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We present a novel approach to reconstruct gas and dark matter projected density maps of galaxy clusters using score-based generative modeling. Our diffusion model takes in mock SZ and X-ray images as conditional inputs, and generates realizations of corresponding gas and dark matter maps by sampling from a learned data posterior. We train and validate the performance of our model by using mock data from a hydrodynamical cosmological simulation. The model accurately reconstructs both the mean and spread of the radial density profiles in the spatial domain, indicating that the model is able to distinguish between clusters of different mass sizes. In the spectral domain, the model achieves close-to-unity values for the bias and cross-correlation coefficients, indicating that the model can accurately probe cluster structures on both large and small scales. Our experiments demonstrate the ability of score models to learn a strong, nonlinear, and unbiased mapping between input observables and fundamental density distributions of galaxy clusters. These diffusion models can be further fine-tuned and generalized to not only take in additional observables as inputs, but also real observations and predict unknown density distributions of galaxy clusters. 

Low-cost sensors enable finer-scale spatiotemporal measurements within the existing methane (CH 4 ) monitoring infrastructure and could help cities mitigate CH 4 emissions to meet their climate goals. While initial studies of low-cost CH 4 sensors have shown potential for effective CH 4 measurement at ambient concentrations, sensor deployment remains limited due to questions about interferences and calibration across environments and seasons. This study evaluates sensor performance across seasons with specific attention paid to the sensor's understudied carbon monoxide (CO) interferences and environmental dependencies through long-term ambient co-location in an urban environment. The sensor was first evaluated in a laboratory using chamber calibration and co-location experiments, and then in the field through two 8 week co-locations with a reference CH 4 instrument. In the laboratory, the sensor was sensitive to CH 4 concentrations below ambient background concentrations. Different sensor units responded similarly to changing CH 4 , CO, temperature, and humidity conditions but required individual calibrations to account for differences in sensor response factors. When deployed in-field, co-located with a reference instrument near Baltimore, MD, the sensor captured diurnal trends in hourly CH 4 concentration after corrections for temperature, absolute humidity, CO concentration, and hour of day. Variable performance was observed across seasons with the sensor performing well ( R 2 = 0.65; percent bias 3.12%; RMSE 0.10 ppm) in the winter validation period and less accurately ( R 2 = 0.12; percent bias 3.01%; RMSE 0.08 ppm) in the summer validation period where there was less dynamic range in CH 4 concentrations. The results highlight the utility of sensor deployment in more variable ambient CH 4 conditions and demonstrate the importance of accounting for temperature and humidity dependencies as well as co-located CO concentrations with low-cost CH 4 measurements. We show this can be addressed via Multiple Linear Regression (MLR) models accounting for key covariates to enable urban measurements in areas with CH 4 enhancement. Together with individualized calibration prior to deployment, the sensor shows promise for use in low-cost sensor networks and represents a valuable supplement to existing monitoring strategies to identify CH 4 hotspots. 

This article synthesizes findings from an international virtual conference, funded by the United States National Science Foundation, focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children’s outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct—focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars.