Interactive quadrangulation with reeb atlases and connectivity textures

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user's own subjective requirements.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Interactive Processes among Babies at a Daycare Center

The paper presents a study regarding babies' interactive processes with peers, which aimed to apprehend some of their qualitative aspects, considering babies' peculiarities. An empirical work was conducted with video recording scenes and interviews, regarding the "Babies' Adaptation to a Daycare Center" project, which followed up 21 babies (4-13 months) at a daycare center. Data analysis was based on the Network of Meanings perspective. Five episodes are here presented regarding three focal subjects and their peers. Analysis indicates the occurrence of interactions; among them it can be highlighted the role of the glance, presence of triadic relations (even among babies younger than nine months old), abbreviation of communicative resources and empathy. Moreover, despite verbal language absence at this age, it was verified meaning processes. Some practical-theoretical implications are pointed out as well.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

DNA-Interactive Properties of Crotamine, a Cell-Penetrating Polypeptide and a Potential Drug Carrier

Crotamine, a 42-residue polypeptide derived from the venom of the South American rattlesnake Crotalus durissus terrificus, has been shown to be a cell-penetrating protein that targets chromosomes, carries plasmid DNA into cells, and shows specificity for actively proliferating cells. Given this potential role as a nucleic acid-delivery vector, we have studied in detail the binding of crotamine to single- and double-stranded DNAs of different lengths and base compositions over a range of ionic conditions. Agarose gel electrophoresis and ultraviolet spectrophotometry analysis indicate that complexes of crotamine with long-chain DNAs readily aggregate and precipitate at low ionic strength. This aggregation, which may be important for cellular uptake of DNA, becomes less likely with shorter chain length. 25-mer oligonucleotides do not show any evidence of such aggregation, permitting the determination of affinities and size via fluorescence quenching experiments. The polypeptide binds non-cooperatively to DNA, covering about 5 nucleotide residues when it binds to single (ss) or (ds) double stranded molecules. The affinities of the protein for ss-vs. ds-DNA are comparable, and inversely proportional to salt levels. Analysis of the dependence of affinity on [NaCl] indicates that there are a maximum of,3 ionic interactions between the protein and DNA, with some of the binding affinity attributable to non-ionic interactions. Inspection of the three-dimensional structure of the protein suggests that residues 31 to 35, Arg-Trp-Arg-Trp-Lys, could serve as a potential DNA-binding site. A hexapeptide containing this sequence displayed a lower DNA binding affinity and salt dependence as compared to the full-length protein, likely indicative of a more suitable 3D structure and the presence of accessory binding sites in the native crotamine. Taken together, the data presented here describing crotamine-DNA interactions may lend support to the design of more effective nucleic acid drug delivery vehicles which take advantage of crotamine as a carrier with specificity for actively proliferating cells. Citation: Chen P-C, Hayashi MAF, Oliveira EB, Karpel RL (2012) DNA-Interactive Properties of Crotamine, a Cell-Penetrating Polypeptide and a Potential Drug Carrier. PLoS ONE 7(11): e48913. doi:10.1371/journal.pone.0048913

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

COMPARISON MEASURES OF MAPS GENERATED BY GEOSTATISTICAL METHODS

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Growth hormone pharmacogenetics: the interactive effect of a microsatellite in the IGF1 promoter region with the GHR-exon 3 and-202 A/C IGFBP3 variants on treatment outcomes of children with severe GH deficiency

Insulin-like growth factor type 1 (IGF1) is a mediator of growth hormone (GH) action, and therefore, IGF1 is a candidate gene for recombinant human GH (rhGH) pharmacogenetics. Lower serum IGF1 levels were found in adults homozygous for 19 cytosine-adenosine (CA) repeats in the IGF1 promoter. The aim of this study was to evaluate the influence of (CA)n IGF1 polymorphism, alone or in combination with GH receptor (GHR)-exon 3 and -202 A/C insulin-like growth factor binding protein-3 (IGFBP3) polymorphisms, on the growth response to rhGH therapy in GH-deficient (GHD) patients. Eighty-four severe GHD patients were genotyped for (CA) n IGF1, -202 A/C IGFBP3 and GHR-exon 3 polymorphisms. Multiple linear regressions were performed to estimate the effect of each genotype, after adjustment for other influential factors. We assessed the influence of genotypes on the first year growth velocity (1st y GV) (n = 84) and adult height standard deviation score (SDS) adjusted for target-height SDS (AH-TH SDS) after rhGH therapy (n = 37). Homozygosity for the IGF1 19CA repeat allele was negatively correlated with 1st y GV (P = 0.03) and AH-TH SDS (P = 0.002) in multiple linear regression analysis. In conjunction with clinical factors, IGF1 and IGFBP3 genotypes explain 29% of the 1st y GV variability, whereas IGF1 and GHR polymorphisms explain 59% of final height-target-height SDS variability. We conclude that homozygosity for IGF1 (CA) 19 allele is associated with less favorable short-and long-term growth outcomes after rhGH treatment in patients with severe GHD. Furthermore, this polymorphism exhibits a non-additive interaction with -202 A/C IGFBP3 genotype on the 1st y GV and with GHR-exon 3 genotype on adult height. The Pharmacogenomics Journal (2012) 12, 439-445; doi:10.1038/tpj.2011.13; published online 5 April 2011

The Interactive Effect of GHR-Exon 3 and -202 A/C IGFBP3 Polymorphisms on rhGH Responsiveness and Treatment Outcomes in Patients with Turner Syndrome

Context: There is great interindividual variability in the response to recombinant human (rh) GH therapy in patients with Turner syndrome (TS). Ascertaining genetic factors can improve the accuracy of growth response predictions. Objective: The objective of the study was to assess the individual and combined influence of GHR-exon 3 and -202 A/C IGFBP3 polymorphisms on the short-and long-term outcomes of rhGH therapy in patients with TS. Design and Patients: GHR-exon 3 and -202 A/C IGFBP3 genotyping (rs2854744) was correlated with height data of 112 patients with TS who remained prepubertal during the first year of rhGH therapy and 65 patients who reached adult height after 5 +/- 2.5 yr of rhGH treatment. Main Outcome Measures: First-year growth velocity and adult height were measured. Results: Patients carrying at least one GHR-d3 or -202 A-IGFBP3 allele presented higher mean first-year growth velocity and achieved taller adult heights than those homozygous for GHR-fl or -202 C-IGFBP3 alleles, respectively. The combined analysis of GHR-exon 3 and -202 A/C IGFBP3 genotypes showed a clear nonadditive epistatic influence on adult height of patients with TS treated with rhGH (GHR-exon 3 alone, R-2 = 0.27; -202 A/C IGFBP3, R-2 = 0.24; the combined genotypes, R-2 = 0.37 at multiple linear regression). Together with clinical factors, these genotypes accounted for 61% of the variability in adult height of patients with TS after rhGH therapy. Conclusion: Homozygosity for the GHR-exon3 full-length allele and/or the -202C-IGFBP3 allele are associated with less favorable short-and long-term growth outcomes after rhGH treatment in patients with TS. (J Clin Endocrinol Metab 97: E671-E677, 2012)