Benchmarking atlas-level data integration in single-cell genomics

Single-cell atlases often include samples that span locations, laboratories and conditions, leading to complex, nested batch effects in data. Thus, joint analysis of atlas datasets requires reliable data integration. To guide integration method choice, we benchmarked 68 method and preprocessing combinations on 85 batches of gene expression, chromatin accessibility and simulation data from 23 publications, altogether representing >1.2 million cells distributed in 13 atlas-level integration tasks. We evaluated methods according to scalability, usability and their ability to remove batch effects while retaining biological variation using 14 evaluation metrics. We show that highly variable gene selection improves the performance of data integration methods, whereas scaling pushes methods to prioritize batch removal over conservation of biological variation. Overall, scANVI, Scanorama, scVI and scGen perform well, particularly on complex integration tasks, while single-cell ATAC-sequencing integration performance is strongly affected by choice of feature space. Our freely available Python module and benchmarking pipeline can identify optimal data integration methods for new data, benchmark new methods and improve method development.

Parametric excitation of a 1D gas in integrable and nonintegrable cases

We study the response of a highly excited 1D gas with pointlike interactions to a periodic modulation of the coupling constant. We calculate the corresponding dynamic structure factors and show that their low-frequency behavior differs dramatically for integrable and nonintegrable models. Nonintegrable systems are sensitive to excitations with frequencies as low as the mean level spacing, whereas much higher frequencies are required to excite an integrable system. This effect can be used as a probe of integrability for mesoscopic 1D systems and can be observed experimentally by measuring the heating rate of a parametrically excited gas.

Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling

We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.