Motion-related artifacts are still a major problem in data analysis of functional magnetic resonance imaging (FMRI) studies of brain activation. However, the traditional image registration algorithm is prone to inaccuracy when there are residual variations owing to counting statistics, partial volume effects or biological variation. In particular, susceptibility artifacts usually result in remarkable signal intensity variance, and they can mislead the estimation of motion parameters. In this study, Two robust estimation algorithms for the registration of FMRI images are described. The first estimation algorithm was based on the Newton method and used Tukey's biweight objective function. The second estimation algorithm was based on the Levenberg-Marquardt technique and used a skipped mean objective function. The robust M-estimators can suppress the effects of the outliers by scaling down their error magnitudes or completely rejecting outliers using a weighting function. The proposed registration methods consisted of the following steps: fast segmentation of the brain region from noisy background as a preprocessing step; pre-registration of the volume centroids to provide a good initial estimation; and two robust estimation algorithms and a voxel sampling technique to find the affine transformation parameters. The accuracy of the algorithms was within 0.5 mm in translation and within 0.5 degrees in rotation. For the FMRI data sets, the performance of the algorithms was visually compared with the AIR 2.0 software, which is a software for image registration, using colour-coded statistical mapping by the Kolmogorov-Smirov method. Experimental results showed, that the algorithms provided significant improvement in correcting motion-related artifacts and can enhance the detection of real brain activation.

In recent years, some researchers used high-order fuzzy time series to deal with forecasting problems. In this paper, we present a new method for forecasting the enrollments of the University of Alabama based on the high-order fuzzy time series. The proposed method uses the socalled "second order differences" of the enrollments of the previous years to determine the trend of the forecasting. The proposed method gets a higher forecasting accuracy rate than the existing methods.

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