This paper presents a new matrix-infinite-product-form (MIP-form) solution for the stationary distribution in upper block-Hessenberg Markov chains (UBH-MCs). The existing MIP-form solution (Masuyama, Queueing Systems 92, 2019, pp. 173–200) requires a certain parameter set that satisfies both a Foster–Lyapunov drift condition and a convergence condition. In contrast, the new MIP-form solution requires no such parameter sets and no other conditions. The new MIP-form solution also has ‘quasi-algorithmic constructibility’, which is a newly introduced feature of being constructed by iterating infinitely many times a recursive procedure of finite complexity per iteration. This feature is not found in the other existing solutions for the stationary distribution in general UBH-MCs.

Our study aimed to investigate the epidemiology of extrapulmonary tuberculosis (EPTB) and analyse the epidemiological characteristics of EPTB patients with or without pulmonary tuberculosis (PTB). EPTB cases admitted in our hospital from January 2015 to December 2020 were included. Uni- and multi-variable logistic regression analysis was carried out to identify risk factors and prognostic factors of concomitant EPTB and PTB or exclusively EPTB. A total of 3488 EPTB patients were reviewed, including 2086 patients with concurrent PTB and EPTB, and 1402 patients with exclusively EPTB. Logistic regression analysis showed that age >60 years (OR = 1.674, 95% CI = 1.438–1.949, P < 0.001) and female (OR = 1.325, 95% CI = 1.155–1.520, P < 0.001) were risk factors of exclusively EPTB, while co-morbidities (OR = 0.676, 95% CI = 0.492–0.929, P = 0.016) and severe symptoms (OR = 0.613, 95% CI = 0.405–0.929, P = 0.021) were risk factors for concurrence of EPTB and PTB. Age >60 years was an independent prognostic factor in EPTB patients with or without PTB (HR = 11.059, 95%CI = 5.097–23.999, P < 0.001; HR = 23.994, 95%CI = 3.093–186.151, P = 0.0020). Female gender was an independent prognostic factor in patients with concurrent PTB and EPTB (HR = 23.994, 95%CI = 3.093–186.151, P = 0.002). Our study disclosed the differential epidemiological characteristics of EPTB patients with or without PTB in China.

The 10-item Autism-Spectrum Quotient (AQ10) is a measure of autistic traits used in research and clinical practice. Recently, the AQ10 has garnered critical attention, with research questioning its psychometric properties and clinical cutoff value. To help inform the utility of the measure, we conducted the first network analysis of the AQ10, with a view to gain a better understanding of its individual items. Using a large dataset of 6,595 participants who had completed the AQ10, we found strongest inter-subscale connections between communication, imagination, and socially relevant items. The nodes with greatest centrality concerned theory of mind differences. Together, these findings align with cognitive explanations of autism and provide clues about which AQ10 items show greatest utility for informing autism-related clinical practice.

We aimed to descriptively analyse the possible impact of the national COVID-19 interventions on the incidence of common infectious diseases in Denmark during spring and summer 2020. This observational study focused on national register data on infections caused by 16 different bacterial and viral pathogens. We included new cases registered between 1 January 2016 and 31 July 2020. The weekly number of new cases were analysed with respect to the COVID-19-related interventions introduced during 2020. We found a marked decrease in infections associated with droplet transmission coinciding with the COVID-19 interventions in spring and summer 2020. These included decreases in both viral and bacterial airway infections and also decreases in invasive infections caused by Streptococcus pneumoniae, Haemophilus influenzae and Neisseria meningitidis. There was also a reduction in cases associated with foodborne transmission during the COVID-19 lockdown period. We found no effect of the lockdown on infections by invasive beta-haemolytic streptococci group B, C and G, Staphylococcus aureus bacteraemia, Neisseria gonorrhoeae or Clostridioides difficile. In conclusion, we found that the widespread interventions such as physical distancing, less travel, hygiene measures and lockdown of schools, restaurants and workplaces together coincided with a marked decline in respiratory infections and, to a smaller extent, some foodborne-transmitted infections.

Hepatitis E is an increasingly serious worldwide public health problem that has attracted extensive attention. It is necessary to accurately predict the incidence of hepatitis E to better plan ahead for future medical care. In this study, we developed a Bi-LSTM model that incorporated meteorological factors to predict the prevalence of hepatitis E. The hepatitis E data used in this study are collected from January 2005 to March 2017 by Jiangsu Provincial Center for Disease Control and Prevention. ARIMA, GBDT, SVM, LSTM and Bi-LSTM models are adopted in this study. The data from January 2009 to September 2014 are used as the training set to fit models, and data from October 2014 to March 2017 are used as the testing set to evaluate the predicting accuracy of different models. Selecting models and evaluating the effectiveness of the models are based on mean absolute per cent error (MAPE), root mean square error (RMSE) and mean absolute error (MAE). A total of 44 923 cases of hepatitis E are detected in Jiangsu Province from January 2005 to March 2017. The average monthly incidence rate is 0.35 per 100 000 persons in Jiangsu Province. Incorporating meteorological factors of temperature, water vapour pressure, and rainfall as a combination into the Bi-LSTM Model achieved the state-of-the-art performance in predicting the monthly incidence of hepatitis E, in which RMSE is 0.044, MAPE is 11.88%, and MAE is 0.0377. The Bi-LSTM model with the meteorological factors of temperature, water vapour pressure, and rainfall can fully extract the linear and non-linear information in the hepatitis E incidence data, and has significantly improved the interpretability, learning ability, generalisability and prediction accuracy.

