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AbstractDuring basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.

Spike Lee, one of the leading African-American filmmakers of all time, speaks with David about his new movie on Chicago gun violence CHI-RAQ, race relations in the U.S., and his love of the New York Knicks.
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Electro- and magnetoencephalography (EEG/MEG) are the means to investigate the dynamics of neuronal activity non-invasively in the human brain. However, both EEG and MEG are also sensitive to non-neural sources, which can severely complicate the interpretation. The saccadic spike potential (SP) at saccade onset has been identified as a particularly problematic artifact in EEG because it closely resembles synchronous neuronal gamma band activity. While the SP and its confounding effects on EEG have been thoroughly characterized, the corresponding artifact in MEG, the saccadic spike field (SF), has not been investigated. Here we provide a detailed characterization of the SF. We simultaneously recorded MEG, EEG, gaze position and electrooculogram (EOG). We compared the SF in MEG for different saccade sizes and directions and contrasted it with the well-known SP in EEG. Our results reveal a saccade amplitude and direction dependent, lateralized saccadic spike artifact, which was most prominent in the gamma frequency range. The SF was strongest at frontal and temporal sensors but unlike the SP in EEG did not contaminate parietal sensors. Furthermore, we observed that the source configurations of the SF were comparable for regular and miniature saccades. Using distributed source analysis we identified the sources of the SF in the extraocular muscles. In summary, our results show that the SF in MEG closely resembles neuronal activity in frontal and temporal sensors. Our detailed characterization of the SF constitutes a solid basis for assessing possible saccadic spike related contamination in MEG experiments. ; the European Union ; the German Federal Ministry of Education and Research ; publisher version