We report the events of an Italian top league soccer club that took place in 1 year (from March 2020 to February 2021) at the time of coronavirus disease 2019 (COVID-19) pandemic. In early March 2020, just before sport competitions were called off due to the national lockdown in Italy, the team, which included 27 players and 26 staff at the time, faced a COVID-19 outbreak, with 16 confirmed and seven probable cases, including three staff members who had to be hospitalised. In May 2020, at the resumption of the training sessions, a high prevalence of anti-severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) immunoglobulin G positivity (35/53, 66%) was detected among the members of the group. In the following months, sport activities were organised behind closed doors with stringent risk mitigation procedures in place. As of February 2021, only two new cases of SARS-CoV-2 infection were detected within the group, against more than 3500 nasopharyngeal swabs and 1000 serological tests.

Experience gained from responding to major outbreaks may have influenced the early coronavirus disease-2019 (COVID-19) pandemic response in several countries across Africa. We retrospectively assessed whether Guinea, Liberia and Sierra Leone, the three West African countries at the epicentre of the 2014–2016 Ebola virus disease outbreak, leveraged the lessons learned in responding to COVID-19 following the World Health Organization's (WHO) declaration of a public health emergency of international concern (PHEIC). We found relatively lower incidence rates across the three countries compared to many parts of the globe. Time to case reporting and laboratory confirmation also varied, with Guinea and Liberia reporting significant delays compared to Sierra Leone. Most of the selected readiness measures were instituted before confirmation of the first case and response measures were initiated rapidly after the outbreak confirmation. We conclude that the rapid readiness and response measures instituted by the three countries can be attributed to their lessons learned from the devastating Ebola outbreak, although persistent health systems weaknesses and the unique nature of COVID-19 continue to challenge control efforts.

Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with the potential to unlock various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems, incorporating machine learning to deal with nonlinearity becomes a new choice for reducing complex problems. These kinds of methods are independent to the numerical solver for the full order model and keep the nonintrusiveness of the whole workflow. Such methods usually consist of two steps. The first step is the dimension reduction by a projection-based method, and the second is the model reconstruction by a neural network (NN). In this work, we apply some modifications for both steps respectively and investigate how they are impacted by testing with three different simulation models. In all cases Proper orthogonal decomposition is used for dimension reduction. For this step, the effects of generating the snapshot database with constant input parameters is compared with time-dependent input parameters. For the model reconstruction step, three types of NN architectures are compared: multilayer perceptron (MLP), explicit Euler NN (EENN), and Runge–Kutta NN (RKNN). The MLPs learn the system state directly, whereas EENNs and RKNNs learn the derivative of system state and predict the new state as a numerical integrator. In the tests, RKNNs show their advantage as the network architecture informed by higher-order numerical strategy.

This paper introduces a dynamic knowledge-graph approach for digital twins and illustrates how this approach is by design naturally suited to realizing the vision of a Universal Digital Twin. The dynamic knowledge graph is implemented using technologies from the Semantic Web. It is composed of concepts and instances that are defined using ontologies, and of computational agents that operate on both the concepts and instances to update the dynamic knowledge graph. By construction, it is distributed, supports cross-domain interoperability, and ensures that data are connected, portable, discoverable, and queryable via a uniform interface. The knowledge graph includes the notions of a “base world” that describes the real world and that is maintained by agents that incorporate real-time data, and of “parallel worlds” that support the intelligent exploration of alternative designs without affecting the base world. Use cases are presented that demonstrate the ability of the dynamic knowledge graph to host geospatial and chemical data, control chemistry experiments, perform cross-domain simulations, and perform scenario analysis. The questions of how to make intelligent suggestions for alternative scenarios and how to ensure alignment between the scenarios considered by the knowledge graph and the goals of society are considered. Work to extend the dynamic knowledge graph to develop a digital twin of the UK to support the decarbonization of the energy system is discussed. Important directions for future research are highlighted.

We propose using fully Bayesian Gaussian process emulation (GPE) as a surrogate for expensive computer experiments of transport infrastructure cut slopes in high-plasticity clay soils that are associated with an increased risk of failure. Our deterioration experiments simulate the dissipation of excess pore water pressure and seasonal pore water pressure cycles to determine slope failure time. It is impractical to perform the number of computer simulations that would be sufficient to make slope stability predictions over a meaningful range of geometries and strength parameters. Therefore, a GPE is used as an interpolator over a set of optimally spaced simulator runs modeling the time to slope failure as a function of geometry, strength, and permeability. Bayesian inference and Markov chain Monte Carlo simulation are used to obtain posterior estimates of the GPE parameters. For the experiments that do not reach failure within model time of 184 years, the time to failure is stochastically imputed by the Bayesian model. The trained GPE has the potential to inform infrastructure slope design, management, and maintenance. The reduction in computational cost compared with the original simulator makes it a highly attractive tool which can be applied to the different spatio-temporal scales of transport networks.

We developed a novel method to align two data sources (TB notifications and the Demographic Health Survey, DHS) captured at different geographic scales. We used this method to identify sociodemographic indicators – specifically population density – that were ecologically correlated with elevated TB notification rates across wards (~100 000 people) in Dhaka, Bangladesh. We found population density was the variable most closely correlated with ward-level TB notification rates (Spearman's rank correlation 0.45). Our approach can be useful, as publicly available data (e.g. DHS data) could help identify factors that are ecologically associated with disease burden when more granular data (e.g. ward-level TB notifications) are not available. Use of this approach might help in designing spatially targeted interventions for TB and other diseases in settings of weak existing data on disease burden at the subdistrict level.

