The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Among other applications, FD has been used to identify abnormalities of the human brain in conventional magnetic resonance imaging (MRI), including white matter abnormalities in patients with Multiple Sclerosis (MS). Extensive grey matter (GM) pathology has been recently identified in MS and it appears to be a key factor in long-term disability. The aim of the present work was to assess whether FD measurement of GM in T1 MRI sequences can identify GM abnormalities in patients with MS in the early phase of the disease. A voxel-based morphometry approach optimized for MS was used to obtain the segmented brain, where we later calculated the three-dimensional FD of the GM in MS patients and healthy controls. We found that patients with MS had a significant increase in the FD of the GM compared to controls. Such differences were present even in patients with short disease durations, including patients with first attacks of MS. In addition, the FD of the GM correlated with T1 and T2 lesion load, but not with GM atrophy or disability. The FD abnormalities of the GM here detected differed from the previously published FD of the white matter in MS, suggesting that different pathological processes were taking place in each structure. These results indicate that GM morphology is abnormal in patients with MS and that this alteration appears early in the course of the disease.

No abstract

Please cite this article in press as: J.A. Adell et al., Estimates for the moments of Bernstein polynomials, J. Math. Anal. Appl. (2015), http://dx. AbstractWe give various explicit estimates for the moments and the absolute moments of Bernstein polynomials. Asymptotically, such estimates are not far from optimality, specially for high moments. As an application, generalized Voronovskaja's formulae for Bernstein polynomials are discussed.

No abstract

No abstract