A uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model more flexible for applications. We analyse the number of leaves, the height, the depth, the number of branches, and the size of the largest branch in these weighted trees.

We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size $b-1$ with $b=O(\sqrt{\log N})$, i.e. a server can have at most one job in service and $b-1$ jobs queued. We focus on the steady-state performance of load-balancing algorithms in the heavy traffic regime such that the load of the system is $\lambda = 1 - \gamma N^{-\alpha}$ for $0<\alpha<0.5$ and $\gamma > 0,$ which we call the sub-Halfin–Whitt regime ($\alpha=0.5$ is the so-called Halfin–Whitt regime). We establish a sufficient condition under which the probability that an incoming job is routed to an idle server is 1 asymptotically (as $N \to \infty$) at steady state. The class of load-balancing algorithms that satisfy the condition includes join-the-shortest-queue, idle-one-first, join-the-idle-queue, and power-of-d-choices with $d\geq \frac{r}{\gamma}N^\alpha\log N$ (r a positive integer). The proof of the main result is based on the framework of Stein’s method. A key contribution is to use a simple generator approximation based on state space collapse.

Let V be an n-set, and let X be a random variable taking values in the power-set of V. Suppose we are given a sequence of random coupons $X_1, X_2, \ldots $, where the $X_i$ are independent random variables with distribution given by X. The covering time T is the smallest integer $t\geq 0$ such that $\bigcup_{i=1}^t X_i=V$. The distribution of T is important in many applications in combinatorial probability, and has been extensively studied. However the literature has focused almost exclusively on the case where X is assumed to be symmetric and/or uniform in some way.

In this paper we study the covering time for much more general random variables X; we give general criteria for T being sharply concentrated around its mean, precise tools to estimate that mean, as well as examples where T fails to be concentrated and when structural properties in the distribution of X allow for a very different behaviour of T relative to the symmetric/uniform case.

Large samples from a light-tailed distribution often have a well-defined shape. This paper examines the implications of the assumption that there is a limit shape. We show that the limit shape determines the upper quantiles for a large class of random variables. These variables may be described loosely as continuous homogeneous functionals of the underlying random vector. They play an important role in evaluating risk in a multivariate setting. The paper also looks at various coefficients of tail dependence and at the distribution of the scaled sample points for large samples. The paper assumes convergence in probability rather than almost sure convergence. This results in an elegant theory. In particular, there is a simple characterization of domains of attraction.

We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. Using potential theory and perturbation theory, we are able to deduce closed-form truncated probability densities, as asymptotics or approximations to the original first passage time densities, for single-side level crossing problems. The framework is applicable to diffusion processes with continuous drift functions; in particular, for bounded drift functions, we show that the perturbation series converges. In the present paper, we demonstrate examples of applying our framework to the Ornstein–Uhlenbeck, Bessel, exponential-Shiryaev, and hypergeometric diffusion processes (the latter two being previously studied by Dassios and Li (2018) and Borodin (2009), respectively). The purpose of this paper is to provide a fast and accurate approach to estimating first passage time densities of various diffusion processes.

R-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations.

Hypertension is a common comorbidity in COVID-19 patients. However, the association of hypertension with the severity and fatality of COVID-19 remain unclear. In the present meta-analysis, relevant studies reported the impacts of hypertension on SARS-CoV-2 infection were identified by searching PubMed, Elsevier Science Direct, Web of Science, Wiley Online Library, Embase and CNKI up to 20 March 2020. As the results shown, 12 publications with 2389 COVID-19 patients (674 severe cases) were included for the analysis of disease severity. The severity rate of COVID-19 in hypertensive patients was much higher than in non-hypertensive cases (37.58% vs 19.73%, pooled OR: 2.27, 95% CI: 1.80–2.86). Moreover, the pooled ORs of COVID-19 severity for hypertension vs. non-hypertension was 2.21 (95% CI: 1.58–3.10) and 2.32 (95% CI: 1.70–3.17) in age <50 years and ⩾50 years patients, respectively. Additionally, six studies with 151 deaths of 2116 COVID-19 cases were included for the analysis of disease fatality. The results showed that hypertensive patients carried a nearly 3.48-fold higher risk of dying from COVID-19 (95% CI: 1.72–7.08). Meanwhile, the pooled ORs of COVID-19 fatality for hypertension vs. non-hypertension was 6.43 (95% CI: 3.40–12.17) and 2.66 (95% CI: 1.27–5.57) in age <50 years and ⩾50 years patients, respectively. Neither considerable heterogeneity nor publication bias was observed in the present analysis. Therefore, our present results provided further evidence that hypertension could significantly increase the risks of severity and fatality of SARS-CoV-2 infection.

