The convergence of first-principles supercell calculations for defects in semiconductors is studied with the vacancy in bulk Si as a test case. The ionic relaxations, defect formation energies, and ionization levels are calculated for supercell sizes of up to 216 atomic sites using several k-point meshes in the Brillouin-zone integrations. The energy dispersion, inherent for the deep defect states in the supercell approximation, and the long range of the ionic relaxations are shown to postpone the convergence so that conclusive results for the physical properties cannot be obtained before the supercell size is of the order of 128-216 atomic sites.

Considering the model fit and repeatability, the kurtosis model seems to be the preferred model for characterization of normal prostate and PCa DWI using b-values up to 2000 s/mm(2) .

The formation and binding energies, the ionization levels, the structures, and the local vibrations of O i , O 2i , O 3i , VO, VO 2 , and V 2 O (Vϭvacancy͒ in silicon are calculated using a self-consistent total-energy pseudopotential method. The most important results are as follows: The ionization levels and associated structures are given for VO and V 2 O as well as the local vibration modes for the negative charge states of VO.

Purpose: To evaluate four mathematical models for diffusion weighted imaging (DWI) of prostate cancer (PCa) in terms of PCa detection and characterization. Methods: Fifty patients with histologically confirmed PCa underwent two repeated 3 Tesla DWI examinations using 12 equally distributed b values, the highest b value of 2000 s/ mm 2 . Normalized mean signal intensities of regions-of-interest were fitted using monoexponential, kurtosis, stretched exponential, and biexponential models. Tumors were classified into low, intermediate, and high Gleason score groups. Areas under receiver operating characteristic curve (AUCs) were estimated to evaluate performance in PCa detection and Gleason score classifications. The fitted parameters were correlated with Gleason score groups by using the Spearman correlation coefficient (r). Coefficient of repeatability and intraclass correlation coefficient [specifically ICC(3,1)], were calculated to evaluate repeatability of the fitted parameters. Results: The AUC and r values were similar between parameters of monoexponential, kurtosis, and stretched exponential (with the exception of the a parameter) models. The absolute r values for ADC m , ADC k , K, and ADC s were in the range from 0.31 to 0.53 (P < 0.01). Parameters of the biexponential model demonstrated low repeatability. Conclusion: In region-of-interest based analysis, the monoexponential model for DWI of PCa using b values up to 2000 s/mm 2 was sufficient for PCa detection and characterization. Magn

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