Metastability in the dilute Ising model

Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalyst effect---rare regions of high dilution speed up the transition from minus phase to plus phase.Comment: 49 page

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples

Vigorous star formation hidden by dust in a galaxy at z=1.4z=1.4

Near-infrared surveys have revealed a substantial population of enigmatic faint galaxies with extremely red optical-to-near-infrared colours and with a sky surface density comparable to that of faint quasars. There are two scenarios for these extreme colours: (i) these distant galaxies have formed virtually all their stars at very high redshifts and, due to the absence of recently formed stars, the colours are extremely red and (ii) these distant galaxies contain large amounts of dust, severely reddening the rest-frame UV--optical spectrum. HR10 ($z = 1.44$) is considered the archetype of the extremely red galaxies. Here we report the detection of the continuum emission from HR10 at 850$\mu$m and at 1250$\mu$m, demonstrating that HR10 is a very dusty galaxy undergoing a major episode of star formation. Our result provides a clear example of a high-redshift galaxy where the star formation rate inferred from the ultraviolet luminosity would be underestimated by a factor up to 1000, and shows that great caution should be used to infer the global star formation history of the Universe from optical observations only.Comment: 12 pages, 1 figure, Nature, in press (30 April 1998

CWRML: representing crop wild relative conservation and use data in XML

Background Crop wild relatives are wild species that are closely related to crops. They are valuable as potential gene donors for crop improvement and may help to ensure food security for the future. However, they are becoming increasingly threatened in the wild and are inadequately conserved, both in situ and ex situ. Information about the conservation status and utilisation potential of crop wild relatives is diverse and dispersed, and no single agreed standard exists for representing such information; yet, this information is vital to ensure these species are effectively conserved and utilised. The European Community-funded project, European Crop Wild Relative Diversity Assessment and Conservation Forum, determined the minimum information requirements for the conservation and utilisation of crop wild relatives and created the Crop Wild Relative Information System, incorporating an eXtensible Markup Language (XML) schema to aid data sharing and exchange. Results Crop Wild Relative Markup Language (CWRML) was developed to represent the data necessary for crop wild relative conservation and ensure that they can be effectively utilised for crop improvement. The schema partitions data into taxon-, site-, and population-specific elements, to allow for integration with other more general conservation biology schemata which may emerge as accepted standards in the future. These elements are composed of sub-elements, which are structured in order to facilitate the use of the schema in a variety of crop wild relative conservation and use contexts. Pre-existing standards for data representation in conservation biology were reviewed and incorporated into the schema as restrictions on element data contents, where appropriate. Conclusion CWRML provides a flexible data communication format for representing in situ and ex situ conservation status of individual taxa as well as their utilisation potential. The development of the schema highlights a number of instances where additional standards-development may be valuable, particularly with regard to the representation of population-specific data and utilisation potential. As crop wild relatives are intrinsically no different to other wild plant species there is potential for the inclusion of CWRML data elements in the emerging standards for representation of biodiversity data

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Interventions to Promote Cancer Awareness and Early Presentation: Systematic Review

Low cancer awareness contributes to delay in presentation for cancer symptoms and may lead to delay in cancer diagnosis. The aim of this study was to review the evidence for the effectiveness of interventions to raise cancer awareness and promote early presentation in cancer to inform policy and future research. We searched bibliographic databases and reference lists for randomised controlled trials of interventions delivered to individuals, and controlled or uncontrolled studies of interventions delivered to communities. We found some evidence that interventions delivered to individuals modestly increase cancer awareness in the short term and insufficient evidence that they promote early presentation. We found limited evidence that public education campaigns reduce stage at presentation of breast cancer, malignant melanoma and retinoblastoma

Application of a Colorimetric Assay to Identify Putative Ribofuranosylaminobenzene 5'-Phosphate Synthase Genes Expressed with Activity in Escherichia coli

Tetrahydromethanopterin (H(4)MPT) is a tetrahydrofolate analog originally discovered in methanogenic archaea, but later found in other archaea and bacteria. The extent to which H(4)MPT occurs among living organisms is unknown. The key enzyme which distinguishes the biosynthetic pathways of H(4)MPT and tetrahydrofolate is ribofuranosylaminobenzene 5'-phosphate synthase (RFAP synthase). Given the importance of RFAP synthase in H(4)MPT biosynthesis, the identification of putative RFAP synthase genes and measurement of RFAP synthase activity would provide an indication of the presence of H(4)MPT in untested microorganisms. Investigation of putative archaeal RFAP synthase genes has been hampered by the tendency of the resulting proteins to form inactive inclusion bodies in Escherichia coli. The current work describes a colorimetric assay for measuring RFAP synthase activity, and two modified procedures for expressing recombinant RFAP synthase genes to produce soluble, active enzyme. By lowering the incubation temperature during expression, RFAP synthase from Archaeoglobus fulgidus was produced in E. coli and purified to homogeneity. The production of active RFAP synthase from Methanothermobacter thermautotrophicus was achieved by coexpression of the gene MTH0830 with a molecular chaperone. This is the first direct biochemical identification of a methanogen gene that codes for an active RFAP synthase

A genetic link between risk for Alzheimer's disease and severe COVID-19 outcomes via the OAS1 gene

Recently, we reported oligoadenylate synthetase 1 (OAS1) contributed to the risk of Alzheimer's disease, by its enrichment in transcriptional networks expressed by microglia. However, the function of OAS1 within microglia was not known. Using genotyping from 1313 individuals with sporadic Alzheimer's disease and 1234 control individuals, we confirm the OAS1 variant, rs1131454, is associated with increased risk for Alzheimer's disease. The same OAS1 locus has been recently associated with severe coronavirus disease 2019 (COVID-19) outcomes, linking risk for both diseases. The single nucleotide polymorphisms rs1131454(A) and rs4766676(T) are associated with Alzheimer's disease, and rs10735079(A) and rs6489867(T) are associated with severe COVID-19, where the risk alleles are linked with decreased OAS1 expression. Analysing single-cell RNA-sequencing data of myeloid cells from Alzheimer's disease and COVID-19 patients, we identify co-expression networks containing interferon (IFN)-responsive genes, including OAS1, which are significantly upregulated with age and both diseases. In human induced pluripotent stem cell-derived microglia with lowered OAS1 expression, we show exaggerated production of TNF-α with IFN-γ stimulation, indicating OAS1 is required to limit the pro-inflammatory response of myeloid cells. Collectively, our data support a link between genetic risk for Alzheimer's disease and susceptibility to critical illness with COVID-19 centred on OAS1, a finding with potential implications for future treatments of Alzheimer's disease and COVID-19, and development of biomarkers to track disease progression

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl