Confidence Bands for Convex Median Curves using Sign-Tests

Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.

The power of emotional valence – from cognitive to affective processes in reading

The comprehension of stories requires the reader to imagine the cognitive and affective states of the characters. The content of many stories is unpleasant, as they often deal with conflict, disturbance or crisis. Nevertheless, unpleasant stories can be liked and enjoyed. In this fMRI study, we used a parametric approach to examine (1) the capacity of increasing negative valence of story contents to activate the mentalizing network (cognitive and affective theory of mind, ToM), and (2) the neural substrate of liking negatively valenced narratives. A set of 80 short narratives was compiled, ranging from neutral to negative emotional valence. For each story mean rating values on valence and liking were obtained from a group of 32 participants in a prestudy, and later included as parametric regressors in the fMRI analysis. Another group of 24 participants passively read the narratives in a three Tesla MRI scanner. Results revealed a stronger engagement of affective ToM-related brain areas with increasingly negative story valence. Stories that were unpleasant, but simultaneously liked, engaged the medial prefrontal cortex (mPFC), which might reflect the moral exploration of the story content. Further analysis showed that the more the mPFC becomes engaged during the reading of negatively valenced stories, the more coactivation can be observed in other brain areas related to the neural processing of affective ToM and empathy.