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Abstract The HH 111 protostellar disk has recently been found to host a pair of spiral arms. Here we report the dust polarization results in the disk as well as the inner envelope around it, obtained with the Atacama Large Millimeter/submillimeter Array in continuum atλ∼ 870μm and ∼0.″05 resolution. In the inner envelope, polarization is detected with a polarization degree of ∼6% and an orientation almost everywhere parallel to the minor axis of the disk and thus likely to be due to the dust grains magnetically aligned mainly by toroidal fields. In the disk, the polarization orientation is roughly azimuthal on the far side and becomes parallel to the minor axis on the near side, with a polarization gap in between on the far side near the central protostar. The disk polarization degree is ∼2%. The polarized intensity is higher on the near side than the far side, showing a near–far side asymmetry. More importantly, the polarized intensity and thus polarization degree are lower in the spiral arms but higher in between the arms, showing an anticorrelation of the polarized intensity with the spiral arms. Our modeling results indicate that this anticorrelation is useful for constraining the polarization mechanism and is consistent with the dust self-scattering by the grains that have grown to a size of ∼150μm. The interarms are sandwiched and illuminated by two brighter spiral arms and thus have higher polarized intensity. Our dust self-scattering model can also reproduce the observed polarization orientation parallel to the minor axis on the near side and the observed azimuthal polarization orientation at the two disk edges in the major axis. Further modeling work is needed to study how to reproduce the observed near–far side asymmetry in the polarized intensity and the observed azimuthal polarization orientation on the far side. 

We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for threshold tests, small-space algorithms, and small-depth circuits. In particular, we obtain small-bias distributions that - achieve an optimal lower bound on their statistical distance to any bounded-uniform distribution. This closes a line of research initiated by Alon, Goldreich, and Mansour in 2003, and improves on a result by O'Donnell and Zhao. - have heavier tail mass than the uniform distribution. This answers a question posed by several researchers including Bun and Steinke. - rule out a popular paradigm for constructing pseudorandom generators, originating in a 1989 work by Ajtai and Wigderson. This again answers a question raised by several researchers. For branching programs, our result matches a bound by Forbes and Kelley. Our small-bias distributions above are symmetric. We show that the xor of any two symmetric small-bias distributions fools any bounded function. Hence our examples cannot be extended to the xor of two small-bias distributions, another popular paradigm whose power remains unknown. We also generalize and simplify the proof of a result of Bazzi. 

The goal of trace reconstruction is to reconstruct an unknown n-bit string x given only independent random traces of x, where a random trace of x is obtained by passing x through a deletion channel. A Statistical Query (SQ) algorithm for trace reconstruction is an algorithm which can only access statistical information about the distribution of random traces of x rather than individual traces themselves. Such an algorithm is said to be 𝓁-local if each of its statistical queries corresponds to an 𝓁-junta function over some block of 𝓁 consecutive bits in the trace. Since several - but not all - known algorithms for trace reconstruction fall under the local statistical query paradigm, it is interesting to understand the abilities and limitations of local SQ algorithms for trace reconstruction. In this paper we establish nearly-matching upper and lower bounds on local Statistical Query algorithms for both worst-case and average-case trace reconstruction. For the worst-case problem, we show that there is an Õ(n^{1/5})-local SQ algorithm that makes all its queries with tolerance τ ≥ 2^{-Õ(n^{1/5})}, and also that any Õ(n^{1/5})-local SQ algorithm must make some query with tolerance τ ≤ 2^{-Ω̃(n^{1/5})}. For the average-case problem, we show that there is an O(log n)-local SQ algorithm that makes all its queries with tolerance τ ≥ 1/poly(n), and also that any O(log n)-local SQ algorithm must make some query with tolerance τ ≤ 1/poly(n). 

We give new upper and lower bounds on the power of several restricted classes of arbitrary-order read-once branching programs (ROBPs) and standard-order ROBPs (SOBPs) that have received significant attention in the literature on pseudorandomness for space-bounded computation. - Regular SOBPs of length n and width ⌊w(n+1)/2⌋ can exactly simulate general SOBPs of length n and width w, and moreover an n/2-o(n) blow-up in width is necessary for such a simulation. Our result extends and simplifies prior average-case simulations (Reingold, Trevisan, and Vadhan (STOC 2006), Bogdanov, Hoza, Prakriya, and Pyne (CCC 2022)), in particular implying that weighted pseudorandom generators (Braverman, Cohen, and Garg (SICOMP 2020)) for regular SOBPs of width poly(n) or larger automatically extend to general SOBPs. Furthermore, our simulation also extends to general (even read-many) oblivious branching programs. - There exist natural functions computable by regular SOBPs of constant width that are average-case hard for permutation SOBPs of exponential width. Indeed, we show that Inner-Product mod 2 is average-case hard for arbitrary-order permutation ROBPs of exponential width. - There exist functions computable by constant-width arbitrary-order permutation ROBPs that are worst-case hard for exponential-width SOBPs. - Read-twice permutation branching programs of subexponential width can simulate polynomial-width arbitrary-order ROBPs. 

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.