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Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property called the semistability of second subderivatives and demonstrate that it is widely satisfied for numerous classes of functions, which is important for applications in constrained and composite optimization problems. Using the latter condition and a certain second-order sufficient condition, we are able to establish Q-linear convergence of the primal-dual sequence for an inexact version of the ALM for composite programs. Funding: Research of the first author is partially supported by Singapore National Academy of Science via SASEAF Programme under the grant RIE2025 NRF International Partnership Funding Initiative. Research of the second author is partially supported by the National Science Foundation under the grant DMS 2108546. 

We discuss a novel approach for imaging local faults inside an infinite bi-periodic layered medium in ℝ3 using acoustic measurements of scattered fields at the bottom or the top of the layer. The faulted area is represented by compactly supported perturbations with erroneous material properties. Our method reconstructs the support of perturbations without knowing or reconstructing the constitutive material parameters of healthy or faulty bi-period layer; only the size of the period is needed. This approach falls under the class of non-iterative imaging methods, known as the generalized linear sampling method with differential measurements, first introduced in [2] and adapted to periodic layers in [25]. The advantage of applying differential measurements to our inverse problem is that instead of comparing the measured data against measurements due to healthy structures, one makes use of periodicity of the layer where the data operator restricted to single Floquet-Bloch modes plays the role of the one corresponding to healthy material. This leads to a computationally efficient and mathematically rigorous reconstruction algorithm. We present numerical experiments that confirm the viability of the approach for various configurations of defects 

Abstract We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the Class 0 protostar IRAS 04166+2706, obtained as part of the ALMA Large Program Early Planet Formation in Embedded Disks. These observations were made in the 1.3 mm dust continuum and molecular lines at angular resolutions of $\sim 0\stackrel{″}{.}05$(∼8 au) and $\sim 0\stackrel{″}{.}16$(∼25 au), respectively. The continuum emission shows a disklike structure with a radius of ∼22 au. Kinematical analysis of¹³CO (2–1), C¹⁸O (2–1), H₂CO (3_0,3–2_0,2), CH₃OH (4₂–3₁) emission demonstrates that these molecular lines trace the infalling-rotating envelope and possibly a Keplerian disk, enabling us to estimate the protostar mass to be 0.15M_⊙ < M_⋆ < 0.39M_⊙. The dusty disk is found to exhibit a brightness asymmetry along its minor axis in the continuum emission, probably caused by a flared distribution of the dust and the high optical depth of the dust emission. In addition, the¹²CO (2–1) and SiO (5–4) emissions show knotty and wiggling motions in the jets. Our high-angular-resolution observations revealed the most recent mass ejection events, which have occurred within the last ∼25 yr. 

Mitochondria play a central role in muscle metabolism and function. A unique family of iron–sulfur proteins, termed CDGSH Iron Sulfur Domain-containing (CISD/NEET) proteins, support mitochondrial function in skeletal muscles. The abundance of these proteins declines during aging leading to muscle degeneration. Although the function of the outer mitochondrial CISD/NEET proteins, CISD1/mitoNEET and CISD2/NAF-1, has been defined in skeletal muscle cells, the role of the inner mitochondrial CISD protein, CISD3/MiNT, is currently unknown. Here, we show that CISD3 deficiency in mice results in muscle atrophy that shares proteomic features with Duchenne muscular dystrophy. We further reveal that CISD3 deficiency impairs the function and structure of skeletal muscles, as well as their mitochondria, and that CISD3 interacts with, and donates its [2Fe-2S] clusters to, complex I respiratory chain subunit NADH Ubiquinone Oxidoreductase Core Subunit V2 (NDUFV2). Using coevolutionary and structural computational tools, we model a CISD3–NDUFV2 complex with proximal coevolving residue interactions conducive of [2Fe-2S] cluster transfer reactions, placing the clusters of the two proteins 10 to 16 Å apart. Taken together, our findings reveal that CISD3/MiNT is important for supporting the biogenesis and function of complex I, essential for muscle maintenance and function. Interventions that target CISD3 could therefore impact different muscle degeneration syndromes, aging, and related conditions. 

Abstract We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We describe the¹²CO (J= 2–1),¹³CO (J= 2–1), C¹⁸O (J= 2–1), H₂CO (J= 3_2,1–2_2,0), and SiO (J= 5–4) molecular lines along with the 1.3 mm continuum at high spatial resolution (∼0.″08 or ∼5 au). Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central compact component and extended continuum emission. The compact components are smooth and show no sign of substructures such as spirals, rings, or gaps. However, there is a brightness asymmetry along the minor axis of the presumed disk in IRS1, possibly indicative of an inclined geometrically and optically thick disk-like component. Using a position–velocity diagram analysis of the C¹⁸O line, clear Keplerian motions were not detected toward either source. If Keplerian rotationally supported disks are present, they are likely deeply embedded in their envelope. However, we can set upper limits of the central protostellar mass of 0.46M_⊙and 0.26M_⊙for BHR 71 IRS1 and BHR 71 IRS2, respectively. Outflows traced by¹²CO and SiO are detected in both sources. The outflows can be divided into two components, a wide-angle outflow and a jet. In IRS1, the jet exhibits a double helical structure, reflecting the removal of angular momentum from the system. In IRS2, the jet is very collimated and shows a chain of knots, suggesting episodic accretion events. 

Abstract Young protostellar binary systems, with expected ages less than ∼10⁵yr, are little modified since birth, providing key clues to binary formation and evolution. We present a first look at the young, Class 0 binary protostellar system R CrA IRAS 32 from the Early Planet Formation in Embedded Disks ALMA large program, which observed the system in the 1.3 mm continuum emission,¹²CO (2−1),¹³CO (2−1), C¹⁸O (2−1), SO (6₅−5₄), and nine other molecular lines that trace disks, envelopes, shocks, and outflows. With a continuum resolution of ∼0.″03 (∼5 au, at a distance of 150 pc), we characterize the newly discovered binary system with a separation of 207 au, their circumstellar disks, and a circumbinary disklike structure. The circumstellar disk radii are 26.9 ± 0.3 and 22.8 ± 0.3 au for sources A and B, respectively, and their circumstellar disk dust masses are estimated as 22.5 ± 1.1M_⊕and 12.4 ± 0.6M_⊕, respectively. The circumstellar disks and the circumbinary structure have well-aligned position angles and inclinations, indicating formation in a smooth, ordered process such as disk fragmentation. In addition, the circumstellar disks have a near/far-side asymmetry in the continuum emission, suggesting that the dust has yet to settle into a thin layer near the midplane. Spectral analysis of CO isotopologues reveals outflows that originate from both of the sources and possibly from the circumbinary disklike structure. Furthermore, we detect Keplerian rotation in the¹³CO isotopologues toward both circumstellar disks and likely Keplerian rotation in the circumbinary structure; the latter suggests that it is probably a circumbinary disk. 

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the inverse problem. The first one employs a 'far-field' transform to the data which we then use to derive and provide an explicit decay rate for the imaging functional. In order to analyze the behavior of this imaging functional we use the factorization of the near field operator as well as the Funk-Hecke integral identity. For the second imaging functional the Cauchy data is used to define the functional and its behavior is analyzed using the Green's identities. Numerical experiments are given in two dimensions for both isotropic and anisotropic scatterers.