Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Evaluation of Indigenous Grains from the Peruvian Andean Region for Antidiabetes and Antihypertension Potential Using In Vitro Methods

The health-relevant functionality of 10 thermally processed Peruvian Andean grains (five cereals, three pseudocereals, and two legumes) was evaluated for potential type 2 diabetes-relevant antihyperglycemia and antihypertension activity using in vitro enzyme assays. Inhibition of enzymes relevant for managing early stages of type 2 diabetes such as hyperglycemia-relevant alpha-glucosidase and alpha-amylase and hypertension-relevant angiotensin I-converting enzyme (ACE) were assayed along with the total phenolic content, phenolic profiles, and antioxidant activity based on the 1,1-diphenyl-2-picrylhydrazyl radical assay. Purple corn (Zea mays L.) (cereal) exhibited high free radical scavenging-linked antioxidant activity (77%) and had the highest total phenolic content (8 +/- 1 mg of gallic acid equivalents/g of sample weight) and alpha-glucosidase inhibitory activity (51% at 5 mg of sample weight). The major phenolic compound in this cereal was protocatechuic acid (287 +/- 15 mu g/g of sample weight). Pseudocereals such as Quinoa (Chenopodium quinoa Willd) and Kaniwa (Chenopodium pallidicaule Aellen) were rich in quercetin derivatives (1,131 +/- 56 and 943 +/- 35 mu g [expressed as quercetin aglycone]/g of sample weight, respectively) and had the highest antioxidant activity (86% and 75%, respectively). Andean legumes (Lupinus mutabilis cultivars SLP-1 and H-6) inhibited significantly the hypertension-relevant ACE (52% at 5 mg of sample weight). No alpha-amylase inhibitory activity was found in any of the evaluated Andean grains. This in vitro study indicates the potential of combination of Andean whole grain cereals, pseudocereals, and legumes to develop effective dietary strategies for managing type 2 diabetes and associated hypertension and provides the rationale for animal and clinical studies.

Hypotheses, rationale, design, and methods for prognostic evaluation in type 2 diabetic patients with angiographically normal coronary arteries. The MASS IV-DM Trial

Background: The MASS IV-DM Trial is a large project from a single institution, the Heart Institute (InCor), University of Sao Paulo Medical School, Brazil to study ventricular function and coronary arteries in patients with type 2 diabetes mellitus. Methods/Design: The study will enroll 600 patients with type 2 diabetes who have angiographically normal ventricular function and coronary arteries. The goal of the MASS IV-DM Trial is to achieve a long-term evaluation of the development of coronary atherosclerosis by using angiograms and coronary-artery calcium scan by electron-beam computed tomography at baseline and after 5 years of follow-up. In addition, the incidence of major cardiovascular events, the dysfunction of various organs involved in this disease, particularly microalbuminuria and renal function, will be analyzed through clinical evaluation. In addition, an effort will be made to investigate in depth the presence of major cardiovascular risk factors, especially the biochemical profile, metabolic syndrome inflammatory activity, oxidative stress, endothelial function, prothrombotic factors, and profibrinolytic and platelet activity. An evaluation will be made of the polymorphism as a determinant of disease and its possible role in the genesis of micro- and macrovascular damage. Discussion: The MASS IV-DM trial is designed to include diabetic patients with clinically suspected myocardial ischemia in whom conventional angiography shows angiographically normal coronary arteries. The result of extensive investigation including angiographic follow-up by several methods, vascular reactivity, pro-thrombotic mechanisms, genetic and biochemical studies may facilitate the understanding of so-called micro- and macrovascular disease of DM.

Hypothalamic-pituitary axis and peripheral tissue responses to TRH stimulation and Liothyronine suppression tests in normal subjects evaluated by current methods

