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The COVID-19 outbreak is asynchronous in US counties. Mitigating the COVID-19 transmission requires not only the state and federal level order of protective measures such as social distancing and testing, but also public awareness of time-dependent risk and reactions at county and community levels. We propose a robust approach to estimate the heterogeneous progression of SARS-CoV-2 at all US counties having no less than 2 COVID-19 associated deaths, and we use the daily probability of contracting (PoC) SARS-CoV-2 for a susceptible individual to quantify the risk of SARS-CoV-2 transmission in a community. We found that shortening by 5 % of the infectious period of SARS-CoV-2 can reduce around 39 % (or 78 K, 95 % CI: [66 K , 89 K ]) of the COVID-19 associated deaths in the US as of 20 September 2020. Our findings also indicate that reducing infection and deaths by a shortened infectious period is more pronounced for areas with the effective reproduction number close to 1, suggesting that testing should be used along with other mitigation measures, such as social distancing and facial mask-wearing, to reduce the transmission rate. Our deliverable includes a dynamic county-level map for local officials to determine optimal policy responses and for the public to better understand the risk of contracting SARS-CoV-2 on each day.

Real-time monitoring of volcanic eruptions involving caldera-forming events are rare (see the Perspective by Sigmundsson). Anderson et al. used several types of geophysical observations to track the caldera-forming collapse at the top of Kīlauea Volcano, Hawai'i, during the 2018 eruption. Gansecki et al. used near–real-time lava composition analysis to determine when magma shifted from highly viscous, slow-moving lava to low-viscosity, fast-moving lava. Patrick et al. used a range of geophysical tools to connect processes at the summit to lava rates coming out of far-away fissures. Together, the three studies improve caldera-collapse models and may help improve real-time hazard responses. Science , this issue p. eaaz0147 , p. eaay9070 ; p. eaaz1822 ; see also p. 1200 Geophysical observations track the caldera collapse event during the 2018 Kīlauea volcanic eruption. Caldera-forming eruptions are among Earth’s most hazardous natural phenomena, yet the architecture of subcaldera magma reservoirs and the conditions that trigger collapse are poorly understood. Observations from the formation of a 0.8–cubic kilometer basaltic caldera at Kīlauea Volcano in 2018 included the draining of an active lava lake, which provided a window into pressure decrease in the reservoir. We show that failure began after <4% of magma was withdrawn from a shallow reservoir beneath the volcano’s summit, reducing its internal pressure by ~17 megapascals. Several cubic kilometers of magma were stored in the reservoir, and only a fraction was withdrawn before the end of the eruption. Thus, caldera formation may begin after withdrawal of only small amounts of magma and may end before source reservoirs are completely evacuated.

Glaucoma is the major cause of irreversible blindness in the world characterized by progressive retinal neurodegeneration, in which local inflammation in retina is involved in persistent loss of retinal ganglion cells (RGCs). In order to explore whether aryl hydrocarbon receptor (AhR) and its agonists tryptophan metabolites are involved in the development of glaucoma, we collected serum and retinas from non-glaucoma controls and patients with glaucoma. Results showed altered serum tryptophan metabolism and reduced retinal AhR expression in glaucoma patients. We also showed intraperitoneally injection of tryptophan metabolite 2-(1′H-indole-3′-carbonyl)-thiazole-4-carboxylic acid methyl ester (ITE) down-regulated retinal local inflammation and protected RGC apoptosis from retinal ischemia/reperfusion (IR) injury via AhR activation. We further revealed that ITE could inhibit inflammation in BV2 microglia and alleviate the neurotoxicity of microglial conditioned medium to RGCs under IR. Finally, we illustrated the possible mechanism that ITE limited ERK and NFκB dependent microglial inflammation. In summary, these findings suggest the critical role of tryptophan metabolism and retinal AhR signaling in modulating local inflammation mediated by microglia in glaucoma, and provide a novel avenue to targeting the intrinsically altered AhR signaling resulted from disturbed tryptophan metabolism for glaucoma treatment.

Purpose To perform an in vivo evaluation of the changes in Schlemm’s canal (SC) among patients with primary angle-closure disease (PACD) using swept-source optical coherence tomography (SS-OCT). Methods Patients diagnosed with PACD who had not undergone surgery were recruited. The SS-OCT quadrants scanned herein included the nasal and temporal sections at 3 and 9 o’clock, respectively. The diameter and cross-sectional area of the SC were measured. A linear mixed-effects model was performed to analyze the effects of parameters on the SC changes. The hypothesis of interest was related to the angle status (iridotrabecular contact, ITC/open angle, OPN), which was further explored with pairwise comparisons of the estimated marginal means (EMMs) of the SC diameter and SC area. In the ITC regions, the relationship between the trabecular-iris contact length (TICL) percentage and SC parameters was also studied by a mixed model. Results A total of 49 eyes of 35 patients were included for measurements and analysis. The percentage of observable SCs in the ITC regions was only 58.5% (24/41), whereas it was 86.0% (49/57) in the OPN regions (χ 2  = 9.44, p  = 0.002). ITC was significantly associated with a decreasing SC size. The EMMs for the diameter and cross-sectional area of SC at the ITC and OPN regions were 203.34 μm versus 261.41 μm ( p  = 0.006) and 3174.43 μm 2 versus 5347.63 μm 2 ( p  = 0.022), respectively. Sex, age, spherical equivalent refraction, intraocular pressure, axial length, extent of angle closure, history of acute attack and treatment with LPI were not significantly associated with SC parameters. In the ITC regions, a larger TICL percentage was significantly associated with a decrease in SC diameter and area ( p  = 0.003 and 0.019, respectively). Conclusions The morphologies of SC could be affected by the angle status (ITC/OPN) in patients with PACD, and ITC was significantly associated with a decreasing SC size. These changes in SC as described by OCT scans might help to elucidate the progression mechanisms of PACD.

