Visual detection and discrimination thresholds are often measured using adaptive staircases, and most studies use transformed (or weighted) up/down methods with fixed step sizes--in the spirit of Wetherill and Levitt (Br J Mathemat Statist Psychol 1965;18:1-10) or Kaernbach (Percept Psychophys 1991;49:227-229)--instead of changing step size at each trial in accordance with best-placement rules-...

Currently, genomic evaluations use multiple-step procedures, which are prone to biases and errors. A single-step procedure may be applicable when genomic predictions can be obtained by modifying the numerator relationship matrix A to H = A + A(Delta), where A(Delta) includes deviations from expected relationships. However, the traditional mixed model equations require H(-1), which is usually di...

Numerical theory provides the basis for quantification of the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for elliptic test problems in two and three space dimensions that demonstrate this theory by computing the convergence order of the F...

The FEM theory provides the basis for quantification on the accuracy and reliability of a numerical solution by the a priori error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents information on the techniques needed in COMSOL 4.2 to enable computational studies that demonstrate this theory for time-dependent problems, in extension of previous work on station...

In this work we introduce volume constraint problems involving the nonlocal operator $$(-\Delta )_{\delta }^{s}$$ , closely related to fractional Laplacian )^{s}$$ and depending upon a parameter $$\delta >0$$ called horizon. We study associated linear spectral behavior of these when \rightarrow 0^+$$ +\infty $$ . Through limit processes on derive convergence local as respectively, well prove so...

The convergence of finite element methods for elliptic and parabolic partial differential equations is well-established if source terms are sufficiently smooth. Noting that finite element computation is easily implemented even when the source terms are measure-valued — for instance, modeling point sources by Dirac delta distributions — we prove new convergence order results in two and three dim...

We investigate the convergence of difference schemes for the one-dimensional heat equation with the coefficient of the time derivative containing a Dirac delta distribution. An abstract operator method is applied for analyzing this equation. The convergence rate estimate of the order O(h) in a special discrete W̃ 2,1 2 Sobolev norm, compatible with the smoothness of the solution, is obtained. 20...