Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

GREEN MACHINING ORIENTED TO DIMINISH DENSITY GRADIENT FOR MINIMIZATION OF DISTORTION IN ADVANCED CERAMICS

After sintering advanced ceramics, there are invariably distortions, caused in large part by the heterogeneous distribution of density gradients along the compacted piece. To correct distortions, machining is generally used to manufacture pieces within dimensional and geometric tolerances. Hence, narrow material removal limit conditions are applied, which minimize the generation of damage. Another alternative is machining the compacted piece before sintering, called the green ceramic stage, which allows machining without damage to mechanical strength. Since the greatest concentration of density gradients is located in the outer-most layers of the compacted piece, this study investigated the removal of different allowance values by means of green machining. The output variables are distortion after sintering, tool wear, cutting force, and the surface roughness of the green ceramics and the sintered ones. The following results have been noted: less distortion is verified in the sintered piece after 1mm allowance removal; and the higher the tool wear the worse the surface roughness of both green and sintered pieces.

Stand-level patterns of carbon fluxes and partitioning in a Eucalyptus grandis plantation across a gradient of productivity, in Sao Paulo State, Brazil

Wood production represents a large but variable fraction of gross primary production (GPP) in highly productive Eucalyptus plantations. Assessing patterns of carbon (C) partitioning (C flux as a fraction of GPP) between above- and belowground components is essential to understand mechanisms driving the C budget of these plantations. Better knowledge of fluxes and partitioning to woody and non-woody tissues in response to site characteristics and resource availability could provide opportunities to increase forest productivity. Our study aimed at investigating how C allocation varied within one apparently homogeneous 90 ha stand of Eucalyptus grandis (W. Hill ex Maiden) in Southeastern Brazil. We assessed annual above-ground net primary production (ANPP: stem, leaf, and branch production) and total belowground C flux (TBCF: the sum of root production and respiration and mycorrhizal production and respiration), GPP (computed as the sum of ANPP, TBCF and estimated aboveground respiration) on 12 plots representing the gradient of productivity found within the stand. The spatial heterogeneity of topography and associated soil attributes across the stand likely explained this fertility gradient. Component fluxes of GPP and C partitioning were found to vary among plots. Stem NPP ranged from 554 g C m(-2) year(-1) on the plot with lowest GPP to 923 g C m(-2) year(-1) on the plot with highest GPP. Total belowground carbon flux ranged from 497 to 1235 g C m(-2) year(-1) and showed no relationship with ANPP or GPP. Carbon partitioning to stem NPP increased from 0.19 to 0.23, showing a positive trend of increase with GPP (R-2 = 0.29, P = 0.07). Variations in stem wood production across the gradient of productivity observed at our experimental site were a result of the variability in C partitioning to different forest system components.

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.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method

There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed.

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

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.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Effects of discontinuous Percoll gradient centrifugation on the quality of bovine spermatozoa evaluated with computer-assisted semen analysis and fluorescent probes association

The objective of this study was to evaluate the quality of bovine frozen-thawed sperm cells after Percoll gradient centrifugation. Frozen semen doses were obtained from six bulls of different breeds, including three taurine and three Zebu animals. Four ejaculates per bull were evaluated before and after discontinuous Percoll gradient centrifugation. Sperm motility was assessed by computer-assisted semen analysis and the integrity of the plasma and acrosomal membranes, as well as mitochondrial function, were evaluated using a combination of fluorescent probes propidium iodide, fluorescein isothiocyanate-conjugated Pisum sativum agglutinin and 5,5',6,6'-tetrachloro-1,1',3,3'-tetraethylbenzimidazolcarbocyanine iodide. The procedure of Percoll gradient centrifugation increased the percentage of total and progressive sperm motility, beat frequency, rectilinear motility, linearity and rapidly moving cells. In addition, the percentage of cells with intact plasma membrane and mitochondrial membrane potential was increased in post-centrifugation samples. However, the percentage of sperm cells with intact acrosomal membrane was markedly reduced. The method used selected the motile cells with intact plasma membrane and higher mitochondrial functionality in frozen-thawed bull semen, but processing, centrifugation and/or the Percoll medium caused damage to the acrosomal membrane.

Bilateral subthalamic nucleus stimulation for generalized dystonia after bilateral pallidotomy

Background: Thalamotomies and pallidotomies were commonly performed before the deep brain stimulation (DBS) era. Although ablative procedures can lead to significant dystonia improvement, longer periods of analysis reveal disease progression and functional deterioration. Today, the same patients seek additional treatment possibilities. Methods: Four patients with generalized dystonia who previously had undergone bilateral pallidotomy came to our service seeking additional treatment because of dystonic symptom progression. Bilateral subthalamic nucleus DBS (B-STN-DBS) was the treatment of choice. The patients were evaluated with the BurkeFahnMarsden Dystonia Rating Scale (BFMDRS) and the Unified Dystonia Rating Scale (UDRS) before and 2 years after surgery. Results: All patients showed significant functional improvement, averaging 65.3% in BFMDRS (P = .014) and 69.2% in UDRS (P = .025). Conclusions: These results suggest that B-STN-DBS may be an interesting treatment option for generalized dystonia, even for patients who have already undergone bilateral pallidotomy. (c) 2012 Movement Disorder Society

