On Lipschitz continuity of nonlinear differential operators

In connection with approximations for nonlinear evolution equations, it is standard to assume that nonlinear terms are at least locally Lipschitz continuous. However, it is shown here that f = f(X,del sub u(X)) is Lipschitz continuous from the subspace W sup 1, infinity is a subset of L sub 2 into W sup 1,2, and maps W sup 2, infinity into W sup 1, infinity, if and only if f is affine with W sup 1, infinity coefficients. In fact, a local version of this claim is proved

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method

Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method

On implicit Runge-Kutta methods for parallel computations

Implicit Runge-Kutta methods which are well-suited for parallel computations are characterized. It is claimed that such methods are first of all, those for which the associated rational approximation to the exponential has distinct poles, and these are called multiply explicit (MIRK) methods. Also, because of the so-called order reduction phenomenon, there is reason to require that these poles be real. Then, it is proved that a necessary condition for a q-stage, real MIRK to be A sub 0-stable with maximal order q + 1 is that q = 1, 2, 3, or 5. Nevertheless, it is shown that for every positive integer q, there exists a q-stage, real MIRK which is I-stable with order q. Finally, some useful examples of algebraically stable MIRKs are given

Impacts of organic and conventional crop management on diversity and activity of free-living nitrogen fixing bacteria and total bacteria are subsidiary to temporal effects

A three year field study (2007-2009) of the diversity and numbers of the total and metabolically active free-living diazotophic bacteria and total bacterial communities in organic and conventionally managed agricultural soil was conducted at the Nafferton Factorial Systems Comparison (NFSC) study, in northeast England. The result demonstrated that there was no consistent effect of either organic or conventional soil management across the three years on the diversity or quantity of either diazotrophic or total bacterial communities. However, ordination analyses carried out on data from each individual year showed that factors associated with the different fertility management measures including availability of nitrogen species, organic carbon and pH, did exert significant effects on the structure of both diazotrophic and total bacterial communities. It appeared that the dominant drivers of qualitative and quantitative changes in both communities were annual and seasonal effects. Moreover, regression analyses showed activity of both communities was significantly affected by soil temperature and climatic conditions. The diazotrophic community showed no significant change in diversity across the three years, however, the total bacterial community significantly increased in diversity year on year. Diversity was always greatest during March for both diazotrophic and total bacterial communities. Quantitative analyses using qPCR of each community indicated that metabolically active diazotrophs were highest in year 1 but the population significantly declined in year 2 before recovering somewhat in the final year. The total bacterial population in contrast increased significantly each year. Seasonal effects were less consistent in this quantitative study

A Modeling Framework to Describe the Transmission of Bluetongue Virus within and between Farms in Great Britain

Recently much attention has been given to developing national-scale micro-simulation models for livestock diseases that can be used to predict spread and assess the impact of control measures. The focus of these models has been on directly transmitted infections with little attention given to vector-borne diseases such as bluetongue, a viral disease of ruminants transmitted by Culicoides biting midges. Yet BT has emerged over the past decade as one of the most important diseases of livestock.We developed a stochastic, spatially-explicit, farm-level model to describe the spread of bluetongue virus (BTV) within and between farms. Transmission between farms was modeled by a generic kernel, which includes both animal and vector movements. Once a farm acquired infection, the within-farm dynamics were simulated based on the number of cattle and sheep kept on the farm and on local temperatures. Parameter estimates were derived from the published literature and using data from the outbreak of bluetongue in northern Europe in 2006. The model was validated using data on the spread of BTV in Great Britain during 2007. The sensitivity of model predictions to the shape of the transmission kernel was assessed.The model is able to replicate the dynamics of BTV in Great Britain. Although uncertainty remains over the precise shape of the transmission kernel and certain aspects of the vector, the modeling approach we develop constitutes an ideal framework in which to incorporate these aspects as more and better data become available. Moreover, the model provides a tool with which to examine scenarios for the spread and control of BTV in Great Britain

A multi-decade record of high quality fCO2 data in version 3 of the Surface Ocean CO2 Atlas (SOCAT)

