Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.

We construct a double common factor model for projecting the mortality of a population using as a reference the minimum death rate at each age among a large number of countries. In particular, the female and male minimum death rates, described as best-performance or best-practice rates, are first modelled by a common factor model structure with both common and sex-specific parameters. The differences between the death rates of the population under study and the best-performance rates are then modelled by another common factor model structure. An important result of using our proposed model is that the projected death rates of the population being considered are coherent with the projected best-performance rates in the long term, the latter of which serves as a very useful reference for the projection based on the collective experience of multiple countries. Our out-of-sample analysis shows that the new model has potential to outperform some conventional approaches in mortality projection.

One of the main concerns about the fast spreading coronavirus disease 2019 (Covid-19) pandemic is how to intervene. We analysed severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) isolates data using the multifractal approach and found a rich in viral genome diversity, which could be one of the root causes of the fast Covid-19 pandemic and is strongly affected by pressure and health index of the hosts inhabited regions. The calculated mutation rate (mr) is observed to be maximum at a particular pressure, beyond which mr maintains diversity. Hurst exponent and fractal dimension are found to be optimal at a critical pressure (Pm), whereas, for P > Pm and P < Pm, we found rich genome diversity relating to complicated genome organisation and virulence of the virus. The values of these complexity measurement parameters are found to be increased linearly with health index values.

In various applications of heavy-tail modelling, the assumed Pareto behaviour is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may, for instance, be subject to a higher level of inspection at highest damage levels leading to weaker tails than apparent from modal claims. Generalizing earlier results of Meerschaert et al. (2012) and Raschke (2020), in this paper we consider tempering of a Pareto-type distribution with a general Weibull distribution in a peaks-over-threshold approach. This requires to modulate the tempering parameters as a function of the chosen threshold. Modelling such a tempering effect is important in order to avoid overestimation of risk measures such as the value-at-risk at high quantiles. We use a pseudo maximum likelihood approach to estimate the model parameters and consider the estimation of extreme quantiles. We derive basic asymptotic results for the estimators, give illustrations with simulation experiments and apply the developed techniques to fire and liability insurance data, providing insight into the relevance of the tempering component in heavy-tail modelling.

We prove the Erdős–Sós conjecture for trees with bounded maximum degree and large dense host graphs. As a corollary, we obtain an upper bound on the multicolour Ramsey number of large trees whose maximum degree is bounded by a constant.

We present the comparative characterisation of 195 non-aureus staphylococci (NAS) isolates obtained from sheep (n = 125) and humans (n = 70) in Sardinia, Italy, identified at the species level by gap gene polymerase chain reaction (PCR) followed by restriction fragment length polymorphism analysis with AluI. Isolates were tested phenotypically with a disc diffusion method and genotypically by PCR, for resistance to 11 antimicrobial agents including cationic antiseptic agents. Among the ovine isolates, Staphylococcus epidermidis (n = 57), S. chromogenes (n = 29), S. haemolyticus (n = 17), S. simulans (n = 8) and S. caprae (n = 6) were the most prevalent species, while among human isolates, S. haemolyticus (n = 28) and S. epidermidis (n = 26) were predominant, followed by S. lugdunensis and S. hominis (n = 4). Of the 125 ovine isolates, 79 (63.2%) did not carry any of the resistance genes tested, while the remainder carried resistance genes for at least one antibiotic. The highest resistance rates among ovine isolates were recorded against tetracycline (20.8%), and penicillin (15.2%); none was resistant to methicillin and two exhibited multidrug resistance (MDR); one of which was positive for the antiseptic resistance smr gene. By contrast, most human isolates (59/70, 84.3%) were resistant to ⩾1 antimicrobials, and 41 (58.6%) were MDR. All 52 (74.3%) penicillin-resistant isolates possessed the blaZ gene, and 33 of 70 (47.1%) harboured the mec gene; of these, seven were characterised by the Staphylococcal Chromosomal Cassette (SCCmec) type IV, 6 the type V, 5 of type III and one representative each of type I and type II. The majority (57.1%) was erythromycin-resistant and 17 isolates carried only the efflux msrA gene, 11 the methylase ermC gene and an equal number harboured both of the latter genes. Moreover, 23 (32.8%) were tetracycline-resistant and all but one possessed only the efflux tetK gene. qacA/B and smr genes were detected in 27 (38.6%) and 18 (25.7%) human NAS, respectively. These results underline a marked difference in species distribution and antimicrobial resistance between ovine and human-derived NAS.