We prove a rate of convergence for the N-particle approximation of a second-order partial differential equation in the space of probability measures, such as the master equation or Bellman equation of the mean-field control problem under common noise. The rate is of order $1/N$ for the pathwise error on the solution v and of order $1/\sqrt{N}$ for the $L^2$-error on its L-derivative $\partial_\mu v$. The proof relies on backward stochastic differential equation techniques.

This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.

New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.

Signature theory plays an important part in the field of reliability. In this paper, the ordered multi-state system signature and its related properties are discussed based on a life-test of independent and non-identical coherent or mixed systems with independent and identical binary-state components. Dynamic properties of these systems are considered through a new notion called dynamic multi-state system signature, and then related comparisons are made based on system lifetimes and costs. Finally, the theoretical results established are illustrated with some specific examples to demonstrate the use of dynamic ordered multi-state system signature in evaluating used multi-state coherent or mixed systems.

Approximately one-quarter of annual global cervical cancer deaths occur in India, possibly due to cultural norms promoting vaccine hesitancy. We sought to determine whether people of Indian ancestry (POIA) in the USA exhibit disproportionately lower human papilloma virus (HPV) vaccination rates than the rest of the US population. We utilised the 2018 National Health Interview Survey to compare HPV vaccine initiation and completion rates between POIA and the general US population and determined factors correlating with HPV vaccine uptake among POIA. Compared to other racial groups, POIA had a significantly lower rate of HPV vaccination (8.18% vs. 12.16%, 14.70%, 16.07% and 12.41%, in White, Black, Other Asian and those of other/mixed ancestry, respectively, P = 0.003), but no statistically significant difference in vaccine series completion among those who received at least one injection (3.17% vs. 4.27%, 3.51%, 4.31% and 5.04%, P = 0.465). Among POIA, younger individuals (vs. older), single individuals (vs. married), those with high English proficiency (vs. low English proficiency), those with health insurance and those born in the USA (vs. those born outside the USA) were more likely to obtain HPV vaccination (P = 0.018, P = 0.006, P = 0.029, P = 0.020 and P = 0.019, respectively). Public health measures promoting HPV vaccination among POIA immigrants may substantially improve vaccination rates among this population.

In this paper, we reconsider the assumptions that ensure the identification of the production function in Olley and Pakes (1996, Econometrica 64, 1263–1297). We show that an index restriction plays a crucial role in the identification, especially if the capital stock is measured by the perpetual inventory method. The index restriction is not sufficient for identification under sample selectivity. The index restriction makes it possible to derive the influence function and the asymptotic variance of the Olley–Pakes estimator.

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameters, and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite-dimensional parameters in the model, we construct nonparametric maximum likelihood estimates for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite-dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. The advantages of our methods are borne out in simulation studies and a real data application.

Let $G=(S,T,E)$ be a bipartite graph. For a matching $M$ of $G$, let $V(M)$ be the set of vertices covered by $M$, and let $B(M)$ be the symmetric difference of $V(M)$ and $S$. We prove that if $M$ is a uniform random matching of $G$, then $B(M)$ satisfies the BK inequality for increasing events.

We use an inequality of Sidorenko to show a general relation between local and global subgraph counts and degree moments for locally weakly convergent sequences of sparse random graphs. This yields an optimal criterion to check when the asymptotic behaviour of graph statistics, such as the clustering coefficient and assortativity, is determined by the local weak limit.

As an application we obtain new facts for several common models of sparse random intersection graphs where the local weak limit, as we see here, is a simple random clique tree corresponding to a certain two-type Galton–Watson branching process.

Given a graph $H$ and a positive integer $n$, the Turán number $\mathrm{ex}(n,H)$ is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. A real number $r\in (1,2)$ is called a Turán exponent if there exists a bipartite graph $H$ such that $\mathrm{ex}(n,H)=\Theta (n^r)$. A long-standing conjecture of Erdős and Simonovits states that $1+\frac{p}{q}$ is a Turán exponent for all positive integers $p$ and $q$ with $q\gt p$.

In this paper, we show that $1+\frac{p}{q}$ is a Turán exponent for all positive integers $p$ and $q$ with $q \gt p^{2}$. Our result also addresses a conjecture of Janzer [18].