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.

Computer simulation study of collective dynamics in the glass former Ca(NO3)(2)center dot 4H(2)O

Time correlation functions of current fluctuations were calculated by molecular dynamics (MD) simulations in order to investigate sound waves of high wavevectors in the glass-forming liquid Ca(NO3)(2)center dot 4H(2)O. Dispersion curves, omega(k), were obtained for longitudinal (LA) and transverse acoustic (TA) modes, and also for longitudinal optic (LO) modes. Spectra of LA modes calculated by MD simulations were modeled by a viscoelastic model within the memory function framework. The viscoelastic model is used to rationalize the change of slope taking place at k similar to 0.3 angstrom(-1) in the omega(k) curve of acoustic modes. For still larger wavevectors, mixing of acoustic and optic modes is observed. Partial time correlation functions of longitudinal mass currents were calculated separately for the ions and the water molecules. The wavevector dependence of excitation energies of the corresponding partial LA modes indicates the coexistence of a relatively stiff subsystem made of cations and anions, and a softer subsystem made of water molecules. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4751548]

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.

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'.

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.

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.

Effect of Si addition on Ca- and P-impregnated implant surfaces with nanometer-scale roughness: an experimental study in dogs

Objectives: To investigate the effect of Si addition on a nanometer-scale roughness Ca and P implant surfaces in a canine tibia model by biomechanical and histomorphometric evaluations. Material and methods: The implant surfaces comprised a resorbable media CaP microblasted (control) and a CaP resorbable media + silica-boost microblasted (experimental) surfaces. Surfaces were characterized by scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and optical interferometry (IFM) down to the nanometric level. The animal model involved the bilateral placement of control (n = 24) and experimental surface (n = 24) implants along the proximal tibiae of six dogs, remaining in vivo for 2 or 4 weeks. After euthanization, half of the specimens were torquedto- interface failure, and the other half was subjected to histomorphologic and bone-to-implant contact (BIC) evaluation. Torque and BIC statistical evaluation was performed by the Friedman test at 95% level of significance, and comparisons between groups was performed by the Dunn test. Results: IFM and SEM observations depicted comparable roughness parameters for both implant surfaces on the micrometer and nanometer scales. XPS analysis revealed similar chemical composition, except for the addition of Si on the experimental group. Torque-to-interface failure and BIC mean values showed no significant differences (P = 0.25 and 0.51, respectively) at both 2- and 4-week evaluation points for experimental and control groups. Early bone healing histomorphologic events were similar between groups. Conclusions: The experimental surface resulted in not significantly different biomechanical fixation and BIC relative to control. Both surfaces were biocompatible and osseoconductive.

Molecular characterization of a phytoplasma of group 16SrIX related to 'Ca. Phytoplasma phoenicium' in periwinkle in Brazil

Periwinkle (Catharanthus roseus), a tropical perennial plant, was found to be infected by a phytoplasma. Plants exhibiting virescence, phyllody and variegation symptoms were collected in the states of Minas Gerais and Sao Paulo, Brazil. The phytoplasma was transmitted by grafting from an infected periwinkle plant to healthy plants and by dodder to a citrus plant. Phytoplasma isolates from periwinkle plants from Brazil had the 16S rDNA gene sequenced and were classified in the 16SrIX group, subgroup A, belonging to the 'Candidatus P. phoenicium' species.

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.

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.

Impaired beta-adrenoceptor-induced relaxation in small mesenteric arteries from DOCA-salt hypertensive rats is due to reduced K-Ca channel activity

beta-Adrenoceptor (beta-AR)-mediated relaxation plays an important role in the regulation of vascular tone. beta-AR-mediated vascular relaxation is reduced in various disease states and aging. We hypothesized that beta-AR-mediated vasodilatation is impaired in DOCA-salt hypertension due to alterations in the cAMP pathway. beta-AR-mediated relaxation was determined in small mesenteric arteries from DOCA-salt hypertensive and control uninephrectomized (Uni) rats. To exclude nitric oxide (NO) and cyclooxygenase (COX) pathways, relaxation responses were determined in the presence of L-NNA and indomethacin, NO synthase inhibitor and COX inhibitors, respectively. Isoprenaline (ISO)-induced relaxation was reduced in arteries from DOCA-salt compared to Uni rats. Protein kinase A (PKA) inhibitors (H89 or Rp-cAMPS) or adenylyl cyclase inhibitor (SQ22536) did not abolish the difference in ISO-induced relaxation between the groups. Forskolin (adenylyl cyclase activator)-induced relaxation was similar between the groups. The inhibition of IKCa/SKCa channels (TRAM-34 plus UCL1684) or BKCa channels (iberiotoxin) reduced ISO-induced relaxation only in Uni rats and abolished the relaxation differences between the groups. The expression of SKCa channel was decreased in DOCA-salt arteries. The expression of BKCa channel a subunit was increased whereas the expression of BKCa channel p subunit was decreased in DOCA-salt arteries. The expression of receptor for activated C kinase 1 (RACK1), which is a binding protein for BKG, channel and negatively modulates its activity, was increased in DOCA-salt arteries. These results suggest that the impairment of beta-AR-mediated relaxation in DOCA-salt mesenteric arteries may be attributable to altered IKCa/SKCa and/or BKCa channels activities rather than cAMP/PKA pathway. Impaired beta-AR-stimulated BKCa channel activity may be due to the imbalance between its subunit expressions and RACK1 upregulation. (C) 2012 Elsevier Ltd. All rights reserved.

Chronic Stress Improves the Myocardial Function without Altering L-type Ca+2 Channel Activity in Rats

Background: Chronic stress is associated with cardiac remodeling; however the mechanisms have yet to be clarified. Objective: The purpose of this study was test the hypothesis that chronic stress promotes cardiac dysfunction associated to L-type calcium Ca2+ channel activity depression. Methods: Thirty-day-old male Wistar rats (70 - 100 g) were distributed into two groups: control (C) and chronic stress (St). The stress was consistently maintained at immobilization during 15 weeks, 5 times per week, 1h per day. The cardiac function was evaluated by left ventricular performance through echocardiography and by ventricular isolated papillary muscle. The myocardial papillary muscle activity was assessed at baseline conditions and with inotropic maneuvers such as: post-rest contraction and increases in extracellular Ca2+ concentration, in presence or absence of specific blockers L-type calcium channels. Results: The stress was characterized for adrenal glands hypertrophy, increase of systemic corticosterone level and arterial hypertension. The chronic stress provided left ventricular hypertrophy. The left ventricular and baseline myocardial function did not change with chronic stress. However, it improved the response of the papillary muscle in relation to positive inotropic stimulation. This function improvement was not associated with the L-type Ca2+ channel. Conclusion: Chronic stress produced cardiac hypertrophy; however, in the study of papillary muscle, the positive inotropic maneuvers potentiated cardiac function in stressed rats, without involvement of L-type Ca2+ channel. Thus, the responsible mechanisms remain unclear with respect to Ca2+ influx alterations. (Arq Bras Cardiol 2012;99(4):907-914)