In a recent study, mid-latitude ionospheric parameters were compared with solar activity; it was suggested that the relationship between these, earlier assumed stable, might be changing with time (Lastovicka, 2019). Here, the information is extended to higher latitude (69.6°N, 19.2E) and further back in time. For the ionospheric F-region (viz. the critical frequency, FoF2) the same behaviour is seen with a change-point around 1996. For the ionospheric E-region (viz. the critical frequency, foE), change-points are less obvious than in the mid-latitude study, presumably owing to the observation site lying under the auroral oval.

Non-typhoidal Salmonella (NTS) serovars, sequences types and antimicrobial susceptibility profiles have specific associations with animal and human infections in Vietnam. Antimicrobial resistance may have an effect on the manifestation of human NTS infections, with isolates from asymptomatic individuals being more susceptible to antimicrobials than those associated with animals and human diarrhoea.

Persistent methicillin-resistant Staphylococcus aureus (MRSA) infection in cystic fibrosis (CF) patients has been associated with a more rapid decline in lung function, increased hospitalisation and mortality. The aim of this study was to evaluate the clonal relationships among 116 MRSA isolates from 12 chronically colonised CF pediatric patients over a 6-year period in a Rio de Janeiro CF specialist centre. Isolates were characterised by antimicrobial resistance, SCCmec type, presence of Panton-Valentine Leukocidin (PVL) genes and grouped according to DNA macrorestriction profile by pulsed-field gel electrophoresis (PFGE) and spa gene type. High resistance rates were detected for erythromycin (78%) and ciprofloxacin (50%) and SCCmec IV was the most common type (72.4%). Only 8.6% of isolates were PVL positive. High genetic diversity was evident by PFGE (39 pulsotypes) and of nine that were identified spa types, t002 (53.1%) and t539 (14.8%) were the most prevalent. We conclude that the observed homogeneity of spa types within patients over the study period demonstrates the persistence of such strain lineages throughout the course of chronic lung infection.

Candida meningitis in neurosurgical patients is relatively unusual but is associated with a high mortality rate. We present our experience with this infection and discuss the clinical characteristics, treatment options and outcomes. We retrospectively reviewed neurosurgical patients with multiple positive cerebrospinal fluid (CSF) culture results in our hospital from January 2013 to December 2019. Nine patients were available for review according to our inclusion and exclusion criteria. Four species of Candida were isolated from the CSF samples and Candida albicans accounted for half of all infections. Eight infections were associated with ventricle peritoneal shunt, lumbar cistern peritoneal shunt or external ventricular drain. All of these foreign intracranial materials were removed or changed and all the patients received antifungal treatment, including fluconazole and/or voriconazole. It is associated with severe long-term outcomes in survivors and a mortality rate that reaches 11.1%. Prior treatments with broad-spectrum and high-grade antibiotics and anaemia are possible risk factors for Candida meningitis. We advise that foreign intracranial material should be removed or changed as early as possible and the timing of re-shunt operation can be 1 month after control of Candida meningitis has been achieved, with several negative CSF culture results.

We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler–Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certain asymptotic regime which includes the case of finite maturity, small vol-of-vol and large initial volatility with fixed product of vol-of-vol and initial volatility. We derive an almost sure limit and a large deviations result for the log-asset price in the limit of a large number of time steps. We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in this regime. Using this representation, we obtain analytical expansions of the implied volatility for small maturity and extreme strikes, which reproduce at leading order known asymptotic results for the continuous time model.

Many cryptocurrencies including Bitcoin are susceptible to a so-called double-spend attack, where someone dishonestly attempts to reverse a recently confirmed transaction. The duration and likelihood of success of such an attack depends on the recency of the transaction and the computational power of the attacker, and these can be related to the distribution of time for counts from one Poisson process to exceed counts from another by some desired amount. We derive an exact expression for this distribution and show how it can be used to obtain efficient simulation estimators. We also give closed-form analytic approximations and illustrate their accuracy.

