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  1. null (Ed.)
    A rapid and cost-effective noninvasive tool to detect and characterize neural silences can be of important benefit in diagnosing and treating many disorders. We propose an algorithm, SilenceMap, for uncovering the absence of electrophysiological signals, or neural silences, using noninvasive scalp electroencephalography (EEG) signals. By accounting for the contributions of different sources to the power of the recorded signals, and using a hemispheric baseline approach and a convex spectral clustering framework, SilenceMap permits rapid detection and localization of regions of silence in the brain using a relatively small amount of EEG data. SilenceMap substantially outperformed existing source localization algorithms in estimating the center-of-mass of the silence for three pediatric cortical resection patients, using fewer than 3 minutes of EEG recordings (13, 2, and 11mm vs. 25, 62, and 53 mm), as well for 100 different simulated regions of silence based on a real human head model (12 ± 0.7 mm vs. 54 ± 2.2 mm). SilenceMap paves the way towards accessible early diagnosis and continuous monitoring of altered physiological properties of human cortical function. 
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  2. 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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