Standard human EEG systems based on spatial Nyquist estimates suggest that 20–30 mm electrode spacing suffices to capture neural signals on the scalp, but recent studies posit that increasing sensor density can provide higher resolution neural information. Here, we compared “super-Nyquist” density EEG (“SND”) with Nyquist density (“ND”) arrays for assessing the spatiotemporal aspects of early visual processing. EEG was measured from 128 electrodes arranged over occipitotemporal brain regions (14 mm spacing) while participants viewed flickering checkerboard stimuli. Analyses compared SND with ND-equivalent subsets of the same electrodes. Frequency-tagged stimuli were classified more accurately with SND than ND arrays in both the time and the frequency domains. Representational similarity analysis revealed that a computational model of V1 correlated more highly with the SND than the ND array. Overall, SND EEG captured more neural information from visual cortex, arguing for increased development of this approach in basic and translational neuroscience.

We present a novel signal processing algorithm for automated, noninvasive detection of Cortical Spreading Depolarizations (CSDs) using electroencephalography (EEG) signals and validate the algorithm on simulated EEG signals. CSDs are waves of neurochemical changes that suppress neuronal activity as they propagate across the brain's cortical surface. CSDs are believed to mediate secondary brain damage after brain trauma and cerebrovascular diseases like stroke. We address key challenges in detecting CSDs from EEG signals: (i) decay of high spatial frequencies as they travel from the cortical surface to the scalp surface; and (ii) presence of sulci and gyri, which makes it difficult to track the CSD waves as they travel across the cortex. Our algorithm detects and tracks "wavefronts" of the CSD wave, and stitches together data across space and time to decide on the presence of a CSD wave. To test our algorithm, we provide different models and complex patterns of CSD waves, including different widths of CSD suppressions, and use these models to simulate scalp EEG signals using head models of 4 subjects from the OASIS dataset. Our results suggest that the average width of suppression that a low-density EEG grid of 40 electrodes can detect is 1.1 cm, which includes a vast majority of CSD suppressions, but not all. A higher density EEG grid having 340 electrodes can detect complex CSD patterns as thin as 0.43 cm (less than minimum widths reported in prior works), among which single-gyrus propagation is the hardest to detect because of its small suppression area.

The needs of a business (e.g., hiring) may require the use of certain features that are critical in a way that any discrimination arising due to them should be exempted. In this work, we propose a novel information-theoretic decomposition of the total discrimination (in a counterfactual sense) into a non-exempt component, which quantifies the part of the discrimination that cannot be accounted for by the critical features, and an exempt component, which quantifies the remaining discrimination. Our decomposition enables selective removal of the non-exempt component if desired. We arrive at this decomposition through examples and counterexamples that enable us to first obtain a set of desirable properties that any measure of non-exempt discrimination should satisfy. We then demonstrate that our proposed quantification of non-exempt discrimination satisfies all of them. This decomposition leverages a body of work from information theory called Partial Information Decomposition (PID). We also obtain an impossibility result showing that no observational measure of non-exempt discrimination can satisfy all of the desired properties, which leads us to relax our goals and examine alternative observational measures that satisfy only some of these properties. We then perform a case study using one observational measure to show how one might train a model allowing for exemption of discrimination due to critical features.

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