We study the geometric and topological features of U-statistics of order k when the k-tuples satisfying geometric and topological constraints do not occur frequently. Using appropriate scaling, we establish the convergence of U-statistics in vague topology, while the structure of a non-degenerate limit measure is also revealed. Our general result shows various limit theorems for geometric and topological statistics, including persistent Betti numbers of Čech complexes, the volume of simplices, a functional of the Morse critical points, and values of the min-type distance function. The required vague convergence can be obtained as a result of the limit theorem for point processes induced by U-statistics. The latter convergence particularly occurs in the $\mathcal M_0$-topology.

Dense networks with weighted connections often exhibit a community-like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node’s community membership. We propose a new framework for generating and estimating dense weighted networks with potentially different connectivity patterns across different communities. The proposed model relies on a particular class of functions which map individual node characteristics to the edges connecting those nodes, allowing for flexibility while requiring a small number of parameters relative to the number of edges. By leveraging the estimation techniques, we also develop a bootstrap methodology for generating new networks on the same set of vertices, which may be useful in circumstances where multiple data sets cannot be collected. Performance of these methods is analyzed in theory, simulations, and real data.

While we know that adolescents tend to befriend peers who share their race and gender, it is unclear whether patterns of homophily vary according to the strength, intimacy, or connectedness of these relationships. By applying valued exponential random graph models to a sample of 153 adolescent friendship networks, I test whether tendencies towards same-race and same-gender friendships differ for strong versus weak relational ties. In nondiverse, primarily white networks, weak ties are more likely to connect same-race peers, while racial homophily is not associated with the formation of stronger friendships. As racial diversity increases, however, strong ties become more likely to connect same-race peers, while weaker bonds are less apt to be defined by racial homophily. Gender homophily defines the patterns of all friendship ties, but these tendencies are more pronounced for weaker connections. My results highlight the empirical value of considering tie strength when examining social processes in adolescent networks.

In this paper we study a class of optimal stopping problems under g-expectation, that is, the cost function is described by the solution of backward stochastic differential equations (BSDEs). Primarily, we assume that the reward process is $L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$-integrable with $\mu>\mu_0$ for some critical value $\mu_0$. This integrability is weaker than $L^p$-integrability for any $p>1$, so it covers a comparatively wide class of optimal stopping problems. To reach our goal, we introduce a class of reflected backward stochastic differential equations (RBSDEs) with $L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$-integrable parameters. We prove the existence, uniqueness, and comparison theorem for these RBSDEs under Lipschitz-type assumptions on the coefficients. This allows us to characterize the value function of our optimal stopping problem as the unique solution of such RBSDEs.

While tetanus toxoid vaccination has reduced the incidence of tetanus in the developed world, this disease remains a substantial health problem in developing nations. Tetanus immune globulin (TIG) is used along with vaccination for prevention of infection after major or contaminated wounds if vaccination status cannot be verified or for active tetanus infection. These studies describe the characterisation of a TIG produced by a caprylate/chromatography process. The TIG potency and presence of plasma protein impurities were analysed at early/late steps in the manufacturing process by chromatography, immunoassay, coagulation and potency tests. The caprylate/chromatography process has been previously shown to effectively eliminate or inactivate potentially transmissible agents from plasma-derived products. In this study, the caprylate/chromatography process was shown to effectively concentrate TIG activity and efficiently remove pro-coagulation factors, naturally present in plasma. This TIG drug product builds on the long-term evidence of the safety and efficacy of TIG by providing a product with higher purity and low pro-coagulant protein impurities.

We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a branching random walk up to generation n—generated by a point process with mean 1. We show that this ‘critical cluster cascade’ converges weakly, and that either the limit point process equals the void process (extinction), or it has the same intensity c as the critical cluster cascade (persistence). We obtain persistence if and only if the Palm version of the outgrown critical branching random walk is locally almost surely finite. This result allows us to give numerous examples for persistent critical cluster cascades.

