In this paper we consider a dynamic Erdős–Rényi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while only observing the aggregate number of edges. This inverse problem is dealt with, in a parametric context, by setting up an estimator based on the method of moments. We provide conditions under which the estimator is asymptotically normal, and we point out how the corresponding covariance matrix can be identified. We also demonstrate how to adapt the estimation procedure if alternative subgraph counts are observed, such as the number of wedges or triangles.

This paper considers two supercritical branching processes with immigration in different random environments, denoted by $\{Z_{1,n}\}$ and $\{Z_{2,m}\}$, with criticality parameters µ1 and µ2, respectively. Under certain conditions, it is known that $\frac{1}{n} \log Z_{1,n} \to \mu_1$ and $\frac{1}{m} \log Z_{2,m} \to \mu_2$ converge in probability as $m, n \to \infty$. We present basic properties about a central limit theorem, a non-uniform Berry–Esseen’s bound, and Cramér’s moderate deviations for $\frac{1}{n} \log Z_{1,n} - \frac{1}{m} \log Z_{2,m}$ as $m, n \to \infty$. To this end, applications to construction of confidence intervals and simulations are also given.

Let $K^r_n$ be the complete $r$-uniform hypergraph on $n$ vertices, that is, the hypergraph whose vertex set is $[n] \, :\! = \{1,2,\ldots ,n\}$ and whose edge set is $\binom {[n]}{r}$. We form $G^r(n,p)$ by retaining each edge of $K^r_n$ independently with probability $p$. An $r$-uniform hypergraph $H\subseteq G$ is $F$-saturated if $H$ does not contain any copy of $F$, but any missing edge of $H$ in $G$ creates a copy of $F$. Furthermore, we say that $H$ is weakly $F$-saturated in $G$ if $H$ does not contain any copy of $F$, but the missing edges of $H$ in $G$ can be added back one-by-one, in some order, such that every edge creates a new copy of $F$. The smallest number of edges in an $F$-saturated hypergraph in $G$ is denoted by ${\textit {sat}}(G,F)$, and in a weakly $F$-saturated hypergraph in $G$ by $\mathop {\mbox{$w$-${sat}$}}\! (G,F)$. In 2017, Korándi and Sudakov initiated the study of saturation in random graphs, showing that for constant $p$, with high probability ${\textit {sat}}(G(n,p),K_s)=(1+o(1))n\log _{\frac {1}{1-p}}n$, and $\mathop {\mbox{$w$-${sat}$}}\! (G(n,p),K_s)=\mathop {\mbox{$w$-${sat}$}}\! (K_n,K_s)$. Generalising their results, in this paper, we solve the saturation problem for random hypergraphs $G^r(n,p)$ for cliques $K_s^r$, for every $2\le r \lt s$ and constant $p$.

In England, Shiga toxin-producing Escherichia coli (STEC) serogroup O26 has recently emerged as a public health concern, despite fewer than half of diagnostic laboratories in England having the capability to detect non-O157 STEC. STEC O26 cases frequently report exposure to farms or nurseries. We describe the epidemiology of STEC O26 and examine evidence for a relationship between O26 and exposure to these settings. We analysed national surveillance data describing laboratory-confirmed STEC cases and public health incidents over the past 10 years to explore the incidence, clinical outcomes, and association with farms and nurseries for STEC O26 cases compared to STEC O157 and other serogroups. Between 2014 and 2023, the proportion of STEC notifications which were STEC O26 increased from 2% (19/956) to 12% (234/1946). After adjusting for age, we found no difference in the likelihood of farm or nursery attendance between O26 and O157 cases but a significantly higher risk of HUS in O26 (adjusted risk ratio 3.13 (2.18–4.51)). We demonstrate that STEC O26 is associated with the same risk of farm or nursery attendance as other STEC serogroups but a higher risk of severe morbidity. Our findings reinforce the need for improved surveillance of non-O157 STEC.

