Let T be the regular tree in which every vertex has exactly $d\ge 3$ neighbours. Run a branching random walk on T, in which at each time step every particle gives birth to a random number of children with mean d and finite variance, and each of these children moves independently to a uniformly chosen neighbour of its parent. We show that, starting with one particle at some vertex 0 and conditionally on survival of the process, the time it takes for every vertex within distance r of 0 to be hit by a particle of the branching random walk is $r + ({2}/{\log(3/2)})\log\log r + {\mathrm{o}}(\log\log r)$.

Modelling and forecasting mortality is a topic of crucial importance to actuaries and demographers. However, forecasts from the majority of mortality projection models are continuations of past trends seen in the data. As such, these models are unable to account for external opinions or expert judgement. In this work, we present a method for the incorporation of deterministic opinions into the smoothing and forecasting of mortality rates using constraints. Not only does our approach yield a smooth transition from the past into the future, but also, the shapes of the resulting forecasts are governed by a combination of the opinion inputs and the speed of improvements observed in the data. In addition, our approach offers the possibility to compute the amount of uncertainty around the projected mortality trends conditional on the opinion inputs, and this allows us to highlight some of the pitfalls of deterministic projection methods.

Asteroid and cometary impacts have been considered one of the possible routes for exogenous delivery of organics to the early Earth. It is well established that amino acids can be synthesized due to impact-driven shock processesing of simple molecules and that amino acids can survive the extreme conditions of impact events. In the present study, we simulate impact-induced shock conditions utilizing a shock tube that can maintain a reflected shock temperature of about 5,500 K for 2 ms time scale. We have performed shock processing of various combinations of amino acids with subsequent morphological analysis carried out using Scanning Electron Microscope (SEM), revealing that the shock processed amino acids demonstrate an extensive range of complex structures. These results provide evidence for the further evolution of amino acids in impact-induced shock environments leading to the formation of complex structures and thus providing a pathway for the origin of life.

Gatherings where people are eating and drinking can increase the risk of getting and spreading SARS-CoV-2 among people who are not fully vaccinated; prevention strategies like wearing masks and physical distancing continue to be important for some groups. We conducted an online survey to characterise fall/winter 2020–2021 holiday gatherings, decisions to attend and prevention strategies employed during and before gatherings. We determined associations between practicing prevention strategies, demographics and COVID-19 experience. Among 502 respondents, one-third attended in person holiday gatherings; 73% wore masks and 84% practiced physical distancing, but less did so always (29% and 23%, respectively). Younger adults were 44% more likely to attend gatherings than adults ≥35 years. Younger adults (adjusted prevalence ratio (aPR) 1.53, 95% CI 1.19–1.97), persons who did not experience COVID-19 themselves or have relatives/close friends experience severe COVID-19 (aPR 1.56, 95% CI 1.18–2.07), and non-Hispanic White persons (aPR 1.57, 95% CI 1.13–2.18) were more likely to not always wear masks in public during the 2 weeks before gatherings. Public health messaging emphasizing consistent application of COVID-19 prevention strategies is important to slow the spread of COVID-19.

This article presents cyclic hardening/softening behaviors (experimental data) of the heat-treated aluminum-matrix nano-clay-composite (AlSi_N_HT6), compared to those of the piston aluminum alloy (AlSi) under strain-controlled loading. For such an objective, standard samples were fabricated by gravity and stir-casting methods. Low-cycle fatigue experiments were carried out under different strain amplitudes (0.20–0.45%) and at various temperatures (25–300°C). Obtained results implied that no obvious change was observed on material properties of aluminum alloy by reinforcements, but a decrement was observed due to increasing the temperature. Results also indicated that the increase of the temperature from 25°C to 200°C has changed the cyclic behavior of both materials (AlSi_N_HT6 and AlSi) from hardening to softening. Moreover, the temperature effect was more significant than the total strain amplitude influences in cyclic behaviors.

