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Abstract A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials. 

In this paper, we develop a novel procedure for low-rank tensor regression, namely Importance Sketching Low-rank Estimation for Tensors (ISLET). The central idea behind ISLET is importance sketching, i.e., carefully designed sketches based on both the responses and low-dimensional structure of the parameter of interest. We show that the proposed method is sharply minimax optimal in terms of the mean-squared error under low-rank Tucker assumptions and under the randomized Gaussian ensemble design. In addition, if a tensor is low-rank with group sparsity, our procedure also achieves minimax optimality. Further, we show through numerical study that ISLET achieves comparable or better mean-squared error performance to existing state-of-the-art methods while having substantial storage and run-time advantages including capabilities for parallel and distributed computing. In particular, our procedure performs reliable estimation with tensors of dimension $p = O(10^8)$ and is 1 or 2 orders of magnitude faster than baseline methods. 

Abstract The dispersive sweep of fast radio bursts (FRBs) has been used to probe the ionized baryon content of the intergalactic medium 1 , which is assumed to dominate the total extragalactic dispersion. Although the host-galaxy contributions to the dispersion measure appear to be small for most FRBs 2 , in at least one case there is evidence for an extreme magneto-ionic local environment 3,4 and a compact persistent radio source 5 . Here we report the detection and localization of the repeating FRB 20190520B, which is co-located with a compact, persistent radio source and associated with a dwarf host galaxy of high specific-star-formation rate at a redshift of 0.241 ± 0.001. The estimated host-galaxy dispersion measure of approximately $${903}_{-111}^{+72}$$ 903 − 111 + 72 parsecs per cubic centimetre, which is nearly an order of magnitude higher than the average of FRB host galaxies 2,6 , far exceeds the dispersion-measure contribution of the intergalactic medium. Caution is thus warranted in inferring redshifts for FRBs without accurate host-galaxy identifications. 

Presentations on ''Structure Functions and Parton Densities'' working group are summarized. They include results from various global analyses for the parton distribution functions (PDFs) inside the proton and nucleus, and the impact of new experimental data and progress in theoretical calculations, on the extraction of PDFs. Various studies were also presented regarding the constraints on the proton and nuclear PDFs from some specific experimental data from the LHC, HERA and RHIC, and elsewhere. 

Design and implementation of the first (asymmetric) Fe-catalyzed intra- and intermolecular difunctionalization of vinyl cyclopropanes (VCPs) with alkyl halides and aryl Grignard reagents has been realized via a mechanistically driven approach. Mechanistic studies support the diffusion of the alkyl radical intermediates out of the solvent cage to participate in an intra- or -intermolecular radical cascade with the VCP followed by re-entering the Fe radical cross-coupling cycle to undergo selective C(sp2)-C(sp3) bond formation. Overall, we provide new design principles for Fe-mediated radical processes and underscore the potential of using combined computations and experiments to accelerate the development of challenging transformations. 

We report the phase-connected timing ephemeris, polarization pulse profiles, Faraday rotation measurements, and Rotating-Vector-Model (RVM) fitting results of 12 millisecond pulsars (MSPs) discovered with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in the Commensal Radio Astronomy FAST survey (CRAFTS). The timing campaigns were carried out with FAST and Arecibo over 3 yr. 11 of the 12 pulsars are in neutron star–white dwarf binary systems, with orbital periods between 2.4 and 100 d. 10 of them have spin periods, companion masses, and orbital eccentricities that are consistent with the theoretical expectations for MSP–Helium white dwarf (He WD) systems. The last binary pulsar (PSR J1912−0952) has a significantly smaller spin frequency and a smaller companion mass, the latter could be caused by a low orbital inclination for the system. Its orbital period of 29 d is well within the range of orbital periods where some MSP–He WD systems have shown anomalous eccentricities, however, the eccentricity of PSR J1912−0952 is typical of what one finds for the remaining MSP–He WD systems.