Astrocytes play a crucial role in regulating sleep‐wake behavior. However, how astrocytes govern a specific sleep‐arousal circuit remains unknown. Here, the authors show that parafacial zone (PZ) astrocytes responded to sleep‐wake cycles with state‐differential Ca2+ activity, peaking during transitions from sleep to wakefulness. Using chemogenetic and optogenetic approaches, they find that activating PZ astrocytes elicited and sustained wakefulness by prolonging arousal episodes while impeding transitions from wakefulness to non‐rapid eye movement (NREM) sleep. Activation of PZ astrocytes specially induced the elevation of extracellular adenosine through the ATP hydrolysis pathway but not equilibrative nucleoside transporter (ENT) mediated transportation. Strikingly, the rise in adenosine levels induced arousal by activating A1 receptors, suggesting a distinct role for adenosine in the PZ beyond its conventional sleep homeostasis modulation observed in the basal forebrain (BF) and cortex. Moreover, at the circuit level, PZ astrocyte activation induced arousal by suppressing the GABA release from the PZGABA neurons, which promote NREM sleep and project to the parabrachial nucleus (PB). Thus, their study unveils a distinctive arousal‐promoting effect of astrocytes within the PZ through extracellular adenosine and elucidates the underlying mechanism at the neural circuit level. This study shows that astrocyte activation in the PZ promotes arousal at the expense of NREM and REM sleep. Adenosine, produced by astrocytes via CD73/39, promotes wakefulness through A1 receptors. Additionally, astrocytes suppress GABA release from PZGABA neurons projecting to the PB, emphasizing astrocyte‐neuron communication in arousal regulation at the circuit level.

We consider the problem of emulating (approximating) computer models (simulators) that produce massive output. The specific simulator we study is a computer model of volcanic pyroclastic flow, a single run of which produces up to 10⁹ outputs over a space-time grid of coordinates. An emulator (essentially a statistical model of the simulator—we use a Gaussian Process) that is computationally suitable for such massive output is developed and studied from practical and theoretical perspectives. On the practical side, the emulator does unexpectedly well in predicting what the simulator would produce, even better than much more flexible and computationally intensive alternatives. This allows the attainment of the scientific goal of this work, accurate assessment of the hazards from pyroclastic flows over wide spatial domains. Theoretical results are also developed that provide insight into the unexpected success of the massive emulator. Generalizations of the emulator are introduced that allow for a nugget, which is useful for the application to hazard assessment.

We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive. The posterior modes that are studied arise from objective priors, such as the reference prior. These priors have been studied in the literature for the situation of an isotropic covariance function or under the assumption of separability in the design of inputs for model runs used in the GaSP construction. In this paper, we consider more general designs (e.g., a Latin Hypercube Design) with a class of commonly used anisotropic correlation functions, which can be written as a product of isotropic correlation functions, each having an unknown range parameter and a fixed roughness parameter. We discuss properties of the objective priors and marginal likelihoods for the parameters of the GaSP and establish the posterior propriety of the GaSP parameters, but our main focus is to demonstrate that certain parameterizations result in more robust estimation of the GaSP parameters than others, and that some parameterizations that are in common use should clearly be avoided. These results are applicable to many frequently used covariance functions, for example, power exponential, Matérn, rational quadratic and spherical covariance. We also generalize the results to the GaSP model with a nugget parameter. Both theoretical and numerical evidence is presented concerning the performance of the studied procedures.

Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field observations. Mathematical models for forward predictions are often written in computer code, and they can be computationally expensive slow to run. To overcome the computational bottleneck from the simulator, we implemented a statistical emulator from the RobustGaSP package for emulating both scalar-valued or vector-valued computer model outputs. Both posterior sampling and maximum likelihood approach are implemented in the RobustCalibration package for parameter estimation. For imperfect computer models, we implement Gaussian stochastic process and the scaled Gaussian stochastic process for modeling the discrepancy function between the reality and mathematical model. This package is applicable to various types of field observations, such as repeated experiments and multiple sources of measurements. We discuss numerical examples of calibrating mathematical models that have closed-form expressions, and differential equations solved by numerical methods.

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference. Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufrière Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.