<b>Motivation:</b> Normalization of microarray data is essential for multiple-array analyses. Several normalization protocols have been proposed based on different biological or statistical assumptions. A fundamental problem arises whether they have effectively normalized arrays. In addition, for a given array, the question arises how to choose a method to most effectively normalize the microarray data.

Dispersive instability appears in time-domain solutions of classical cochlear models. In this letter, a derivation of optimal initial data is presented to minimize the effect of instability. A second-order accurate implicit boundary integral method is introduced. Numerical solutions of two-dimensional models show that the optimal initial conditions work successfully in time-domain steady-state computations for both the zero Neumann and zero Dirichlet fluid pressure boundary conditions at the helicotrema.

In an event-related functional MRI data analysis, an accurate and robust extraction of the hemodynamic response function (HRF) and its associated statistics (e.g., magnitude, width, and time to peak) is critical to infer quantitative information about the relative timing of the neuronal events in different brain regions. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) to accurately estimate HRFs pertaining to each stimulus sequence across all voxels. MASM explicitly accounts for both spatial and temporal smoothness information, while incorporating such information to adaptively estimate HRFs in the frequency domain. One simulation study and a real data set are used to demonstrate the methodology and examine its finite sample performance in HRF estimation, which confirms that MASM significantly outperforms the existing methods including the smooth finite impulse