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Use of passive diffusion sampling method for defining NO2 concentrations gradient in São Paulo, Brazil

Abstract Background Air pollution in São Paulo is constantly being measured by the State of Sao Paulo Environmental Agency, however there is no information on the variation between places with different traffic densities. This study was intended to identify a gradient of exposure to traffic-related air pollution within different areas in São Paulo to provide information for future epidemiological studies. Methods We measured NO2 using Palmes' diffusion tubes in 36 sites on streets chosen to be representative of different road types and traffic densities in São Paulo in two one-week periods (July and August 2000). In each study period, two tubes were installed in each site, and two additional tubes were installed in 10 control sites. Results Average NO2 concentrations were related to traffic density, observed on the spot, to number of vehicles counted, and to traffic density strata defined by the city Traffic Engineering Company (CET). Average NO2concentrations were 63μg/m3 and 49μg/m3 in the first and second periods, respectively. Dividing the sites by the observed traffic density, we found: heavy traffic (n = 17): 64μg/m3 (95% CI: 59μg/m3 – 68μg/m3); local traffic (n = 16): 48μg/m3 (95% CI: 44μg/m3 – 52μg/m3) (p < 0.001). Conclusion The differences in NO2 levels between heavy and local traffic sites are large enough to suggest the use of a more refined classification of exposure in epidemiological studies in the city. Number of vehicles counted, traffic density observed on the spot and traffic density strata defined by the CET might be used as a proxy for traffic exposure in São Paulo when more accurate measurements are not available.

A note on the use of the generalized odds ratio in meta-analysis of association studies involving bi- and tri-allelic polymorphisms

Abstract Background The generalized odds ratio (GOR) was recently suggested as a genetic model-free measure for association studies. However, its properties were not extensively investigated. We used Monte Carlo simulations to investigate type-I error rates, power and bias in both effect size and between-study variance estimates of meta-analyses using the GOR as a summary effect, and compared these results to those obtained by usual approaches of model specification. We further applied the GOR in a real meta-analysis of three genome-wide association studies in Alzheimer's disease. Findings For bi-allelic polymorphisms, the GOR performs virtually identical to a standard multiplicative model of analysis (e.g. per-allele odds ratio) for variants acting multiplicatively, but augments slightly the power to detect variants with a dominant mode of action, while reducing the probability to detect recessive variants. Although there were differences among the GOR and usual approaches in terms of bias and type-I error rates, both simulation- and real data-based results provided little indication that these differences will be substantial in practice for meta-analyses involving bi-allelic polymorphisms. However, the use of the GOR may be slightly more powerful for the synthesis of data from tri-allelic variants, particularly when susceptibility alleles are less common in the populations (≤10%). This gain in power may depend on knowledge of the direction of the effects. Conclusions For the synthesis of data from bi-allelic variants, the GOR may be regarded as a multiplicative-like model of analysis. The use of the GOR may be slightly more powerful in the tri-allelic case, particularly when susceptibility alleles are less common in the populations.

Tracing latitudinal gradient, river discharge and water masses along the subtropical South American coast using benthic Foraminifera assemblages

More than 30% of Buccella peruviana (D'Orbigny), Globocassidulina crassa porrecta (Earland & Heron-Allen), Cibicides mackannai (Galloway & Wissler) and C. refulgens (Montfort) indicate the presence of cold Sub Antarctic Shelf Water in winter, from 33.5 to 38.3º S, deeper than 100 m, in the southern part of the study area. In summer, the abundance of this association decreases to less than 15% around 37.5-38.9º S where two species (Globocassidulina subglobosa (Brady), Uvigerina peregrina (Cushman) take over. G. subglobosa, U. peregrina, and Hanzawaia boueana (D'Orbigny) are found at 27-33º S in both seasons in less than 55 m deep in the northern part, and are linked with warm Subtropical Shelf Water and Tropical Water. Freshwater influence was signalized by high silicate concentration and by the presence of Pseudononion atlanticum (Cushman), Bolivina striatula (Cushman), Buliminella elegantissima (D'Orbigny), Bulimina elongata (D'Orbigny), Elphidium excavatum (Terquem), E. poeyanum (D'Orbigny), Ammobaculites exiguus (Cushman & Brönnimann), Arenoparrella mexicana (Kornfeld), Gaudryina exillis (Cushman & Brönnimann), Textularia earlandi (Parker) and thecamoebians in four sectors of the shelf. The presence of Bulimina marginata (D'Orbigny) between 34.1-32.8º S in the winter and 34.2-32.7º S in the summer indicates that the influence of the Subtropical Shelf Front on the sediment does not change seasonally, otherwise, the presence of Angulogerina angulosa (Williamson) in the winter, only in Mar del Plata (38.9º S), show that Malvinas currents are not influencing the sediment in the summer.