Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Effect of 15n-labeled hairy vetch and nitrogen fertilization on maize nutrition and yield under no-tillage¹

This study evaluated the effect of hairy vetch (Vicia villosa Roth) as cover crop on maize nutrition and yield under no tillage using isotope techniques. For this purpose, three experiments were carried out: 1) quantification of biological nitrogen fixation (BNF) in hairy vetch; 2) estimation of the N release rate from hairy vetch residues on the soil surface; 3) quantification of 15N recovery by maize from labeled hairy vetch under three rates of mineral N fertilization. This two-year field experiment was conducted on a sandy Acrisol (FAO soil classification) or Argissolo Vermelho distrófico arênico (Brazilian Soil Classification), at a mean annual temperature of 18 ºC and mean annual rainfall of 1686 mm. The experiment was arranged in a double split-plot factorial design with three replications. Two levels of hairy vetch residue (50 and 100 % of the aboveground biomass production) were distributed on the surface of the main plots (5 x 12 m). Maize in the sub-plots (5 x 4 m) was fertilized with three N rates (0, 60, and 120 kg ha-1 N), with urea as N source. The hairy vetch-derived N recovered by maize was evaluated in microplots (1.8 x 2.2 m). The BFN of hairy vetch was on average 72.4 %, which represents an annual input of 130 kg ha-1 of atmospheric N. The N release from hairy vetch residues was fast, with a release of about 90 % of total N within the first four weeks after cover crop management and soil residue application. The recovery of hairy vetch 15N by maize was low, with an average of 12.3 % at harvest. Although hairy vetch was not directly the main source of maize N nutrition, the crop yield reached 8.2 Mg ha-1, without mineral fertilization. There was an apparent synergism between hairy vetch residue application and the mineral N fertilization rate of 60 kg ha-1, confirming the benefits of the combination of organic and inorganic N sources for maize under no tillage.

Nutrition, dry matter accumulation and partitioning and phosphorus use efficiency of potato grown at different phosphorus levels in nutrient solution

High rates of phosphate fertilizers are applied to potato (Solanum tuberosum L.), which may cause antagonistic interactions with other nutrients and limit crop yields when over-supplied. The purpose of this study was to evaluate the influence of phosphorus (P) levels in nutrient solution on P use efficiency, nutritional status and dry matter (DM) accumulation and partitioning of potato plants cv. Ágata. The experiment was carried out in a greenhouse, arranged in a completely randomized block design with four replications. Treatments consisted of seven P levels in nutrient solution (0, 2, 4, 8, 16, 31, and 48 mg L-1). Plants were harvested after 28 days of growth in nutrient solution, and separated in roots, stems and leaves for evaluations. The treatment effects were analyzed by regression analysis. Phosphorus levels of up to 8 mg L-1 increased the root and shoot DM accumulation, but drastically decreased the root/shoot ratio of potato cv. Ágata. Higher P availability increased P concentration, accumulation and absorption efficiency, but decreased P use efficiency. Higher P levels increased the N, P, Mg, Fe, and Mn concentrations in roots considerably and decreased K, S, Cu, and Zn concentrations. In shoot biomass, N, P, K, and Ca concentrations were significantly increased by P applied in solution, unlike Mg and Cu concentrations. Although higher P levels (> 8 mg L-1) in nutrient solution increased P concentration, accumulation and absorption efficiency, the DM accumulation and partitioning of potato cv. Ágata were not affected.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Influence of age on retinochoroidal healing processes after argon photocoagulation in C57bl/6j mice.

