Let $(Z_n)_{n\geq 0}$ be a critical branching process in a random environment defined by a Markov chain $(X_n)_{n\geq 0}$ with values in a finite state space $\mathbb{X}$. Let $ S_n = \sum_{k=1}^n \ln f_{X_k}^{\prime}(1)$ be the Markov walk associated to $(X_n)_{n\geq 0}$, where $f_i$ is the offspring generating function when the environment is $i \in \mathbb{X}$. Conditioned on the event $\{ Z_n>0\}$, we show the nondegeneracy of the limit law of the normalized number of particles ${Z_n}/{e^{S_n}}$ and determine the limit of the law of $\frac{S_n}{\sqrt{n}} $ jointly with $X_n$. Based on these results we establish a Yaglom-type theorem which specifies the limit of the joint law of $ \log Z_n$ and $X_n$ given $Z_n>0$.

This paper discusses a general class of replicator–mutator equations on a multidimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fokker–Planck–Kolmogorov (FPK) equations and a martingale extraction approach. We provide examples with closed-form probabilistic solutions for different fitness functions considered in the existing literature. We also construct a particle system and prove a general convergence result to the unique solution of the FPK equation associated with the extended replicator–mutator equation with respect to a Wasserstein-like metric adapted to our probabilistic framework.

A continuum of stochastic dominance rules, also referred to as fractional stochastic dominance (SD), was introduced by Müller, Scarsini, Tsetlin, and Winkler (2017) to cover preferences from first- to second-order SD. Fractional SD can be used to explain many individual behaviors in economics. In this paper we introduce the concept of fractional pure SD, a special case of fractional SD. We investigate further properties of fractional SD, for example the generating processes of fractional pure SD via $\gamma$-transfers of probability, Yaari’s dual characterization by utilizing the special class of distortion functions, the separation theorem in terms of first-order SD and fractional pure SD, Strassen’s representation, and bivariate characterization. We also establish several closure properties of fractional SD under quantile truncation, under comonotonic sums, and under distortion, as well as its equivalence characterization. Examples of distributions ordered in the sense of fractional SD are provided.

Signal-to-interference-plus-noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unlike in earlier works, in the present paper the transmitted signal powers of the devices of the network are assumed random, independent and identically distributed, and possibly unbounded. Additionally, we assume that the devices form a stationary Cox point process, i.e., a Poisson point process with stationary random intensity measure, in two or more dimensions. We present the following main results. First, under suitable moment conditions on the signal powers and the intensity measure, there is percolation in the SINR graph given that the device density is high and interferences are sufficiently reduced, but not vanishing. Second, if the interference cancellation factor $\gamma$ and the SINR threshold $\tau$ satisfy $\gamma \geq 1/(2\tau)$, then there is no percolation for any intensity parameter. Third, in the case of a Poisson point process with constant powers, for any intensity parameter that is supercritical for the underlying Gilbert graph, the SINR graph also percolates with some small but positive interference cancellation factor.

This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\!=\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$, $u\rightarrow\infty$, where $X_i(t)$, $t\ge0$, $i=1,2,\ldots,n$, are independent centered Gaussian processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \ldots, \mathcal{T}_n)$ is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$, $a_i>0$, $i=1,2,\ldots,n$. Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$. We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.

Rubella is a highly contagious mild viral illness. It is a leading cause of congenital rubella syndrome (CRS). Routine data of rubella do not exist in Ethiopia. However, laboratory-based conformation of rubella cases from measles negative samples were collected from a measles surveillance system. The current study was to analyse the epidemiological distribution of rubella cases from measles-suspected cases in Ethiopia from 2011 to 2015. National-based secondary data analysis of rubella through measles-based surveillances was carried out. Measles-suspected cases were investigated using the case investigation form, and a serum sample collected and sent to the Ethiopian laboratory for conformation. Samples tested for measles immunoglobulin M (IgM) were tested for rubella. The investigation results were entered into an electronic database using SPSS version 25 for analysis. Out of 11749 samples tested for rubella IgM from 2011 to 2015, 2295 (19.5%) were positive for rubella IgM and 51% of rubella-positive cases were female. Five per cent of all cases were female aged between 15 and 49. Cases were confirmed from all regions, two administrative towns and seasonal variations were observed with peaks in the first and fourth seasonal periods of the years. As fear of congenital abnormality (CRS), the Ethiopian government should focus on rubella syndrome surveillance with the aim of starting a rubella vaccine.

After the introduction of the 13-valent pneumococcal conjugate vaccine (PCV13), serotype replacement has occurred in Japan, and serotype 24 has become the most common serotype in paediatric invasive pneumococcal disease (IPD). To understand the characteristics of serotype 24-IPD in Japanese children in the post-PCV13 era, we conducted a retrospective study in children aged ≤15 years from 2010 to 2020 using a database of paediatric IPD surveillance in Chiba prefecture, Japan. We identified a total of 357 IPD cases and collected clinical information on 225 cases (24: 32 cases, non-24: 193 cases). Compared with the non-serotype 24-IPD, serotype 24-IPD was independently related to be <2 years of age [odds ratio (OR) 3.91, 95% confidence interval (CI) 1.47–10.44; P = 0.0064] and bacteremia (OR 2.28, 95% CI 1.01–5.13; P = 0.0475), as a result of the multivariate regression analysis. We also conducted a bacterial analysis, and the isolates of serotype 24-IPD had tendencies of PCG-susceptible (24: 100.0%, non-24: 61.3%; P < 0.0001) and macrolide-resistance (24: 100.0%, non-24: 87.3%; P = 0.0490). Their multilocus sequence typing was mostly ST2572 and the variants, which were unique to Japan. This tendency might have been a result of the progress made in the Japanese PCV13 immunisation programme.

