Statistical analysis of stochastic resonance in a simple setting

A subthreshold signal may be detected if noise is added to the data. We stu dy a simple model, consisting of a constant signal to which at uniformly sp aced times independent and identically distributed noise variables with kno wn distribution are added. A detector records the times at which the noisy signal exceeds a threshold. There is an optimal noise level, called stochas tic resonance. We explore the detectability of the signal in a system with one or more detectors, with different thresholds. We use a statistical dete ctability measure, the asymptotic variance of the best estimator of the sig nal from the thresholded data, or equivalently, the Fisher information in t he data. In particular, we determine optimal configurations of detectors, v arying the distances between the thresholds and the signal, as well as the noise level: The approach generalizes to nonconstant signals. [S1063-651X(9 9)17110-1].At certain experimental conditions, foam films drawn from aqueou s surfactant solutions can form highly stable Newtonian films. We show that the origin of the film stability can be attributed to specific patterning of surfactant molecules. Due to high dielectric contrast, the charges, toge ther with their electrostatic images, interact as needlelike charged polyme rs. Below a critical thickness, such quasipolyelectrolytes undergo the Bere zinskii-Kosterlitz-Thouless transition from a plasmalike state to a charge neutral one. In the latter, all the charges are bound into dipole pairs. In herent only in thin films, the effect leads to the surfactant condensation into spots that cannot be observed on a single interface at the same surfac tant concentration. We quantify a film resistance to rupture in terms of a pore line tension and show that the corresponding energy barrier needed for pore creation is much greater than the energy of thermal excitations. [S10 63-651X(99)04110-0].