The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

BOWIE-ALIGN: How formation and migration histories of giant planets impact atmospheric compositions

This is the final version. Available on open access from Oxford University Press via the DOI in this recordData availability: The data underlying this article will be shared on reasonable request to the corresponding author. The code to reproduce the models can be found here: https://github.com/miosta/drift_composition/Hot Jupiters present a unique opportunity for measuring how planet formation history shapes present-day atmospheric composition. However, due to the myriad pathways influencing composition, a well-constructed sample of planets is needed to determine whether formation history can be accurately traced back from atmospheric composition. To this end, the BOWIE-ALIGN survey will compare the compositions of 8 hot Jupiters around F stars, 4 with orbits aligned with the stellar rotation axis and 4 misaligned. Using the alignment as an indicator for planets that underwent disc migration or high-eccentricity migration, one can determine whether migration history produces notable differences in composition between the two samples of planets. This paper describes the planet formation model that motivates our observing programme. Our model traces the accretion of chemical components from the gas and dust in the disc over a broad parameter space to create a full, unbiased model sample from which we can estimate the range of final atmospheric compositions. For high metallicity atmospheres (O/H ≥ 10× solar), the C/O ratios of aligned and misaligned planets diverge, with aligned planets having lower C/O (< 0.25) due to the accretion of oxygen-rich silicates from the inner disc. However, silicates may rain out instead of releasing their oxygen into the atmosphere. This would significantly increase the C/O of aligned planets (C/O > 0.6), inverting the trend between the aligned and misaligned planets. Nevertheless, by comparing statistically significant samples of aligned and misaligned planets, we expect atmospheric composition to constrain how planets form.Royal SocietyEuropean Union Horizon 2020Imperial College LondonUKRIScience and Technology Facilities Council (STFC)Leverhulme Trus

Implications of CTL-Mediated Killing of HIV-Infected Cells during the Non-Productive Stage of Infection

Patients infected with HIV exhibit orders of magnitude differences in their set-point levels of the plasma viral load. As to what extent this variation is due to differences in the efficacy of the cytotoxic T lymphocyte (CTL) response in these patients is unclear. Several studies have shown that HIV-infected CD4+ T cells also present viral epitopes that are recognized by CTLs before the productive stage of infection, i.e., during the intracellular eclipse phase before the infected cell starts to produce new viral particles. Here, we use mathematical modeling to investigate the potential impact of early killing of HIV-infected cells on viral replication. We suggest that the majority of CTL-mediated killing could occur during the viral eclipse phase, and that the killing of virus-producing cells could be substantially lower at later stages due to MHC-I-down-regulation. Such a mechanism is in agreement with several experimental observations that include CD8+ T cell depletion and antiretroviral drug treatment. This indicates a potentially important role of CTL-mediated killing during the non-productive stage of HIV-infected cells

Heterogeneously catalyzed lignin depolymerization

Biomass offers a unique resource for the sustainable production of bio-derived chemical and fuels as drop-in replacements for the current fossil fuel products. Lignin represents a major component of lignocellulosic biomass, but is particularly recalcitrant for valorization by existing chemical technologies due to its complex cross-linking polymeric network. Here, we highlight a range of catalytic approaches to lignin depolymerisation for the production of aromatic bio-oil and monomeric oxygenates

The origin of multicellularity in cyanobacteria

Background: Cyanobacteria are one of the oldest and morphologically most diverse prokaryotic phyla on our planet. The early development of an oxygen-containing atmosphere approximately 2.45 - 2.22 billion years ago is attributed to the photosynthetic activity of cyanobacteria. Furthermore, they are one of the few prokaryotic phyla where multicellularity has evolved. Understanding when and how multicellularity evolved in these ancient organisms would provide fundamental information on the early history of life and further our knowledge of complex life forms. Results: We conducted and compared phylogenetic analyses of 16S rDNA sequences from a large sample of taxa representing the morphological and genetic diversity of cyanobacteria. We reconstructed ancestral character states on 10,000 phylogenetic trees. The results suggest that the majority of extant cyanobacteria descend from multicellular ancestors. Reversals to unicellularity occurred at least 5 times. Multicellularity was established again at least once within a single-celled clade. Comparison to the fossil record supports an early origin of multicellularity, possibly as early as the “Great Oxygenation Event” that occurred 2.45 - 2.22 billion years ago. Conclusions: The results indicate that a multicellular morphotype evolved early in the cyanobacterial lineage and was regained at least once after a previous loss. Most of the morphological diversity exhibited in cyanobacteria today —including the majority of single-celled species— arose from ancient multicellular lineages. Multicellularity could have conferred a considerable advantage for exploring new niches and hence facilitated the diversification of new lineages

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO’s second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h95%0=3.47×10−25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering