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Abstract In 2021, Chen proved that the size of any connected component of the Markoff mod$$p$$ $p$graph is divisible by$$p$$ $p$. In combination with the work of Bourgain, Gamburd, and Sarnak, Chen’s result resolves a conjecture of Baragar for all but finitely many primes: the Markoff mod$$p$$ $p$graph is connected. In particular, strong approximation for Markoff triples holds for all but finitely many primes. We provide an alternative proof of Chen’s theorem. 

Abstract For 𝓞 an imaginary quadratic ring, we compute a fundamental polyhedron in hyperbolic 3-space for the action of PE₂(𝓞), the projective elementary subgroup of PSL₂(𝓞). This allows for new, simplified proofs of theorems of Cohn, Nica, Fine, and Frohman. Namely, we obtain a presentation for PE₂(𝓞), show that it has infinite index and is its own normalizer in PSL₂(𝓞), and split PSL₂(𝓞) into a free product with amalgamation that has PE₂(𝓞) as one of its factors. 

We propose and demonstrate a general method to calibrate the frequency-dependent response of selfcompensating noble-gas–alkali-metal comagnetometers to arbitrary spin perturbations. This includes magnetic and nonmagnetic perturbations such as rotations and exotic spin interactions. The method is based on a fit of the magnetic field response to an analytical model. The frequency-dependent response of the comagnetometer to arbitrary spin perturbations can be inferred using the fit parameters. We demonstrate the effectiveness of this method by comparing the inferred rotation response to an experimental measurement of the rotation response. Our results show that experiments relying on zero-frequency calibration of the comagnetometer response can over- or underestimate the comagnetometer sensitivity by orders of magnitude over a wide frequency range. Moreover, this discrepancy accumulates over time as operational parameters tend to drift during comagnetometer operation. The demonstrated calibration protocol enables accurate prediction and control of comagnetometer sensitivity to, for example, ultralight bosonic dark-matter fields coupling to electron or nuclear spins, as well as accurate monitoring and control of the relevant system parameters. 

ABSTRACT Histone-like nucleoid structuring (H-NS) and H-NS-like proteins serve as global gene silencers and work with antagonistic transcriptional activators (counter-silencers) to properly coordinate the expression of virulence genes in pathogenic bacteria. InBrucella, MucR has been proposed as a novel H-NS-like gene silencer, but direct experimental evidence is lacking. Here, we show that MucR serves as an H-NS-like silencer of theBrucella abortusgenes encoding the polar autotransporter adhesins BtaE and BmaC, the c-di-GMP-specific phosphodiesterase BpdB, and the quorum-sensing regulator BabR. We also demonstrate that the MarR-type transcriptional activator MdrA can displace MucR from thebtaEpromoter, supporting the existence of MucR counter-silencers inBrucella. Moreover, our chromatin immunoprecipitation (ChIP)-seq analysis identified 546 MucR enrichment peaks along the genome, including in the promoters of the genes encoding the Type IV secretion machinery and effectors and the quorum-sensing regulator VjbR. Importantly, MucR ChIP-seq peaks overlap with the previously described binding sites for the transcriptional activators VjbR, BvrR, and CtrA suggesting that these regulators serve as MucR counter-silencers and work in concert with MucR to coordinate virulence gene expression inBrucella. In addition, using chromosome conformation capture (Hi-C), we show that like H-NS inEscherichia coli, MucR alters the global structure of theBrucellanucleoid. Finally, a copy of theE. coli hnsrescues the distinctive growth defect and elevatedbtaEexpression of aB. abortus mucRmutant. Together, these findings solidify the role of MucR as a novel type of H-NS-like protein and suggest that MucR’s gene-silencing properties play a key role in virulence inBrucella. IMPORTANCEHistone-like nucleoid structuring (H-NS) and H-NS-like proteins coordinate host-associated behaviors in many pathogenic bacteria, often through forming silencer/counter-silencer pairs with signal-responsive transcriptional activators to tightly control gene expression.Brucellaand related bacteria do not encode H-NS or homologs of known H-NS-like proteins, and it is unclear if they have other proteins that perform analogous functions during pathogenesis. In this work, we provide compelling evidence for the role of MucR as a novel H-NS-like protein inBrucella. We show that MucR possesses many of the known functions attributed to H-NS and H-NS-like proteins, including the formation of silencer/counter-silencer pairs to control virulence gene expression and global structuring of the nucleoid. These results uncover a new role for MucR as a nucleoid structuring protein and support the importance of temporal control of gene expression inBrucellaand related bacteria. 

Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.