We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in which neighbours must have a height difference of exactly one. The local law is uniform by definition. We prove that the height variance of this model is bounded, uniformly over all boundary conditions (both in terms of location and boundary heights). This implies a strong notion of localisation, uniformly over all extremal Gibbs measures of the system. For the second model, we consider directed trees, in which each vertex has exactly one parent and at least two children. We consider the locally uniform law on height functions which are monotone, that is, such that the height of the parent vertex is always at least the height of the child vertex. We provide a complete classification of all extremal gradient Gibbs measures, and describe exactly the localisation-delocalisation transition for this model. Typical extremal gradient Gibbs measures are localised also in this case. Localisation in both models is consistent with the observation that the Gaussian free field is localised on trees, which is an immediate consequence of transience of the random walk.

In this paper, a new point process is introduced. It combines the nonhomogeneous Poisson process with the generalized Polya process (GPP) studied in recent literature. In reliability interpretation, each event (failure) from this process is minimally repaired with a given probability and GPP-repaired with the complementary probability. Characterization of the new process via the corresponding bivariate point process is presented. The mean numbers of events for marginal processes are obtained via the corresponding rates, which are used for considering an optimal replacement problem as an application.

Acute pyelonephritis (AP) epidemiology has been sparsely described. This study aimed to describe the evolution of AP patients hospitalised in France and identify the factors associated with urinary diversion and fatality, in a cross-sectional study over the 2014–2019 period. Adult patients hospitalised for AP were selected by algorithms of ICD-10 codes (PPV 90.1%) and urinary diversion procedure codes (PPV 100%). 527,671 AP patients were included (76.5% female: mean age 66.1, 48.0% Escherichia coli), with 5.9% of hospital deaths. In 2019, the AP incidence was 19.2/10,000, slightly increasing over the period (17.3/10,000 in 2014). 69,313 urinary diversions (13.1%) were performed (fatality rate 6.7%), mainly in males, increasing over the period (11.7% to 14.9%). Urolithiasis (OR [95% CI] =33.1 [32.3–34.0]), sepsis (1.73 [1.69–1.77]) and a Charlson index ≥3 (1.32 [1.29–1.35]) were significantly associated with urinary diversion, whereas E. coli (0.75 [0.74–0.77]) was less likely associated. The same factors were significantly associated with fatality, plus old age and cancer (2.38 [2.32–2.45]). This nationwide study showed an increase in urolithiasis and identified, for the first time, factors associated with urinary diversion in AP along with death risk factors, which may aid urologists in clinical decision-making.

In 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\unicode{x2124}$: in this model, the probability that the walk moves from a point of $\unicode{x2124}$ to a given neighbor depends on the number of previous crossings of the directed edge from the initial point to the target, called the local time of the edge. Tóth and Vető found that this model exhibited very peculiar behavior, as the process formed by the local times of all the edges, evaluated at a stopping time of a certain type and suitably renormalized, converges to a deterministic process, instead of a random one as in similar models. In this work, we study the fluctuations of the local times process around its deterministic limit, about which nothing was previously known. We prove that these fluctuations converge in the Skorokhod $M_1$ topology, as well as in the uniform topology away from the discontinuities of the limit, but not in the most classical Skorokhod topology. We also prove the convergence of the fluctuations of the aforementioned stopping times.

The global prevalence and spread of multidrug-resistant organisms (MDROs) represent an emerging public health threat. Day care centre (DCC) attendance is a risk factor for MDRO carriage in children and their environment. This study aimed to map the epidemiology of carriage and potential transmission of these organisms within 18 Flemish DDCs (Belgium). An MDRO prevalence survey was organised between November 2018 and February 2019 among children attending the centres. Selective chromogenic culture media were used for the detection of extended-spectrum beta-lactamase-producing Enterobacterales (ESBL-E), carbapenemase-producing Enterobacterales (CPE), and vancomycin-resistant Enterococci (VRE) in faecal swabs obtained from diapers or jars (n = 448). All isolated MDROs were subjected to resistance gene sequencing. A total of 71 of 448 samples (15.8%) yielded isolates of ESBL-E with a predominance of Escherichia coli (92.2% of ESBL-E) and ESBL resistance gene blaCTX-M-15 (50.7% of ESBL coding genes in E. coli). ESBL-E prevalence varied between DCCs, ranging from 0 to 50%. Transmission, based on the clonal relatedness of ESBL-E strains, was observed. CPE was identified in only one child carrying an E. coli with an OXA-244 gene. VRE was absent from all samples. The observed prevalence of ESBL-E in Flemish DCCs is high compared with previous studies, and our findings re-emphasise the need for rigorous hygiene measures within such centres to control the further spread of MDROs in the community.

