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.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

HEALTH BELIEFS REGARDING DIET: A PERSPECTIVE OF HYPERTENSIVE BLACK INDIVIDUALS

The objective of this descriptive-exploratory study was to identify the health beliefs of black individuals with hypertension regarding the barriers and benefits of diet for controlling the disease, including the sociodemographic factors associated with the health beliefs surrounding diet control. One hundred and six black adults with hypertension were interviewed using a specific instrument. The data were analyzed considering the percentages, frequency of the cases, scores and prevalence ratio. The global analysis of beliefs showed a preponderance of beliefs regarding the benefits of diet control. It was observed that men, younger individuals, lack of a partner and low educational level and income were related to the beliefs regarding the benefits of adopting a healthy diet. In conclusion, health promotion among the black population requires an interdisciplinary approach and specific health policies addressing this populations' needs, aimed at preventive and curative aspects.

Lithium in M 67: From the main sequence to the red giant branch

Context. Lithium abundances in open clusters are a very effective probe of mixing processes, and their study can help us to understand the large depletion of lithium that occurs in the Sun. Owing to its age and metallicity, the open cluster M 67 is especially interesting on this respect. Many studies of lithium abundances in M 67 have been performed, but a homogeneous global analysis of lithium in stars from subsolar masses and extending to the most massive members, has yet to be accomplished for a large sample based on high-quality spectra. Aims. We test our non-standard models, which were calibrated using the Sun with observational data. Methods. We collect literature data to analyze, for the first time in a homogeneous way, the non-local thermal equilibrium lithium abundances of all observed single stars in M 67 more massive than similar to 0.9 M-circle dot. Our grid of evolutionary models is computed assuming a non-standard mixing at metallicity [Fe/H] = 0.01, using the Toulouse-Geneva evolution code. Our analysis starts from the entrance into the zero-age main-sequence. Results. Lithium in M 67 is a tight function of mass for stars more massive than the Sun, apart from a few outliers. A plateau in lithium abundances is observed for turn-off stars. Both less massive (M >= 1.10 M-circle dot) and more massive (M >= 1.28 M-circle dot) stars are more depleted than those in the plateau. There is a significant scatter in lithium abundances for any given mass M <= 1.1 M-circle dot. Conclusions. Our models qualitatively reproduce most of the features described above, although the predicted depletion of lithium is 0.45 dex smaller than observed for masses in the plateau region, i.e. between 1.1 and 1.28 solar masses. More work is clearly needed to accurately reproduce the observations. Despite hints that chromospheric activity and rotation play a role in lithium depletion, no firm conclusion can be drawn with the presently available data.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Xylella fastidiosa: An in vivo system to study possible survival strategies within citrus xylem vessels based on global gene expression analysis

Xylella fastidiosa inhabits the plant xylem, a nutrient-poor environment, so that mechanisms to sense and respond to adverse environmental conditions are extremely important for bacterial survival in the plant host. Although the complete genome sequences of different Xylella strains have been determined, little is known about stress responses and gene regulation in these organisms. In this work, a DNA microarray was constructed containing 2,600 ORFs identified in the genome sequencing project of Xylella fastidiosa 9a5c strain, and used to check global gene expression differences in the bacteria when it is infecting a symptomatic and a tolerant citrus tree. Different patterns of expression were found in each variety, suggesting that bacteria are responding differentially according to each plant xylem environment. The global gene expression profile was determined and several genes related to bacterial survival in stressed conditions were found to be differentially expressed between varieties, suggesting the involvement of different strategies for adaptation to the environment. The expression pattern of some genes related to the heat shock response, toxin and detoxification processes, adaptation to atypical conditions, repair systems as well as some regulatory genes are discussed in this paper. DNA microarray proved to be a powerful technique for global transcriptome analyses. This is one of the first studies of Xylella fastidiosa gene expression in vivo which helped to increase insight into stress responses and possible bacterial survival mechanisms in the nutrient-poor environment of xylem vessels.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Extensive cross-talk and global regulators identified from an analysis of the integrated transcriptional and signaling network in Escherichia coli

To understand the regulatory dynamics of transcription factors (TFs) and their interplay with other cellular components we have integrated transcriptional, protein-protein and the allosteric or equivalent interactions which mediate the physiological activity of TFs in Escherichia coli. To study this integrated network we computed a set of network measurements followed by principal component analysis (PCA), investigated the correlations between network structure and dynamics, and carried out a procedure for motif detection. In particular, we show that outliers identified in the integrated network based on their network properties correspond to previously characterized global transcriptional regulators. Furthermore, outliers are highly and widely expressed across conditions, thus supporting their global nature in controlling many genes in the cell. Motifs revealed that TFs not only interact physically with each other but also obtain feedback from signals delivered by signaling proteins supporting the extensive cross-talk between different types of networks. Our analysis can lead to the development of a general framework for detecting and understanding global regulatory factors in regulatory networks and reinforces the importance of integrating multiple types of interactions in underpinning the interrelationships between them.

Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.