We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtained from an iteration process. This algorithm is easily numerically implementable. We present two concrete applications of our method: the product of two free operator-valued semicircular elements and the calculation of the distribution of dcd + d 2 cd 2 for scalar-valued c and d, which are free. Comparision between the solution obtained by our methods and simulations of random matrices shows excellent agreement. arXiv:1209.3508v1 [math.OA]

This work addresses multi-class liver tissue classification from multi-parameter MRI in patients with hepatocellular carcinoma (HCC), and is among the first to do so. We propose a structured prediction framework to simultaneously classify parenchyma, blood vessels, viable tumor tissue, and necrosis, which overcomes limitations related to classifying these tissue classes individually and consecutively. A novel classification framework is introduced, based on the integration of multi-scale shape and appearance features to initiate the classification, which is iteratively refined by augmenting the feature space with both structured and rotationally invariant label context features. We study further the topic of rotationally invariant label context feature representations, and introduce a method for this purpose based on computing the energies of the spherical harmonic decompositions computed at different frequencies and radii. We test our method on full 3D multi-parameter MRI volumes from 47 patients with HCC and achieve promising results.

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Purpose To investigate whether Bevacizumab compromises early response assessment after Transarterial Chemoembolization (TACE) in patients with hepatocellular carcinoma by 3D quantitative European Association for the Study of the Liver (qEASL) criteria in comparison to other imaging-based criteria. Materials and Methods Each of 14 patients receiving TACE and bevacizumab was matched with two patients receiving TACE alone. Baseline and Follow-up MRI was retrospectively analyzed regarding qEASL and other imaging-based criteria. Results Percentage-based qEASL achieved significant separation in both therapy arms (p=0.046 and p=0.015). Response and Overall Survival showed similar association among treatment groups (p=0.749). Conclusions Anti-angiogenic therapy with bevacizumab does not impede early response assessment by qEASL.

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