A novel approach to analyzing mirrored stimuli in chronometric mental rotation and description of a flexible extended library of stimuli Mirrored stimuli in chronometric mental rotation tests cannot be rotated into congruence and are typically discarded from analysis. We present a novel design using three figures, such that congruence is achieved for all stimuli. For design construction, we consider the geometrical properties of rotation and mirroring.We have experimentally tested the approach with forty-one German sport students.Results analyzed with linear mixed modeling show small differences but are comparable to the classical two-figure design. Based on our findings we suggest our new layout for future chronometric mental rotation. This will improve analysis of accuracies while increasing power.Moreover, we present a database of cube figures and code for flexible generation of stimuli, which we make available on GitHub at

Mirrored stimuli in chronometric mental rotation tests cannot be rotated into congruence and are typically discarded from analysis. We present a novel design using three figures, such that congruence is achieved for all stimuli. For design construction, we consider the geometrical properties of rotation and mirroring.We have experimentally tested the approach with forty-one German sport students. Results analyzed with linear mixed modeling show small differences but are comparable to the classical two-figure design. Based on our findings we suggest our new layout for future chronometric mental rotation. This will improve analysis of accuracies while increasing power.Moreover, we present a database of cube figures and code for flexible generation of stimuli, which we make available on GitHub at https://github.com/LeonardoJost/MRlibrary.

Studies have demonstrated that manual and mental rotation show common processes. Training studies have shown that a manual and concurrent visual rotation improves mental rotation performance. In this study, we separated the visual rotation from the manual rotation. 121 participants were randomly assigned to visual training, manual rotation training, or manual training without rotational movement. Before and after the training session of 30 minutes, they had to solve a chronometric mental rotation test. Data were analyzed with linear mixed models and showed an improvement in mental rotation performance for all groups. However, this improvement did not differ between groups. Due to the independence of the form and occurrence of the manual activity, this suggests that it is not the motor activity but the concurrent visual rotation that leads to improvements in mental rotation tasks. Therefore, the visual component in mental rotation tasks has to be investigated in more detail.

We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triple-wise joint measurability. Particularly, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triple-wise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pair wise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.

It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis of the properties and the convergence behavior of these algorithms and then discuss their application in the area of balanced graph cuts.