Acute gastrointestinal illness (AGI) remains a significant public health issue and differences in risk based on a comprehensive set of sociodemographic characteristics remain poorly understood. Thus, this retrospective cohort study was conducted to identify the risk of incurring an AGI-related emergency department (ED) visit or inpatient hospitalization based on various sociodemographic factors. Linked respondents of Canadian Community Health Survey cycles 2.1, 3.1, and 2007–2015 were followed from their interview date until 31 December 2017, using the National Ambulatory Care Reporting System (NACRS) and the Discharge Abstract Database (DAD) to capture emergency ED visits and hospitalizations due to AGI, respectively. Effects of identified potential risk factors for the incidence of AGI-related ED visits or hospitalizations were estimated Cox proportional hazards regression to generate hazard ratios (HRs) with 95% confidence intervals (CIs). A total of 190,700 respondents were linked to NACRS and 470,700 were linked to DAD. Six per cent of respondents visited an ED and 2% were hospitalized for AGI. Fully-adjusted estimates revealed that high-risk groups with the strongest effects were people with poor self-perceived health (ED visits: HR 1.47 (95% CI 1.40–1.54), hospitalizations: HR 1.92 (95% CI 1.82–2.02)), and people living with at least one chronic condition (ED visits: HR 1.54 (95% CI 1.47–1.61), hospitalizations: HR 1.65 (95% CI 1.57–1.73)). This study identified risk factors for requiring hospital care for AGI in the Canadian context. Additional research is needed to investigate mechanisms for differential exposure to pathogens by sociodemographic characteristics that might lead to increased risks of AGI.

Mpox (formerly called monkeypox) is a zoonotic viral disease caused by the monkeypox virus (MPXV) that has recently emerged as a notable global health issue by spreading beyond its typical geographical zones in Central and West Africa. In this study, we conducted a phylogenetic and evolutionary investigation of MPXV in West Africa. We focussed on 167 complete genome sequences collected from human infections in Nigeria and Cameroon between 2019 and 2024, all of which were retrieved from the GSAID database. To analyse these sequences, we employed multiple sequence alignment using fast Fourier transform (MAFFT) and maximum likelihood techniques to identify conserved genomic variants and trace evolutionary patterns within the virus. Our findings revealed that all the MPXV strains studied belong to clade II, which is further subdivided into two subclades. Notably, this study documents the presence of two distinct subclades IIa and IIb, reflecting the complex and ongoing evolution of the virus in the region. The phylogenetic analysis reveals rapid mutations and suggests that MPXV is being transmitted from multiple lineages between Nigeria and Cameroon. This demands the need to further strengthen the surveillance and containment efforts in West Africa. This study highlights the role of genomic surveillance in monitoring the evolution and spread of the MPXV, particularly in regions with limited available data.

The objective of this study was to evaluate the impact on SARS-CoV-2 transmission prevention of mask wearing by index cases and their household contacts. A prospective study of SARS-CoV-2 transmission to household contacts aged ≥18 years was conducted between May 2022 and February 2024 in Spain. Contacts underwent a rapid antigen test on day zero and a real-time polymerase chain reaction test 7 days later if results were negative. The dependent variable was SARS-CoV-2 infection in contacts. Index case and contact mask use effects were estimated using the adjusted odds ratio (aOR) and its 95% confidence interval (CI). Studied were 230 household contacts, mean (standard deviation) age 53.3 (16.6) years, and 47.8% (110/230) women. Following index case diagnosis, 36.1% of contacts (83/230) used a mask, and 54.3% (125/230) were exposed to a mask-wearing index case. Infection incidence in contacts was 45.2% (104/230) and was lower in contacts exposed to mask-wearing index cases (36.0% vs. 56.2%; p < 0.002). The logistic regression model indicated a protective effect for contacts of both index case mask use (aOR = 0.31; 95% CI: 0.15–0.65) and vaccination (aOR = 0.24; 95% CI: 0.08–0.77). Index case mask use reduced SARS-CoV-2 transmission to contacts, while mask effectiveness was not observed for contacts.

