ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

Saccharification of Brazilian sisal pulp: evaluating the impact of mercerization on non-hydrolyzed pulp and hydrolysis products

Cultivation of sisal, a plant with a short growth cycle, is highly productive in Brazil. This work is part of extensive research in which sisal is valued. In these studies, sisal fibers are used in the preparation of bio-based composites and in the derivatization of the pulp, including posterior preparation of films. This study aimed to examine the use of sisal pulp in the production of bioethanol, which can potentially be a high efficiency process because of the cellulose content of this fiber. A previous paper addressed the hydrolysis of sisal pulp using sulfuric acid as a catalyst. In the present study, the influence of the mercerization process on the acid hydrolysis of sisal pulp was evaluated. Mercerization was achieved in a 20% wt NaOH solution, and the cellulosic pulp was suspended and vigorously mixed for 1, 2 and 3 h, at 50 A degrees C. The previously characterized mercerized pulps were hydrolyzed (100 A degrees C, 30% H2SO4, v/v), and the results are compared with those obtained for unmercerized pulp (described in a companion paper). The starting sample was characterized by viscometry, alpha-cellulose content, crystallinity index and scanning electron microscopy. During the reactions, aliquots were withdrawn, and the liquor was analyzed by HPLC. The residual pulps (non-hydrolyzed) were also characterized by the techniques described for the initial sample. The results revealed that pretreatment decreases the polyoses content as well as causes a decrease of up to 23% in the crystallinity and up to 21% in the average molar mass of cellulose after 3 h of mercerization. The mercerization process proved to be very important to achieve the final target. Under the same reaction conditions (30% and 100 A degrees C, 6 h), the hydrolysis of mercerized pulp generated yields of up to 50% more glucose. The results of this paper will be compared with the results of subsequent studies obtained using other acids, and enzymes, as catalysts.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.

Correlation between carotid bifurcation calcium burden on non-enhanced CT and percentage stenosis, as confirmed by digital subtraction angiography

Objectives: Previous evidence supports a direct relationship between the calcium burden (volume) on post-contrast CT with the percent internal carotid artery (ICA) stenosis at the carotid bifurcation. We sought to further investigate this relationship by comparing non-enhanced CT (NECT) and digital subtraction angiography (DSA). Methods: 50 patients (aged 41-82 years) were retrospectively identified who had undergone cervical NECT and DSA. A 64-multidetector array CT (MDCT) scanner was utilised and the images reviewed using preset window widths/levels (30/300) optimised to calcium, with the volumes measured via three-dimensional reconstructive software. Stenosis measurements were performed on DSA and luminal diameter stenoses >40% were considered "significant". Volume thresholds of 0.01, 0.03, 0.06, 0.09 and 0.12 cm(3) were utilised and Pearson's correlation coefficient (r) was calculated to correlate the calcium volume with percent stenosis. Results: Of 100 carotid bifurcations, 88 were available and of these 7 were significantly stenotic. The NECT calcium volume moderately correlated with percent stenosis on DSA r=0.53 (p<0.01). A moderate-strong correlation was found between the square root of calcium volume on NECT with percent stenosis on DSA (r=0.60, p<0.01). Via a receiver operating characteristic curve, 0.06 cm(3) was determined to be the best threshold (sensitivity 100%, specificity 90.1%, negative predictive value 100% and positive predictive value 46.7%) for detecting significant stenoses. Conclusion: This preliminary investigation confirms a correlation between carotid bifurcation calcium volume and percent ICA stenosis and is promising for the optimal threshold for stenosis detection. Future studies could utilise calcium volumes to create a "score" that could predict high grade stenosis.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Simcluster: clustering enumeration gene expression data on the simplex space

