Pharmacokinetic/pharmacodynamic data are often analysed using nonlinear mixed-effect models, and model evaluation should be an important part of the analysis. Recently, normalised prediction distribution errors (npde) have been proposed as a model evaluation tool. In this paper, we describe an add-on package for the open source statistical package R, designed to compute npde. npde take into acc...

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or “nanodozer”. From our simulations we extract the nonequilibrim density profile c(x, t) of the squeezed molecule along the channel axis (x-coordinate) and th...

Purpose. To evaluate by simulation the statistical properties of normalized prediction distribution errors (NPDE), prediction discrepancies (pd), standardized prediction errors (SPE), numerical predictive check (NPC) and decorrelated NPC (NPC dec) for the external evaluation of a population pharmacokinetic analysis, and to illustrate the use of NPDE for the evaluation of covariate models. Metho...

In this paper the classical Lie group formalism is applied to deduce new classes of solutions of a less studied nonlinear partial differential equation (nPDE) of the third order. The nPDE under consideration is closely related to motions of plane curves. Up to now no carefully performed symmetry analysis is available. Therefore we determine the classical Lie point symmetries including algebraic...

Identifying differentially expressed (DE) genes across conditions or treatments is a typical problem in microarray experiments. In time course microarray experiments (under two or more conditions/treatments), it is sometimes of interest to identify two classes of DE genes: those with no time-condition interactions (called parallel DE genes, or PDE), and those with time-condition interactions (n...

Recently we introduced a nonlinear partial differential equation (nPDE) of the third order for the first time. This new model equation allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. This also leads to a new formulation in the meaning of the nonlinear Poisson-Boltzmann Equation (nPBE) and therefore we call it the modified PoissonBoltzmann Equation (...

A multivariable technique has been incorporated for guesstimating solutions of Nonlinear Partial Differential Equations (NPDE) using bases set B-Polynomials (B-polys). To approximate the anticipated solution NPD equation, a linear product variable coefficients ai(t) and Bi(x) B-polys employed. Additionally, quantities in are determined Galerkin method minimizing errors. Before minimization proc...

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

In this paper a new algebraic procedure is introduced to compute new classes of solutions of (1+1)-nonlinear partial differential equations (nPDEs) of scientific and technical relevance. The crucial step of the method is the basic assumption that the unknown solution of the nPDE under consideration satisfies an ordinary differential equation (ODE) of the first order that can be integrated compl...

In this paper the physical meaning of a nonlinear partial differential equation (nPDE) of the fourth order relating to wave theory is deduced to the first time. The equation under consideration belongs to a class of less studied nPDEs and an explicit physical meaning is not known until now. This paper however bridges the gap between some known results and a concrete application concerning wave ...