Hepatitis E virus infection is a major cause of acute hepatitis, typically self-limiting but occasionally leading to liver failure. Understanding disease progression factors could inform prevention strategies. This study aimed to analyse the characteristics of a large cohort of hospitalised hepatitis E patients in Tianjin, China, and explore factors influencing their progression to liver failure. A total of 1279 hospitalised patients with hepatitis E were included in this cross-sectional study in Tianjin, China. Student's t-test and the Mann–Whitney U-test were used for comparisons. Multiple logistic regression analysis was used to explore the association. Among these 1279 patients, 107 (8.4%) developed liver failure. Patients with diabetes mellitus (DM) (95% confidence interval [CI] 1.150–2.887, p = 0.011), liver cirrhosis (95% [CI] 2.229–7.224, p < 0.001), and hepatitis B (95% [CI] 1.159–4.512, p = 0.017) were more likely to progress to liver failure. Hepatitis E patients with comorbid DM, liver cirrhosis, or hepatitis B virus co-infection have higher risks of developing liver failure. Hepatitis E vaccination may be recommended for these vulnerable patients to curb disease severity.

A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to pathwise-control the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions of switching processes in the spirit of Skorokhod’s representation theorem varying according to the problem being dealt with. In particular, this method can cope with switching processes in an infinite state space and not necessarily of birth–death type. As an application, some known results on the ergodicity and stability of state-dependent regime-switching processes can be improved.

Available data suggest that the immunogenicity of COVID-19 vaccines might decrease in the immunocompromised population, but data on vaccine immunogenicity and safety among people living with HIV (PLWH) are still lacking. The purpose of this meta-analysis is to compare the immunogenicity and safety of COVID-19 vaccines in PLWH with healthy controls. We comprehensively searched the following databases: PubMed, Cochrane Library, and EMBASE. The risk ratio (RR) of seroconversion after the first and second doses of a COVID-19 vaccine was separately pooled using random-effects meta-analysis. Seroconversion rate was lower among PLWH compared with healthy individuals after the first (RR = 0.77, 95% confident interval (CI) 0.64–0.92) and second doses (RR = 0.97, 95%CI 0.95–0.99). The risk of total adverse reactions among PLWH is similar to the risk in the healthy group, after the first (RR = 0.87, 95%CI 0.70–1.10) and second (RR = 0.83, 95%CI 0.65–1.07) doses. This study demonstrates that the immunogenicity and safety of SARS-CoV-2 vaccine in fully vaccinated HIV-infected patients were generally satisfactory. A second dose was related to seroconversion enhancement. Therefore, we considered that a booster dose may provide better seroprotection for PLWH. On the basis of a conventional two-dose regimen for COVID-19 vaccines, the booster dose is very necessary.

The coronavirus pandemic has created a new awareness of epidemics, and insurance companies have been reminded to consider the risk related to infectious diseases. This paper extends the traditional multi-state models to include epidemic effects. The main idea is to specify the transition intensities in a Markov model such that the impact of contagion is explicitly present in the same way as in epidemiological models. Since we can study the Markov model with contagious effects at an individual level, we consider individual risk and reserves relating to insurance products, conforming with the standard multi-state approach in life insurance mathematics. We compare our notions with other but related notions in the literature and perform numerical illustrations.

