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.

External dichotomous noise: The problem of the mean-first-passage time

A retarded backward equation for a non-Markovian process induced by dichotomous noise (the random telegraphic signal) is deduced. The mean-first-passage time of this process is exactly obtained. The Gaussian white noise and the white shot noise limits are studied. Explicit physical results in first approximation are evaluated.

Passage times for the decay of an unstable state triggered by colored noise

We study the decay of an unstable state in the presence of colored noise by calculating the moment generating function of the passage-time distribution. The problems of the independence of the initial condition in this non-Markovian process and that of nonlinear effects are addressed. Our results are compared with recent analog simulations.

Transient and preparation colored-noise effects: The nonlinear relaxation-time approach

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

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.

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.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Generation of spatiotemporal colored noise

We develop an algorithm to simulate a Gaussian stochastic process that is non-¿-correlated in both space and time coordinates. The colored noise obeys a linear reaction-diffusion Langevin equation with Gaussian white noise. This equation is exactly simulated in a discrete Fourier space.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.

Free conjunctival autologous graft for bleb repair and bleb reduction after trabeculectomy and nonpenetrating filtering surgery.

PURPOSE: To describe methods and outcomes of excisional revision of a filtering bleb (bleb revision) using free conjunctival autologous graft either for bleb repair or for bleb reduction after trabeculectomy and deep sclerectomy with an implant. METHODS: Retrospective medical records were reviewed for a consecutive non-comparative case series comprising patients who underwent excisional revision of a filtering bleb between May 1998-January 2001. Excisional revision using free conjunctival autologous graft (bleb revision) was performed either for bleb repair, to treat early and late leaks and hypotony with maculopathy, or for bleb reduction, to improve ocular pain, discomfort, burning, foreign body sensation, tearing, and fluctuations of visual acuity. The revision consisted of bleb excision and free conjunctival autologous graft. The bleb histopathology was analyzed in patients who underwent bleb repair. RESULTS: Sixteen patients were included in the study, consisting of nine patients who had a trabeculectomy and seven patients who had a deep sclerectomy with an implant. Bleb revision was necessary in 14 patients due to leaking filtering bleb (bleb repair), and in 2 patients due to bleb dysesthesia (bleb reduction). After a follow-up of 15.1 +/- 8.4 months, the mean intraocular pressure (IOP) rose from 7.8 +/- 6.3 mm Hg to 14.3 +/- 6.5 mm Hg, and the visual acuity from 0.4 +/- 0.3 to 0.7 +/- 0.3, with a P value of 0.008 and 0.03, respectively. The complete success rate at 32 months, according to the Kaplan-Meier survival curve, was 38.3%, and the qualified success rate was 83.3%. Four patients (25%) required additional suturing for persistent bleb leak. To control IOP, antiglaucoma medical therapy was needed for six patients (37.5%) and repeated glaucoma surgery was needed for one patient. CONCLUSION: Free conjunctival autologous graft is a safe and successful procedure for bleb repair and bleb reduction. However, patients should be aware of the postoperative possibility of requiring medical or surgical intervention for IOP control after revision.

Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Feasibility of non-invasive pressure support ventilation in infants with respiratory failure after extubation: a pilot study.

OBJECTIVE: To evaluate the feasibility and effects of non-invasive pressure support ventilation (NIV) on the breathing pattern in infants developing respiratory failure after extubation. DESIGN: Prospective pilot clinical study; each patient served as their own control. SETTING: A nine-bed paediatric intensive care unit of a tertiary university hospital. PATIENTS: Six patients (median age 5 months, range 0.5-7 months; median weight 4.2 kg, range 3.8-5.1 kg) who developed respiratory failure after extubation. INTERVENTIONS: After a period of spontaneous breathing (SB), children who developed respiratory failure were treated with NIV. MEASUREMENTS AND RESULTS: Measurements included clinical dyspnoea score (DS), blood gases and oesophageal pressure recordings, which were analysed for respiratory rate (RR), oesophageal inspiratory pressure swing (dPes) and oesophageal pressure-time product (PTPes). All data were collected during both periods (SB and NIV). When comparing NIV with SB, DS was reduced by 44% (P < 0.001), RR by 32% (P < 0.001), dPes by 45% (P < 0.01) and PTPes by 57% (P < 0.001). A non-significant trend for decrease in PaCO(2) was observed. CONCLUSION: In these infants, non-invasive pressure support ventilation with turbine flow generator induced a reduction of breathing frequency, dPes and PTPes, indicating reduced load of the inspiratory muscles. NIV can be used with some benefits in infants with respiratory failure after extubation.

Relationship between autonomic neuropathy and thermogenesis in non diabetic and diabetic obese patients.

