The organization of basic functions of the human brain, particularly in the right hemisphere, remains poorly understood. Recent advances in functional neuroimaging have improved our understanding of cortical organization but do not allow for direct interrogation or determination of essential (versus participatory) cortical regions. Direct cortical stimulation represents a unique opportunity to provide novel insights into the functional distribution of critical epicentres. Direct cortical stimulation (bipolar, 60 Hz, 1-ms pulse) was performed in 165 consecutive patients undergoing awake mapping for resection of low-grade gliomas. Tasks included motor, sensory, counting, and picture naming. Stimulation sites eliciting positive (sensory/motor) or negative (speech arrest, dysarthria, anomia, phonological and semantic paraphasias) findings were recorded and mapped onto a standard Montreal Neurological Institute brain atlas. Montreal Neurological Institute-space functional data were subjected to cluster analysis algorithms (K-means, partition around medioids, hierarchical Ward) to elucidate crucial network epicentres. Sensorimotor function was observed in the pre/post-central gyri as expected. Articulation epicentres were also found within the pre/post-central gyri. However, speech arrest localized to ventral premotor cortex, not the classical Broca's area. Anomia/paraphasia data demonstrated foci not only within classical Wernicke's area but also within the middle and inferior frontal gyri. We report the first bilateral probabilistic map for crucial cortical epicentres of human brain functions in the right and left hemispheres, including sensory, motor, and language (speech, articulation, phonology and semantics). These data challenge classical theories of brain organization (e.g. Broca's area as speech output region) and provide a distributed framework for future studies of neural networks.

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Studies of the optimal multiplier (or optimal step size) modification to the standard Newton-Raphson (NR) load flow have mainly focused on highly stressed and unsolvable systems. This paper extends these previous studies by comparing performance of the NR load flow with and without optimal multipliers for a variety of unstressed, stressed, and unsolvable systems. Also, the impact of coordinate system choice in representing the voltage phasor at each bus is considered. In total, four solution methods are compared: the NR algorithm with and without optimal multipliers using polar and rectangular coordinates. This comparison is carried out by combining analysis of the optimal multiplier technique with empirical results for two-bus, 118-bus, and 10 274-bus test cases. These results indicate that the polar NR load flow with optimal multipliers is the best method of solution for both solvable and unsolvable cases.