Healthcare workers (HCWs) have increased exposure and subsequent risk of infection with severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). This case-control study was conducted to investigate the contemporaneous risks associated with confirmed SARS-CoV-2 infection amongst HCWs following in-work exposure to a confirmed coronavirus disease-2019 (COVID-19) case. We assessed the influence of demographic (age, sex, nationality, high risk co-morbidities and vaccination status) and work-related factors (job role, exposure location, contact type, personal protective equipment (PPE) use) on infection risk following nosocomial SARS-CoV-2 exposure. All contact tracing records within the hospital site during waves 1–3 of the COVID-19 pandemic in Ireland were screened to identify exposure events, cases and controls. In total, 285 cases and 1526 controls were enrolled, as a result of 1811 in-work exposure events with 745 index cases. We demonstrate that male sex, Eastern European nationality, exposure location, PPE use and vaccination status all impact the likelihood of SARS-CoV-2 infection following nosocomial SARS-CoV-2 exposure. The findings draw attention to the need for continuing emphasis on PPE use and its persisting benefit in the era of COVID-19 vaccinations. We suggest that non-work-related factors may influence infection risk seen in certain ethnic groups and that infection risk in high-risk HCW roles (e.g. nursing) may be the result of repeated exposures rather than risks inherent to a single event.

Campylobacter spp. are one of the most common causes of bacterial gastroenteritis in Canada and worldwide. Fluoroquinolones are often used to treat complicated human campylobacteriosis and strains of Campylobacter spp. resistant to these drugs are emerging along the food chain. A scoping review was conducted to summarise how human (fluoro)quinolone-resistant (FQR; quinolones including fluoroquinolones) Campylobacter spp. infections are characterised in the literature by describing how burden of illness (BOI) associated with FQR is measured and reported, describing the variability in reporting of study characteristics, and providing a narrative review of literature that compare BOI measures of FQR Campylobacter spp. infections to those with susceptible infections. The review identified 26 studies that yielded many case reports, a lack of recent literature and a lack of Canadian data. Studies reported 26 different BOI measures and the most common were hospitalisation, diarrhoea, fever and duration of illness. There were mixed results as BOI measures reported in literature were inconsistently defined and there were limited comparisons between resistant and susceptible infections. This presents a challenge when attempting to assess the magnitude of the BOI due to FQR Campylobacter spp., highlighting the need for more research in this area.

In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our method to a model of a random intersection graph, a random graph obtained through p-bond percolation on a general d-regular graph, and a model of an inhomogeneous random graph.

We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cramér–Lundberg model, namely the constant intensity of the Poisson process. Due to this structure, we can apply the theory of piecewise deterministic Markov processes on a multivariate process containing the intensity and the reserve process, which allows us to identify a family of martingales. Eventually, we use change of measure techniques to derive an upper bound for the ruin probability in this model. Exploiting a recurrent structure of the shot-noise process, even the asymptotic behaviour of the ruin probability can be determined.

In this article we provide new results for the asymptotic behavior of a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities $\mathbb{P}[N_{\alpha}(t)=\,j\mid N_{\alpha}(0)=i]$ are governed by a time-fractional system of differential equations, under the condition that it is not killed. More specifically, we prove that the concepts of quasi-limiting distribution and quasi-stationary distribution do not coincide, which is a consequence of the long-memory nature of the process. In addition, exact formulas for the quasi-limiting distribution and its rate convergence are presented. In the first sections, we revisit the two equivalent characterizations for this process: the first one is a time-changed classic birth and death process, whereas the second one is a Markov renewal process. Finally, we apply our main theorems to the linear model originally introduced by Orsingher and Polito [23].

