Consider a well-shuffled deck of cards of n different types where each type occurs m times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in the past few decades. Under different regimes of m, n, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper we establish a central limit theorem with Berry–Esseen bounds when m is fixed and n is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions.

Dengue, chikungunya, and Zika are arboviruses that cause 390 million infections annually. Risk factors for hospitalization are poorly understood. Communities affected by these diseases have an escalating prevalence of allergies and obesity, which are linked to immune dysfunction. We assessed the association of allergies or body mass with hospitalization for an arbovirus infection. From 2014 to 2017, we recruited participants with a clinical diagnosis of arbovirus infection. Arbovirus infections were laboratory-confirmed and allergies were self-reported. Mid-upper arm circumference (MUAC), weight, and height were measured. We used two logistic regression models to assess the relationships between hospitalization and allergies and between hospitalization and body mass (MUAC for participants <20 years old and body mass index (BMI) for adults ≥20 years old). Models were stratified by age group and adjusted for confounders. For allergies, 41 of 265 were hospitalized. There was no association between allergies and hospitalization. For body mass, 34 of 251 were hospitalized. There was a 43% decrease in hospitalization odds for each additional centimetre MUAC among children (aOR 0.566, 95% CI 0.252–1.019) and a 12% decrease in hospitalization odds for each additional BMI unit among adults (aOR 0.877, 95% CI 0.752–0.998). Our work encourages the exploration of the underlying mechanisms.

Wild rabbits in Australia developed genetic resistance to the myxoma virus, which was introduced as a biological control agent. However, little is known about the rate at which this evolutionary change occurred. We collated data from challenge trials that estimated rabbit resistance to myxomatosis in Australia and expressed resistance on a continuous scale, enabling trends in its development to be assessed over 45 years up to 1995. Resistance initially increased rapidly, followed by a plateau lasting ten years, before a second rapid increase occurred associated with the introduction of European rabbit fleas as myxoma virus vectors. By contrast, in the United Kingdom, where rabbit flea vectors were already present when the myxoma virus initially spread, resistance developed more slowly. No estimates of rabbit resistance to myxomatosis have been made for almost 30 years, despite other highly lethal rabbit pathogens becoming established worldwide. Continued testing of wild-caught rabbits in Australia to determine current levels of resistance to myxomatosis is recommended to assess its current effectiveness for managing pest rabbits. Given the economic and environmental significance of invasive rabbits, it would be remiss to manage such biological resources and ecosystem services poorly.

The aim of this study was to evaluate the impact of coronavirus disease 2019 (COVID-19) on treatment outcomes in critically ill patients with carbapenem-resistant Acinetobacter baumannii (CRAB) bloodstream infection (BSI). This single-centre, retrospective cohort study was conducted in a 1,048-bed university-affiliated tertiary hospital in the Republic of Korea from January 2021 to March 2022. The study participants included consecutive hospitalised adult patients (aged ≥18 years) in the intensive care unit with CRAB monomicrobial BSI. During the study period, a total of 70 patients were included in our study, and 24 (34.3%) were diagnosed with COVID-19. The 28-day mortality rate was 64.3%. In the multivariate Cox proportional hazard regression analysis, diagnosis of COVID-19 (hazard ratio (HR), 2.91; 95% confidence interval (CI): 1.45–5.87), neutropenia (HR, 2.76; 95% CI: 1.04–7.29), Pitt bacteraemia score (per point; HR, 1.30; 95% CI: 1.19–1.41), and appropriate definite antibiotic therapy (HR, 0.31; 95% CI: 0.15–0.62) were independent predictors of 28-day mortality in patients with CRAB BSI. In conclusion, our findings suggested that COVID-19 has a negative prognostic impact on patients with CRAB BSI. Further study is needed to investigate the specific mechanisms of how COVID-19 worsens the prognosis of CRAB infection.

