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.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Coherent stochastic resonance

We consider Brownian motion on a line terminated by two trapping points. A bias term in the form of a telegraph signal is applied to this system. It is shown that the first two moments of survival time exhibit a minimum at the same resonant frequency.

Stochastic resonance in a suspension of magnetic dipoles under shear flow

We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e., the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss the limitations and role of the linear response theory in its applications to the theory of stochastic resonance.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

Stochastic resonance in a system of magnetic particles

We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times, and the mean first passage time. The behavior of these quantities is similar to the behavior of corresponding quantities in other systems where stochastic resonance has also been observed.

Coherence and anticoherence resonance tunned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Thermal resonance in signal transmission

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.

Nuclear magnetic resonance

This article reviews the principles and methods of nuclear magnetic resonance spectroscopy, and gives examples of applications carried out at ourFacility, which illustrate the capabilities of the technique.

Stochastic resonance in a dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a nonzero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e., when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.

Entropic stochastic resonance

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

Endorectal Magnetic Resonance Imaging and Spectroscopy Are Useful for Selecting Candidates for Biopsy among Patients with Persistently Elevated Prostate Specific Antigen

To evaluate the efficacy of endorectal Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spetroscopic Imaging (MRSI) combined with total prostate-specific antigen (tPSA) and free prostate-specific antigen (fPSA) in selecting candidates for biopsy. Subjects and Methods: 246 patients with elevated tPSA (median: 7.81 ng/ml) underwent endorectal MRI and MRSI before Transrectal Ultrasound (TRUS) biopsy (10 peripheral + 2 central cores); patients with positive biopsies were treated with radical intention; those with negative biopsies were followed up and underwent MRSI before each additional biopsy if tPSA rose persistently. Mean follow-up: 27.6 months. We compared MRI, MRSI, tPSA, and fPSA with histopathology by sextant and determined the association between the Gleason score and MRI and MRSI. We determined the most accurate combination to detect prostate cancer (PCa) using receiver operating curves; we estimated the odds ratios (OR) and calculated sensitivity, specificity, and positive and negative predictive values. Results: No difference in tPSA was found between patients with and without PCa (p = 0.551). In the peripheral zone, the risk of PCa increased with MRSI grade; patients with high-grade MRSI had the greatest risk of PCa over time (OR = 328.6); the model including MRI, MRSI, tPSA, and fPSA was more accurate (Area under Curve: AUC = 95.7%) than MRI alone (AUC = 85.1%) or fPSA alone (AUC = 78.1%), but not than MRSI alone (94.5%). In the transitional zone, the model was less accurate (AUC = 84.4%). The association (p = 0.005) between MRSI and Gleason score was significant in both zones. Conclusions: MRSI is useful in patients with elevated tPSA. High-grade MRSI lesions call for repeated biopsies. Men with negative MRSI may forgo further biopsies because a significantly high Gleason lesion is very unlikely

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.