Objective: To reevaluate the responses of thyrotropin-releasing hormone ( TRH) stimulation test in baseline condition as well as after the administration of graded supraphysiological doses of liothyronine ( L- T-3) in normal subjects. Design: To assess various parameters related to the hypothalamic-pituitary axis and peripheral tissue responses to L- T-3 in 22 normal individuals ( median age: 30.5 years). Subjects were submitted to an intravenous TRH test at baseline condition and also to the oral administration of sequential and graded doses of L- T-3 ( 50, 100, and 200 mu g/day), each given over 3 days, at an outpatient clinic. Blood samples were obtained for thyrotropin (TSH) and prolactin (PRL) at basal and then 15, 30, and 60 minutes after the TRH injection. Effects of L- T3 administration on cholesterol, creatine kinase, retinol, ferritin, and sex hormone-binding globulin ( SHBG) were also measured at basal and after the oral administration of L- T-3. Main outcome: TRH administration resulted in an increase of 4-to 14-fold rise in serum TSH ( 8.3 +/- 2.5-fold), and in a slight rise in serum PRL concentrations ( 3.8 +/- 1.5-fold). Administration of graded doses of triiodothyronine ( T-3) resulted in a dose-dependent suppression of TSH and PRL. Basal thyroxine- binding globulin (TBG) and cholesterol levels decreased, and ferritin and SHBG increased after L- T-3 administration, while creatine kinase and retinol did not change throughout the study. There was a positive correlation between basal TSH and TSH peak response to TRH at basal condition and after each sequential L- T-3 doses. On the other hand, TSH peak response to the TRH test did not predict cholesterol, TBG, ferritin, or SHBG values. Conclusion: Using the current methods on hormone and biochemical analysis, we standardized the response of many parameters to TRH stimulation test after sequential and graded T-3 suppression test in normal subjects. Our data suggest that the evaluation of the responses of the hypothalamus-pituitary axis to TRH test as well as the impact of L- T-3 on peripheral tissues were not modified by the current methods.

Fossil groups in the Millennium simulation Their environment and its evolution

Context. Fossil systems are defined to be X- ray bright galaxy groups ( or clusters) with a two- magnitude difference between their two brightest galaxies within half the projected virial radius, and represent an interesting extreme of the population of galaxy agglomerations. However, the physical conditions and processes leading to their formation are still poorly constrained. Aims. We compare the outskirts of fossil systems with that of normal groups to understand whether environmental conditions play a significant role in their formation. We study the groups of galaxies in both, numerical simulations and observations. Methods. We use a variety of statistical tools including the spatial cross- correlation function and the local density parameter Delta(5) to probe differences in the density and structure of the environments of "" normal"" and "" fossil"" systems in the Millennium simulation. Results. We find that the number density of galaxies surrounding fossil systems evolves from greater than that observed around normal systems at z = 0.69, to lower than the normal systems by z = 0. Both fossil and normal systems exhibit an increment in their otherwise radially declining local density measure (Delta(5)) at distances of order 2.5 r(vir) from the system centre. We show that this increment is more noticeable for fossil systems than normal systems and demonstrate that this difference is linked to the earlier formation epoch of fossil groups. Despite the importance of the assembly time, we show that the environment is different for fossil and non- fossil systems with similar masses and formation times along their evolution. We also confirm that the physical characteristics identified in the Millennium simulation can also be detected in SDSS observations. Conclusions. Our results confirm the commonly held belief that fossil systems assembled earlier than normal systems but also show that the surroundings of fossil groups could be responsible for the formation of their large magnitude gap.

Fast ray-tracing algorithm for circumstellar structures (FRACS) II. Disc parameters of the B[e] supergiant CPD-57 degrees 2874 from VLTI/MIDI data

Context. B[e] supergiants are luminous, massive post-main sequence stars exhibiting non-spherical winds, forbidden lines, and hot dust in a disc-like structure. The physical properties of their rich and complex circumstellar environment (CSE) are not well understood, partly because these CSE cannot be easily resolved at the large distances found for B[e] supergiants (typically greater than or similar to 1 kpc). Aims. From mid-IR spectro-interferometric observations obtained with VLTI/MIDI we seek to resolve and study the CSE of the Galactic B[e] supergiant CPD-57 degrees 2874. Methods. For a physical interpretation of the observables (visibilities and spectrum) we use our ray-tracing radiative transfer code (FRACS), which is optimised for thermal spectro-interferometric observations. Results. Thanks to the short computing time required by FRACS (<10 s per monochromatic model), best-fit parameters and uncertainties for several physical quantities of CPD-57 degrees 2874 were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, and disc inclination. Conclusions. The analysis of VLTI/MIDI data with FRACS allowed one of the first direct determinations of physical parameters of the dusty CSE of a B[e] supergiant based on interferometric data and using a full model-fitting approach. In a larger context, the study of B[e] supergiants is important for a deeper understanding of the complex structure and evolution of hot, massive stars.

