Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

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Finding familial relatives using DNA have multiple applications, in genetic genealogy, population genetics, and forensics. So far, most relative matching algorithms rely on detecting identity-by-descent (IBD) segments with high quality genotype data. Recently, low coverage sequencing (LCS) has received growing attention as a promising cost-effective method to ascertain genomic information. However, with higher error rates, it is unclear whether existing IBD detection can work on LCS datasets. Here, we developed and tested a framework for relative matching using sequencing with 1× coverage (1×LCS). We started by exploring the error characteristics of this method compared to array data. Our results show that after some optimization 1×LCS can exhibit the same genotyping discordance rates as the discordance between two array platforms. Using this observation, we developed a hybrid framework for relative matching and tuned this framework with >2,700 pairs of confirmed genealogical relatives that were genotyped using heterogenous datasets. We then obtained array and 1×LCS on 19 samples and use our framework to find relatives in a database of over 3 million individuals. The total length of shared segments obtained by 1×LCS was virtually indistinguishable to genotyping arrays for matches with a total sharing >200cM (second cousins or closer). For more distant relatives, as long as those were detected by both technologies, the total length obtained by LCS and by genotyping arrays was highly correlated, with no evidence of over- or underestimation. Taken together, our results show that 1×LCS can be a valid alternative to arrays for relative matching, opening the possibility for further democratization of genomic data.

An abelian differential on a surface defines a flat metric and a vector field on the complement of a finite set of points. The vertical flow that can be defined on the surface has two kinds of invariant closed sets (i.e. invariant components) -periodic components and minimal components. We give upper bounds on the number of minimal components, on the number of periodic components and on the total number of invariant components in every stratum of abelian differentials. We also show that these bounds are tight in every stratum.