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Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in social systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable that splits the population into distinct partitions to estimate causal effects. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities that balance the gain and loss in the effect size. We also develop a computationally-efficient reinforcement learning algorithm for the dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital. 

Abstract In this paper we present the derivation of two new forms of the Kalman filter equations; the first is for a pure lognormally distributed random variable, while the second set of Kalman filter equations will be for a combination of Gaussian and lognormally distributed random variables. We show that the appearance is similar to that of the Gaussian-based equations, but that the analysis state is a multivariate median and not the mean. We also show results of the mixed distribution Kalman filter with the Lorenz 1963 model with lognormal errors for the background and observations of the z component, and compare them to analysis results from a traditional Gaussian-based extended Kalman filter and show that under certain circumstances the new approach produces more accurate results. 

Marine oil contamination remediation remains a worldwide challenge. Siphon action provides a spontaneous, continuous, low-cost and green route for oil recovery. However, it is still limited by the low oil recovery rate due to insufficient internal pathways for oil transport. In this paper, a graphene petal foam (GPF)-based oil skimmer is designed and fabricated by plasma-enhanced chemical vapor deposition (PECVD) for ultrafast self-pumping oil recovery from oil/water mixtures. The hierarchical structure, containing micro- and nano-channels formed by interconnected graphene networks and vertically aligned graphene petals (GPs), respectively, and micro-pores inherited from the 3D interconnected structure of Ni foam, provides multiple fast passages for oil transport. An oil recovery rate of 135.2 L m −2 h −1 is achieved in dark conditions for such oil skimmers, while the value is increased to 318.8 L m −2 h −1 under solar irradiation of 1 kW m −2 because of the excellent solar-heating effect of GPs. Quantitative analyses suggest that 68.8% of such a high oil recovery rate is contributed by the nano-channels and micro-pores, while 31.2% arises from the micro-channels. Our demonstrated GPF oil skimmers exhibit great promise for fast spontaneous and continuous oil contamination cleanup. 

We observed two Terrestrial Gamma‐ray Flashes (TGFs) in Uchinada, Japan associated with negative cloud‐to‐ground lightning strokes exactly 1 year apart on 18 December 2020 and 2021. The events were remarkable for their lateral distance from the associated strokes—each about 5 km away from the detector site. Not only was that lateral distance remarkable on its own for a ground based detection, but the low‐altitude profile of winter thunderstorms in Japan would suggest the detections occurred at unprecedented nadir angles—73.3° off axis for the 2020 event with the standard assumption of a vertically oriented TGF. Unsurprisingly, Monte Carlo simulations of the straightforward interpretation of these events yield fluences 2 orders of magnitude lower than observed data. We investigate a variety of ways to attempt to resolve the contradiction between expected and observed behavior.