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Time synchronized measurements of voltage magnitudes or phasors are increasingly common in electrical networks. Voltage measurement statistics are informative of the underlying network structure or topology making them useful for grid monitoring. However, this connection is poorly understood and many proposed voltage analytics are purely heuristic. We use graph theory to establish sound theoretical connections between voltage measurements and the structure of the underlying network. Our results are important for many applications, from topology estimation to missing data recovery. Based on this new theory, we discuss existing analytics, transforming them from heuristic to theoretically justified approaches, and introduce new analytics. We clarify all assumptions made, to indicate when analytics may fail or perform poorly. Our work enables voltage measurement streams to be transformed into physically meaningful, intuitive, visualizable, actionable information through simple algorithms. 

Phytochrome proteins control the growth, reproduction, and photosynthesis of plants, fungi, and bacteria. Light is detected by a bilin cofactor, but it remains elusive how this leads to activation of the protein through structural changes. We present serial femtosecond X-ray crystallographic data of the chromophore-binding domains of a bacterial phytochrome at delay times of 1 ps and 10 ps after photoexcitation. The data reveal a twist of the D-ring, which leads to partial detachment of the chromophore from the protein. Unexpectedly, the conserved so-called pyrrole water is photodissociated from the chromophore, concomitant with movement of the A-ring and a key signaling aspartate. The changes are wired together by ultrafast backbone and water movements around the chromophore, channeling them into signal transduction towards the output domains. We suggest that the observed collective changes are important for the phytochrome photoresponse, explaining the earliest steps of how plants, fungi and bacteria sense red light. 

Phytochromes are red-light photoreceptors that were first characterized in plants, with homologs in photosynthetic and non-photosynthetic bacteria known as bacteriophytochromes (BphPs). Upon absorption of light, BphPs interconvert between two states denoted Pr and Pfr with distinct absorption spectra in the red and far-red. They have recently been engineered as enzymatic photoswitches for fluorescent-marker applications in non-invasive tissue imaging of mammals. This article presents cryo- and room-temperature crystal structures of the unusual phytochrome from the non-photosynthetic myxobacteriumStigmatella aurantiaca(SaBphP1) and reveals its role in the fruiting-body formation of this photomorphogenic bacterium. SaBphP1 lacks a conserved histidine (His) in the chromophore-binding domain that stabilizes the Pr state in the classical BphPs. Instead it contains a threonine (Thr), a feature that is restricted to several myxobacterial phytochromes and is not evolutionarily understood. SaBphP1 structures of the chromophore binding domain (CBD) and the complete photosensory core module (PCM) in wild-type and Thr-to-His mutant forms reveal details of the molecular mechanism of the Pr/Pfr transition associated with the physiological response of this myxobacterium to red light. Specifically, key structural differences in the CBD and PCM between the wild-type and the Thr-to-His mutant involve essential chromophore contacts with proximal amino acids, and point to how the photosignal is transduced through the rest of the protein, impacting the essential enzymatic activity in the photomorphogenic response of this myxobacterium.