The Surface Ocean CO2 Atlas (SOCAT) is a synthesis of quality-controlled fCO2 (fugacity of carbon dioxide) values for the global surface oceans and coastal seas with regular updates. Version 3 of SOCAT has 14.7 million fCO2 values from 3646 data sets covering the years 1957 to 2014. This latest version has an additional 4.6 million fCO2 values relative to version 2 and extends the record from 2011 to 2014. Version 3 also significantly increases the data availability for 2005 to 2013. SOCAT has an average of approximately 1.2 million surface water fCO2 values per year for the years 2006 to 2012. Quality and documentation of the data has improved. A new feature is the data set quality control (QC) flag of E for data from alternative sensors and platforms. The accuracy of surface water fCO2 has been defined for all data set QC flags. Automated range checking has been carried out for all data sets during their upload into SOCAT. The upgrade of the interactive Data Set Viewer (previously known as the Cruise Data Viewer) allows better interrogation of the SOCAT data collection and rapid creation of high-quality figures for scientific presentations. Automated data upload has been launched for version 4 and will enable more frequent SOCAT releases in the future. High-profile scientific applications of SOCAT include quantification of the ocean sink for atmospheric carbon dioxide and its long-term variation, detection of ocean acidification, as well as evaluation of coupled-climate and ocean-only biogeochemical models. Users of SOCAT data products are urged to acknowledge the contribution of data providers, as stated in the SOCAT Fair Data Use Statement. This ESSD (Earth System Science Data) “living data” publication documents the methods and data sets used for the assembly of this new version of the SOCAT data collection and compares these with those used for earlier versions of the data collection (Pfeil et al., 2013; Sabine et al., 2013; Bakker et al., 2014). Individual data set files, included in the synthesis product, can be downloaded here: doi:10.1594/PANGAEA.849770. The gridded products are available here: doi:10.3334/CDIAC/OTG.SOCAT_V3_GRID

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

A method of determining where to target surveillance efforts in heterogeneous epidemiological systems

The spread of pathogens into new environments poses a considerable threat to human, animal, and plant health, and by extension, human and animal wellbeing, ecosystem function, and agricultural productivity, worldwide. Early detection through effective surveillance is a key strategy to reduce the risk of their establishment. Whilst it is well established that statistical and economic considerations are of vital importance when planning surveillance efforts, it is also important to consider epidemiological characteristics of the pathogen in question—including heterogeneities within the epidemiological system itself. One of the most pronounced realisations of this heterogeneity is seen in the case of vector-borne pathogens, which spread between ‘hosts’ and ‘vectors’—with each group possessing distinct epidemiological characteristics. As a result, an important question when planning surveillance for emerging vector-borne pathogens is where to place sampling resources in order to detect the pathogen as early as possible. We answer this question by developing a statistical function which describes the probability distributions of the prevalences of infection at first detection in both hosts and vectors. We also show how this method can be adapted in order to maximise the probability of early detection of an emerging pathogen within imposed sample size and/or cost constraints, and demonstrate its application using two simple models of vector-borne citrus pathogens. Under the assumption of a linear cost function, we find that sampling costs are generally minimised when either hosts or vectors, but not both, are sampled

Using a real-world network to model localized COVID-19 control strategies

Case isolation and contact tracing can contribute to the control of COVID-19 outbreaks1,2. However, it remains unclear how real-world social networks could influence the effectiveness and efficiency of such approaches. To address this issue, we simulated control strategies for SARS-CoV-2 transmission in a real-world social network generated from high-resolution GPS data that were gathered in the course of a citizen-science experiment3,4. We found that tracing the contacts of contacts reduced the size of simulated outbreaks more than tracing of only contacts, but this strategy also resulted in almost half of the local population being quarantined at a single point in time. Testing and releasing non-infectious individuals from quarantine led to increases in outbreak size, suggesting that contact tracing and quarantine might be most effective as a ‘local lockdown’ strategy when contact rates are high. Finally, we estimated that combining physical distancing with contact tracing could enable epidemic control while reducing the number of quarantined individuals. Our findings suggest that targeted tracing and quarantine strategies would be most efficient when combined with other control measures such as physical distancing