In the classical gambler’s ruin problem, the gambler plays an adversary with initial capitals z and $a-z$, respectively, where $a>0$ and $0< z < a$ are integers. At each round, the gambler wins or loses a dollar with probabilities p and $1-p$. The game continues until one of the two players is ruined. For even a and $0<z\leq {a}/{2}$, the family of distributions of the duration (total number of rounds) of the game indexed by $p \in [0,{\frac{1}{2}}]$ is shown to have monotone (increasing) likelihood ratio, while for ${a}/{2} \leq z<a$, the family of distributions of the duration indexed by $p \in [{\frac{1}{2}}, 1]$ has monotone (decreasing) likelihood ratio. In particular, for $z={a}/{2}$, in terms of the likelihood ratio order, the distribution of the duration is maximized over $p \in [0,1]$ by $p={\frac{1}{2}}$. The case of odd a is also considered in terms of the usual stochastic order. Furthermore, as a limit, the first exit time of Brownian motion is briefly discussed.

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, for continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity or moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth–death processes. Our approach, together with the identities, easily extends to discrete-time Markov chains.

Older adults and people of colour are vulnerable to the COVID-19 pandemic, and mitigation behaviours reduce COVID-19 infection. We examined racial and ethnic differences in COVID-19 diagnosis and adherence to COVID-19 mitigation behaviours among U.S. older adults. Data were retrieved from the National Health and Aging Trends Study, a nationally representative prospective cohort with 3257 U.S. Medicare beneficiaries aged 65+. COVID-19 variables were collected in 2020; all other data in 2019. Odds of COVID-19 diagnosis and adherence to mitigation behaviours (handwashing, masking, social distancing) were analysed using logistic regression. Compared to White older adults, only Hispanic respondents had 2.7 times significantly higher odds of COVID-19 after adjusting for sociodemographics, health, and mitigation behaviours (aOR = 2.71, 95% CI = 1.20-6.12). Black older adults had 7.9 times significantly higher odds of masking (aOR = 7.94, 95% CI = 2.33-27.04) and 2.3 times higher odds of social distancing (aOR = 2.33, 95% CI = 1.28-4.24), after adjusting for sociodemographics and health. Among all racial and ethnic groups, only Hispanic older adults had a significantly elevated COVID-19 diagnosis. Despite higher adherence to COVID-19 mitigation behaviours among racial and ethnic minorities, especially Black older adults, odds of COVID-19 remained elevated. Research is needed to explore potential mechanisms for higher odds of COVID-19 among minority older adults.

This paper sets out the working party’s view that for a defined benefit pension scheme’s commutation rate the appropriate starting point should be to set it in line with the scheme’s cash equivalent transfer value basis. We recognise that there may be several reasons why an actuary in their advice may deviate from that starting point and we explore these in detail, giving our views on when deviation is and is not justified, noting that many common reasons used such as selection risk are often used without (in our view) adequate justification. We also cover frequency of review – our view is that commutation rates should be reviewed at least every 3 years and actuaries should consider performing a high-level review of commutation rates annually. We suggest that actuaries should consider proposing market-related commutation rates especially in periods of volatile market conditions. In terms of timing, there are good arguments to review commutation terms either following or during a valuation. Finally, we set out some considerations on how actuaries should present their advice, such as clearly setting out all the information required to take key decisions, following up with any actuarial certification in writing (if necessary) and illustrating the impact on members for changing commutation rates.

Let $(X_{1},\ldots,X_{n})$ be a random vector distributed according to a time-transformed exponential model. This is a special class of exchangeable models, which, in particular, includes multivariate distributions with Schur-constant survival functions. Let for $1\leq i\leq n$, $X_{i:n}$ denote the corresponding ith-order statistic. We consider the problem of comparing the strength of dependence between any pair of Xi’s with that of the corresponding order statistics. It is in particular proved that for $m=2,\ldots,n$, the dependence of $X_{2:m}$ on $X_{1:m}$ is more than that of X2 on X1 according to more stochastic increasingness (positive monotone regression) order, which in turn implies that $(X_{1:m},X_{2:m})$ is more concordant than $(X_{1},X_{2})$. It will be interesting to examine whether these results can be extended to other exchangeable models.