutation in the triple helical domain. However, a significantly higher proportion of myopia in patients with mutations located in this domain was observed in relation to those with the mutation in the non-tripe helical domain (c.556G>T; P < 0.04). A trend towards a higher prevalence of glaucoma, although not statistically significant, was observed in the presence of the mutation c.556G>T. It is possible. that this mutation alters the splicing of the mRNA instead of only creating a premature stop codon and therefore it can lead to protein products of different ocular effects. One novel DNA variation (c.1266+7G>C) occurs near a splice site and it was observed to co-segregate with the phenotype in one of the two families with this DNA variation. As in silico analysis predicted that the c.1266+7G>C DNA variation can affect the efficiency of the splicing, we still cannot rule it out as non-pathogenic. Our study also showed that ascertainment through cleft palate associated to other craniofacial signs can be very efficient for identification of Stickler syndrome patients. Still, high frequency of familial cases and high frequency of underdevelopment of distal lateral tibial epiphyses observed in our patients suggested that the inclusion of this information can improve the clinical diagnosis of Stickler syndrome. (C) 2008 Elsevier Masson SAS. All rights reserved.

Alcantarea (Bromeliaceae) leaf anatomical characterization and its systematic implications

Alcantarea (Bromeliaceae) has 26 species that are endemic to eastern Brazil, occurring mainly on gneiss-granitic rock outcrops (`inselbergs`). Alcantarea has great ornamental potential and several species are cultivated in gardens. Limited data is available in the literature regarding the leaf anatomical features of the genus, though it has been shown that it may provide valuable information for characterizing of Bromeliaceae taxa. In the present work, we employed leaf anatomy to better characterize the genus and understand its radiation into harsh environments, such as inselbergs. We also searched for characteristics potentially useful in phylogenetic analyses and in delimiting Alcantarea and Vriesea. The anatomical features of the leaves, observed for various Alcantarea species, are in accordance with the general pattern shown by other Bromeliaceae members. However, some features are notable for their importance for sustaining life on rock outcrops, such as: small epidermal thick-walled cells, uneven sinuous epidermal walls, hypodermis often differentiated into lignified layers with thick-walled cells, aquiferous hypodermis bearing collapsible cells, and the presence of well developed epicuticular stratum. Alcantarea leaves tend to show different shapes in the spongy parenchyma, and have chlorenchymatous palisade parenchyma arranged in more well-defined arches, when compared to Vriesea species from the same habitat.

Morphology and anatomy of inflorescence and inflorescence axis in Paepalanthus sect. Diphyomene Ruhland (Eriocaulaceae, Poales) and its taxonomic implications

Paepalanthus sect. Diphyomene has inflorescences arranged in umbels. The underlying bauplan seems however to be more complex and composed of several distinct subunits. Despite appearing superficially very similar, the morphology and anatomy of the inflorescences can supply useful information for the understanding of the phylogeny and taxonomy of the group. Inflorescences of Paepalanthus erectifolius, Paepalanthus flaccidus, Paepalanthus giganteus, and Paepalanthus polycladus were analyzed in regard to branching pattern and anatomy. In P. erectifolius, P. giganteus and P. polycladus the structure is a tribotryum, with terminal dibotryum, and with pherophylls bearing lateral dibotrya. In P. flaccidus, the inflorescence is a pleiobotryum, with terminal subunit, and without pherophylls. Secondary inflorescences may occur in all species without regular pattern. Especially when grown in sites without a pronounced seasonality, the distinction between enrichment zone (part of the same inflorescence) and new inflorescences may be obscured. The main anatomical features supplying diagnostic and phylogenetic information are as follows: (a) in the elongated axis, the thickness of the epidermal cell walls and the cortex size; (b) in the bracts, the quantity of parenchyma cells (c) in the scapes, the shape and the presence of a pith tissue. Therefore, P. sect. Diphyomene can be divided in two groups; group A is represented by P. erectifolius, P. giganteus and P. polycladus, and group B is represented by P. flaccidus. The differentiation is based in both, inflorescence structure and anatomy. Group A presents a life cycle and anatomical features similar to species of Actinocephalus. Molecular trees also point that these two groups are closely related. However, inflorescence morphology and blooming sequence are different. Species of group B present an inflorescence structure and anatomical features shared with many genera and species in Eriocaulaceae. The available molecular and morphology based phylogenies still do not allow a precise allocation of the group in the bulk of basal species of Paepalanthus collocated in P. sect. Variabiles. The characters described and used here supply however important information towards this goal. (C) 2009 Elsevier GmbH. All rights reserved.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of Sao Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model. (C) 2008 Elsevier B.V. All rights reserved.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Effect of SO(2) on the Transport Properties of an Imidazolium Ionic Liquid and Its Lithium Solution

Transport coefficients have been measured as a function of the concentration of sulfur dioxide, SO(2), dissolved in 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)-imide, [BMMI][Tf(2)N], as well as in its lithium salt solution, Li[Tf(2)N]. The SO(2) reduces viscosity and density and increases conductivity and diffusion coefficients in both the neat [BMMI] [Tf(2)N] and the [BMMI][Tf(2)N]-Li[Tf(2)N] solution. The conductivity enhancement is not assigned to a simple viscosity effect; the weakening of ionic interactions upon SO(2) addition also plays a role. Microscopic details of the SO(2) effect were unraveled using Raman spectroscopy and molecular dynamics (MD) simulations. The Raman spectra suggest that the Li(+)-[Tf(2)N] interaction is barely affected by SO(2), and the SO(2)-[Tf(2)N] interaction is weaker than previously observed in an investigation of an ionic liquid containing the bromide anion. Transport coefficients calculated by MD simulations show the same trend as the experimental data with respect to SO(2) content. The MD simulations provide structural information on SO(2) molecules around [Tf(2)N], in particular the interaction of the sulfur atom of SO(2) with oxygen and fluorine atoms of the anion. The SO(2)-[BMMI] interaction is also important because the [BMMI] cations with above-average mobility have a larger number of nearest-neighbor SO(2) molecules.