In this paper we consider the problem of averaging for a class of piecewise deterministic Markov processes (PDMPs) whose dynamic is constrained by the presence of a boundary. On reaching the boundary, the process is forced to jump away from it. We assume that this boundary is attractive for the process in question in the sense that its averaged flow is not tangent to it. Our averaging result relies strongly on the existence of densities for the process, allowing us to study the average number of crossings of a smooth hypersurface by an unconstrained PDMP and to deduce from this study averaging results for constrained PDMPs.

This article analyzes raw driving data of passenger cars in the city of Semnan in Iran, with the objective of understanding the impact of traffic conditions at different times of day (morning, noon, evening, and night). For this study, two cars, the Toyota Prius and the Peugeot Pars (or the IKCO Persia), were used, and the data of speed, longitude, latitude, and altitude of the vehicles were acquired. This data was collected over a week (July 21–28, 2022) for a distance of 670 km (13 hr), with the help of the Global Positioning System application, and were presented for both cars. In addition to this, the data on fuel consumption and average speed, based on the Electronic Control Unit in the Prius, was also collected. Finally, a sensitivity analysis was done on the features of the raw data, based on the Principal Component Analysis method.

The world has suffered a lot from COVID-19 and is still on the verge of a new outbreak. The infected regions of coronavirus have been classified into four categories: SIRD model, (1) suspected, (2) infected, (3) recovered, and (4) deaths, where the COVID-19 transmission is evaluated using a stochastic model. A study in Pakistan modeled COVID-19 data using stochastic models like PRM and NBR. The findings were evaluated based on these models, as the country faces its third wave of the virus. Our study predicts COVID-19 casualties in Pakistan using a count data model. We’ve used a Poisson process, SIRD-type framework, and a stochastic model to find the solution. We took data from NCOC (National Command and Operation Center) website to choose the best prediction model based on all provinces of Pakistan, On the values of log L and AIC criteria. The best model among PRM and NBR is NBR because when over-dispersion happens; NBR is the best model for modelling the total suspected, infected, and recovered COVID-19 occurrences in Pakistan as it has the maximum log L and smallest AIC of the other count regression model. It was also observed that the active and critical cases positively and significantly affect COVID-19-related deaths in Pakistan using the NBR model.

To develop a machine learning model and nomogram to predict the probability of persistent virus shedding (PVS) in hospitalized patients with coronavirus disease 2019 (COVID-19), the clinical symptoms and signs, laboratory parameters, cytokines, and immune cell data of 429 patients with nonsevere COVID-19 were retrospectively reviewed. Two models were developed using the Akaike information criterion (AIC). The performance of these two models was analyzed and compared by the receiver operating characteristic (ROC) curve, calibration curve, net reclassification index (NRI), and integrated discrimination improvement (IDI). The final model included the following independent predictors of PVS: sex, C-reactive protein (CRP) level, interleukin-6 (IL-6) level, the neutrophil-lymphocyte ratio (NLR), monocyte count (MC), albumin (ALB) level, and serum potassium level. The model performed well in both the internal validation (corrected C-statistic = 0.748, corrected Brier score = 0.201) and external validation datasets (corrected C-statistic = 0.793, corrected Brier score = 0.190). The internal calibration was very good (corrected slope = 0.910). The model developed in this study showed high discriminant performance in predicting PVS in nonsevere COVID-19 patients. Because of the availability and accessibility of the model, the nomogram designed in this study could provide a useful prognostic tool for clinicians and medical decision-makers.

We propose a new Kalikow decomposition for continuous-time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a finite network and with empty past before zero. The Kalikow decomposition is not unique, and we discuss the choice of the decomposition in terms of algorithmic efficiency in certain cases. We apply these methods to several examples: the linear Hawkes process, the age-dependent Hawkes process, the exponential Hawkes process, and the Galves–Löcherbach process.

Suppose that a system is affected by a sequence of random shocks that occur over certain time periods. In this paper we study the discrete censored $\delta$-shock model, $\delta \ge 1$, for which the system fails whenever no shock occurs within a $\delta$-length time period from the last shock, by supposing that the interarrival times between consecutive shocks are described by a first-order Markov chain (as well as under the binomial shock process, i.e., when the interarrival times between successive shocks have a geometric distribution). Using the Markov chain embedding technique introduced by Chadjiconstantinidis et al. (Adv. Appl. Prob. 32, 2000), we study the joint and marginal distributions of the system’s lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system. The joint and marginal probability generating functions of these random variables are obtained, and several recursions and exact formulae are given for the evaluation of their probability mass functions and moments. It is shown that the system’s lifetime follows a Markov geometric distribution of order $\delta$ (a geometric distribution of order $\delta$ under the binomial setup) and also that it follows a matrix-geometric distribution. Some reliability properties are also given under the binomial shock process, by showing that a shift of the system’s lifetime random variable follows a compound geometric distribution. Finally, we introduce a new mixed discrete censored $\delta$-shock model, for which the system fails when no shock occurs within a $\delta$-length time period from the last shock, or the magnitude of the shock is larger than a given critical threshold $\gamma >0$. Similarly, for this mixed model, we study the joint and marginal distributions of the system’s lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system, under the binomial shock process.