A foodborne outbreak related to milk cartons served in school lunches occurred in June 2021, which involved more than 1,800 cases from 25 schools. The major symptoms were abdominal pain, diarrhoea, vomiting, and fever. Although major foodborne toxins and pathogens were not detected, a specific Escherichia coli strain, serotype OUT (OgGp9):H18, was predominantly isolated from milk samples related to the outbreak and most patients tested. The strains from milk and patient stool samples were identified as the same clone by core genome multilocus sequence typing and single-nucleotide polymorphism analysis. The strain was detected in milk samples served for two days related to the foodborne outbreak at a rate of 69.6% and levels of less than ten most probable number/100 mL but not on days unrelated to the outbreak. The acid tolerance of the strain for survival in the stomach was similar to that of enterohaemorrhagic E. coli O157:H7, and the same inserts in the chu gene cluster in the acid fitness island were genetically revealed. The pathogenicity of the strain was not clear; however, it was indicated that the causative pathogen was atypical diarrhoeagenic E. coli OUT (OgGp9):H18.

In resource-limited countries, the lack of widespread screening masks the true situation of COVID-19. We conducted this study to assess SARS-CoV-2 spread by detection of specific antibodies and to determine associated factors. A population-based cross-sectional study was conducted. Subjects were tested for the presence of two antibodies (IgM and IgG) specific to SARS-CoV-2. Data collection was done using a smartphone with the KoboCollect application. Prevalence of antibodies was estimated with 95% confidence intervals. Logistic regression was used to determine factors associated with positive serological test. A total of 9,094 persons were tested in 4,340 households. The mean age was 30.18 ± 18.65 years, 46.5% male. The overall seroprevalence (prevalence, 95% CI) of SARS-CoV-2 antibodies was (48.2% [47.2%–49.2%]). Being vaccinated, having been in contact with a COVID-19 patient, being older than 50 years, living in a union, having secondary education and having tertiary education were factors independently associated with the likelihood of having anti-sars-CoV-2. We estimate in February 2022 that 48% persons had antibodies against the COVID-19 virus, more among those vaccinated. Vaccination intensification in low prevalence departments will reduce the risk of new outbreaks.

The SARS-CoV-2 pandemic persists with global repercussions. Initial COVID-19 symptoms encompass pneumonia, fever, myalgia, and fatigue. The human immune system produces IgM and IgG antibodies in response to SARS-CoV-2. Despite previous research, a comprehensive understanding of the interplay between clinical manifestations and humoral immune responses remains elusive. This study aims to scrutinize this association. 134 COVID-19 patients were enrolled, and stratified into mild, moderate, and severe symptom groups. Serum IgM and IgG levels were assessed thrice at one-month intervals using ELISA. The findings reveal significant elevation in serum IgG levels in moderate compared to mild cases (P < 0.001). Additionally, IgG production was significantly heightened in severe cases compared to both mild (P < 0.0001) and moderate (P < 0.05) groups. IgM and IgG levels peaked initially and diminished over time. While anti-SARS-CoV-2 antibodies are expected to confer protection, the direct correlation between IgG levels and symptom severity may arise from delayed immune activation, resulting in an intense antibody response in severe cases. Given evidence linking delayed immune function with a dysregulated innate immune response, comprehensive data collection should encompass not only serum IgG and IgM, but also early measurement of type I interferons at symptom onset. This could provide a more thorough understanding of COVID-19 progression.

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions, and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to overrejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.

We show that an $n$-uniform maximal intersecting family has size at most $e^{-n^{0.5+o(1)}}n^n$. This improves a recent bound by Frankl ((2019) Comb. Probab. Comput. 28(5) 733–739.). The Spread Lemma of Alweiss et al. ((2020) Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing.) plays an important role in the proof.

Clostridium botulinum causes infant botulism by colonising the intestines and producing botulinum neurotoxin in situ. Previous reports have linked infant botulism cases to C. botulinum spores in household dust, yet the baseline incidence of C. botulinum spores in residential households is currently unknown. Vacuum cleaner dust from 963 households in 13 major Canadian cities was tested for C. botulinum using a novel real-time PCR assay directed against all known subtypes of the botulinum neurotoxin gene. None of the samples tested positive for C. botulinum. Analysis of a random subset of samples by MALDI Biotyper revealed that the most common anaerobic bacterial isolates were of the genus Clostridium and the most common species recovered overall was Clostridium perfringens. Dust that was spiked with C. botulinum spores of each toxin type successfully produced positive real-time PCR reactions. These control experiments indicate that this is a viable method for the detection of C. botulinum spores in household dust. We make several recommendations for future work that may help discover a common environmental source of C. botulinum spores that could lead to effective preventative measures for this rare but deadly childhood disease.