Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.

Parcellation of fMRI datasets with ICA and PLS: a data driven approach

Inter-subject parcellation of functional Magnetic Resonance Imaging (fMRI) data based on a standard General Linear Model (GLM) and spectral clustering was recently proposed as a means to alleviate the issues associated with spatial normalization in fMRI. However, for all its appeal, a GLM-based parcellation approach introduces its own biases, in the form of a priori knowledge about the shape of Hemodynamic Response Function (HRF) and task-related signal changes, or about the subject behaviour during the task. In this paper, we introduce a data-driven version of the spectral clustering parcellation, based on Independent Component Analysis (ICA) and Partial Least Squares (PLS) instead of the GLM. First, a number of independent components are automatically selected. Seed voxels are then obtained from the associated ICA maps and we compute the PLS latent variables between the fMRI signal of the seed voxels (which covers regional variations of the HRF) and the principal components of the signal across all voxels. Finally, we parcellate all subjects data with a spectral clustering of the PLS latent variables. We present results of the application of the proposed method on both single-subject and multi-subject fMRI datasets. Preliminary experimental results, evaluated with intra-parcel variance of GLM t-values and PLS derived t-values, indicate that this data-driven approach offers improvement in terms of parcellation accuracy over GLM based techniques.