Sexual propagation of Agave plants is an incipient cultivation method, these plants withstand drought and adverse growing conditions; therefore, research on Agave’s diversity, seed processing, and storage could support its cultivation on marginal lands. The aim of this work was to evaluate seed morphology, germination, and seedling genetic diversity of six seed origins (species × provenance) of Agave plants collected in five provenances from Mexico. Seed longevity was evaluated in two seed origins after a 10-year storage period. Seed morphology and seedling genetic variation results demonstrated intra- and interspecific variation within Agave salmiana and with the other seed origins, respectively. After a 10-year storage period seed germination of two A. salmiana seed origins remained relatively stable, storage conditions, and seed variables of this work can serve as reference parameters for future analyses. To the best authors’ knowledge, this is the first report of Agave’s seed longevity evaluation after a 10-year storage period.

Researchers have found that although external attacks, exogenous shocks, and node knockouts can disrupt networked systems, they rarely lead to the system’s collapse. Although these processes are widely understood, most studies of how exogenous shocks affect networks rely on simulated or observational data. Thus, little is known about how groups of real individuals respond to external attacks. In this article, we employ an experimental design in which exogenous shocks, in the form of the unexpected removal of a teammate, are imposed on small teams of people who know each other. This allows us to causally identify the removed individual’s contribution to the team structure, the effect that an individual had on those they were connected, and the effect of the node knockout on the team. At the team level, we find that node knockouts decrease overall internal team communication. At the individual level, we find that node knockouts cause the remaining influential players to become more influential, while the remaining peripheral players become more isolated within their team. In addition, we also find that node knockouts may have a nominal influence on team performance. These findings shed light on how teams respond and adapt to node knockouts.

This paper provides a full classification of the dynamics for continuous-time Markov chains (CTMCs) on the nonnegative integers with polynomial transition rate functions and without arbitrary large backward jumps. Such stochastic processes are abundant in applications, in particular in biology. More precisely, for CTMCs of bounded jumps, we provide necessary and sufficient conditions in terms of calculable parameters for explosivity, recurrence versus transience, positive recurrence versus null recurrence, certain absorption, and implosivity. Simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions as well as existence and nonexistence of moments of hitting times are also obtained. Similar simple sufficient conditions for the aforementioned dynamics together with their opposite dynamics are established for CTMCs with unbounded forward jumps. Finally, we apply our results to stochastic reaction networks, an extended class of branching processes, a general bursty single-cell stochastic gene expression model, and population processes, none of which are birth–death processes. The approach is based on a mixture of Lyapunov–Foster-type results, the classical semimartingale approach, and estimates of stationary measures.

In this study, we tested the validity across two scales addressing conspiratorial thinking that may influence behaviours related to public health and the COVID-19 pandemic. Using the COVIDiSTRESSII Global Survey data from 12 261 participants, we validated the 4-item Conspiratorial Thinking Scale and 3-item Anti-Expert Sentiment Scale across 24 languages and dialects that were used by at least 100 participants per language. We employed confirmatory factor analysis, measurement invariance test and measurement alignment for internal consistency testing. To test convergent validity of the two scales, we assessed correlations with trust in seven agents related to government, science and public health. Although scalar invariance was not achieved when measurement invariance test was conducted initially, we found that both scales can be employed in further international studies with measurement alignment. Moreover, both conspiratorial thinking and anti-expert sentiments were significantly and negatively correlated with trust in all agents. Findings from this study provide supporting evidence for the validity of both scales across 24 languages for future large-scale international research.

Measles resurged in Vietnam between 2018 and 2020, especially in the Southern region. The proportion of children with measles infection showed quite some variation at the provincial level. We applied a spatio-temporal endemic–epidemic modelling framework for age-stratified infectious disease counts using measles surveillance data collected in Southern Vietnam between 1 January 2018 and 30 June 2020. We found that disease transmission within age groups was greatest in young children aged 0–4 years whereas a relatively high between-group transmission was observed in older age groups (5–14 years, 15–24 years and 25+ years groups). At the provincial level, spatial transmission followed an age-dependent distance decay with measles spread mainly depending on local and neighbouring transmission. Our study helped to clarify the measles transmission dynamics in a more detailed fashion with respect to age strata, time and space. Findings from this study may help determine proper strategies in measles outbreak control including promotion of age-targeted intervention programmes in specific areas.