We investigated whether household to clinic distance was a risk factor for death on tuberculosis (TB) treatment in Malawi. Using enhanced TB surveillance data, we recorded all TB treatment initiations and outcomes between 2015 and 2018. Household locations were geolocated, and distances were measured by a straight line or shortest road network. We constructed Bayesian multi-level logistic regression models to investigate associations between distance and case fatality. A total of 479/4397 (10.9%) TB patients died. Greater distance was associated with higher (odds ratio (OR) 1.07 per kilometre (km) increase, 95% credible interval (CI) 0.99–1.16) odds of death in TB patients registered at the referral hospital, but not among TB patients registered at primary clinics (OR 0.98 per km increase, 95% CI 0.92–1.03). Age (OR 1.02 per year increase, 95% CI 1.01–1.02) and HIV-positive status (OR 2.21, 95% CI 1.73–2.85) were also associated with higher odds of death. Model estimates were similar for both distance measures. Distance was a risk factor for death among patients at the main referral hospital, likely due to delayed diagnosis and suboptimal healthcare access. To reduce mortality, targeted community TB screening interventions for TB disease and HIV, and expansion of novel sensitive diagnostic tests are required.

Given a hereditary property of graphs $\mathcal{H}$ and a $p\in [0,1]$, the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically the maximum proportion of edge additions plus edge deletions applied to a graph of edge density p sufficient to ensure that the resulting graph satisfies $\mathcal{H}$. The edit distance function is directly related to other well-studied quantities such as the speed function for $\mathcal{H}$ and the $\mathcal{H}$-chromatic number of a random graph.

Let $\mathcal{H}$ be the property of forbidding an Erdős–Rényi random graph $F\sim \mathbb{G}(n_0,p_0)$, and let $\varphi$ represent the golden ratio. In this paper, we show that if $p_0\in [1-1/\varphi,1/\varphi]$, then a.a.s. as $n_0\to\infty$,

\begin{align*}{\textrm{ed}}_{\mathcal{H}}(p) = (1+o(1))\,\frac{2\log n_0}{n_0}\cdot\min\left\{\frac{p}{-\log(1-p_0)},\frac{1-p}{-\log p_0}\right\}.\end{align*}

$p\in [1/3,2/3]$

$p_0\in (0,1)$

A primary tool in the proof is the categorization of p-core coloured regularity graphs in the range $p\in[1-1/\varphi,1/\varphi]$. Such coloured regularity graphs must have the property that the non-grey edges form vertex-disjoint cliques.

Consumption of pork and pork products can be associated with outbreaks of human salmonellosis. Salmonella infection is usually subclinical in pigs, and farm-based control measures are challenging to implement. To obtain data on Salmonella prevalence, samples can be collected from pigs during the slaughter process. Here we report the results of a Great Britain (GB) based abattoir survey conducted by sampling caecal contents from pigs in nine British pig abattoirs during 2019. Samples were collected according to a randomised stratified scheme, and pigs originating from 286 GB farms were included in this survey. Salmonella was isolated from 112 pig caecal samples; a prevalence of 32.2% [95% confidence interval (CI) 27.4–37.4]. Twelve different Salmonella serovars were isolated, with the most common serovars being S. 4,[5],12:i:-, a monophasic variant of Salmonella Typhimurium (36.6% of Salmonella-positive samples), followed by S. Derby (25.9% of Salmonella-positive samples). There was no significant difference compared to the estimate of overall prevalence (30.5% (95% CI 26.5–34.6)) obtained in the last abattoir survey conducted in the UK (2013). Abattoir-based control measures are often effective in the reduction of Salmonella contamination of carcasses entering the food chain. In this study, the effect of abattoir hygiene practices on the prevalence of Salmonella on carcasses was not assessed. Continuing Salmonella surveillance at slaughter is recommended to assess effect of farm-based and abattoir-based interventions and to monitor potential public health risk associated with consumption of Salmonella-contaminated pork products.

In this paper we consider the one-dimensional, biased, randomly trapped random walk with infinite-variance trapping times. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton–Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime.

This note corrects an error in the definition of the rate function in Jacquier, Pakkanen, and Stone (2018) and slightly simplifies some proofs.

Motivated by the problem of variance allocation for the sum of dependent random variables, Colini-Baldeschi, Scarsini and Vaccari (2018) recently introduced Shapley values for variance and standard deviation games. These Shapley values constitute a criterion satisfying nice properties useful for allocating the variance and the standard deviation of the sum of dependent random variables. However, since Shapley values are in general computationally demanding, Colini-Baldeschi, Scarsini and Vaccari also formulated a conjecture about the relation of the Shapley values of two games, which they proved for the case of two dependent random variables. In this work we prove that their conjecture holds true in the case of an arbitrary number of independent random variables but, at the same time, we provide counterexamples to the conjecture for the case of three dependent random variables.

This paper considers logarithmic asymptotics of tails of randomly stopped sums. The stopping is assumed to be independent of the underlying random walk. First, finiteness of ordinary moments is revisited. Then the study is expanded to more general asymptotic analysis. Results are applicable to a large class of heavy-tailed random variables. The main result enables one to identify if the asymptotic behaviour of a stopped sum is dominated by its increments or the stopping variable. As a consequence, new sufficient conditions for the moment determinacy of compounded sums are obtained.

It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$-mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$-mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$-mixing results for the self-exciting threshold autoregressive model.