This paper describes the epidemiology of coronavirus disease 2019 (COVID-19) in Northern Ireland (NI) between 26 February 2020 and 26 April 2020, and analyses enhanced surveillance and contact tracing data collected between 26 February 2020 and 13 March 2020 to estimate secondary attack rates (SAR) and relative risk of infection among different categories of contacts of individuals with laboratory confirmed severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) infection. Our results show that during the study period COVID-19 cumulative incidence and mortality was lower in NI than the rest of the UK. Incidence and mortality were also lower than in the Republic of Ireland (ROI), although these observed differences are difficult to interpret given considerable differences in testing and surveillance between the two nations. SAR among household contacts was 15.9% (95% CI 6.6%–30.1%), over 6 times higher than the SAR among ‘high-risk’ contacts at 2.5% (95% CI 0.9%–5.4%). The results from logistic regression analysis of testing data on contacts of laboratory-confirmed cases show that household contacts had 11.0 times higher odds (aOR: 11.0, 95% CI 1.7–70.03, P-value: 0.011) of testing positive for SARS-CoV-2 compared to other categories of contacts. These results demonstrate the importance of the household as a locus of SARS-CoV-2 transmission, and the urgency of identifying effective interventions to reduce household transmission.

Algorithmic decision tools (ADTs) are being introduced into public sector organizations to support more accurate and consistent decision-making. Whether they succeed turns, in large part, on how administrators use these tools. This is one of the first empirical studies to explore how ADTs are being used by Street Level Bureaucrats (SLBs). The author develops an original conceptual framework and uses in-depth interviews to explore whether SLBs are ignoring ADTs (algorithm aversion); deferring to ADTs (automation bias); or using ADTs together with their own judgment (an approach the author calls “artificing”). Interviews reveal that artificing is the most common use-type, followed by aversion, while deference is rare. Five conditions appear to influence how practitioners use ADTs: (a) understanding of the tool (b) perception of human judgment (c) seeing value in the tool (d) being offered opportunities to modify the tool (e) alignment of tool with expectations.

This systematic review and meta-analysis aimed to evaluate thrombocytopenia as a prognostic biomarker in patients with coronavirus disease 2019 (COVID-19). We performed a systematic literature search using PubMed, Embase and EuropePMC. The main outcome was composite poor outcome, a composite of mortality, severity, need for intensive care unit care and invasive mechanical ventilation. There were 8963 patients from 23 studies. Thrombocytopenia occurred in 18% of the patients. Male gender (P = 0.037) significantly reduce the incidence. Thrombocytopenia was associated with composite poor outcome (RR 1.90 (1.43–2.52), P < 0.001; I2: 92.3%). Subgroup analysis showed that thrombocytopenia was associated with mortality (RR 2.34 (1.23–4.45), P < 0.001; I2: 96.8%) and severity (RR 1.61 (1.33–1.96), P < 0.001; I2: 62.4%). Subgroup analysis for cut-off <100 × 109/l showed RR of 1.93 (1.37–2.72), P < 0.001; I2: 83.2%). Thrombocytopenia had a sensitivity of 0.26 (0.18–0.36), specificity of 0.89 (0.84–0.92), positive likelihood ratio of 2.3 (1.6–3.2), negative likelihood ratio of 0.83 (0.75–0.93), diagnostic odds ratio of 3 (2, 4) and area under curve of 0.70 (0.66–0.74) for composite poor outcome. Meta-regression analysis showed that the association between thrombocytopenia and poor outcome did not vary significantly with age, male, lymphocyte, d-dimer, hypertension, diabetes and CKD. Fagan's nomogram showed that the posterior probability of poor outcome was 50% in patients with thrombocytopenia, and 26% in those without thrombocytopenia. The Deek's funnel plot was relatively symmetrical and the quantitative asymmetry test was non-significant (P = 0.14). This study indicates that thrombocytopenia was associated with poor outcome in patients with COVID-19.

PROSPERO ID: CRD42020213974

A set of integers is primitive if it does not contain an element dividing another. Let f(n) denote the number of maximum-size primitive subsets of {1,…,2n}. We prove that the limit α = limn→∞f(n)1/n exists. Furthermore, we present an algorithm approximating α with (1 + ε) multiplicative error in N(ε) steps, showing in particular that α ≈ 1.318. Our algorithm can be adapted to estimate the number of all primitive sets in {1,…,n} as well.

We address another related problem of Cameron and Erdős. They showed that the number of sets containing pairwise coprime integers in {1,…n} is between ${2^{\pi (n)}} \cdot {e^{(1/2 + o(1))\sqrt n }}$ and ${2^{\pi (n)}} \cdot {e^{(2 + o(1))\sqrt n }}$. We show that neither of these bounds is tight: there are in fact ${2^{\pi (n)}} \cdot {e^{(1 + o(1))\sqrt n }}$ such sets.

