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.

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.

Diabetic patients who report receiving processes of diabetic care do not express a better quality of life

Background: Chronic disease management initiatives emphasize patient-centered care, and quality of life (QoL) is increasingly considered a representative outcome in that context. In this study we evaluated the association between receipt of processes of diabetic care and QoL. Methods: This cross-sectional population-based study (2011) used self-reported data from non-institutionalized, adult diabetics, recruited from randomly selected community pharmacies in Vaud. Outcomes included the physical and mental composites of the SF-36 (PCS, MCS) and the disease-specific Audit of Diabetes-Dependent QoL (ADDQoL). Main exposure variables were receipt of six diabetes processes-of care in the past 12 months. We also evaluated whether the association between care received and QoL was congruent with the chronic care model, when assessed by the Patient Assessment of Chronic Illness Care (PACIC). We used linear regressions to examine the association between process measures and the three composites of health-related QoL. Analyses were adjusted for age, gender, socioeconomic status, living companion, BMI, alcohol, smoking, physical activity, co-morbidities and diabetes mellitus (DM) characteristics (type, insulin use, complications, duration). Results: Mean age of the 519 diabetic patients was 64.4 years (SD 11.3), 60% were male and 73% had a living companion; 87% reported type 2 DM, half of respondents required insulin treatment, 48% had at least one DM complication, and 48% had DM over 10 years. Crude overall mean QoL scores were PCS: 43.4 (SD 10.5), MCS: 47.0 (SD 11.2) and ADDQoL: -1.56 (SD 1.6). In bivariate analyses, patients who received the influenza vaccine versus those who did not, had lower ADDQoL and PCS scores; there were no other indicator differences. In adjusted models including all processes, receipt of influenza vaccine was associated with lower ADDQoL (β= - 0.41, p=.01); there were no other associations between process indicators and QoL composites. There was no process association even when these were reported as combined measures of processes of care. PACIC score was associated only with the MCS (β= 1.57, p=.004). Conclusions: Process indicators for diabetes care did not show an association with QoL. This may represent an effect lag time between time of process received and quality of life; or that treatment may be related with inconvenience and patient worry. Further research is needed to explore these unexpected findings.

Hydrological processes obtained on the plot scale under four simulated rainfall tests during the cycle of different crop systems

The cropping system influences the interception of water by plants, water storage in depressions on the soil surface, water infiltration into the soil and runoff. The aim of this study was to quantify some hydrological processes under no tillage cropping systems at the edge of a slope, in 2009 and 2010, in a Humic Dystrudept soil, with the following treatments: corn, soybeans, and common beans alone; and intercropped corn and common bean. Treatments consisted of four simulated rainfall tests at different times, with a planned intensity of 64 mm h-1 and 90 min duration. The first test was applied 18 days after sowing, and the others at 39, 75 and 120 days after the first test. Different times of the simulated rainfall and stages of the crop cycle affected soil water content prior to the rain, and the time runoff began and its peak flow and, thus, the surface hydrological processes. The depth of the runoff and the depth of the water intercepted by the crop + soil infiltration + soil surface storage were affected by the crop systems and the rainfall applied at different times. The corn crop was the most effective treatment for controlling runoff, with a water loss ratio of 0.38, equivalent to 75 % of the water loss ratio exhibited by common bean (0.51), the least effective treatment in relation to the others. Total water loss by runoff decreased linearly with an increase in the time that runoff began, regardless of the treatment; however, soil water content on the gravimetric basis increased linearly from the beginning to the end of the rainfall.

First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.