In the present study, I explored the relationship between people's trust in different agents related to the prevention of the spread of coronavirus disease 2019 (COVID-19) and their compliance with pharmaceutical and non-pharmaceutical preventive measures. The COVIDiSTRESSII Global Survey dataset, which was collected from international samples, was analysed to examine the aforementioned relationship across different countries. For data-driven exploration, network analysis and Bayesian generalised linear model (GLM) analysis were performed. The result from network analysis demonstrated that trust in the scientific research community was most central in the network of trust and compliance. In addition, the outcome from Bayesian GLM analysis indicated that the same factor, trust in the scientific research community, was most fundamental in predicting participants' intent to comply with both pharmaceutical and non-pharmaceutical preventive measures. I briefly discussed the implications of the findings, the importance of trust in the scientific research community in explaining people's compliance with a measure to prevent the spread of COVID-19.

We consider a continuous Gaussian random field living on a compact set $T\subset \mathbb{R}^{d}$. We are interested in designing an asymptotically efficient estimator of the probability that the integral of the exponential of the Gaussian process over T exceeds a large threshold u. We propose an Asmussen–Kroese conditional Monte Carlo type estimator and discuss its asymptotic properties according to the assumptions on the first and second moments of the Gaussian random field. We also provide a simulation study to illustrate its effectiveness and compare its performance with the importance sampling type estimator of Liu and Xu (2014a).

Log-concavity of a joint survival function is proposed as a model for bivariate increasing failure rate (BIFR) distributions. Its connections with or distinctness from other notions of BIFR are discussed. A necessary and sufficient condition for a bivariate survival function to be log-concave (BIFR-LCC) is given that elucidates the impact of dependence between lifetimes on ageing. Illustrative examples are provided to explain BIFR-LCC for both positive and negative dependence.

Theoretical results of frequentist model averaging mainly focus on asymptotic optimality and asymptotic distribution of the model averaging estimator. However, even for basic least squares model averaging, many theoretical problems have not been well addressed yet. This article discusses asymptotic properties of a class of least squares model averaging methods with nested candidate models that includes the Mallows model averaging (MMA) of Hansen (2007, Econometrica 75, 1175–1189) as a special case. Two scenarios are considered: (i) all candidate models are under-fitted; and (ii) the true model is included in the candidate models. We find that in the first scenario, the least squares model averaging method asymptotically assigns weight one to the largest candidate model and the resulting model averaging estimator is asymptotically normal. In the second scenario with a slightly special weight space, if the penalty factor in the weight selection criterion is diverging with certain order, the model averaging estimator is asymptotically optimal by putting weight one to the true model. However, MMA with fixed model dimensions is not asymptotically optimal since it puts nonnegligible weights to over-fitted models. The theoretical results are clearly summarized with their restrictions, and some critical implications are discussed. Monte Carlo simulations confirm our theoretical results.

Asymptotics deviation probabilities of the sum $S_n=X_1+\dots+X_n$ of independent and identically distributed real-valued random variables have been extensively investigated, in particular when $X_1$ is not exponentially integrable. For instance, Nagaev (1969a, 1969b) formulated exact asymptotics results for $\mathbb{P}(S_n>x_n)$ with $x_n\to \infty$ when $X_1$ has a semiexponential distribution. In the same setting, Brosset et al. (2020) derived deviation results at logarithmic scale with shorter proofs relying on classical tools of large-deviation theory and making the rate function at the transition explicit. In this paper we exhibit the same asymptotic behavior for triangular arrays of semiexponentially distributed random variables.

Bullfrog is one of the most important economic aquatic animals in China that is widely cultured in southern China and is a key breed recommended as an industry of poverty alleviation in China. During recent years, a fatal bacterial disease has often been found in cultured bullfrogs. The clinical manifestations of the diseased bullfrogs were severe intestinal inflammation and an anal prolapse. A bacterial pathogen was isolated from the diseased bullfrog intestines. The bacterium was identified as Vibrio cholerae using morphological, biochemical and 16S rRNA phylogenetic analysis. In this study, V. cholerae was isolated and identified in diseased bullfrogs for the first time, providing a basis for the diagnosis and control of the disease. Therefore, attention should be paid to the modes of transmission of V. cholerae from bullfrog and formulate reasonable safety measures.

Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let $\nu$ be the extinction time. Under certain conditions, we show that both $\mathbb{P}(\nu=n)$ and $\mathbb{P}(\nu>n)$ are asymptotically the same as some functions of the products of spectral radii of the mean matrices. We also give an example for which $\mathbb{P}(\nu=n)$ decays with various speeds such as ${c}/({n^{1/2}\log n)^2}$, ${c}/{n^\beta}$, $\beta >1$, which are very different from those of homogeneous multitype Galton–Watson processes.