This descriptive and exploratory observational case series examined intestinal colonisation and subsequent bacteraemia due to ESBL-producing Klebsiella pneumoniae (ESBL-Kp) in preterm neonates in Morocco. Prospective bacteriological cultures and antibiotic susceptibility testing were supported by phenotypic methods, including Brilliance ESBL Agar and the NG-Test CARBA-5 assay, for the rapid detection of ESBL and carbapenemase producers. Molecular analysis using PCR was also undertaken to identify specific resistance genes. A total of 567 rectal swabs were collected from 339 preterm neonates, yielding 293 K. pneumoniae isolates. ESBL-producing strains were identified in 53.6% of the neonates (182/339). Detected resistance genes included blaSHV (26.3%), blaCTX-M-1 (42.8%), blaTEM (30.2%), blaOXA-48 (50.0%), blaNDM(15.3%), and blaVIM (4.9%). Principal risk factors for colonisation were low birth weight (OR 1.69), very preterm birth (OR 6.24), enteral tube feeding (OR 2.02), and prolonged use of third-generation cephalosporins (OR 1.26). Among the neonates studied, 32 (9.4%) developed healthcare-associated bacteraemia, with 56.2% of these cases preceded by intestinal colonisation with ESBL-Kp. Clinically, severe respiratory distress and alveolar haemorrhage were strongly associated with increased mortality (aRR = 29.32 and 4.45, respectively). The findings highlight the clinical importance of early screening to guide infection control and antimicrobial stewardship in neonatal intensive care settings.

A non-uniqueness phase for infinite clusters is proven for a class of marked random connection models (RCMs) on the d-dimensional hyperbolic space, ${\mathbb{H}^d}$, in a high volume-scaling regime. The approach taken in this paper utilizes the spherical transform on ${\mathbb{H}^d}$ to diagonalize convolution by the adjacency function and the two-point function and bound their $L^2\to L^2$ operator norms. Under some circumstances, this spherical transform approach also provides bounds on the triangle diagram that allows for a derivation of certain mean-field critical exponents. In particular, the results are applied to some Boolean and weight-dependent hyperbolic RCMs. While most of the paper is concerned with the high volume-scaling regime, the existence of the non-uniqueness phase is also proven without this scaling for some RCMs whose resulting graphs are almost surely not locally finite.

The matrixdist R package provides a comprehensive suite of tools for the statistical analysis of matrix distributions, including phase-type, inhomogeneous phase-type, discrete phase-type, and related multivariate distributions. This paper introduces the package and its key features, including the estimation of these distributions and their extensions through expectation-maximization algorithms, as well as the implementation of regression through the proportional intensities and mixture-of-experts models. Additionally, the paper provides an overview of the theoretical background, discusses the algorithms and methods implemented in the package, and offers practical examples to illustrate the application of matrixdist in real-world actuarial problems. The matrixdist R package aims to provide researchers and practitioners a wide set of tools for analyzing and modeling complex data using matrix distributions.

We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e. when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e. there is exactly one hidden layer), the large and moderate principles hold for quite general pre-activation functions.

We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the support of a point process. We show that if the expected number of crossings converges to a positive but finite value, this point process converges to a Poisson point process in the Kantorovich–Rubinstein distance. We further show a multivariate central limit theorem between the number of crossings and a second variable called the stress that holds when the expected vertex degree in the random geometric graph converges to a positive finite value.

This paper introduces the general ideas for parametric integral stochastic orders, with which a continuum of parametric functions are defined as a bridge between different classes of non-parametric functions. This approach allows one to identify a parametric function class over which two given random variables may violate the non-parametric stochastic order with specific patterns. The parameter used to name the parametric function class also measures the ratio of dominance violation for the corresponding non-parametric stochastic orders. Our framework, expanding the domain of stochastic orders, covers the existing studies of almost stochastic dominance. This leads to intuitive explanations and simpler proofs of existing results and their extensions.

We establish a novel duality relationship between continuous/discrete non-negative non-decreasing functionals of stochastic (not necessarily Markovian) processes and their right inverses, and further discuss its applications. For general Markov processes, we develop a theoretical and computational framework for the transform analysis via an operator-based approach, i.e. through the infinitesimal generators. More precisely, we characterize the joint double transforms of additive functionals of Markov processes and the terminal values in continuous/discrete time. Under the continuous-time Markov chain (CTMC) setting, we obtain single Laplace transforms for continuous/discrete additive functionals and their inverses. We apply the proposed transform methodology to computing option prices related to the occupation time of the underlying asset price process.

We prove a scaling limit theorem for two-type Galton–Watson branching processes with interaction. The limit theorem gives rise to a class of mixed-state branching processes with interaction used to simulate evolution for cell division affected by parasites. Such processes can also be obtained by the pathwise-unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability 1 and the exponential ergodicity in the $L^1$-Wasserstein distance of such processes in some cases.

