The study of random Fourier series, linear combinations trigonometric functions whose coefficients are independent (in our case Gaussian) variables with polynomially bounded means and standard deviations, dates back to Norbert Wiener in one the original constructions Brownian motion. A geometric generalization -- relevant e.g.\ Euclidean quantum field theory an infrared cutoff is Gaussian eigen...

We wish to discriminate spike sequences based on the degree of irregularity. For this purpose, we search for a rational expressions of quadratic functions of consecutive interspike intervals that efficiently measures spiking irregularity. Under natural assumptions, the functional form of the coefficient can be parameterized by a single parameter. The parameter is determined so as to maximize th...

Implantable devices capable of several modes of therapy will require differentiation of various ventricular tachyarrhythmias. Three methods of arrhythmia analysis, magnitude-squared coherence, ventricular rate, and irregularity of cycle length were performed for 45 episodes of induced ventricular tachyarrhythmia in 15 patients. Differentiation of monomorphic ventricular tachycardia from polymor...

AIMS To quantitatively evaluate the changes in corneal irregular astigmatism after laser in situ keratomileusis (LASIK) in relation to the amount of laser ablation. METHODS In 189 eyes of 116 patients undergoing LASIK for myopia, corneal topography was obtained before and 1 month after surgery. Using Fourier harmonic analysis of the topography data, corneal irregular astigmatism (asymmetry an...

The action potential activity of single cortical neurons can evoke measurable sensory effects, but it is not known how spiking parameters and neuronal subtypes affect the evoked sensations. Here, we examined the effects of spike train irregularity, spike frequency, and spike number on the detectability of single-neuron stimulation in rat somatosensory cortex. For regular-spiking, putative excit...

We consider the Navier-Stokes equation in a domain with rough boundaries. The small irregularity is modeled by a small amplitude and small wavelength boundary, with typical lengthscale ε ¿ 1. For periodic roughness, it is well-known that the best homogenized (that is regular in ε) boundary condition is of Navier type. Such result still holds for random stationary irregularities, as shown recent...