Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation n. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by the moment method, based on the spinal decomposition and the many-to-few formula. As a result, we give explicit integral representations of all quasi-stationary distributions of $(Z_n)_{n\in\mathbb{N}}$, whose proofs are direct and probabilistic, and do not rely on Martin boundary theory.

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments.

In this paper, we investigate a class of McKean–Vlasov stochastic differential equations (SDEs) with Lévy-type perturbations. We first establish the existence and uniqueness theorem for the solutions of the McKean–Vlasov SDEs by utilizing an Eulerlike approximation. Then, under suitable conditions, we demonstrate that the solutions of the McKean–Vlasov SDEs can be approximated by the solutions of the associated averaged McKean–Vlasov SDEs in the sense of mean square convergence. In contrast to existing work, a novel feature of this study is the use of a much weaker condition, locally Lipschitz continuity in the state variables, allowing for possibly superlinearly growing drift, while maintaining linearly growing diffusion and jump coefficients. Therefore, our results apply to a broader class of McKean–Vlasov SDEs.

This paper investigates the asymptotic properties of parameter estimation for the Ewens–Pitman partition with parameters $0\lt\alpha\lt1$ and $\theta\gt-\alpha$. Specifically, we show that the maximum-likelihood estimator (MLE) of $\alpha$ is $n^{\alpha/2}$-consistent and converges to a variance mixture of normal distributions, where the variance is governed by the Mittag-Leffler distribution. Moreover, we show that a proper normalization involving a random statistic eliminates the randomness in the variance. Building on this result, we construct an approximate confidence interval for $\alpha$. Our proof relies on a stable martingale central limit theorem, which is of independent interest.

We consider the random series–parallel graph introduced by Hambly and Jordan (2004 Adv. Appl. Probab. 36, 824–838), which is a hierarchical graph with a parameter $p\in [0, \, 1]$. The graph is built recursively: at each step, every edge in the graph is either replaced with probability p by a series of two edges, or with probability $1-p$ by two parallel edges, and the replacements are independent of each other and of everything up to then. At the nth step of the recursive procedure, the distance between the extremal points on the graph is denoted by $D_n (p)$. It is known that $D_n(p)$ possesses a phase transition at $p=p_c \;:\!=\;\frac{1}{2}$; more precisely, $\frac{1}{n}\log {{\mathbb{E}}}[D_n(p)] \to \alpha(p)$ when $n \to \infty$, with $\alpha(p) >0$ for $p>p_c$ and $\alpha(p)=0$ for $p\le p_c$. We study the exponent $\alpha(p)$ in the slightly supercritical regime $p=p_c+\varepsilon$. Our main result says that as $\varepsilon\to 0^+$, $\alpha(p_c+\varepsilon)$ behaves like $\sqrt{\zeta(2) \, \varepsilon}$, where $\zeta(2) \;:\!=\; \frac{\pi^2}{6}$.

In this paper, we study ordering properties of vectors of order statistics and sample ranges arising from bivariate Pareto random variables. Assume that $(X_1,X_2)\sim\mathcal{BP}(\alpha,\lambda_1,\lambda_2)$ and $(Y_1,Y_2)\sim\mathcal{BP}(\alpha,\mu_1,\mu_2).$ We then show that $(\lambda_1,\lambda_2)\stackrel{m}{\succ}(\mu_1,\mu_2)$ implies $(X_{1:2},X_{2:2})\ge_{st}(Y_{1:2},Y_{2:2}).$ Under bivariate Pareto distributions, we prove that the reciprocal majorization order between the two vectors of parameters is equivalent to the hazard rate and usual stochastic orders between sample ranges. We also show that the weak majorization order between two vectors of parameters is equivalent to the likelihood ratio and reversed hazard rate orders between sample ranges.

We consider an optimal stopping problem of a linear diffusion under Poisson constraint where the agent can adjust the arrival rate of new stopping opportunities. We assume that the agent may switch the rate of the Poisson process between two values. Maintaining the lower rate incurs no cost, whereas the higher rate requires effort that is captured by a cost function c. We study a broad class of payoff functions, cost functions and diffusion dynamics, for which we explicitly characterize the solution to the constrained stopping problem. We also characterize the case where switching to the higher rate is always suboptimal. The results are illustrated with two examples.

