It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.

There is an unmet medical need to identify neuroimaging biomarkers that is able to accurately diagnose and monitor Alzheimer's disease (AD) at very early stages and assess the response to AD-modifying therapies. To a certain extent, volumetric and functional magnetic resonance imaging (fMRI) studies can detect changes in structure, cerebral blood flow and blood oxygenation that are able to distinguish AD and mild cognitive impairment (MCI) subjects from normal controls. However, it has been challenging to use fully automated MRI analytic methods to identify potential AD neuroimaging biomarkers. We have thus proposed a method based on independent component analysis (ICA), for studying potential AD-related MR image features, coupled with the use of support vector machine (SVM) for classifying scans into categories of AD, MCI, and normal control (NC) subjects. The MRI data were selected from Open Access Series of Imaging Studies (OASIS) and the Alzheimer's Disease Neuroimaging Initiative (ADNI) databases. The experimental results showed that our ICA-based method can differentiate AD and MCI subjects from normal controls, although further methodological improvement in the analytic method and inclusion of additional variables may be required for optimal classification.

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Given a fixed$p$≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $ , provided that the dimension$d$is sufficiently large. The method also yields new$L$^{$q$}space-time regularity results for solutions of the wave equation in high dimensions.

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