Cyclospora cayetanensis is a parasite causing cyclosporiasis (an illness in humans). Produce (fruits, vegetables, herbs), water and soil contaminated with C. cayetanensis have been implicated in human infection. The objective was to conduct a scoping review of primary research in English on the detection, epidemiology and control of C. cayetanensis with an emphasis on produce, water and soil. MEDLINE® (Web of ScienceTM), Agricola (ProQuest), CABI Global Health, and Food Science and Technology Abstracts (EBSCOhost) were searched from 1979 to February 2020. Of the 349 relevant primary research studies identified, there were 75 detection-method studies, 40 molecular characterisation studies, 38 studies of Cyclospora in the environment (33 prevalence studies, 10 studies of factors associated with environmental contamination), 246 human infection studies (212 prevalence/incidence studies, 32 outbreak studies, 60 studies of environmental factors associated with non-outbreak human infection) and eight control studies. There appears to be sufficient literature for a systematic review of prevalence and factors associated with human infection with C. cayetanensis. There is a dearth of publicly available detection-method studies in soil (n = 0) and water (n = 2), prevalence studies on soil (n = 1) and studies of the control of Cyclospora (particularly on produce prior to retail (n = 0)).

Tick-borne encephalitis (TBE) is a vector-borne infection associated with a variety of potentially serious complications and sequelae. Vaccination against TBE is strongly recommended for people living in endemic areas. There are two TBE vaccination schemes – standard and rapid – which differ in the onset of protection. With vaccination in a rapid schedule, protection starts as early as 4 weeks after the first dose and is therefore especially recommended for non-immune individuals travelling to endemic areas. Both schemes work reliably in immunocompetent individuals, but only little is known about how TBE vaccination works in people with HIV infection. Our aim was to assess the immunogenicity and safety of the rapid scheme of TBE vaccination in HIV-1 infected individuals. Concentrations of TBE-specific IgG > 126 VIEU/ml were considered protective. The seroprotection rate was 35.7% on day 28 and 39.3% on day 60. There were no differences between responders and non-responders in baseline and nadir CD4 + T lymphocytes. No serious adverse events were observed after vaccination. The immunogenicity of the TBE vaccination was unsatisfactory in our study and early protection was only achieved in a small proportion of vaccinees. Therefore, TBE vaccination with the rapid scheme cannot be recommended for HIV-1 infected individuals.

In the group testing problem the aim is to identify a small set of k ⁓ nθ infected individuals out of a population size n, 0 < θ < 1. We avail ourselves of a test procedure capable of testing groups of individuals, with the test returning a positive result if and only if at least one individual in the group is infected. The aim is to devise a test design with as few tests as possible so that the set of infected individuals can be identified correctly with high probability. We establish an explicit sharp information-theoretic/algorithmic phase transition minf for non-adaptive group testing, where all tests are conducted in parallel. Thus with more than minf tests the infected individuals can be identified in polynomial time with high probability, while learning the set of infected individuals is information-theoretically impossible with fewer tests. In addition, we develop an optimal adaptive scheme where the tests are conducted in two stages.

Let ${\mathbb{P}}(ord\pi = ord\pi ')$ be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that ${\mathbb{P}}(ord\pi = ord\pi ') = {n^{ - 2 + o(1)}}$ and that ${\mathbb{P}}(ord\pi = ord\pi ') \ge {1 \over 2}{n^{ - 2}}lg*n$ for infinitely many n. (Here lg*n is the height of the tallest tower of twos that is less than or equal to n.)

Bollobás and Riordan, in their paper ‘Metrics for sparse graphs’, proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to sparse graphs. We refute these conjectures by exhibiting a sequence of graphs with convergent normalized subgraph densities (and pseudorandom C4-counts), but with no limit expressible as a kernel.

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. A new test for linear cointegration against nonlinear departures is developed based on a simple linearized pseudo-model that is very convenient for practical implementation and has standard normal limit theory in the strictly exogenous regressor case. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semimartingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.

Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. For instance, a closely connected social communities exhibit faster rate of transmission of information in comparison to loosely connected communities. Moreover, many machine learning algorithms and tools that are developed for complex networks try to take advantage of the existence of communities to improve their performance or speed. As a result, there are many competing algorithms for detecting communities in large networks. Unfortunately, these algorithms are often quite sensitive and so they cannot be fine-tuned for a given, but a constantly changing, real-world network at hand. It is therefore important to test these algorithms for various scenarios that can only be done using synthetic graphs that have built-in community structure, power law degree distribution, and other typical properties observed in complex networks. The standard and extensively used method for generating artificial networks is the LFR graph generator. Unfortunately, this model has some scalability limitations and it is challenging to analyze it theoretically. Finally, the mixing parameter μ, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally defined networks. In this paper, we provide an alternative random graph model with community structure and power law distribution for both degrees and community sizes, the Artificial Benchmark for Community Detection (ABCD graph). The model generates graphs with similar properties as the LFR one, and its main parameter ξ can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. We show that the new model solves the three issues identified above and more. In particular, we test the speed of our algorithm and do a number of experiments comparing basic properties of both ABCD and LFR. The conclusion is that these models produce graphs with comparable properties but ABCD is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (independent) communities and random graph with no community structure.

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.