Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Carbon balance and crop residue management in dynamic equilibrium under a no-till system in Campos Gerais

The adoption of no-tillage systems (NT) and the maintenance of crop residues on the soil surface result in the long-term increase of carbon (C) in the system, promoting C sequestration and reducing C-CO2 emissions to the atmosphere. The purpose of this study was to evaluate the C sequestration rate and the minimum amount of crop residues required to maintain the dynamic C equilibrium (dC/dt = 0) of two soils (Typic Hapludox) with different textural classes. The experiment was arranged in a 2 x 2 x 2 randomized block factorial design. The following factors were analyzed: (a) two soil types: Typic Hapludox (Oxisol) with medium texture (LVTM) and Oxisol with clay texture (LVTA), (b) two sampling layers (0-5 and 5-20 cm), and (c) two sampling periods (P1 - October 2007; P2 - September 2008). Samples were collected from fields under a long-term (20 years) NT system with the following crop rotations: wheat/soybean/black oat + vetch/maize (LVTM) and wheat/maize/black oat + vetch/soybean (LVTA). The annual C sequestration rates were 0.83 and 0.76 Mg ha-1 for LVTM and LVTA, respectively. The estimates of the minimum amount of crop residues required to maintain a dynamic equilibrium (dC/dt = 0) were 7.13 and 6.53 Mg ha-1 year-1 for LVTM and LVTA, respectively. The C conversion rate in both studied soils was lower than that reported in other studies in the region, resulting in a greater amount of crop residues left on the soil surface.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Combination of MRI and dynamic FET PET for initial glioma grading.

AIM: MRI and PET with 18F-fluoro-ethyl-tyrosine (FET) have been increasingly used to evaluate patients with gliomas. Our purpose was to assess the additive value of MR spectroscopy (MRS), diffusion imaging and dynamic FET-PET for glioma grading. PATIENTS, METHODS: 38 patients (42 ± 15 aged, F/M: 0.46) with untreated histologically proven brain gliomas were included. All underwent conventional MRI, MRS, diffusion sequences, and FET-PET within 3±4 weeks. Performances of tumour FET time-activity-curve, early-to-middle SUVmax ratio, choline / creatine ratio and ADC histogram distribution pattern for gliomas grading were assessed, as compared to histology. Combination of these parameters and respective odds were also evaluated. RESULTS: Tumour time-activity-curve reached the best accuracy (67%) when taken alone to distinguish between low and high-grade gliomas, followed by ADC histogram analysis (65%). Combination of time-activity-curve and ADC histogram analysis improved the sensitivity from 67% to 86% and the specificity from 63-67% to 100% (p < 0.008). On multivariate logistic regression analysis, negative slope of the tumour FET time-activity-curve however remains the best predictor of high-grade glioma (odds 7.6, SE 6.8, p = 0.022). CONCLUSION: Combination of dynamic FET-PET and diffusion MRI reached good performance for gliomas grading. The use of FET-PET/MR may be highly relevant in the initial assessment of primary brain tumours.

Endocytic and secretory traffic in Arabidopsis merge in the trans-Golgi network/early endosome, an independent and highly dynamic organelle.

Plants constantly adjust their repertoire of plasma membrane proteins that mediates transduction of environmental and developmental signals as well as transport of ions, nutrients, and hormones. The importance of regulated secretory and endocytic trafficking is becoming increasingly clear; however, our knowledge of the compartments and molecular machinery involved is still fragmentary. We used immunogold electron microscopy and confocal laser scanning microscopy to trace the route of cargo molecules, including the BRASSINOSTEROID INSENSITIVE1 receptor and the REQUIRES HIGH BORON1 boron exporter, throughout the plant endomembrane system. Our results provide evidence that both endocytic and secretory cargo pass through the trans-Golgi network/early endosome (TGN/EE) and demonstrate that cargo in late endosomes/multivesicular bodies is destined for vacuolar degradation. Moreover, using spinning disc microscopy, we show that TGN/EEs move independently and are only transiently associated with an individual Golgi stack.

Revisiting the S-index for soil physical quality and its use in Brazil

The S-index was introduced in 2004 in a publication by A.R. Dexter. S was proposed as an indicator of soil physical quality. A critical value delimiting soils with rich and poor physical quality was proposed. At present, Brazil is world leader in citations of Dexter's publication. In this publication the S-theory is mathematically revisited and extended. It is shown that S is mathematically correlated to bulk density and total porosity. As an absolute indicator, the value of S alone has proven to be incapable of predicting soil physical quality. The critical value does not always hold under boundary conditions described in the literature. This is to be expected because S is a static parameter, therefore implicitly unable to describe dynamic processes. As a relative indicator of soil physical quality, the S-index has no additional value over bulk density or total porosity. Therefore, in the opinion of the author, the fact that bulk density or total porosity are much more easily determined than the water retention curve for obtaining S disqualifies S as an advantageous indicator of relative soil physical quality. Among the several equations available for the fitting of water retention curves, the Groenevelt-Grant equation is preferable for use with S since one of its parameters and S are linearly correlated. Since efforts in soil physics research have the purpose of describing dynamic processes, it is the author's opinion that these efforts should shift towards mechanistic soil physics as opposed to the search for empirical correlations like S which, at present, represents far more than its reasonable share of soil physics in Brazil.

Dynamic, auxin-responsive plasma membrane-to-nucleus movement of Arabidopsis BRX.

In Arabidopsis, interplay between nuclear auxin perception and trans-cellular polar auxin transport determines the transcriptional auxin response. In brevis radix (brx) mutants, this response is impaired, probably indirectly because of disturbed crosstalk between the auxin and brassinosteroid pathways. Here we provide evidence that BRX protein is plasma membrane-associated, but translocates to the nucleus upon auxin treatment to modulate cellular growth, possibly in conjunction with NGATHA class B3 domain-type transcription factors. Application of the polar auxin transport inhibitor naphthalene phthalamic acid (NPA) resulted in increased BRX abundance at the plasma membrane. Thus, nuclear translocation of BRX could depend on cellular auxin concentration or on auxin flux. Supporting this idea, NPA treatment of wild-type roots phenocopied the brx root meristem phenotype. Moreover, BRX is constitutively turned over by the proteasome pathway in the nucleus. However, a stabilized C-terminal BRX fragment significantly rescued the brx root growth phenotype and triggered a hypocotyl gain-of-function phenotype, similar to strong overexpressors of full length BRX. Therefore, although BRX activity is required in the nucleus, excess activity interferes with normal development. Finally, similar to the PIN-FORMED 1 (PIN1) auxin efflux carrier, BRX is polarly localized in vascular cells and subject to endocytic recycling. Expression of BRX under control of the PIN1 promoter fully rescued the brx short root phenotype, suggesting that the two genes act in the same tissues. Collectively, our results suggest that BRX might provide a contextual readout to synchronize cellular growth with the auxin concentration gradient across the root tip.

Collective dynamic properties in simple crystals: Influence of the structural disorder

Collective dynamic properties in Lennard-Jones crystals are investigated by molecular dynamics simulation. The study is focused on properties such as the dynamic structure factors, the longitudinal and transverse currents and the density of states. The influence on these properties of the structural disorder is analyzed by comparing the results for one-component crystals with those for liquids and supercooled liquids at analogous conditions. The effects of species-disorder on the collective properties of binary crystals are also discussed.

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.