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  1. We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable in nite dimensional C*-algebra A is asymptotically tracially in the class of C-algebras with nite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear Z-stable C-algebras. 1
  2. We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method, thereby providing a systematic way for deriving several well-known decentralized algorithms including EXTRA [41] and SSDA [37]. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds. We provide experimental results that demonstrate the effectiveness of the proposed algorithm on highly ill-conditioned problems.
  3. Abstract On 2019 August 14 at 21:10:39 UTC, the LIGO/Virgo Collaboration (LVC) detected a possible neutron star–black hole merger (NSBH), the first ever identified. An extensive search for an optical counterpart of this event, designated GW190814, was undertaken using the Dark Energy Camera on the 4 m Victor M. Blanco Telescope at the Cerro Tololo Inter-American Observatory. Target of Opportunity interrupts were issued on eight separate nights to observe 11 candidates using the 4.1 m Southern Astrophysical Research (SOAR) telescope’s Goodman High Throughput Spectrograph in order to assess whether any of these transients was likely to be an optical counterpartmore »of the possible NSBH merger. Here, we describe the process of observing with SOAR, the analysis of our spectra, our spectroscopic typing methodology, and our resultant conclusion that none of the candidates corresponded to the gravitational wave merger event but were all instead other transients. Finally, we describe the lessons learned from this effort. Application of these lessons will be critical for a successful community spectroscopic follow-up program for LVC observing run 4 (O4) and beyond.« less
    Free, publicly-accessible full text available April 1, 2023
  4. We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed approach allows one to use them without assuming any knowledge about the convexity of the objective. In general, the scheme is guaranteed to produce a stationary point with a worst-case efficiency typical of first-order methods, and when the objective turns out to be convex, it automatically accelerates in the sense of Nesterov and achieves near-optimal convergence rate in function values. We conclude the paper by showing promising experimental resultsmore »obtained by applying our approach to incremental algorithms such as SVRG and SAGA for sparse matrix factorization and for learning neural networks« less