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.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Microstructure of highly oriented, hexagonal, boron nitride thin films grown on crystalline silicon by radio frequency plasma-assisted chemical vapor deposition

We present a high‐resolution electron microscopy study of the microstructure of boron nitride thin films grown on silicon (100) by radio‐frequency plasma‐assisted chemical vapor deposition using B2H6 (1% in H2) and NH3 gases. Well‐adhered boron nitride films grown on the grounded electrode show a highly oriented hexagonal structure with the c‐axis parallel to the substrate surface throughout the film, without any interfacial amorphous layer. We ascribed this textured growth to an etching effect of atomic hydrogen present in the gas discharge. In contrast, films grown on the powered electrode, with compressive stress induced by ion bombardment, show a multilayered structure as observed by other authors, composed of an amorphous layer, a hexagonal layer with the c‐axis parallel to the substrate surface and another layer oriented at random

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.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

First-passage times for non-Markovian processes: Shot noise

The stochastic-trajectory-analysis technique is applied to the calculation of the mean¿first-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes.

First-passage times for non-Markovian processes: Multivalued noise

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

Divergent signal-to-noise ratio and stochastic resonance in monostable systems

We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the signal-to-noise ratio and implies the appearance of stochastic resonance in some monostable systems. We outline applications of our results to a wide variety of systems pertaining to different scientific areas. Two particular examples are discussed in detail.

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.

Noise suppression by noise

We have analyzed the interplay between an externally added noise and the intrinsic noise of systems that relax fast towards a stationary state, and found that increasing the intensity of the external noise can reduce the total noise of the system. We have established a general criterion for the appearance of this phenomenon and discussed two examples in detail.

Effects of strontium ranelate and alendronate on bone microstructure in women with osteoporosis. Results of a 2-year study.

A Strontium ranelate appears to influence more than alendronate distal tibia bone microstructure as assessed by high-resolution peripheral quantitative computed tomography (HR-pQCT), and biomechanically relevant parameters as assessed by micro-finite element analysis (mu FEA), over 2 years, in postmenopausal osteoporotic women.Introduction Bone microstructure changes are a target in osteoporosis treatment to increase bone strength and reduce fracture risk.Methods Using HR-pQCT, we investigated the effects on distal tibia and radius microstructure of strontium ranelate (SrRan; 2 g/day) or alendronate (70 mg/week) for 2 years in postmenopausal osteoporotic women. This exploratory randomized, double-blind trial evaluated HR-pQCT and FEA parameters, areal bone mineral density (BMD), and bone turnover markers.Results In the intention-to-treat population (n = 83, age: 64 +/- 8 years; lumbar T-score: -2.8 +/- 0.8 [DXA]), distal tibia Cortical Thickness (CTh) and Density (DCort), and cancellous BV/TV increased by 6.3%, 1.4%, and 2.5%, respectively (all P < 0.005), with SrRan, but not with alendronate (0.9%, 0.4%, and 0.8%, NS) (P < 0.05 for all above between-group differences). Difference for CTh evaluated with a distance transformation method was close to significance (P = 0.06). The estimated failure load increased with SrRan (+2.1%, P < 0.005), not with alendronate (-0.6%, NS) (between-group difference, P < 0.01). Cortical stress was lower with SrRan (P < 0.05); both treatments decreased trabecular stress. At distal radius, there was no between-group difference other than DCort (P < 0.05). Bone turnover markers decreased with alendronate; bALP increased (+21%) and serum-CTX-I decreased (-1%) after 2 years of SrRan (between-group difference at each time point for both markers, P < 0.0001). Both treatments were well tolerated.Conclusions Within the constraints of HR-pQCT method, and while a possible artefactual contribution of strontium cannot be quantified, SrRan appeared to influence distal tibia bone microstructure and FEA-determined biomechanical parameters more than alendronate. However, the magnitude of the differences is unclear and requires confirmation with another method.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.