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Context. A large fraction of stars form in clusters containing high-mass stars, which subsequently influences the local and galaxy-wide environment. Aims. Fundamental questions about the physics responsible for fragmenting molecular parsec-scale clumps into cores of a few thousand astronomical units (au) are still open, that only a statistically significant investigation with ALMA is able to address; for instance: the identification of the dominant agents that determine the core demographics, mass, and spatial distribution as a function of the physical properties of the hosting clumps, their evolutionary stage and the different Galactic environments in which they reside. The extent to which fragmentation is driven by clumps dynamics or mass transport in filaments also remains elusive. Methods. With the ALMAGAL project, we observed the 1.38 mm continuum and lines toward more than 1000 dense clumps in our Galaxy, withM≥ 500 M_⊙, Σ ≥ 0.1 g cm⁻²andd≤ 7.5 kiloparsec (kpc). Two different combinations of ALMA Compact Array (ACA) and 12-m array setups were used to deliver a minimum resolution of ∼1000 au over the entire sample distance range. The sample covers all evolutionary stages from infrared dark clouds (IRDCs) to H IIregions from the tip of the Galactic bar to the outskirts of the Galaxy. With a continuum sensitivity of 0.1 mJy, ALMAGAL enables a complete study of the clump-to-core fragmentation process down toM∼ 0.3 M_⊙across the Galaxy. The spectral setup includes several molecular lines to trace the multiscale physics and dynamics of gas, notably CH₃CN, H₂CO, SiO, CH₃OH, DCN, HC₃N, and SO, among others. Results. We present an initial overview of the observations and the early science product and results produced in the ALMAGAL Consortium, with a first characterization of the morphological properties of the continuum emission detected above 5σin our fields. We used “perimeter-versus-area” and convex hull-versus-area metrics to classify the different morphologies. We find that more extended and morphologically complex (significantly departing from circular or generally convex) shapes are found toward clumps that are relatively more evolved and have higher surface densities. Conclusions. ALMAGAL is poised to serve as a game-changer for a number of specific issues in star formation: clump-to-core fragmentation processes, demographics of cores, core and clump gas chemistry and dynamics, infall and outflow dynamics, and disk detections. Many of these issues will be covered in the first generation of papers that closely follow on the present publication. 

We consider the problem of velocity inversion/calibration in passive survey, where the seismic source is also an unknown. In earthquake detection or microseismic localization, the major task is to reconstruct the passive seismic sources, but due to the source-velocity coupling, source reconstructions are inherently affected by inaccurate knowledge of the velocity, bringing the need of velocity calibration. We propose a source independent velocity calibration method that recovers the velocity without the source information, thus providing a better ground for source inversion. Unlike existing methods that assume sources to be a linear combination of separated point sources, the proposed method allows sources to lie on a line singularity (representing rock cracks), as long as the activation time is relatively brief. The proposed approach is based on the observation that the spatial distribution of the source is separable from the velocity model after a proper Helmholtz domain projection. 

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.