In this paper, we consider an extended class of univariate and multivariate generalized Pólya processes and study its properties. In the generalized Pólya process considered in [8], each occurrence of an event increases the stochastic intensity of the counting process. In the extended class studied in this paper, on the contrary, it decreases the stochastic intensity of the process, which induces a kind of negative dependence in the increments in the disjoint time intervals. First, we define the extended class of generalized Pólya processes and derive some preliminary results which will be used in the remaining part of the paper. It is seen that the extended class of generalized Pólya processes can be viewed as generalized pure death processes, where the death rate depends on both the state and the time. Based on the preliminary results, the main properties of the multivariate extended generalized Pólya process and meaningful characterizations are obtained. Finally, possible applications to reliability modeling are briefly discussed.

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022, Preprint, arXiv:1812.04195v4 [stat.ME]), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.

Consider a finite or infinite collection of urns, each with capacity r, and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain r balls. When $r=1$, this is the number of balls landing in non-empty urns, which has been studied in the past. Our aim here is to use martingale methods to study the asymptotics of the overflow in the general situation, i.e. for arbitrary r. In particular, we provide sufficient conditions for both Poissonian and normal asymptotics.

Recently, there is a growing interest to study the variability of uncertainty measure in information theory. For the sake of analyzing such interest, varentropy has been introduced and examined for one-sided truncated random variables. As the interval entropy measure is instrumental in summarizing various system and its components properties when it fails between two time points, exploring variability of such measure pronounces the extracted information. In this article, we introduce the concept of varentropy for doubly truncated random variable. A detailed study of theoretical results taking into account transformations, monotonicity and other conditions is proposed. A simulation study has been carried out to investigate the behavior of varentropy in shrinking interval for simulated and real-life data sets. Furthermore, applications related to the choice of most acceptable system and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process are illustrated.

In daycare centres, the close contact of children with other children and employees favours the transmission of infections. The majority of children <6 years attend daycare programmes in Germany, but the role of daycare centres in the SARS-CoV-2 pandemic is unclear. We investigated the transmission risk in daycare centres and the spread of SARS-CoV-2 to associated households. 30 daycare groups with at least one recent laboratory-confirmed SARS-CoV-2 case were enrolled in the study (10/2020–06/2021). Close contact persons within daycare and households were examined over a 12-day period (repeated SARS-CoV-2 PCR tests, genetic sequencing of viruses, symptom diary). Households were interviewed to gain comprehensive information on each outbreak. We determined primary cases for all daycare groups. The number of secondary cases varied considerably between daycare groups. The pooled secondary attack rate (SAR) across all 30 daycare centres was 9.6%. The SAR tended to be higher when the Alpha variant was detected (15.9% vs. 5.1% with evidence of wild type). The household SAR was 53.3%. Exposed daycare children were less likely to get infected with SARS-CoV-2 than employees (7.7% vs. 15.5%). Containment measures in daycare programmes are critical to reduce SARS-CoV-2 transmission, especially to avoid spread to associated households.

In this study, we aimed to examine the association between gastrointestinal (GI) symptom presence during severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and the prevalence of GI symptoms and the development of post-infectious irritable bowel syndrome (PI-IBS). We used data from a prospective cohort and logistic regression to examine the association between GI symptom status during confirmed SARS-CoV-2 infection and prevalence of persistent GI symptoms at ≥45 days. We also report the incidence of PI-IBS following SARS-CoV-2 infection. Of the 1475 participants in this study, 33.8% (n = 499) had GI symptoms during acute infection. Cases with acute GI symptoms had an odds of persisting GI symptoms 4 times higher than cases without acute GI symptoms (odds ratio (OR) 4.29, 95% confidence interval (CI) 2.45–7.53); symptoms lasted on average 8 months following infection. Of those with persisting GI symptoms, 67% sought care for their symptoms and incident PI-IBS occurred in 3.0% (n = 15) of participants. Those with acute GI symptoms after SARS-CoV-2 infection are likely to have similar persistent symptoms 45 days and greater. These data indicate that attention to a potential increase in related healthcare needs is warranted.

We study supercritical branching processes under the influence of an independent and identically distributed (i.i.d.) emigration component. We provide conditions under which the lifetime of the process is finite or has a finite expectation. A theorem of Kesten–Stigum type is obtained, and the extinction probability for a large initial population size is related to the tail behaviour of the emigration.

This article examines large-time behaviour of finite-state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) of the time required for convergence of the empirical measure process of the N-particle system to its invariant measure; we show that when time is of the order $\exp\{N\Lambda\}$ for a suitable constant $\Lambda > 0$, the process has mixed well and it is close to its invariant measure. We then obtain large-N asymptotics of the second-largest eigenvalue of the generator associated with the empirical measure process when it is reversible with respect to its invariant measure. We show that its absolute value scales as $\exp\{{-}N\Lambda\}$. The main tools used in establishing our results are the large deviation properties of the empirical measure process from its large-N limit. As an application of the study of large-time behaviour, we also show convergence of the empirical measure of the system of particles to a global minimum of a certain ‘entropy’ function when particles are added over time in a controlled fashion. The controlled addition of particles is analogous to the cooling schedule associated with the search for a global minimum of a function using the simulated annealing algorithm.

