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Covering integers by x2 + dy2
Get PDFWhat proportion of integers n ⩽ N may be expressed as x
2 + dy2
for some d ⩽ ∆,
with x, y integers? Writing ∆ = (log N)
log 22
α
√
log log N for some α ∈ (−∞, ∞), we show that the
answer is Φ(α) + o(1), where Φ is the Gaussian distribution function Φ(α) = √1
2π
R α
−∞ e
−x
2/2
dx.
A consequence of this is a phase transition: almost none of the integers n ⩽ N can be represented
by x
2 + dy2 with d ⩽ (log N)
log 2−ε
, but almost all of them can be represented by x
2 + dy2 with
d ⩽ (log N)
log 2+ε
New directions in competition policy: an overview
Get PDFCompetition policy has faced increasing scrutiny in recent years, with growing tension between
traditional antitrust frameworks and contemporary critiques, including the "hipster antitrust"
movement. Some of the critics contend that competition policy has failed to address the
growing market power of dominant firms, especially in the digital sector. This issue of the
Oxford Review of Economic Policy explores the validity of these claims and their potential
implications for the future of competition policy. It also examines how emerging
methodologies, particularly those rooted in data science, can enhance our understanding both
of how firms behave and how competition authorities and courts make decisions. This article
summarises a diverse range of contributions from academics, regulators, and practitioners in
law and economics. It concludes with a discussion of how competition economics might adapt
to the challenges posed by the hipster antitrust movement and the rapid changes in how firms
compete
Epigenetic age acceleration and methylation differences in IgG4-related cholangitis and primary sclerosing cholangitis
Get PDFBackground: IgG4-related cholangitis (IgG4-SC) and primary sclerosing cholangitis (PSC) are chronic fibro-inflammatory hepatobiliary conditions, with genetic, environmental, and immunologic risk factors, in which epigenetic alterations may provide insights into pathophysiology and novel biomarkers. This study is the first to assess methylation signatures in IgG4-SC. Results: Whole blood DNA methylation profiling and genotyping was performed in 264 individuals; 47 with IgG4-SC, 65 with PSC, 64 with ulcerative colitis (UC), and 88 healthy controls. We identified 19 significant methylation differences between IgG4-SC and controls and 38 between PSC and controls. IgG4-SC and PSC shared 8 probes. Inflammatory genes (including CEP97, IFNAR1, TXK, HERC6, C5orf36, PYY, and MTRNR2L1) were predominantly involved in dysregulated methylation. Epigenetic age acceleration was observed in patients with IgG4-SC, but not in those with PSC or UC. meQTL analyses to identify genetic determinants of methylation revealed a strong human leucocyte antigen (HLA) signal in both PSC and IgG4-SC (HLA-DQB2, HLA-DPA1, HLA-F and HLA-DRA). Conclusions: We identify novel epigenetic alterations in IgG4-SC and PSC, with biological age acceleration in IgG4-SC, providing insights into disease pathogenesis, and highlight the role of genetic variation especially within the HLA region in shaping the methylome
Transport and inhibition of the sphingosine-1-phosphate exporter SPNS2
Get PDFSphingosine-1-phosphate (S1P) is a signaling lysolipid critical to heart development, immunity, and hearing. Accordingly, mutations in the S1P transporter SPNS2 are associated with reduced white cell count and hearing defects. SPNS2 also exports the S1P-mimicking FTY720-P (Fingolimod) and thereby is central to the pharmacokinetics of this drug when treating multiple sclerosis. Here, we use a combination of cryo-electron microscopy, immunofluorescence, in vitro binding and in vivo S1P export assays, and molecular dynamics simulations to probe SPNS2’s substrate binding and transport. These results reveal the transporter’s binding mode to its native substrate S1P, the therapeutic FTY720-P, and the reported SPNS2-targeting inhibitor 33p. Further capturing an inward-facing apo state, our structures illuminate the protein’s mechanism for exchange between inward-facing and outward-facing conformations. Finally, using these structural, localization, and S1P transport results, we identify how pathogenic mutations ablate the protein’s export activity and thereby lead to hearing loss
The impact of structured higher order interactions on ecological network stability
Get PDFThe impact of higher-order interactions, those involving more than two species, is increasingly appreciated as having the potential to strongly influence the dynamics of complex ecological systems. However, although the critical importance of the structure of pairwise interaction networks is well established, studies of higher-order interactions still largely assume random structures. Here, we demonstrate the strong impact of structured higher-order interactions on simulated ecological communities. We focus on effects caused by interaction modifications within food webs, where a consumer resource interaction is modified by a third species, and for which plausible structures can be hypothesised. We show how interaction modifications introduced under a range of non-random distributions may impact the overall network structure. Local stability and the size of the feasibility domain are critically dependent on the inter-relationship between trophic and non-trophic effects. Where interaction modifications are structured into mutual interference motifs (associated with consumers switching between resources) synergistic signs and topological effects have particularly consequential impacts. Furthermore, we show that previous results of the impact of higher-order interactions on diversity-stability relationships can be reversed when higher-order interactions are structured, not random. Empirical data on interaction modifications will be a key part of improving understanding the dynamics of communities, particularly the distribution of interaction modification signs across networks
Detection of low frequency artemisinin resistance mutations, C469Y, P553L and A675V, and fixed antifolate resistance mutations in asymptomatic primary school children in Kenya