In this paper, we introduce a unified framework based on the pathwise expansion method to derive explicit recursive formulas for cumulative distribution functions, option prices, and transition densities in multivariate diffusion models. A key innovation of our approach is the introduction of the quasi-Lamperti transform, which normalizes the diffusion matrix at the initial time. This transformation facilitates expansions using uncorrelated Brownian motions, effectively reducing multivariate problems to one-dimensional computations. Consequently, both the analysis and the computation are significantly simplified. We also present two novel applications of the pathwise expansion method. Specifically, we employ the proposed framework to compute the value-at-risk for stock portfolios and to evaluate complex derivatives, such as forward-starting options. Our method has the flexibility to accommodate models with diverse features, including stochastic risk premiums, stochastic volatility, and nonaffine structures. Numerical experiments demonstrate the accuracy and computational efficiency of our approach. In addition, as a theoretical contribution, we establish an equivalence between the pathwise expansion method and the Hermite polynomial-based expansion method in the literature.

In large public health jurisdictions, only a small proportion of people infected with Salmonella are interviewed due to resource constraints. As such, sources of illness are rarely found, and preventative action not implemented. We trialled alternative methods to contact notified salmonellosis cases to collect information on exposures and risks, focusing particularly on the feasibility of SMS (short message service)-based surveillance. Over five-years period we sequentially mailed letters, sent online surveys, and then text messages. The SMS approach was designed to assess the efficiency of a two-way personalized messaging model in gathering actionable public health data. The personalized SMS-follow-up model demonstrated the highest success: 56% of cases responded, enabling the identification and intervention of 10 distinct point-source outbreaks of Salmonella. SMS-based surveillance offers a novel, efficient, and acceptable method for collecting critical food exposure data in Salmonella cases. In settings where resources are constrained, SMS can complement traditional case follow-up methods, enhancing both the timeliness and effectiveness of outbreak detection. Integrating this follow-up with routine clinical care could further enhance the acceptance and success of this method. This study highlights the promise of SMS in streamlining surveillance efforts and warrants further exploration for application to other infectious diseases.

Embracing the potential of foresight in migration policy, North Macedonia has embarked on a ground-breaking journey to institutionalize anticipatory governance through extensive capacity-building activities, imparting foresight methods to stakeholders responsible for shaping migration policies. This research provides a comprehensive overview, detailing the initiative’s origins, alignment with the Resolution on Migration Policy 2021–2025, and the accompanying Action Plan. The study assesses the impact and potential of the Anticipatory Governance in Migration in North Macedonia when fully integrated with the action plan, which focuses on data-based management that oversees the migration policy resolution and the migration policy milieu. Through a comprehensive analysis of the foresight interventions, training programs, and stakeholder engagements, this study unveils the potential impact of forward-looking planning on North Macedonia’s migration policy landscape. The conclusion and recommendations have broader significance, extending beyond North Macedonia to serve as a model for other countries confronting migration challenges in our rapidly changing world.

We consider a population consisting of two types of individuals, each of which can produce offspring on two different islands (in particular, the islands can be interpreted as active or dormant individuals). We model the evolution of the population of each type using a two-type Feller diffusion with immigration and study the frequency of one type on each island, when the total population size on each island is forced to be constant at a dense set of times. This leads to the solution of a stochastic differential equation, which we call the asymmetric two-island frequency process. We derive properties of this process and obtain a large population limit as the total size of each island tends to infinity. Additionally, we compute the fluctuations of the process around its deterministic limit. We establish conditions under which the asymmetric two-island frequency process has a moment dual. The dual is a continuous-time two-dimensional Markov chain that can be interpreted in terms of mutation, branching, pairwise branching, coalescence, and a novel mixed selection–migration term.

This article proposes a novel method for estimating quantile regression models that account for sample selection. Unlike the approach by Arellano and Bonhomme (2017, Econometrica 85(1), 1–28; hereafter referred to as AB17), which employs a parametric selection equation, our method utilizes a standard binary quantile regression model to handle the selection issue, thereby accommodating general heterogeneity in both the selection and outcome equations. We adopt a semiparametric estimation technique for the outcome quantile regression by integrating local moment conditions, resulting in $\sqrt {n}$-consistent estimators for the quantile coefficients and copula parameter. Monte Carlo simulation results demonstrate that our estimator performs well in finite samples. Additionally, we apply our method to examine the wage distribution among women using a randomly simulated sample from the US General Social Survey. Our key finding is the presence of significant positive selection among women in the US, which is notably more pronounced than the estimates produced by the AB17’s model.