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Obtaining effective representations of DNA sequences is crucial for genome analysis. Metagenomic binning, for instance, relies on genome representations to cluster complex mixtures of DNA fragments from biological samples with the aim of determining their microbial compositions. In this paper, we revisit k-mer-based representations of genomes and provide a theoretical analysis of their use in representation learning. Based on the analysis, we propose a lightweight and scalable model for performing metagenomic binning at the genome read level, relying only on the k-mer compositions of the DNA fragments. We compare the model to recent genome foundation models and demonstrate that while the models are comparable in performance, the proposed model is significantly more effective in terms of scalability, a crucial aspect for performing metagenomic binning of real-world datasets., Comment: Accepted to the Thirty-Eighth Annual Conference on Neural Information Processing Systems (NeurIPS 2024)

Superlattices from twisted graphene mono- and bi-layer systems give rise to on-demand many-body states such as Mott insulators and unconventional superconductors. These phenomena are ascribed to a combination of flat bands and strong Coulomb interactions. However, a comprehensive understanding is lacking because the low-energy band structure strongly changes when the electron filling is varied. Here, we gain direct access to the filling-dependent low energy bands of twisted bilayer graphene (TBG) and twisted double bilayer graphene (TDBG) by applying micro-focused angle-resolved photoemission spectroscopy to in situ gated devices. Our findings for the two systems are in stark contrast: The doping dependent dispersion for TBG can be described in a simple model, combining a filling-dependent rigid band shift with a many-body related bandwidth change. In TDBG, on the other hand, we find a complex behaviour of the low-energy bands, combining non-monotonous bandwidth changes and tuneable gap openings. Our work establishes the extent of electric field tunability of the low energy electronic states in twisted graphene superlattices and can serve to underpin the theoretical understanding of the resulting phenomena., Comment: 26 pages, 4 main figures and 7 supplementary figures