The coronavirus disease 2019 (COVID-19), with new variants, continues to be a constant pandemic threat that is generating socio-economic and health issues in manifold countries. The principal goal of this study is to develop a machine learning experiment to assess the effects of vaccination on the fatality rate of the COVID-19 pandemic. Data from 192 countries are analysed to explain the phenomena under study. This new algorithm selected two targets: the number of deaths and the fatality rate. Results suggest that, based on the respective vaccination plan, the turnout in the participation in the vaccination campaign, and the doses administered, countries under study suddenly have a reduction in the fatality rate of COVID-19 precisely at the point where the cut effect is generated in the neural network. This result is significant for the international scientific community. It would demonstrate the effective impact of the vaccination campaign on the fatality rate of COVID-19, whatever the country considered. In fact, once the vaccination has started (for vaccines that require a booster, we refer to at least the first dose), the antibody response of people seems to prevent the probability of death related to COVID-19. In short, at a certain point, the fatality rate collapses with increasing doses administered. All these results here can help decisions of policymakers to prepare optimal strategies, based on effective vaccination plans, to lessen the negative effects of the COVID-19 pandemic crisis in socioeconomic and health systems.

For the measles-mumps-rubella (MMR) vaccine, the World Health Organization-recommended coverage for herd protection is 95% for measles and 80% for rubella and mumps. However, a national vaccine coverage does not reflect social clustering of unvaccinated children, e.g. in schools of Orthodox Protestant or Anthroposophic identity in The Netherlands. To fully characterise this clustering, we estimated one-dose MMR vaccination coverages at all schools in the Netherlands. By combining postcode catchment areas of schools and school feeder data, each child in the Netherlands was characterised by residential postcode, primary and secondary school (referred to as school career). Postcode-level vaccination data were used to estimate vaccination coverages per school career. These were translated to coverages per school, stratified by school identity. Most schools had vaccine coverages over 99%, but major exceptions were Orthodox Protestant schools (63% in primary and 58% in secondary schools) and Anthroposophic schools (67% and 78%). School-level vaccine coverage estimates reveal strong clustering of unvaccinated children. The school feeder data reveal strongly connected Orthodox Protestant and Anthroposophic communities, but separated from one another. This suggests that even at a national one-dose MMR coverage of 97.5%, thousands of children per cohort are not protected by herd immunity.

There is a lack of publicly available information covering the practices insurers employ to manage their exposure to reinsurance recapture risk. A working party was set-up to shed light on the different approaches insurers use to mitigate this complicated to manage risk. This report is intended to form part of a publicly available information repository that market practitioners can refer to and reflect on as best practice evolves and develops.

In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.

In this paper, we study the optimal multiple stopping problem under the filtration-consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions, rather than a process that is right-continuous with left limits. We first construct the optimal stopping time for the single stopping problem, which is no longer given by the first hitting time of processes. We then prove by induction that the value function of the multiple stopping problem can be interpreted as the one for the single stopping problem associated with a new reward family, which allows us to construct the optimal multiple stopping times. If the reward family satisfies some strong regularity conditions, we show that the reward family and the value functions can be aggregated by some progressive processes. Hence, the optimal stopping times can be represented as hitting times.

Sensor placement optimization (SPO) is usually applied during the structural health monitoring sensor system design process to collect effective data. However, the failure of a sensor may significantly affect the expected performance of the entire system. Therefore, it is necessary to study the optimal sensor placement considering the possibility of sensor failure. In this article, the research focusses on an SPO giving a fail-safe sensor distribution, whose sub-distributions still have good performance. The performance of the fail-safe sensor distribution with multiple sensors placed in the same position will also be studied. The adopted data sets include the mode shapes and corresponding labels of structural states from a series of tests on a glider wing. A genetic algorithm is used to search for sensor deployments, and the partial results are validated by an exhaustive search. Two types of optimization objectives are investigated, one for modal identification and the other for damage identification. The results show that the proposed fail-safe sensor optimization method is beneficial for balancing the system performance before and after sensor failure.