We estimate variation with respect to half-spaces in terms of "flows through hyperplanes". Our estimate is derived from an integral representation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequently we obtain conditions which guarantee approximation error rate of order O by one-hidden-layer networks with n sigmoid...

The contribution is focused on multiple change point detection in a onedimensional stochastic process by sparse parameter estimation from an overparametrized model. Stochastic process with changes in the mean is estimated using dictionary consisting of Heaviside functions. The basis pursuit algorithm is used to get sparse parameter estimates. Some properties of mentioned method are studied by s...

A connection is investigated between integral formulas and neural networks based on the Heaviside function. The integral formula developed by Kůrková, Kainen and Kreinovich is derived in a new way for odd dimensions and extended to even dimensions. In particular, it is shown that well-behaved functions of d variables can be represented by integral combinations of Heavisides with weights dependi...

We find the polynomials of the best one-sided approximation to the Heaviside and sign functions. The polynomials are obtained by Hermite interpolation at the zeros of some Jacobi polynomials. Also we give an estimate of the error of approximation and characterize the extremal points of the convex set of the best approximants. c ⃝ 2012 Elsevier Inc. All rights reserved.

A new approach for analyzing cracked problems in 2D orthotropic materials using the well-known element free Galerkin method and orthotropic enrichment functions is proposed. The element free Galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. In this study, element free Galerkin is extrinsically enriched by the recently developed crack-tip orthot...

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the ...

Topology optimization is formulated in terms of the nodal variables that control an implicit function description of the shape. The implicit function is constrained by upper and lower bounds, so that only a band of nodal variables needs to be considered in each step of the optimization. The weak form of the equilibrium equation is expressed as a Heaviside function of the implicit function; the ...

Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz continuous but steep firing rate function is employed, then standard ODE theory implies that such models are well-posed and can thus, approximately, be solved with finite precision arithmetic. We investigate whether ...

Pharmacokinetic compartment models are the only that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions drug concentration AUC form mathematical series Heaviside functions for repetitive intermittent infusions one- two-compart...