PURPOSE: To analyze the influence of age on retinochoroidal wound healing processes and on glial growth factor and cytokine mRNA expression profiles observed after argon laser photocoagulation. METHODS: A cellular and morphometric study was performed that used 44 C57Bl/6J mice: 4-week-old mice (group I, n=8), 6-week-old mice (group II, n=8), 10-12-week-old mice (group III, n=14), and 1-year-old mice (group IV, n=14). All mice in these groups underwent a standard argon laser photocoagulation (50 microm, 400 mW, 0.05 s). Two separated lesions were created in each retina using a slit lamp delivery system. At 1, 3, 7, 14, 60 days, and 4 months after photocoagulation, mice from each of the four groups were sacrificed by carbon dioxide inhalation. Groups III and IV were also studied at 6, 7, and 8 months after photocoagulation. At each time point the enucleated eyes were either mounted in Tissue Tek (OCT), snap frozen and processed for immunohistochemistry or either flat mounted (left eyes of groups III and IV). To determine, by RT-PCR, the time course of glial fibrillary acidic protein (GFAP), vascular endothelial growth factor (VEGF), and monocyte chemotactic protein-1 (MCP-1) gene expression, we delivered ten laser burns (50 microm, 400 mW, 0.05 s) to each retina in 10-12-week-old mice (group III', n=10) and 1-year-old mice (group IV', n=10). Animals from Groups III' and IV' had the same age than those from Groups III and IV, but they received ten laser impacts in each eye and served for the molecular analysis. Mice from Groups III and IV received only two laser impacts per eye and served for the cellular and morphologic study. Retinal and choroidal tissues from these treated mice were collected at 16 h, and 1, 2, 3, and 7 days after photocoagulation. Two mice of each group did not receive photocoagulation and were used as controls. RESULTS: In the cellular and morphologic study, the resultant retinal pigment epithelium interruption expanse was significantly different between the four groups. It was more concise and smaller in the oldest group IV (112.1 microm+/-11.4 versus 219.1 microm+/-12.2 in group III) p<0.0001 between groups III and IV. By contrast, while choroidal neovascularization (CNV) was mild and not readily identifiable in group I, at all time points studied, CNV was more prominent in the (1-year-old mice) Group IV than in the other groups. For instance, up to 14 days after photocoagulation, CNV reaction was statistically larger in group IV than in group III ((p=0.0049 between groups III and IV on slide sections and p<0.0001 between the same groups on flat mounts). Moreover, four months after photocoagulation, the CNV area (on slide sections) was 1,282 microm(2)+/-90 for group III and 2,999 microm(2)+/-115 for group IV (p<0.0001 between groups III and IV). Accordingly, GFAP, VEGF, and MCP-1 mRNA expression profiles, determined by RT-PCR at 16 h, 1, 2, 3, and 7 days postphotocoagulation, were modified with aging. In 1-year-old mice (group IV), GFAP mRNA expression was already significantly higher than in the younger (10-12 week) group III before photocoagulation. After laser burns, GFAP mRNA expression peaked at 16-24 h and on day 7, decreasing thereafter. VEGF mRNA expression was markedly increased after photocoagulation in old mice eyes, reaching 2.7 times its basal level at day 3, while it was only slightly increased in young mice (1.3 times its level in untreated young mice 3 days postphotocoagulation). At all time points after photocoagulation, MCP-1 mRNA expression was elevated in old mice, reaching high levels of expression at 16 h and day 3 respectively. CONCLUSIONS: Our results were based on the study of four different age groups and included not only data from morphological observations but also from a molecular analysis of the various alterations of cytokine signaling and expression. One-year-old mice demonstrated more extensive CNV formation and a slower pace of regression after laser photocoagulation than younger mice. These were accompanied by differences in growth factors and cytokine expression profiles indicate that aging is a factor that aggravates CNV. The above results may provide some insight into possible therapeutic strategies in the future.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Processes models, environmental analyses, and cognitive architectures: Quo vadis quantum probability theory? (Commentary on Pothos and Busemeyer)

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.

Effect of fertilization at sowing on nutrition and yield of crambe in second season

The interest in crambe (Crambe abyssinica ) cultivation in Brazil is on the rise, whereas information on the nutrient requirements for this crop is scarce. The objective of this work was to evaluate the effect of nitrogen-phosphorus-potassium (N-P2O5-K2O formula 8:28:16) fertilization (0, 150, and 300 kg ha-1) on crambe shoot biomass production, grain and oil yields, and nutrient extraction and exportation in the second growing season after soybean. The experiment with a Haplorthox (Dystroferric Red Latosol) was carried out for two years in Botucatu, São Paulo State, Brazil. A randomized complete block design with eight replications was used. Fertilization with NPK at sowing increased the shoot biomass production, grain yield, grain oil content, as well as nutrient extraction and exportation at harvest. In the fertilized treatments, the average amounts of nutrients extracted per hectare were 91 kg K, 71 kg N, 52 kg Ca, 9.4 kg P, 9.4 kg Mg, 7.9 kg S, 2,348 g Fe, 289 g Zn, 135 g Mn, and 18.2 g Cu; while the average values of nutrient exportation per hectare were 54 kg N, 20 kg K, 12.3 kg Ca, 10 kg P, 6.6 kg S, 3.2 kg Mg, 365 g Zn, 60 g Fe, 50 g Mn, and 7.3 g Cu, with NPK fertilizer application.