In this editorial, Guest Editors Richard Benjamins (Telefónica), Jeanine Vos (GSMA), and Stefaan Verhulst (Data & Policy Editor-in-Chief) draw insights from a set of peer-reviewed, open access articles in a Data & Policy special collection dedicated to the use of Telco Big Data Analytics for COVID-19.

We revisit the so-called cat-and-mouse Markov chain, studied earlier by Litvak and Robert (2012). This is a two-dimensional Markov chain on the lattice $\mathbb{Z}^2$, where the first component (the cat) is a simple random walk and the second component (the mouse) changes when the components meet. We obtain new results for two generalisations of the model. First, in the two-dimensional case we consider far more general jump distributions for the components and obtain a scaling limit for the second component. When we let the first component be a simple random walk again, we further generalise the jump distribution of the second component. Secondly, we consider chains of three and more dimensions, where we investigate structural properties of the model and find a limiting law for the last component.

Veterinary healthcare workers are in close contact with many different animals and might be at an increased risk of acquiring Clostridioides difficile. In this cross-sectional study, we assessed the prevalence and risk factors of C. difficile carriage in Dutch veterinary healthcare workers. Participants provided a faecal sample and filled out a questionnaire covering potential risk factors for C. difficile carriage. C. difficile culture positive isolates were polymerase chain reaction (PCR) ribotyped and the presence of toxin genes tcdA, tcdB and cdtA/cdtB was determined. Eleven of 482 [2.3%; 95% confidence interval (CI) 1.3–4.0] veterinary healthcare workers were carriers of C. difficile. Three persons carried C. difficile ribotype 078 (0.6%; 95% CI 0.2–1.8). Risk factors for carriage were health/medication and hygiene related, including poor hand hygiene after patient (animal) contact, and did not include occupational contact with certain animal species. In conclusion, the prevalence of C. difficile carriage in veterinary healthcare workers was low and no indications were found that working in veterinary care is a risk for C. difficile carriage.

For a one-locus haploid infinite population with discrete generations, the celebrated model of Kingman describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability. This paper generalises Kingman’s model by using independent and identically distributed random mutation probabilities, to reflect the influence of a random environment. The weak convergence of fitness distributions to the globally stable equilibrium is proved. Condensation occurs when almost surely a positive proportion of the population travels to and condenses at the largest fitness value. Condensation may occur when selection is favoured over mutation. A criterion for the occurrence of condensation is given.

Outbreaks caused by Chlamydia psittaci and other chlamydial species have recently been reported in poultry farms worldwide, causing considerable economic losses. The objective of this study was to determine the presence of chlamydial species in these birds in Costa Rica. One hundred and fifty pools of lung tissue samples from industrial poultry with respiratory problems and 112 pools of tracheal swabs from asymptomatic backyard poultry were analysed by real-time quantitative polymerase chain reaction (qPCR), end-point PCR and sequencing. A total of 16.8% (44/262) samples were positive for Chlamydia spp., most of them detected in asymptomatic backyard poultry (28.6%, 32/112) and fewer in industrial poultry (8%, 12/150). Of these positive samples, 45.5% (20/44) were determined to be C. psittaci. For the first time C. psittaci genotype A is reported in poultry in Latin America. In addition, the presence of Chlamydia gallinacea in backyard poultry and of Chlamydia muridarum in industrial and backyard poultry is reported for the first time in Central America. In 40.9% (18/44) of the positive samples, it was not possible to identify the infecting chlamydial species. These findings reveal a zoonotic risk, particularly for poultry farm and slaughterhouse workers having direct contact with these birds.

Preterm infants show postnatal deficits of long-chain polyunsaturated fatty acids (LCPUFAs) which are essential for adequate growth and neurodevelopment. Human milk is a primary source of fatty acids (FAs) for the preterm infant, and therefore, knowledge about milk FA levels is required to design appropriate supplementation strategies. Here, we expanded on our previous study (Nilsson et al., 2018, Acta Paediatrica, 107, 1020–1027) determining FA composition in milk obtained from mothers of extremely low gestational age (<28 weeks) infants on three occasions during lactation. There was a clear difference in FA composition in milk collected at Day 7 and milk collected at postmenstrual weeks (PMW) 32 or PMW 40. Notably, the proportion of LCPUFAs was low and declined significantly during milk maturation. These results strengthen previous data that the content of FAs required by the preterm infant is not supplied in sufficient amounts when the mother’s own milk is the sole source of these essential nutrients.

We investigate random minimal factorizations of the n-cycle, that is, factorizations of the permutation $(1 \, 2 \cdots n)$ into a product of cycles $\tau_1, \ldots, \tau_k$ whose lengths $\ell(\tau_1), \ldots, \ell(\tau_k)$ satisfy the minimality condition $\sum_{i=1}^k(\ell(\tau_i)-1)=n-1$. By associating to a cycle of the factorization a black polygon inscribed in the unit disk, and reading the cycles one after another, we code a minimal factorization by a process of colored laminations of the disk. These new objects are compact subsets made of red noncrossing chords delimiting faces that are either black or white. Our main result is the convergence of this process as $n \rightarrow \infty$, when the factorization is randomly chosen according to Boltzmann weights in the domain of attraction of an $\alpha$-stable law, for some $\alpha \in (1,2]$. The limiting process interpolates between the unit circle and a colored version of Kortchemski’s $\alpha$-stable lamination. Our principal tool in the study of this process is a new bijection between minimal factorizations and a model of size-conditioned labeled random trees whose vertices are colored black or white, as well as the investigation of the asymptotic properties of these trees.