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Context. The Milky Way’s central molecular zone (CMZ) has been measured to form stars ten times less efficiently than in the Galactic disk, based on emission from high-mass stars. However, the CMZ’s low-mass (⩽2M_⊙) protostellar population, which accounts for most of the initial stellar mass budget and star formation rate (SFR), is poorly constrained observationally due to limited sensitivity and resolution. Aims. We aim to perform a cloud-wide census of the protostellar population in three massive CMZ clouds. Methods. We present the Dual-band Unified Exploration of three CMZ Clouds (DUET) survey, targeting the 20 km s⁻¹cloud, Sgr C, and the dust ridge cloud “e” using the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.3 and 3 mm. The mosaicked observations achieve a comparable resolution of 0.^′′2–0.^′′3 (∼2000 au) and a sky coverage of 8.3–10.4 arcmin², respectively. Results. We report 563 continuum sources at 1.3 mm and 330 at 3 mm, respectively, and a dual-band catalog with 450 continuum sources. These sources are marginally resolved at a resolution of 2000 au. We find a universal deviation (>70% of the source sample) from commonly used dust modified blackbody (MBB) models, characterized by either low spectral indices or low brightness temperatures. Conclusions. Three possible explanations are discussed for the deviation. (1) Optically thick class 0/I young stellar objects (YSOs) with a very small beam filling factor can lead to lower brightness temperatures than what MBB models predict. (2) Large dust grains with millimeter or centimeter in size have more significant self-scattering, and frequency-dependent albedo could therefore cause lower spectral indices. (3) Free-free emission over 30 μJy can severely contaminate dust emission and cause low spectral indices for milliJansky sources, although the number of massive protostars (embedded UCHIIregions) needed is infeasibly high for the normal stellar initial mass function. A reliable measurement of the SFR at low protostellar masses will require future work to distinguish between these possible explanations. 

Promoting well-being is one of the key targets of the Sustainable Development Goals at the United Nations. Many national and city governments worldwide are incorporating Subjective Well-Being (SWB) indicators into their agenda, to complement traditional objective development and economic metrics. In this study, we introduce the Twitter Sentiment Geographical Index (TSGI), a location-specific expressed sentiment database with SWB implications, derived through deep-learning-based natural language processing techniques applied to 4.3 billion geotagged tweets worldwide since 2019. Our open-source TSGI database represents the most extensive Twitter sentiment resource to date, encompassing multilingual sentiment measurements across 164 countries at the admin-2 (county/city) level and daily frequency. Based on the TSGI database, we have created a web platform allowing researchers to access the sentiment indices of selected regions in the given time period.