We consider various aspects of longevity trend risk viewed through the prism of a finite time window. We show the broad equivalence of value-at-risk (VaR) capital requirements at a p-value of 99.5% to conditional tail expectations (CTEs) at 99%. We also show how deferred annuities have higher risk, which can require double the solvency capital of equivalently aged immediate anuities. However, results vary considerably with the choice of model and so longevity trend-risk capital can only be determined through consideration of multiple models to inform actuarial judgement. This model risk is even starker when trying to value longevity derivatives. We briefly discuss the importance of using smoothed models and describe two methods to considerably shorten VaR and CTE run times.

This abstract relates to the following papers: Spender, A., Bullen, C., Altmann-Richer, L., Cripps, J., Duffy, R., Falkous, C., Farrell, M., Horn, T. and Wigzell, J. Wearables and the Internet of things: considerations for the life and health insurance industry. British Actuarial Journal, 24. doi: 10.1017/S1357321719000072.

The coronavirus disease 2019 (COVID-19) outbreak caused by the severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2 virus) has been sustained in China since December 2019, and has become a pandemic. The mental health of frontline medical staff is a concern. In this study, we aimed to identify the factors influencing medical worker anxiety in China during the COVID-19 outbreak. We conducted a cross-sectional study to estimate the prevalence of anxiety among medical staff in China from 10 February 2020 to 20 February 2020 using the Zung Self-rating Anxiety Scale (SAS) to assess anxiety, with the criteria of normal (⩽49), mild (50–59), moderate (60–70) and severe anxiety (⩾70). We used multivariable linear regression to determine the factors (e.g. having direct contact when treating infected patients, being a medical staff worker from Hubei province, being a suspect case) for anxiety. We also used adjusted models to confirm independent factors for anxiety after adjusting for gender, age, education and marital status. Of 512 medical staff in China, 164 (32.03%) had had direct contact treating infected patients. The prevalence of anxiety was 12.5%, with 53 workers suffering from mild (10.35%), seven workers suffering from moderate (1.36%) and four workers suffering from severe anxiety (0.78%). After adjusting for sociodemographic characteristics (gender, age, education and marital status), medical staff who had had direct contact treating infected patients experienced higher anxiety scores than those who had not had direct contact (β value = 2.33, confidence interval (CI) 0.65–4.00; P = 0.0068). A similar trend was observed in medical staff from Hubei province, compared with those from other parts of China (β value = 3.67, CI 1.44–5.89; P = 0.0013). The most important variable was suspect cases with high anxiety scores, compared to non-suspect cases (β value = 4.44, CI 1.55–7.33; P = 0.0028). In this survey of hospital medical workers during the COVID-19 outbreak in China, we found that study participants experienced anxiety symptoms, especially those who had direct clinical contact with infected patients; as did those in the worst affected areas, including Hubei province; and those who were suspect cases. Governments and healthcare authorities should proactively implement appropriate psychological intervention programmes, to prevent, alleviate or treat increased anxiety.

The aim of this study was to determine the most cost-effective strategy for the prevention and control of multidrug-resistant organisms (MDROs) in intensive care units (ICUs) in areas with limited health resources. The study was conducted in 12 ICUs of four hospitals. The total cost for the prevention of MDROs and the secondary attack rate (SAR) of MDROs for each strategy were collected retrospectively from 2046 subjects from January to December 2017. The average cost-effectiveness ratio (CER), incremental cost-effectiveness ratio (ICER) and cost-effectiveness acceptability curve were calculated. Hand hygiene (HH) had the lowest total cost (2149.6 RMB) and SAR of MDROs (8.8%) while single-room isolation showed the highest cost (33 700.2 RMB) and contact isolation had the highest SAR of MDROs (31.8%). The average cost per unit infection prevention was 24 427.8 RMB, with the HH strategy followed by the environment disinfection strategy (CER = 21 314.67). HH had the highest iterative cost effect under willingness to pay less than 2000 RMB. Due to the low cost for repeatability and obvious effectiveness, we conclude that HH is the optimal strategy for MDROs infections in ICUs in developing countries. The cost-effectiveness of the four prevention strategies provides some reference for developing countries but multiple strategies remain to be examined.