The intracellular signalling network of the p53 protein plays important roles in genome protection and the control of cell cycle phase transitions. Recently observed oscillatory behaviour in single cells under stress conditions has inspired several research groups to simulate and study the dynamics of the protein with the aim of gaining a proper understanding of the physiological meanings of the oscillations.

The paper deals with the numerical solution of a nonstandard Sturm-Liouville boundary value problem on the half line where the coefficients of the differential terms depend on the unknown function by means of a scalar integral operator. By using a finite difference discretization, a truncated quadrature rule and an iterative procedure, we construct a numerical method, whose convergence is proved. The order of convergence and the truncation at infinity are also discussed. Finally, some numerical tests are given to show the performance of the method. © 2013 Elsevier B.V. All rights reserved.

The modeling of various physical questions often leads to nonlinear boundary value problems involving a nonlocal operator, which depends on the unknown function in the entire domain, rather than at a single point. In order to answer an open question posed by J.R. Cannon and D.J. Galiffa, we study the numerical solution of a special class of nonlocal nonlinear boundary value problems, which involve the integral of the unknown solution over the integration domain.

We present a comparison of three methods for the solution of the magnetoencephalography inverse problem. The methods are: a linearly constrained minimum variance beamformer, an algorithm implementing multiple signal classification with recursively applied projection and a particle filter for Bayesian tracking. Synthetic data with neurophysiological significance are analyzed by the three methods to recover position, orientation and amplitude of the active sources. Finally, a real data set evoked by a simple auditory stimulus is considered.

Within the complex pathological picture associated to diabetes, high glucose (HG) has ". per se" effects on cells and tissues that involve epigenetic reprogramming of gene expression. In fetal tissues, epigenetic changes occur genome-wide and are believed to induce specific long term effects. Human umbilical vein endothelial cells (HUVEC) obtained at delivery from gestational diabetic women were used to study the transcriptomic effects of chronic hyperglycemia in fetal vascular cells using Affymetrix microarrays.

We develop a mathematical model for a three-phase free boundary problem in one dimension that involves interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also dissolves within the meltwater. The model incorporates the Stefan condition at the water-ice interface along with Henry's law for dissolution of gas at the gas-water interface. We employ a quasi-steady approximation for the phase temperatures and then derive a series solution for the interface positions.