Spiral-like structure at the centre of nearby clusters of galaxies

Context. X-ray data analysis have found that fairly complex structures at cluster centres are more common than expected. Many of these structures have similar morphologies, which exhibit spiral-like substructure. Aims. It is not yet well known how these structures are formed or maintained. Understanding the origin of these spiral-like features at the centre of some clusters is the major motivation behind this work. Methods. We analyse deep Chandra observations of 15 nearby galaxy clusters ( 0.01 < z < 0.06), and use X-ray temperature and substructure maps to detect small features at the cores of the clusters. Results. We detect spiral-like features at the centre of 7 clusters: A85, A426, A496, Hydra A cluster, Centaurus, Ophiuchus, and A4059. These patterns are similar to those found in numerical hydrodynamic simulations of cluster mergers with non-zero impact parameter. In some clusters of our sample, a strong radio source also occupies the inner region of the cluster, which indicates a possible connection between the two. Our investigation implies that these spiral-like structures may be caused by off-axis minor mergers. Since these features occur in regions of high density, they may confine radio emission from the central galaxy producing, in some cases, unusual radio morphology.

TURBULENCE AND THE FORMATION OF FILAMENTS, LOOPS, AND SHOCK FRONTS IN NGC 1275

NGC 1275, the central galaxy in the Perseus cluster, is the host of gigantic hot bipolar bubbles inflated by active galactic nucleus (AGN) jets observed in the radio as Perseus A. It presents a spectacular H alpha-emitting nebulosity surrounding NGC 1275, with loops and filaments of gas extending to over 50 kpc. The origin of the filaments is still unknown, but probably correlates with the mechanism responsible for the giant buoyant bubbles. We present 2.5 and three-dimensional magnetohydrodynamical (MHD) simulations of the central region of the cluster in which turbulent energy, possibly triggered by star formation and supernovae (SNe) explosions, is introduced. The simulations reveal that the turbulence injected by massive stars could be responsible for the nearly isotropic distribution of filaments and loops that drag magnetic fields upward as indicated by recent observations. Weak shell-like shock fronts propagating into the intracluster medium (ICM) with velocities of 100-500 km s(-1) are found, also resembling the observations. The isotropic outflow momentum of the turbulence slows the infall of the ICM, thus limiting further starburst activity in NGC 1275. As the turbulence is subsonic over most of the simulated volume, the turbulent kinetic energy is not efficiently converted into heat and additional heating is required to suppress the cooling flow at the core of the cluster. Simulations combining the MHD turbulence with the AGN outflow can reproduce the temperature radial profile observed around NGC 1275. While the AGN mechanism is the main heating source, the SNe are crucial to isotropize the energy distribution.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri II. Testing the 2D global disk oscillation model

Context. About 2/3 of the Be stars present the so-called V/R variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the HI emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years. Aims. This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star zeta Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disk model for zeta Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations in the H alpha and Br gamma lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Recovery of the star formation history of the LMC from the VISTA survey of the Magellanic system

The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJK(s) photometry reaching stars in the oldest turn-off point throughout the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy in the star formation history (SFH) that can be expected from VMC data, in particular for the Large Magellanic Cloud (LMC). To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground Milky Way (MW) stars and background galaxies. The simulations cover the whole range of density of LMC field stars. We then perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimisation of a chi-squared-like statistics. We verify that the foreground MW stars are accurately recovered by the minimisation algorithms, whereas the background galaxies can be largely eliminated from the CMD analysis due to their particular colours and morphologies. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known age-metallicity relation (AMR). It turns out that, for a given sky area, the random errors for ages older than similar to 0.4 Gyr seem to be independent of the crowding. This can be explained by a counterbalancing effect between the loss of stars from a decrease in the completeness and the gain of stars from an increase in the stellar density. For a spatial resolution of similar to 0.1 deg(2), the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the lower stellar statistics for stars younger than similar to 0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR( t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that these parameters can be determined with (relative) accuracies of Delta(m-M)(0) similar to 0.02 mag and Delta E(B-V) similar to 0.01 mag, for each individual field over the LMC. The propagation of these errors in the SFR(t) implies systematic errors below 30%. This level of accuracy in the SFR(t) can reveal significant imprints in the dynamical evolution of this unique and nearby stellar system, as well as possible signatures of the past interaction between the MCs and the MW.