Asymptotic dimension and Assouad–Nagata dimension are measures of the large-scale shape of a class of graphs. Bonamy, Bousquet, Esperet, Groenland, Liu, Pirot, and Scott [J. Eur. Math. Society] showed that any proper minor-closed class has asymptotic dimension 2, dropping to 1 only if the treewidth is bounded. We improve this result by showing it also holds for the stricter Assouad–Nagata dimension. We also characterise when subdivision-closed classes of graphs have bounded Assouad–Nagata dimension.

Salmonella Typhimurium sequence type (ST) 36 is a rare sequence type in Sweden. During August–November 2024, 100 cases of Salmonella Typhimurium ST36 were reported nationwide. The highest proportions of cases were observed among individuals aged 0–10 years (17%) and 41–50 years (20%), with females representing 65% of the total cases. Microbiological analysis of the S. Typhimurium ST36 isolates identified nine clusters and five individual strains clustering within 53 single-nucleotide polymorphisms. A matched case–control study found cases to be associated with the consumption of alfalfa sprouts (adjusted odds ratio = 8.94, 95% CI: 2.96–27.1). Trace-back investigation identified seeds used by two alfalfa sprout producers in Sweden as the likely source of the outbreak, although microbiological analysis of sprouted alfalfa seeds from the producers did not detect Salmonella. However, continued international investigations further implicated seeds sourced from the same origin, supporting that alfalfa seeds were the ultimate source of the Swedish outbreak. Our investigation and findings indicate that alfalfa sprouts may contain Salmonella and thus pose a health risk to consumers. We emphasize the need for primary producers of alfalfa seeds and sprouts to identify and prevent possible contamination points.

This surveillance report describes the epidemiology and clinical outcomes of carbapenem-resistant Enterobacterales (CRE) infections in Tennessee from 2016 to 2022, analysing 570 cases and 406 isolates. The incidence of CRE infections per 100 000 population showed an upward trend. Enterobacter species were the most common organisms, whereas Klebsiella species were the main carbapenemase-producing CRE (CP-CRE). Klebsiella pneumoniae carbapenemase was the most common mechanism contributing to this resistance. Demographic characteristics of patients with identified isolates demonstrated a median age of 69.5 years. There were no significant differences in CP-CRE infection by sex or race. Patients with CP-CRE were more likely to be hospitalized than those with non-CP-CRE, at 60.9% and 43.9%, respectively. Multivariable analysis indicated that patients with CP-CRE had significantly higher odds of 90-day mortality (odds ratio, 2.22; 95% confidence interval, 1.12–4.42; p < 0.0001) than non-CP-CRE patients. Individuals with a higher Charlson Comorbidity Index score exhibited an increased odds of dying within 30- and 90-day post-specimen collection and had a greater likelihood of requiring intensive care unit admission. This report underscores the need to understand the epidemiology and risk factors linked to CRE infections to improve prevention strategies and patient care.

Toxoplasmosis during pregnancy can cause congenital malformations and fetal death. This study aimed to estimate the Toxoplasma gondii seroprevalence among pregnant women participating in the 2021 French national perinatal survey and identify associated factors. All women giving birth in France during the study period were invited to participate. Data collected included demographic information, nationality, socio-economic status, education level, and Toxoplasma gondii serological status. Women were classified as seropositive if IgG antibodies were present or if seroconversion occurred during pregnancy. Univariate and multivariate Poisson regression analyses with robust error variance were used to estimate prevalence ratios and identify factors associated with seropositivity. Among 12,612 women, the overall seroprevalence was 25.9%, and 0.22% seroconverted during pregnancy. Seroprevalence increased by 5% with every 5-year age increment and was significantly higher in the French overseas territories of Mayotte (75.0%), La Réunion (35.8%), and French Guiana (33.3%). Seroprevalence was also higher among women with lower educational levels (47.4% for primary education) and those of Sub-Saharan African nationality (52.0%). Geographic and socio-demographic variations may reflect dietary and environmental diversity. Despite declining seroprevalence in France, continued public health efforts, particularly among high-risk populations, remain critical to minimize the impact of congenital toxoplasmosis.