In this paper, we study the pricing of vulnerable Asian options with liquidity risk. We employ general Lévy processes to capture the changes in the liquidity discount factors and the information processes of all assets. In the proposed pricing model, we obtain the closed-form pricing formula of vulnerable Asian options using the Fourier transform methods. Finally, the derived pricing formula is used to illustrate the effects of asymmetric jump risk, and the effects are relatively stable on (vulnerable) Asian options with different moneynesses.

The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, DeepLearning, and especially convolutional neural networks (CNNs), has been introduced to solve this equation, leading to significant inference time reduction at the cost of a lack of guarantee on the accuracy of the solution.This drawback might lead to inaccuracies, potentially unstable simulations and prevent performing fair assessments of the CNN speedup for different network architectures. To circumvent this issue, a hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level. The CNN hybrid method is tested on two flow cases: (a) the flow around a 2D cylinder and (b) the variable-density plumes with and without obstacles (both 2D and 3D), demonstrating remarkable generalization capabilities, ensuring both the accuracy and stability of the simulations. The error distribution of the predictions using several network architectures is further investigated in the plume test case. The introduced hybrid strategy allows a systematic evaluation of the CNN performance at the same accuracy level for various network architectures. In particular, the importance of incorporating multiple scales in the network architecture is demonstrated, since improving both the accuracy and the inference performance compared with feedforward CNN architectures. Thus, in addition to the pure networks’ performance evaluation, this study has also led to numerous guidelines and results on how to build neural networks and computational strategies to predict unsteady flows with both accuracy and stability requirements.

Potentialdata breach losses represent a significant part of operational risk and can be a serious concern for risk managers and insurers. In this paper, we employ the vine copulas under a Bayesian framework to co-model incidences from different data breach types. A full Bayesian approach can allow one to select both the copulas and margins and estimate their parameters in a coherent fashion. In particular, it can incorporate process, parameter, and model uncertainties, and this is very important for applications in risk management under current regulations. We also conduct a series of sensitivity tests on the Bayesian modelling results. Using two public data sets of data breach losses, we find that the overall dependency structure and tail dependence vary significantly between different types of data breaches. The optimally selected vine structure and pairwise copulas suggest more conservative value-at-risk estimates when compared to the other suboptimal copula models.

In the literature, some stochastic orders have been extended to the higher orders in different scenarios. In this paper, inspired by interesting properties of the excess wealth order and its wide range application particularly in comparing the tail variability of risks, we consider the second-order excess wealth order and study its main properties. We obtain two results characterizing the proposed order. We also investigate its relationship with other well-known variability orders and criteria to compare risks. An application of the results in comparing the epoch times of two nonhomogeneous poisson processes is also given.

The study aim was to examine the incidence and risk factors of respiratory syncytial virus (RSV) bronchiolitis hospitalisations and disease severity among infants. We compared demographic and health characteristics of children aged 0–23 hospitalised for RSV bronchiolitis (cases, n = 1227) during 2008–2018 and control children (n = 554) of the same age admitted for non-respiratory disease. RSV antigen was detected in nasal swabs by immunochromatography. Multiple logistic regression models were applied. The average annual incidence of hospitalisation for RSV bronchiolitis was 12.6 per 1000 and 1.7 per 1000 (P < 0.001) among infants and toddlers, respectively, with winter seasonality (November–March). The risk of hospitalisation for RSV bronchiolitis increased among children aged 0–5 months (OR 7.66; 95% CI 5.61–10.45) and 6–11 months (OR 12.88, 95% CI 8.48–19.55), compared to those aged 12–23 months. Additional risk factors were living in low vs. higher socio-economic status towns (OR 1.49; 95% CI 1.14–1.95), having chronic medical conditions (OR 2.75; 95% CI 1.61–4.70), birth month (October–January vs. June–September) (OR 2.19; 95% CI 1.60–2.99) and history of stay in neonatal intensive care unit at birth (OR 2.37; 95% CI 1.27–4.41). Male children and those who had pneumonia were more likely to have severe RSV bronchiolitis. In conclusion, the burden of hospitalisations for RSV bronchiolitis is high, especially in young infants. Effective preventive measures such as RSV active vaccines can reduce the risk of hospitalisations for RSV bronchiolitis among these vulnerable groups.