Evaluation of the carbon content of aerosols from the burning of biomass in the Brazilian Amazon using thermal, optical and thermal-optical analysis methods

Aerosol samples were collected at a pasture site in the Amazon Basin as part of the project LBA-SMOCC-2002 (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall and Climate: Aerosols from Biomass Burning Perturb Global and Regional Climate). Sampling was conducted during the late dry season, when the aerosol composition was dominated by biomass burning emissions, especially in the submicron fraction. A 13-stage Dekati low-pressure impactor (DLPI) was used to collect particles with nominal aerodynamic diameters (D(p)) ranging from 0.03 to 0.10 mu m. Gravimetric analyses of the DLPI substrates and filters were performed to obtain aerosol mass concentrations. The concentrations of total, apparent elemental, and organic carbon (TC, EC(a), and OC) were determined using thermal and thermal-optical analysis (TOA) methods. A light transmission method (LTM) was used to determine the concentration of equivalent black carbon (BC(e)) or the absorbing fraction at 880 nm for the size-resolved samples. During the dry period, due to the pervasive presence of fires in the region upwind of the sampling site, concentrations of fine aerosols (D(p) < 2.5 mu m: average 59.8 mu g m(-3)) were higher than coarse aerosols (D(p) > 2.5 mu m: 4.1 mu g m(-3)). Carbonaceous matter, estimated as the sum of the particulate organic matter (i.e., OC x 1.8) plus BC(e), comprised more than 90% to the total aerosol mass. Concentrations of EC(a) (estimated by thermal analysis with a correction for charring) and BC(e) (estimated by LTM) averaged 5.2 +/- 1.3 and 3.1 +/- 0.8 mu g m(-3), respectively. The determination of EC was improved by extracting water-soluble organic material from the samples, which reduced the average light absorption Angstrom exponent of particles in the size range of 0.1 to 1.0 mu m from >2.0 to approximately 1.2. The size-resolved BC(e) measured by the LTM showed a clear maximum between 0.4 and 0.6 mu m in diameter. The concentrations of OC and BC(e) varied diurnally during the dry period, and this variation is related to diurnal changes in boundary layer thickness and in fire frequency.

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

On the influence of non-thermal pressure on the mass determination of galaxy clusters

Aims. Given that in most cases just thermal pressure is taken into account in the hydrostatic equilibrium equation to estimate galaxy cluster mass, the main purpose of this paper is to consider the contribution of all three non-thermal components to total mass measurements. The non-thermal pressure is composed by cosmic rays, turbulence and magnetic pressures. Methods. To estimate the thermal pressure we used public XMM-Newton archival data of five Abell clusters to derive temperature and density profiles. To describe the magnetic pressure, we assume a radial distribution for the magnetic field, B(r) proportional to rho(alpha)(g). To seek generality we assume alpha within the range of 0.5 to 0.9, as indicated by observations and numerical simulations. Turbulent motions and bulk velocities add a turbulent pressure, which is considered using an estimate from numerical simulations. For this component, we assume an isotropic pressure, P(turb) = 1/3 rho(g)(sigma(2)(r) + sigma(2)(t)). We also consider the contribution of cosmic ray pressure, P(cr) proportional to r(-0.5). Thus, besides the gas (thermal) pressure, we include these three non-thermal components in the magnetohydrostatic equilibrium equation and compare the total mass estimates with the values obtained without them. Results. A consistent description for the non-thermal component could yield a variation in mass estimates that extends from 10% to similar to 30%. We verified that in the inner parts of cool core clusters the cosmic ray component is comparable to the magnetic pressure, while in non-cool core clusters the cosmic ray component is dominant. For cool core clusters the magnetic pressure is the dominant component, contributing more than 50% of the total mass variation due to non-thermal pressure components. However, for non-cool core clusters, the major influence comes from the cosmic ray pressure that accounts for more than 80% of the total mass variation due to non-thermal pressure effects. For our sample, the maximum influence of the turbulent component to the total mass variation can be almost 20%. Although all of the assumptions agree with previous works, it is important to notice that our results rely on the specific parametrization adopted in this work. We show that this analysis can be regarded as a starting point for a more detailed and refined exploration of the influence of non-thermal pressure in the intra-cluster medium (ICM).