The present paper, which composes a broader research agenda developed by Data Privacy Brasil Research Association, aims to conduct a descriptive and qualitative study of the Brazilian National Identity System through a data protection and data justice perspective. For this purpose, a desk research and legislation analyses were conducted to answer the following question: is the Brazilian National Civil Identification System (Identificação Civil Nacional or ICN) framework adequate with the Brazilian data protection general legislation and its principles—especially regarding its information architecture? As a result, we found that the current information architecture of the ICN, as well as its current use, may reveal a set of concerns related to data protection and data justice.

Let $X_1,X_2, \ldots, X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density f. Under some conditions on f, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability kth-nearest neighbor balls of $X_1,\ldots, X_n$. Our result generalizes Theorem 2.2 of [11], which refers to the special case $k=1$. Our proof is completely different since it employs the Chen–Stein method instead of the method of moments. Moreover, we obtain a rate of convergence for the Poisson approximation.

The clustered chromatic number of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$. We determine the clustered chromatic number of any minor-closed class with bounded treedepth, and prove a best possible upper bound on the clustered chromatic number of any minor-closed class with bounded pathwidth. As a consequence, we determine the fractional clustered chromatic number of every minor-closed class.

We study the problem of finding pairwise vertex-disjoint triangles in the randomly perturbed graph model, which is the union of any $n$-vertex graph $G$ satisfying a given minimum degree condition and the binomial random graph $G(n,p)$. We prove that asymptotically almost surely $G \cup G(n,p)$ contains at least $\min \{\delta (G), \lfloor n/3 \rfloor \}$ pairwise vertex-disjoint triangles, provided $p \ge C \log n/n$, where $C$ is a large enough constant. This is a perturbed version of an old result of Dirac.

Our result is asymptotically optimal and answers a question of Han, Morris, and Treglown [RSA, 2021, no. 3, 480–516] in a strong form. We also prove a stability version of our result, which in the case of pairwise vertex-disjoint triangles extends a result of Han, Morris, and Treglown [RSA, 2021, no. 3, 480–516]. Together with a result of Balogh, Treglown, and Wagner [CPC, 2019, no. 2, 159–176], this fully resolves the existence of triangle factors in randomly perturbed graphs.

We believe that the methods introduced in this paper are useful for a variety of related problems: we discuss possible generalisations to clique factors, cycle factors, and $2$-universality.

Hepatitis B virus-related acute-on-chronic liver failure (HBV-ACLF) is a severe and life-threatening complication, characterised by multi-organ failure and high short-term mortality. However, there is limited information on the impact of various comorbidities on HBV-ACLF in a large population. This study aimed to investigate the relationship between comorbidities, complications and mortality. In this retrospective observational study, we identified 2166 cases of HBV-ACLF hospitalised from January 2010 to March 2018. Demographic data from the patients, medical history, treatment, laboratory indices, comorbidities and complications were collected. The mortality rate in our study group was 47.37%. Type 2 diabetes mellitus was the most common comorbidity, followed by alcoholic liver disease. Spontaneous bacterial peritonitis, pneumonia and hepatic encephalopathy (HE) were common in these patients. Diabetes mellitus and hyperthyroidism are risk factors for death within 90 days, together with gastrointestinal bleeding and HE at admission, HE and hepatorenal syndrome during hospitalisation. Knowledge of risk factors can help identify HBV-ACLF patients with a poor prognosis for HBV-ACLF with comorbidities and complications.

Trustworthiness is typically regarded as a desirable feature of national identification systems (NISs); but the variegated nature of the trustor communities associated with such systems makes it difficult to see how a single system could be equally trustworthy to all actual and potential trustors. This worry is accentuated by common theoretical accounts of trustworthiness. According to such accounts, trustworthiness is relativized to particular individuals and particular areas of activity, such that one can be trustworthy with regard to some individuals in respect of certain matters, but not trustworthy with regard to all trustors in respect of every matter. The present article challenges this relativistic approach to trustworthiness by outlining a new account of trustworthiness, dubbed the expectation-oriented account. This account allows for the possibility of an absolutist (or one-place) approach to trustworthiness. Such an account, we suggest, is the approach that best supports the effort to develop NISs. To be trustworthy, we suggest, is to minimize the error associated with trustor expectations in situations of social dependency (commonly referred to as trust situations), and to be trustworthy in an absolute sense is to assign equal value to all expectation-related errors in all trust situations. In addition to outlining the features of the expectation-oriented account, we describe some of the implications of this account for the design, development, and management of trustworthy NISs.