Digital Twinning (DT) has become a main instrument for Industry 4.0 and the digital transformation of manufacturing and industrial processes. In this statement paper, we elaborate on the potential of DT as a valuable tool in support of the management of intelligent infrastructures throughout all stages of their life cycle. We highlight the associated needs, opportunities, and challenges and discuss the needs from both the research and applied perspectives. We elucidate the transformative impact of digital twin applications for strategic decision-making, discussing its potential for situation awareness, as well as enhancement of system resilience, with a particular focus on applications that necessitate efficient, and often real-time, or near real-time, diagnostic and prognostic processes. In doing so, we elaborate on the separate classes of DT, ranging from simple images of a system, all the way to interactive replicas that are continually updated to reflect a monitored system at hand. We root our approach in the adoption of hybrid modeling as a seminal tool for facilitating twinning applications. Hybrid modeling refers to the synergistic use of data with models that carry engineering or empirical intuition on the system behavior. We postulate that modern infrastructures can be viewed as cyber-physical systems comprising, on the one hand, an array of heterogeneous data of diversified granularity and, on the other, a model (analytical, numerical, or other) that carries information on the system behavior. We therefore propose hybrid digital twins (HDT) as the main enabler of smart and resilient infrastructures.

The Kerridge [(1961). Inaccuracy and inference. Journal of the Royal Statistical Society: Series B 23(1): 184-194] inaccuracy measure is the mathematical expectation of the information content of the true distribution with respect to an assumed distribution, reflecting the inaccuracy introduced when the assumed distribution is used. Analyzing the dispersion of information around such measures helps us understand their consistency. The study of dispersion of information around the inaccuracy measure is termed varinaccuracy. Recently, Balakrishnan et al. [(2024). Dispersion indices based on Kerridge inaccuracy measure and Kullback–Leibler divergence. Communications in Statistics – Theory and Methods 53(15): 5574-5592] introduced varinaccuracy, to compare models where lower variance indicates greater precision. As interval inaccuracy is crucial for analyzing the evolution of system reliability over time, examining its variability strengthens the validity of the extracted information. This article introduces the varinaccuracy measure for doubly truncated random variables and demonstrates its significance. The measure has been studied under transformations, and bounds are also provided to broaden the applicability of the measure where direct evaluation is challenging. Additionally, an estimator for the measure is proposed, and its consistency is analyzed using simulated data through a kernel-smoothed nonparametric estimation technique. The estimator is validated on real data sets of COVID-19 mortality rates for Mexico and Italy. Furthermore, the article illustrates the practical value of the measure in selecting the best alternative to a given distribution within an interval, following the minimum information discrimination principle, thereby highlighting the effectiveness of the study.

The bonus-malus system (BMS) is a widely recognized and commonly employed risk management tool. A well-designed BMS can match expected insurance payments with estimated claims even in a diverse group of risks. Although there has been abundant research on improving bonus-malus (BM) systems, one important aspect has been overlooked: the stationary probability of a BMS satisfies the monotone likelihood ratio property. The monotone likelihood ratio for stationary probabilities allows us to better understand how riskier policyholders are more likely to remain in higher premium categories, while less risky policyholders are more likely to move toward lower premiums. This study establishes this property for BMSs that are described by an ergodic Markov chain with one possible claim and a transition rule +1/-d. We derive this result from the linear recurrences that characterize the stationary distribution; this represents a novel analytical approach in this domain. We also illustrate the practical implications of our findings: in the BM design problem, the premium scale is automatically monotonic.

Networks describe complex relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a data set well, and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodness-of-fit (GoF) test for dyadic data. We show that our method, when applied to a specific model of interest, provides a straightforward, computationally fast way of selecting parameters in a number of commonly used network models. For example, we show how to select the dimension of the latent space in latent space models. Unlike other network GoF methods, our general approach does not require simulating from a candidate parametric model, which can be cumbersome with large graphs, and eliminates the need to choose a particular set of statistics on the graph for comparison. It also allows us to perform GoF tests on partial network data, such as Aggregated Relational Data. We show with simulations that our method performs well in many situations of interest. We analyze several empirically relevant networks and show that our method leads to improved community detection algorithms.

