High-resolution computer simulation of the dynamics of isoelectric focusing using carrier ampholytes: focusing with concurrent electrophoretic mobilization is an isotachophoretic process

Focusing of four hemoglobins with concurrent electrophoretic mobilization was studied by computer simulation. A dynamic electrophoresis simulator was first used to provide a detailed description of focusing in a 100-carrier component, pH 6-8 gradient using phosphoric acid as anolyte and NaOH as catholyte. These results are compared to an identical simulation except that the catholyte contained both NaOH and NaCl. A stationary, steady-state distribution of carrier components and hemoglobins is produced in the first configuration. In the second, the chloride ion migrates into and through the separation space. It is shown that even under these conditions of chloride ion flux a pH gradient forms. All amphoteric species acquire a slight positive charge upon focusing and the whole pattern is mobilized towards the cathode. The cathodic gradient end is stable whereas the anodic end is gradually degrading due to the continuous accumulation of chloride. The data illustrate that the mobilization is a cationic isotachophoretic process with the sodium ion being the leading cation. The peak height of the hemoglobin zones decreases somewhat upon mobilization, but the zones retain a relatively sharp profile, thus facilitating detection. The electropherograms that would be produced by whole column imaging and by a single detector placed at different locations along the focusing column are presented and show that focusing can be commenced with NaCl present in the catholyte at the beginning of the experiment. However, this may require detector placement on the cathodic side of the catholyte/sample mixture interface.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.