We study an example of a hit-and-run random walk on the symmetric group $\mathbf S_n$. Our starting point is the well-understood top-to-random shuffle. In the hit-and-run version, at each single step, after picking the point of insertion j uniformly at random in $\{1,\ldots,n\}$, the top card is inserted in the jth position k times in a row, where k is uniform in $\{0,1,\ldots,j-1\}$. The question is, does this accelerate mixing significantly or not? We show that, in $L^2$ and sup-norm, this accelerates mixing at most by a constant factor (independent of n). Analyzing this problem in total variation is an interesting open question. We show that, in general, hit-and-run random walks on finite groups have non-negative spectrum.

In October 2021, the WHO published an ambitious strategy to ensure that all countries had vaccinated 40% of their population by the end of 2021 and 70% by mid-2022. The end of June 2022 marks 18 months of implementation of coronavirus disease 2019 (COVID-19) vaccination in the African region and provides an opportunity to look back and think ahead about COVID-19 vaccine set targets, demand and delivery strategies. As of 26 June 2022 two countries in the WHO African region have achieved this target (Mauritius and Seychelles) and seven are on track, having vaccinated between 40% and 69% of their population. By the 26 June 2022, seven among the 20 countries that had less than 10% of people fully vaccinated at the end of January 2022, have surpassed 15% of people fully vaccinated at the end of June 2022. This includes five targeted countries, which are being supported by the WHO Regional Office for Africa through the Multi-Partners' Country Support Team Initiative. As we enter the second semester of 2022, a window of opportunity has opened to provide new impetus to COVID-19 vaccination rollout in the African region guided by the four principles: Scale-up, Transition, Consolidation and Communication. Member States need to build on progress made to ensure that this impetus is not lost and that the African region does not remain the least vaccinated global region, as economies open up and world priorities change.

Simulated tempering is a popular method of allowing Markov chain Monte Carlo algorithms to move between modes of a multimodal target density $\pi$. Tawn, Moores and Roberts (2021) introduces the Annealed Leap-Point Sampler (ALPS) to allow for rapid movement between modes. In this paper we prove that, under appropriate assumptions, a suitably scaled version of the ALPS algorithm converges weakly to skew Brownian motion. Our results show that, under appropriate assumptions, the ALPS algorithm mixes in time $O(d [\log d]^2)$ or O(d), depending on which version is used.

The US government invests substantial sums to control the HIV/AIDS epidemic. To monitor progress toward epidemic control, PEPFAR, or the President’s Emergency Plan for AIDS Relief, oversees a data reporting system that includes standard indicators, reporting formats, information systems, and data warehouses. These data, reported quarterly, inform understanding of the global epidemic, resource allocation, and identification of trouble spots. PEPFAR has developed tools to assess the quality of data reported. These tools made important contributions but are limited in the methods used to identify anomalous data points. The most advanced consider univariate probability distributions, whereas correlations between indicators suggest a multivariate approach is better suited. For temporal analysis, the same tool compares values to the averages of preceding periods, though does not consider underlying trends and seasonal factors. To that end, we apply two methods to identify anomalous data points among routinely collected facility-level HIV/AIDS data. One approach is Recommender Systems, an unsupervised machine learning method that captures relationships between users and items. We apply the approach in a novel way by predicting reported values, comparing predicted to reported values, and identifying the greatest deviations. For a temporal perspective, we apply time series models that are flexible to include trend and seasonality. Results of these methods were validated against manual review (95% agreement on non-anomalies, 56% agreement on anomalies for recommender systems; 96% agreement on non-anomalies, 91% agreement on anomalies for time series). This tool will apply greater methodological sophistication to monitoring data quality in an accelerated and standardized manner.

While incidence studies based on hospitalisation counts are commonly used for public health decision-making, no standard methodology to define hospitals' catchment population exists. We conducted a review of all published community-acquired pneumonia studies in England indexed in PubMed and assessed methods for determining denominators when calculating incidence in hospital-based surveillance studies. Denominators primarily were derived from census-based population estimates of local geographic boundaries and none attempted to determine denominators based on actual hospital access patterns in the community. We describe a new approach to accurately define population denominators based on historical patient healthcare utilisation data. This offers benefits over the more established methodologies which are dependent on assumptions regarding healthcare-seeking behaviour. Our new approach may be applicable to a wide range of health conditions and provides a framework to more accurately determine hospital catchment. This should increase the accuracy of disease incidence estimates based on hospitalised events, improving information available for public health decision making and service delivery planning.

A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the pathwise uniqueness of a system of stochastic partial differential equations, which is satisfied by the corresponding system of distribution function-valued processes.

$U{\hbox{-}}\textrm{max}$ statistics were introduced by Lao and Mayer in 2008. Such statistics are natural in stochastic geometry. Examples are the maximal perimeters and areas of polygons and polyhedra formed by random points on a circle, ellipse, etc. The main method to study limit theorems for $U{\hbox{-}}\textrm{max}$ statistics is via a Poisson approximation. In this paper we consider a general class of kernels defined on a circle, and we prove a universal limit theorem with the Weibull distribution as a limit. Its parameters depend on the degree of the kernel, the structure of its points of maximum, and the Hessians of the kernel at these points. Almost all limit theorems known so far may be obtained as simple special cases of our general theorem. We also consider several new examples. Moreover, we consider not only the uniform distribution of points but also almost arbitrary distribution on a circle satisfying mild additional conditions.

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.