Abstract Background Transcript enumeration methods such as SAGE, MPSS, and sequencing-by-synthesis EST "digital northern", are important high-throughput techniques for digital gene expression measurement. As other counting or voting processes, these measurements constitute compositional data exhibiting properties particular to the simplex space where the summation of the components is constrained. These properties are not present on regular Euclidean spaces, on which hybridization-based microarray data is often modeled. Therefore, pattern recognition methods commonly used for microarray data analysis may be non-informative for the data generated by transcript enumeration techniques since they ignore certain fundamental properties of this space. Results Here we present a software tool, Simcluster, designed to perform clustering analysis for data on the simplex space. We present Simcluster as a stand-alone command-line C package and as a user-friendly on-line tool. Both versions are available at: http://xerad.systemsbiology.net/simcluster. Conclusion Simcluster is designed in accordance with a well-established mathematical framework for compositional data analysis, which provides principled procedures for dealing with the simplex space, and is thus applicable in a number of contexts, including enumeration-based gene expression data.

The Impact of Regulatory Heterogeneity on Agri-food Trade

We estimate the impact of regulatory heterogeneity on agri-food trade using a gravity analysis that relies on detailed data on non-tariff measures (NTMs) collected by the NTM-Impact project. The data cover a broad range of import requirements for agricultural and food products for the EU and nine of its major trade partners. We find that trade is significantly reduced when importing countries have stricter maximum residue limits (MRLs) for plant products than exporting countries. For most other measures, due to their qualitative nature, we were unable to infer whether the importer has stricter standards relative to the exporter, and we do not find a robust relationship between these measures and trade. Our findings suggest that, at least for some import standards, harmonising regulations will increase trade. We also conclude that tariff reductions remain an effective means to increase trade even when NTMs abound.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Association of Proton Pump Inhibitor Use on Cardiovascular Outcomes With Clopidogrel and Ticagrelor Insights From the Platelet Inhibition and Patient Outcomes Trial

Background-The clinical significance of the interaction between clopidogrel and proton pump inhibitors (PPIs) remains unclear. Methods and Results-We examined the relationship between PPI use and 1-year cardiovascular events (cardiovascular death, myocardial infarction, or stroke) in patients with acute coronary syndrome randomized to clopidogrel or ticagrelor in a prespecified, nonrandomized subgroup analysis of the Platelet Inhibition and Patient Outcomes (PLATO) trial. The primary end point rates were higher for individuals on a PPI (n = 6539) compared with those not on a PPI (n = 12 060) at randomization in both the clopidogrel (13.0% versus 10.9%; adjusted hazard ratio [HR], 1.20; 95% confidence interval [CI], 1.04 -1.38) and ticagrelor (11.0% versus 9.2%; HR, 1.24; 95% CI, 1.07-1.45) groups. Patients on non-PPI gastrointestinal drugs had similar primary end point rates compared with those on a PPI (PPI versus non-PPI gastrointestinal treatment: clopidogrel, HR, 0.98; 95% CI, 0.79-1.23; ticagrelor, HR, 0.89; 95% CI, 0.73-1.10). In contrast, patients on no gastric therapy had a significantly lower primary end point rate (PPI versus no gastrointestinal treatment: clopidogrel, HR, 1.29; 95% CI, 1.12-1.49; ticagrelor, HR, 1.30; 95% CI, 1.14-1.49). Conclusions-The use of a PPI was independently associated with a higher rate of cardiovascular events in patients with acute coronary syndrome receiving clopidogrel. However, a similar association was observed between cardiovascular events and PPI use during ticagrelor treatment and with other non-PPI gastrointestinal treatment. Therefore, in the PLATO trial, the association between PPI use and adverse events may be due to confounding, with PPI use more of a marker for, than a cause of, higher rates of cardiovascular events.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

Light emission and current rectification in a molecular device: Experiment and theory

We have investigated optical and transport properties of the molecular structure 2,3,4,5-tetraphenyl-1-phenylethynyl-cyclopenta-2,4-dienol experimentally and theoretically. The optical spectrum was calculated using Hartree-Fock-intermediate neglect of differential overlap-configuration interaction model. The experimental photoluminescence spectrum showed a peak around 470nm which was very well described by the modeling. Electronic transport measurements showed a diode-like effect with a strong current rectification. A phenomenological microscopic model based on non-equilibrium Green's function technique was proposed and a very good description electronic transport was obtained. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767457]

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.