Autonomic neuropathy is a well known complication of diabetes. Diabetes is often superimposed on obesity. A reduction in the variability of the heart rate in the resting state has been demonstrated in 16 obese diabetic subjects as well as in 34 obese non-diabetic subjects. The coefficient of variation (CV) of the heart rate during 30 minutes of resting was significantly decreased in both obese groups (3.9 +/- 0.2% for the diabetics; 5.2 +/- 0.2%, p less than 0.01 for the non diabetics) as compared to their own controls (4.5 +/- 0.6% and 6.5 +/- 0.4%, respectively). Age also contributes to decreased heart rate variability. Furthermore, this defect of autonomic function has been correlated with the blunted glucose-induced thermogenesis (GIT) seen in both obese groups (r = 0.52, p. less than 0.001): the increase in energy expenditure over basal values following a 100 g oral glucose load was only 4.8 +/- 0.8% for the diabetic obese group (p less than 0.001), and 8.5 +/- 0.7% for the non-diabetic obese group (p less than 0.001) as opposed to their own controls (12.4 +/- 1.3% and 13.3 +/- 0.6% respectively). Measurement of the variability of heart rate in obese individuals may be of predictive value in assessing blunted glucose-induced thermogenesis in non diabetic and diabetic obese patients.

Mechanism of reduction of virus release and cell-cell fusion in persistent canine distemper virus infection.

Canine distemper virus (CDV), a mobillivirus related to measles virus causes a chronic progressive demyelinating disease, associated with persistence of the virus in the central nervous system (CNS). CNS persistence of morbilliviruses has been associated with cell-to-cell spread, thereby limiting immune detection. The mechanism of cell-to-cell spread remains uncertain. In the present study we studied viral spread comparing a cytolytic (non-persistent) and a persistent CDV strain in cell cultures. Cytolytic CDV spread in a compact concentric manner with extensive cell fusion and destruction of the monolayer. Persistent CDV exhibited a heterogeneous cell-to-cell pattern of spread without cell fusion and 100-fold reduction of infectious viral titers in supernatants as compared to the cytolytic strain. Ultrastructurally, low infectious titers correlated with limited budding of persistent CDV as compared to the cytolytic strain, which shed large numbers of viral particles. The pattern of heterogeneous cell-to-cell viral spread can be explained by low production of infectious viral particles in only few areas of the cell membrane. In this way persistent CDV only spreads to a small proportion of the cells surrounding an infected one. Our studies suggest that both cell-to-cell spread and limited production of infectious virus are related to reduced expression of fusogenic complexes in the cell membrane. Such complexes consist of a synergistic configuration of the attachment (H) and fusion (F) proteins on the cell surface. F und H proteins exhibited a marked degree of colocalization in cytolytic CDV infection but not in persistent CDV as seen by confocal laser microscopy. In addition, analysis of CDV F protein expression using vaccinia constructs of both strains revealed an additional large fraction of uncleaved fusion protein in the persistent strain. This suggests that the paucity of active fusion complexes is due to restricted intracellular processing of the viral fusion protein.

MDCT arthrography of the hip: value of the adaptive statistical iterative reconstruction technique and potential for radiation dose reduction.

OBJECTIVE: The purpose of this article is to assess the effect of the adaptive statistical iterative reconstruction (ASIR) technique on image quality in hip MDCT arthrography and to evaluate its potential for reducing radiation dose. SUBJECTS AND METHODS: Thirty-seven patients examined with hip MDCT arthrography were prospectively randomized into three different protocols: one with a regular dose (volume CT dose index [CTDIvol], 38.4 mGy) and two with a reduced dose (CTDIvol, 24.6 or 15.4 mGy). Images were reconstructed using filtered back projection (FBP) and four increasing percentages of ASIR (30%, 50%, 70%, and 90%). Image noise and contrast-to-noise ratio (CNR) were measured. Two musculoskeletal radiologists independently evaluated several anatomic structures and image quality parameters using a 4-point scale. They also jointly assessed acetabular labrum tears and articular cartilage lesions. RESULTS: With decreasing radiation dose level, image noise statistically significantly increased (p=0.0009) and CNR statistically significantly decreased (p=0.001). We also found a statistically significant reduction in noise (p=0.0001) and increase in CNR (p≤0.003) with increasing percentage of ASIR; in addition, we noted statistically significant increases in image quality scores for the labrum and cartilage, subchondral bone, overall diagnostic quality (up to 50% ASIR), and subjective noise (p≤0.04), and statistically significant reductions for the trabecular bone and muscles (p≤0.03). Regardless of the radiation dose level, there were no statistically significant differences in the detection and characterization of labral tears (n=24; p=1) and cartilage lesions (n=40; p≥0.89) depending on the ASIR percentage. CONCLUSION: The use of up to 50% ASIR in hip MDCT arthrography helps to reduce radiation dose by approximately 35-60%, while maintaining diagnostic image quality comparable to that of a regular-dose protocol using FBP.