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{"Abstract":["We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: \r\n1) We consider read-once group-products over a finite group G, i.e., tests of the form ∏_{i=1}^n (g_i)^{x_i} where g_i ∈ G, a special case of read-once permutation branching programs. We give generators with optimal seed length c_G log(n/ε) over any p-group. The proof uses the small-bias plus noise paradigm, but derandomizes the noise to avoid the recursion in previous work. Our generator works when the bits are read in any order. Previously for any non-commutative group the best seed length was ≥ log n log(1/ε), even for a fixed order.\r\n2) We give a reduction that "lifts" suitable generators for group products over G to a generator that fools width-w block products, i.e., tests of the form ∏ (g_i)^{f_i} where the f_i are arbitrary functions on disjoint blocks of w bits. Block products generalize several previously studied classes. The reduction applies to groups that are mixing in a representation-theoretic sense that we identify.\r\n3) Combining (2) with (1) and other works we obtain new generators for block products over the quaternions or over any commutative group, with nearly optimal seed length. In particular, we obtain generators for read-once polynomials modulo any fixed m with nearly optimal seed length. Previously this was known only for m = 2.\r\n4) We give a new generator for products over "mixing groups." The construction departs from previous work and uses representation theory. For constant error, we obtain optimal seed length, improving on previous work (which applied to any group). \r\nThis paper identifies a challenge in the area that is reminiscent of a roadblock in circuit complexity - handling composite moduli - and points to several classes of groups to be attacked next."]} 

Abstract Jets can facilitate the mass accretion onto the protostars in star formation. They are believed to be launched from accretion disks around the protostars by magnetocentrifugal force, as supported by the detections of rotation and magnetic fields in some of them. Here we report a radial flow of the textbook-case protostellar jet HH 212 at the base to further support this jet-launching scenario. This radial flow validates a central prediction of the magnetocentrifugal theory of jet formation and collimation, namely, the jet is the densest part of a wide-angle wind that flows radially outward at distances far from the (small, sub-au) launching region. Additional evidence for the radially flowing wide-angle component comes from its ability to reproduce the structure and kinematics of the shells detected around the HH 212 jet. This component, which can transport material from the inner to outer disk, could account for the chondrules and Ca–Al-rich inclusions detected in the solar system at large distances. 

Abstract We have obtained sensitive dust continuum polarization observations at 850 μ m in the B213 region of Taurus using POL-2 on SCUBA-2 at the James Clerk Maxwell Telescope as part of the B -fields in STar-forming Region Observations (BISTRO) survey. These observations allow us to probe magnetic field ( B -field) at high spatial resolution (∼2000 au or ∼0.01 pc at 140 pc) in two protostellar cores (K04166 and K04169) and one prestellar core (Miz-8b) that lie within the B213 filament. Using the Davis–Chandrasekhar–Fermi method, we estimate the B -field strengths in K04166, K04169, and Miz-8b to be 38 ± 14, 44 ± 16, and 12 ± 5 μ G, respectively. These cores show distinct mean B -field orientations. The B -field in K04166 is well ordered and aligned parallel to the orientations of the core minor axis, outflows, core rotation axis, and large-scale uniform B -field, in accordance with magnetically regulated star formation via ambipolar diffusion taking place in K04166. The B -field in K04169 is found to be ordered but oriented nearly perpendicular to the core minor axis and large-scale B -field and not well correlated with other axes. In contrast, Miz-8b exhibits a disordered B -field that shows no preferred alignment with the core minor axis or large-scale field. We found that only one core, K04166, retains a memory of the large-scale uniform B -field. The other two cores, K04169 and Miz-8b, are decoupled from the large-scale field. Such a complex B -field configuration could be caused by gas inflow onto the filament, even in the presence of a substantial magnetic flux.