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The problems of recovering the state of power systems and detecting the instances of bad data have been widely studied in literature. Nevertheless, these two operations have been designed and optimized for the most part in isolation. Specifically, state estimators are optimized based on the minimum mean-square error criteria, which is only optimal when the source of distortions in the data is Gaussian random noise. Hence, the state estimators fail to perform optimality when the data is further contaminated by bad data, which cannot necessarily be modeled by additive Gaussian terms. The problem of power state estimation has been studied extensively. But the fundamental performance limits and the attendant decision rules are unknown when the data is potentially compromised by random bad data (due to sensor failures) or structured bad data (due to cyber attacks, which are also referred to false data injection attacks). This paper provides a general framework that formalizes the underlying connection between state estimation and bad data detection routines. We aim to carry out the combined tasks of detecting the presence of random and structured bad data, and form accurate estimations for the state of power grid. This paper characterizes the optimal detectors and estimators. Furthermore, the gains with respect to the existing state estimators and bad data detectors are established through numerical evaluations.

Background Neuro-axonal brain damage releases neurofilament light chain (NfL) proteins, which enter the blood. Serum NfL has recently emerged as a promising biomarker for grading axonal damage, monitoring treatment responses, and prognosis in neurological diseases. Importantly, serum NfL levels also increase with aging, and the interpretation of serum NfL levels in neurological diseases is incomplete due to lack of a reliable model for age-related variation in serum NfL levels in healthy subjects. Methods Graph signal processing (GSP) provides analytical tools, such as graph Fourier transform (GFT), to produce measures from functional dynamics of brain activity constrained by white matter anatomy. Here, we leveraged a set of features using GFT that quantified the coupling between blood oxygen level dependent signals and structural connectome to investigate their associations with serum NfL levels collected from healthy subjects and former athletes with history of concussions. Results Here we show that GSP feature from isthmus cingulate in the right hemisphere (r-iCg) is strongly linked with serum NfL in healthy controls. In contrast, GSP features from temporal lobe and lingual areas in the left hemisphere and posterior cingulate in the right hemisphere are the most associated with serum NfL in former athletes. Additional analysis reveals that the GSP feature from r-iCg is associated with behavioral and structural measures that predict aggressive behavior in healthy controls and former athletes. Conclusions Our results suggest that GSP-derived brain features may be included in models of baseline variance when evaluating NfL as a biomarker of neurological diseases and studying their impact on personality traits.

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