Let $V_{(r,n,\tilde {m}_n,k)}^{(p)}$ and $W_{(r,n,\tilde {m}_n,k)}^{(p)}$ be the $p$-spacings of generalized order statistics based on absolutely continuous distribution functions $F$ and $G$, respectively. Imposing some conditions on $F$ and $G$ and assuming that $m_1=\cdots =m_{n-1}$, Hu and Zhuang (2006. Stochastic orderings between p-spacings of generalized order statistics from two samples. Probability in the Engineering and Informational Sciences 20: 475) established $V_{(r,n,\tilde {m}_n,k)}^{(p)} \leq _{{\rm hr}} W_{(r,n,\tilde {m}_n,k)}^{(p)}$ for $p=1$ and left the case $p\geq 2$ as an open problem. In this article, we not only resolve it but also give the result for unequal $m_i$'s. It is worth mentioning that this problem has not been proved even for ordinary order statistics so far.

We provide a general purpose result for the coupling of exploration processes of random graphs, both undirected and directed, with their local weak limits when this limit is a marked Galton–Watson process. This class includes in particular the configuration model and the family of inhomogeneous random graphs with rank-1 kernel. Vertices in the graph are allowed to have attributes on a general separable metric space and can potentially influence the construction of the graph itself. The coupling holds for any fixed depth of a breadth-first exploration process.

This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak, Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method.

We present an affine-invariant random walk for drawing uniform random samples from a convex body $\mathcal{K} \subset \mathbb{R}^n$ that uses maximum-volume inscribed ellipsoids, known as John’s ellipsoids, for the proposal distribution. Our algorithm makes steps using uniform sampling from the John’s ellipsoid of the symmetrization of $\mathcal{K}$ at the current point. We show that from a warm start, the random walk mixes in ${\widetilde{O}}\!\left(n^7\right)$ steps, where the log factors hidden in the ${\widetilde{O}}$ depend only on constants associated with the warm start and desired total variation distance to uniformity. We also prove polynomial mixing bounds starting from any fixed point x such that for any chord pq of $\mathcal{K}$ containing x, $\left|\log \frac{|p-x|}{|q-x|}\right|$ is bounded above by a polynomial in n.

This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a nonlinear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Itô model. Given the autoregressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite-sample performance of the proposed model and an empirical study with 50 assets among the S&P 500 compositions. Numerical studies show the advantages of the proposed model.

As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples.

We study semiparametric inference in a small-dimensional vector autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q. This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multistep procedure in closed-form, which combines an eigenvalue–eigenvector matrix decomposition and a linear instrumental variable estimation allowing for Hansen–Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical illustration, we investigate the dynamic common factors and the spillover effects that explain the co-movements among the log daily realized volatilities of four European stock market indices.

This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when a large set of instruments with potential invalidity is present. We establish theoretical results on the higher-order mean-squared error (MSE) approximation of the two-stage least-squares (2SLS), the limited information maximum likelihood (LIML), the Fuller (FULL), the bias-adjusted 2SLS, and jackknife version of the LIML and FULL estimators by allowing for local violations of the instrument exogeneity conditions. Based on the approximation to the higher-order MSE, we consider the instrument selection criteria that can be used to choose among the set of available instruments. We demonstrate the asymptotic optimality of the instrument selection procedure proposed by Donald and Newey (2001, Econometrica 69, 1161–1191) in the presence of locally (faster than $N^{-1/2}$) invalid instruments in the sense that the dominant term in the MSE with the chosen instrument is asymptotically equivalent to the infeasible optimum. Furthermore, we propose instrument selection procedures to choose instruments among the sets of conservative (known) valid instruments and potentially locally ($N^{-1/2}$) invalid instruments based on the higher-order MSE of the IV estimators by considering the bias-variance trade-off.

Using one-dimensional branching Brownian motion in a periodic environment, we give probabilistic proofs of the asymptotics and uniqueness of pulsating traveling waves of the Fisher–Kolmogorov–Petrovskii–Piskounov (F-KPP) equation in a periodic environment. This paper is a sequel to ‘Branching Brownian motion in a periodic environment and existence of pulsating travelling waves’ (Ren et al., 2022), in which we proved the existence of the pulsating traveling waves in the supercritical and critical cases, using the limits of the additive and derivative martingales of branching Brownian motion in a periodic environment.

Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of certain curves in statistical physics models. In this note, we describe a new growth-fragmentation process connected to random planar maps with faces of large degree, having as a key ingredient the ricocheted stable process recently discovered by Budd. The process has applications to the excursions of planar Brownian motion and Liouville quantum gravity.

Episodes of bacterial superinfections have been well identified for several respiratory viruses, notably influenza. In this retrospective study, we compared the frequency of superinfections in COVID-19 patients to those found in influenza-positive patients, and to controls without viral infection. We included 42 468 patients who had been diagnosed with COVID-19 and 266 261 subjects who had tested COVID-19 negative between 26 February 2020 and 1 May 2021. In addition, 4059 patients were included who had tested positive for the influenza virus between 1 January 2017 and 31 December 2019. Bacterial infections in COVID-19 patients were more frequently healthcare-associated, and acquired in ICUs, were associated with longer ICU stays, and occurred in older and male patients when compared to controls and to influenza patients (P < 0.0001 for all). The most common pathogens proved to be less frequent in COVID-19 patients, including fewer cases of bacteraemia involving E. coli (P < 0.0001) and Klebsiella pneumoniae (P = 0.027) when compared to controls. In respiratory specimens Haemophilus influenzae (P < 0.0001) was more frequent in controls, while Streptococcus pneumoniae (P < 0.0001) was more frequent in influenza patients. Likewise, species associated with nosocomial transmission, such as Pseudomonas aeruginosa and Staphylococcus epidermidis, were more frequent among COVID-19 patients. Finally, we observed a high frequency of Enterococcus faecalis bacteraemia among COVID-19 patients, which were mainly ICU-acquired and associated with a longer timescale to acquisition.

To reappraise pre-exposure prophylaxis (PrEP) eligibility criteria towards the men who have sex with men (MSM) with highest HIV-risk, we assessed PrEP need (i.e. HIV-risk) using Amsterdam Cohort Studies data from 2011–2017 for all non-PrEP using MSM. Outcomes were incident HIV-infection and newly-diagnosed anal STI. Determinants were current PrEP eligibility criteria (anal STI and condomless sex (CAS)) and additional determinants (age, education, group sex, alcohol use during sex and chemsex). We used targeted maximum likelihood estimation (TMLE) to estimate the relative risk (RR) and 95% confidence intervals (CI) of determinants on outcomes, and calculated population attributable fractions (PAFs) with 95% CI using RRs from TMLE. Among 810 included MSM, 22 HIV-infections and 436 anal STIs (n = 229) were diagnosed during follow-up. Chemsex (RR = 5.8 (95% CI 2.0–17.0); PAF = 55.3% (95% CI 43.3–83.4)), CAS with a casual partner (RR = 3.3 (95% CI 1.3–8.7); PAF = 38.0% (95% CI 18.3–93.6)) and anal STI (RR = 5.3 (95% CI 1.7–16.7); PAF = 22.0 (95% CI −16.8 to 100.0)) were significantly (P < 0.05) associated with and had highest attributable risk fractions for HIV. Chemsex (RR = 2.0 (95% CI 1.6–2.4); PAF = 19.5 (95% CI 10.6–30.6)) and CAS with a casual partner (RR = 2.5 (95% CI 2.0–3.0); PAF = 28.0 (95% CI 21.0–36.4)) were also significantly associated with anal STI, as was younger age (16–34/≥35; RR = 1.7 (95% CI 1.4–2.1); PAF = 15.5 (95% CI 6.4–27.6)) and group sex (RR = 1.3 (95% CI 1.1–1.6); PAF = 9.0 (95% CI −2.3 to 23.7)). Chemsex should be an additional PrEP eligibility criterion.