Get PDFBackground: To understand the emergence and spread of drug-resistant parasites in malaria-endemic areas, accurate assessment and monitoring of antimalarial drug resistance markers is critical. Recent advances in next-generation sequencing (NGS) technologies have enabled the tracking of drug-resistant malaria parasites. Methods: In this study, we used Targeted Amplicon Deep Sequencing (TADS) to characterise the genetic diversity of the Pfk13, Pfdhfr, Pfdhps, and Pfmdr1 genes among primary school-going children in 15 counties in Kenya (Bungoma, Busia, Homa Bay, Migori, Kakamega, Kilifi, Kirinyaga, Kisii, Kisumu, Kwale, Siaya, Tana River, Turkana, Vihiga and West Pokot). A total of 920 dried blood spot (DBS) samples collected from 121 selected primary schools within the country were used to extract genomic DNA. A nested polymerase chain reaction (PCR) was used to generate amplicons that were sequenced to determine the prevalence of known and novel polymorphisms. Results: Pfk13 mutations associated with artemisinin resistance were present as mixed genotype infections for the C469Y mutation in 23 samples (4%), the A675V mutation in 2 samples (1.7%), and the P553L mutation in 7 samples (1.2%). The A578S mutation, was also identified in mixed infections, appearing in 15.2% of the 87 samples analysed. The Pfdhfr 51I and 108 N pyrimethamine-resistance mutations were at fixation (100% frequency), and the Pfmdr1 Y184F mutation, which is linked to reduced susceptibility to several antimalarial drugs, especially those used in combination therapies for malaria treatment, was detected in 97.5% of the samples as mixed-genotype infections. Conclusion: The genomic surveillance of asymptomatic school children in Kenya provides an early warning signal of at least 1 of the 3 validated artemisinin resistance mutations circulating in all regions in Western Kenya sampled except Homa Bay and Kisii Counties. These signals in asymptomatic and mixed infections would have been missed without deep sequencing
Enhancing single-cell transcriptomics using interposed anchor oligonucleotide sequences
Get PDFSingle-cell transcriptomics, which utilises barcodes and unique molecular identifiers (UMIs) for polyA+ mRNA capture, is compromised by oligonucleotide synthesis errors. To address this, we modified the oligonucleotide capture design and integrated an interposed anchor between the barcode and the UMI. This design significantly reduces the need to discard reads due to synthesis inaccuracies. Our results demonstrate that this anchor-enhanced design substantially improves gene expression profiles in droplet-based single-cell sequencing analyses
PlomBOX: a low cost bioassay for the sensitive detection of lead in drinking water
Get PDFThis paper reports the design of a biosensor for sensitive, low-cost measurement of lead in drinking water. The biosensor uses a genetically-modified strain of Escherichia coli, which serves as both signal amplifier and reporter of lead in water, measured via colour change. We developed the PlomBOX measurement platform to image this colour change and we demonstrate its capability to detect concentrations as low as the World Health Organisation upper limit for drinking water of 10 ppb. Our approach does not require expensive infrastructure or expert operators, and its automated sensing, detection and result visualisation platform is user-friendly and robust compared to existing lead biosensors—critical features to enable measurement by non-experts at the point of use
Disruption of seasonal influenza circulation and evolution during the 2009 H1N1 and COVID-19 pandemics in Southeastern Asia
Get PDFEast, South, and Southeast Asia (together referred to as Southeastern Asia hereafter) have been recognized as critical areas fuelling the global circulation of seasonal influenza. However, the seasonal influenza migration network within Southeastern Asia remains unclear, including how pandemic-related disruptions altered this network. We leveraged genetic, epidemiological, and airline travel data between 2007-2023 to characterise the dispersal patterns of influenza A/H3N2 and B/Victoria viruses both out of and within Southeastern Asia, including during perturbations by the 2009 A/H1N1 and COVID-19 pandemics. During the COVID-19 pandemic, consistent autumn-winter movement waves from Southeastern Asia to temperate regions were interrupted for both subtype/lineages, however the A/H1N1 pandemic only disrupted A/H3N2 spread. We find a higher persistence of A/H3N2 than B/Victoria circulation in Southeastern Asia and identify distinct pandemic-related disruptions in A/H3N2 antigenic evolution between two pandemics, compared to interpandemic levels; similar patterns are observed in B/Victoria using genetic distance. The internal movement structure within Southeastern Asia markedly diverged during the COVID-19 pandemic season, and to a lesser extent, during the 2009 A/H1N1 pandemic season. Our findings provide insights into the heterogeneous impact of two distinct pandemic-related disruptions on influenza circulation, which can help anticipate the effects of future pandemics and potential mitigation strategies on influenza dynamics
Cross-national measures of the intensity of COVID-19 public health policies
Get PDFWe show in this research note that the complex nature of COVID-19 policy responses means that models trying to identify the effect of individual policies can produce spurious results unless they take into account systematic measurement error. Employing a simulation of the policymaking process, we find that regression analyses of multiple related policy indicators results in spurious inferences due to measurement error. To remedy this issue, we estimate six new indices of the overall intensity of different types of COVID-19 restrictions that incorporate policymaker intentions behind the design of similar policies. These indices are derived from novel granular data on COVID-19 restrictions from the CoronaNet dataset, and we augment this data with the Oxford COVID-19 Government dataset. To gain estimates with uncertainty, we use a Bayesian time-varying measurement model that provides time-varying policy intensity scores from 1 January, 2020 to 1 May, 2021 for over 180 countries. We show with these measures that regression models of policy scores on important pandemic outcomes are robust to measurement error and fully incorporate uncertainty. Supplementary material for this article is available in the appendix in the online edition