Pneumococcal conjugate vaccines (PCVs) have influenced population dynamics of Streptococcus pneumoniae in the nasopharynx and may have contributed to increased Staphylococcus aureus colonization. This study assessed the prevalence of colonization, antibiotic resistance patterns, and associated risk factors for colonization and co-colonization of S. aureus and S. pneumoniae in healthy Peruvian children post-PCV introduction. Nasopharyngeal swabs from children <24 months were collected in five hospitals in Lima (2018–2019). Microbiological identification and antibiotic susceptibility tests were performed, and multinomial regression evaluated factors influencing colonization. Among 894 children, 19.7% were colonized with S. aureus, 20.3% with S. pneumoniae, and 2.9% co-colonized. Of the 176 S. aureus strains isolated, 1.7% were methicillin resistant and 20.5% were clindamycin resistant; no resistance to trimethoprim-sulfamethoxazole (SXT) was found. Among 182 S. pneumoniae strains isolated, 48.9% were resistant to macrolides, 74.7% to SXT; no resistance to penicillin was found. Breastfeeding and vaccination with PCV13 were associated with a reduced prevalence of S. aureus colonization, while vaccination with PCV13 increased the prevalence of S. pneumoniae colonization, mainly by non-vaccine serotypes. This study highlights the need to continue monitoring the changes in colonization dynamics and antimicrobial resistance patterns after vaccine introduction, to guide empirical therapy and future vaccine strategies.

Invasive Escherichia coli disease (IED) is associated with high hospitalization and mortality rates, particularly among adults aged ≥60 years. O-antigens are virulence factors required for E. coli survival. To inform EXPEC9V development, a novel glycoconjugate vaccine targeting E. coli O-antigens that is no longer in active clinical development, this retrospective observational study describes O-serotype prevalence among E. coli isolates from IED patients. Eligible patients were identified from medical record databases (9 January 2018–8 November 2019) across 17 tertiary care hospitals in Europe, North America, and Asia. To estimate vaccine serotype coverage of EXPEC9V, E. coli isolates were O-serotyped using whole-genome sequencing and agglutination. Antimicrobial susceptibility testing was also performed. Nine hundred and two patients were enrolled, of whom 690 (76.5%) were aged ≥60 years. Common serotypes were O25, O2, O6, O1, O15, O75, O16, O4, and O18, with O25 being the most reported (17.3%). In patients aged ≥60 years, 422/637 E. coli isolates were EXPEC9V O-serotypes. EXPEC9V O-serotype prevalence did not substantially differ when stratified according to sex, presence of a positive blood culture, sepsis, fatality, or multidrug resistance. Consistent with previous studies, serotype O25 was most prevalent and associated with ~20% of cases. An EXPEC9V vaccine serotype coverage of 66.2% was observed for IED patients aged ≥60 years.

This paper investigates the time N until a random walk first exceeds some specified barrier. Letting $X_i, i \geq 1,$ be a sequence of independent, identically distributed random variables with a log-concave density or probability mass function, we derive both lower and upper bounds on the probability $P(N \gt n),$ as well as bounds on the expected value $E[N].$ On barriers of the form $a + b \sqrt{k},$ where a is nonnegative, b is positive, and k is the number of steps, we provide additional bounds on $E[N].$

Introduced over a century ago, Whittaker–Henderson smoothing remains widely used by actuaries in constructing one-dimensional and two-dimensional experience tables for mortality, disability, and other life insurance risks. In this paper, we reinterpret this smoothing technique within a modern statistical framework and address six practically relevant questions about its use. First, we adopt a Bayesian perspective on this method to construct credible intervals. Second, in the context of survival analysis, we clarify how to choose the observation and weight vectors by linking the smoothing technique to a maximum likelihood estimator. Third, we improve accuracy by relaxing the method’s reliance on an implicit normal approximation. Fourth, we select the smoothing parameters by maximizing a marginal likelihood function. Fifth, we improve computational efficiency when dealing with numerous observation points and consequently parameters. Finally, we develop an extrapolation procedure that ensures consistency between estimated and predicted values through constraints.

In our digital world, reusing data to inform: decisions, advance science, and improve people’s lives should be easier than ever. However, the reuse of data remains limited, complex, and challenging. Some of this complexity requires rethinking consent and public participation processes about it. First, to ensure the legitimacy of uses, including normative aspects like agency and data sovereignty. Second, to enhance data quality and mitigate risks, especially since data are proxies that can misrepresent realities or be oblivious to the original context or use purpose. Third, because data, both as a good and infrastructure, are the building blocks of both technologies and knowledge of public interest that can help societies work towards the well-being of their people and the environment. Using the case study of the European Health Data Space, we propose a multidimensional, polytopic framework with multiple intersections to democratising decision-making and improving the way in which meaningful participation and consent processes are conducted at various levels and from the point of view of institutions, regulations, and practices.