We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V]=(1/T)integral(T)(0)dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T-->infinity at fixed r we obtain P(r,T) approximately exp[-theta(r)T], where theta(r) is a large-deviatio...

We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might become discontinuous in finite time. Consequently, if finite precision arithmetic is used, then it is virtually impossible to guarantee the accurate numerical solution of such models. If a smooth firing rate function is employed, then standard O...

One method of solving the single-image super-resolution problem is to use Heaviside functions. This has been done previously by making a binary classification of image components as "smooth" and "non-smooth", describing these with approximated Heaviside functions (AHFs), and iteration including l1 regularization. We now introduce a new method in which the binary classification of image componen...

This study explored the free vibration problem in relation to glass fiber reinforced polymer (GFRP) plates with central cutouts and free boundaries using theoretical, experimental, and numerical methods. The theoretical formulations were derived from the classical lamination plate theory. The rectangular cutout was mathematically modeled into the stiffness matrix of the plate by multiplying Hea...

• An improved level-set model is proposed for honing groove feature segmentation. The Heaviside function approximated using a piecewise linear function. A 30% accuracy improvement over the best-tested algorithms has been observed. folder metal characterization case study validates algorithm’s performance. Honing features of cylinder liner surface contain helpful information on Traditional evalu...

Abstract Fractional calculus (FC) is useful in studying physical phenomena with memory effect. In this paper, a fractional form of Ambartsumian equation considered utilizing the Caputo derivative. The Heaviside expansion formula classical (CC) extended/developed view FC. Then, extended applied to obtain exact solution simplest form. Several theorems and lemmas are proved facilitate evaluation i...

We consider one-dimensional biased voter models, where 1’s replace 0’s at a faster rate than the other way round, started in Heaviside initial state describing interface between two infinite populations of and 1’s. In limit weak bias, for diffusively rescaled process, we measure-valued process local fraction type 1 sites as function time. Under finite second moment condition on rates, show that...

Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. Two classes of such networks are considered: voltage and activity based. In both cases, our networks contain an arbitrary number, n, of interacting neuron populations. Spatial nonsymmetric connectivity functions represent cortico-cortical, local connections, and external inputs represent nonloc...