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  1. Abstract

    Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

     
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  2. Summary

    Emiliania huxleyiis a calcifying haptophyte, contributing to both the organic and inorganic marine carbon cycles. In marine ecosystems, light is a major driver of phytoplankton physiology and ultimately carbon flow through the ecosystem. Here, we analysed a Lagrangian time‐series of metatranscriptomes collected in the North Pacific Subtropical Gyre (NPSG) to examine howin situpopulations ofE.huxleyimodulate gene expression over day–night transitions. ManyE.huxleyicontigs had a diel expression pattern, with 61% of contigs clustering into modules with statistically significant diel periodicity. Contigs involved in processes that build up energy stores, like carbon fixation and lipid synthesis, peaked around dawn. In contrast, contigs involved in processes that released energy stores, like respiration and lipid degradation, peaked mid‐day and towards dusk. These patterns suggest an orchestrated cycle of building, then consuming energy stores inE.huxleyipopulations in the NPSG. Selected contigs related to the cell cycle also exhibited significant diel periodicity consistent with phased modulations of division observed in culture. Overall, these patterns of gene expression suggest a daily metabolic cascade that could contribute to both organic and inorganic carbon flow in this nutrient depleted ecosystem.

     
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  3. ABSTRACT White dwarfs are one of the few types of stellar object for which we have yet to confirm the existence of companion planets. Recent evidence for metal contaminated atmospheres, circumstellar debris discs, and transiting planetary debris all indicates that planets may be likely. However, white dwarf transit surveys are challenging due to the intrinsic faintness of such objects, the short time-scale of the transits, and the low transit probabilities due to their compact radii. The Large Synoptic Survey Telescope (LSST) offers a remedy to these problems as a deep, half-sky survey with fast exposures encompassing approximately 10 million white dwarfs with r < 24.5 apparent magnitude (mr). We simulate LSST photometric observations of 3.5 million white dwarfs over a 10 yr period and calculate the detectability of companion planets with P < 10 d via transits. We find typical detection rates in the range of 5 × 10−6 to 4 × 10−4 for Ceres-sized bodies to Earth-sized worlds, yielding ∼50–$4000$ detections for a 100 per cent occurrence rate of each. For terrestrial planets in the continuously habitable zone, we find detection rates of ∼10−3 indicating that LSST would reveal hundreds of such worlds for occurrence rates in the range of 1–10 per cent. 
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