Here we consider the hypergraph Turán problem in uniformly dense hypergraphs as was suggested by Erdős and Sós. Given a $3$-graph $F$, the uniform Turán density $\pi _{\boldsymbol{\therefore }}(F)$ of $F$ is defined as the supremum over all $d\in [0,1]$ for which there is an $F$-free uniformly $d$-dense $3$-graph, where uniformly $d$-dense means that every linearly sized subhypergraph has density at least $d$. Recently, Glebov, Král’, and Volec and, independently, Reiher, Rödl, and Schacht proved that $\pi _{\boldsymbol{\therefore }}(K_4^{(3)-})=\frac {1}{4}$, solving a conjecture by Erdős and Sós. Despite substantial attention, the uniform Turán density is still only known for very few hypergraphs. In particular, the problem due to Erdős and Sós to determine $\pi _{\boldsymbol{\therefore }}(K_4^{(3)})$ remains wide open.

In this work, we determine the uniform Turán density of the $3$-graph on five vertices that is obtained from $K_4^{(3)-}$ by adding an additional vertex whose link forms a matching on the vertices of $K_4^{(3)-}$. Further, we point to two natural intermediate problems on the way to determining $\pi _{\boldsymbol{\therefore }}(K_4^{(3)})$, and solve the first of these.

This study assesses the seroprevalence of Rift Valley fever (RVF) in ruminants in Dhobley, Somalia, following a 2021 outbreak in Kenya. Among 142 ruminants sampled, 4.9% were seropositive for RVF virus (RVFV) antibody, with IgM antibodies (1.4%) indicating recent exposure, though no cases were RT-PCR-positive. Unregulated livestock movement and limited surveillance pose significant risks for future outbreaks, underscoring the need for enhanced surveillance systems and One Health strategies.

In this paper we study one-sided hypothesis testing under random sampling without replacement, which frequently appears in the cryptographic problem setting, including the verification of measurement-based quantum computation. Suppose that $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ follow a permutation invariant distribution and n binary random variables $X_1,\ldots, X_{n}$ are observed. Then, we propose randomized tests with a randomization parameter for the expectation of the $(n+1)$th random variable $X_{n+1}$ under a given significance level $\delta>0$. Our randomized tests significantly improve the upper confidence limit over deterministic tests. Our problem setting commonly appears in machine learning in addition to cryptographic scenarios by considering adversarial examples. Such studies are essential for expanding the applicable area of statistics. Although this paper addresses only binary random variables, a similar significant improvement by randomized tests can be expected for general non-binary random variables.

We prove that for every locally stable and tempered pair potential $\phi$ with bounded range, there exists a unique infinite-volume Gibbs point process on $\mathbb{R}^{d}$ for every activity $\lambda < ({e}^{L} \hat{C}_{\phi})^{-1}$, where L is the local stability constant and $\hat{C}_{\phi} \,:\!=\, \sup_{x \in \mathbb{R}^{d}} \int_{\mathbb{R}^{d}} 1 - {e}^{-\left\lvert \phi(x, y) \right\rvert} \mathrm{d} y$ is the (weak) temperedness constant. Our result extends the uniqueness regime that is given by the classical Ruelle–Penrose bound by a factor of at least ${e}$, where the improvements become larger as the negative parts of the potential become more prominent (i.e. for attractive interactions at low temperature). Our technique is based on the approach of Dyer et al. (2004 Random Structures & Algorithms 24, 461–479): We show that for any bounded region and any boundary condition, we can construct a Markov process (in our case spatial birth–death dynamics) that converges rapidly to the finite-volume Gibbs point process while the effects of the boundary condition propagate sufficiently slowly. As a result, we obtain a spatial mixing property that implies uniqueness of the infinite-volume Gibbs measure.

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.

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.