The gyral morphology of the region of the primary auditory cortex (PAC) in the human brain is highly variable, and possible asymmetries between the hemispheres have been noted since the beginning of the century. We mapped the location and extent of PAC as identified from gross anatomical landmarks in magnetic resonance scans that had been transformed into Talairach-Tournoux stereotaxic space. Individual maps were averaged to produce a probabilistic map of the region which can be co-registered with any image of brain structure or function that has been similarly transformed. The map can be used to localize a region of interest, such as a lesion, or an activation focus from position omission tomography or functional magnetic resonance imaging, within a specified range of probability. We also measured the total volume of the region and found a significant L > R asymmetry both on average and in the majority of subjects. Automatic segmentation of the volumes into grey and white matter revealed larger volumes of white, but not grey matter on the left. This larger volume of cortical connecting fibres may be related to the known left-hemisphere dominance for speech, and a preferential role for left PAC in processing temporal aspects of auditory stimuli is suggested.

The pars opercularis occupies the posterior part of the inferior frontal gyrus. Electrical stimulation or damage of this region interferes with language production. The present study investigated the morphology and morphometry of the pars opercularis in 108 normal adult human cerebral hemispheres by means of magnetic resonance imaging. The brain images were transformed into a standardized proportional steoreotaxic space (i.e. that of Talairach and Tournoux) in order to minimize interindividual brain size variability. There was considerable variability in the shape and location of the pars opercularis across brains and between cerebral hemispheres. There was no significant difference or correlation between left and right hemisphere grey matter volumes. There was also no significant difference between sex and side of asymmetry of the pars opercularis. A probability map of the pars opercularis was constructed by averaging its location and extent in each individual normalized brain into Talairach space to aid in localization of activity changes in functional neuroimaging studies.

For finitely generated nilpotent groups, we employ Mal'cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and quasilinear time. Logarithmic space presentation-uniform versions of these algorithms are provided. Compressed-word versions of the same problems, in which each input word is provided as a straight-line program, are solved in polynomial time.