We propose a test for anticipated changes in spot volatility, either due to continuous or discontinuous price moves, at the times of realization of event risk in the form of pre-scheduled releases of economic information such as earnings announcements by firms and macroeconomic news announcements. These events can generate nontrivial volatility in asset returns, which does not scale even locally in time. Our test is based on short-dated options written on an underlying asset subject to event risk, which takes place after the options’ observation time and prior to or after their expiration. We use options with different tenors to estimate the conditional (risk-neutral) characteristic functions of the underlying asset log-returns over the horizons of the options. Using these estimates and a relationship between the conditional characteristic functions with three different tenors, which holds true if and only if continuous and discontinuous spot volatility does not change at the event time, we design a test for this hypothesis. In an empirical application, we study anticipated individual stocks’ volatility changes following earnings announcements for a set of stocks with good option coverage.

This study aimed to determine the impact of current hepatitis B virus (HBV) infection on patients hospitalised with sepsis. This was a retrospective cohort study. Patients from three medical centres in Suzhou from 10 January 2016 to 23 July 2022 participated in this study. Demographic characteristics and clinical characteristics were collected. A total of 945 adult patients with sepsis were included. The median age was 66.0 years, 68.6% were male, 13.1% presented with current HBV infection, and 34.9% of all patients died. In the multivariable-adjusted Cox model, patients with current HBV infection had significantly higher mortality than those without (hazard ratio (HR) 1.50, 95% confidence interval (CI) 1.11–2.02). A subgroup analysis showed that being infected with HBV significantly increased in-hospital mortality in patients younger than 65 years old (HR 1.74, 95% CI 1.16–2.63), whereas no significant impact was observed in patients ≥65 years. The propensity score-matched case–control analysis showed that the rate of septic shock (91.4% vs. 62.1%, P < 0.001) and in-hospital mortality (48.3% vs. 35.3%, P = 0.045) were much higher in the propensity score-matched HBV infection group compared with the control group. In conclusion, current HBV infection was associated with mortality in adults with sepsis.

We investigate jointly modelling age–year-specific rates of various causes of death in a multinational setting. We apply multi-output Gaussian processes (MOGPs), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death mortality rates across several countries and both genders. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Cause-of-Death Database (HCD). We discuss a case study involving cancer variations in three European nations and a US-based study that considers eight top-level causes and includes comparison to all-cause analysis. Our models provide insights into the commonality of cause-specific mortality trends and demonstrate the opportunities for respective data fusion.

We study the problem of determining the minimum number $f(n,k,d)$ of affine subspaces of codimension $d$ that are required to cover all points of $\mathbb{F}_2^n\setminus \{\vec{0}\}$ at least $k$ times while covering the origin at most $k - 1$ times. The case $k=1$ is a classic result of Jamison, which was independently obtained by Brouwer and Schrijver for $d = 1$. The value of $f(n,1,1)$ also follows from a well-known theorem of Alon and Füredi about coverings of finite grids in affine spaces over arbitrary fields. Here we determine the value of this function exactly in various ranges of the parameters. In particular, we prove that for $k\geq 2^{n-d-1}$ we have $f(n,k,d)=2^d k-\left\lfloor{\frac{k}{2^{n-d}}}\right\rfloor$, while for $n \gt 2^{2^d k-k-d+1}$ we have $f(n,k,d)=n + 2^d k -d-2$, and obtain asymptotic results between these two ranges. While previous work in this direction has primarily employed the polynomial method, we prove our results through more direct combinatorial and probabilistic arguments, and also exploit a connection to coding theory.

Severe infections and psychiatric disorders have a large impact on both society and the individual. Studies investigating these conditions and the links between them are therefore important. Most past studies have focused on binary phenotypes of particular infections or overall infection, thereby losing some information regarding susceptibility to infection as reflected in the number of specific infection types, or sites, which we term infection load. In this study we found that infection load was associated with increased risk for attention-deficit/hyperactivity disorder, autism spectrum disorder, bipolar disorder, depression, schizophrenia and overall psychiatric diagnosis. We obtained a modest but significant heritability for infection load (h2 = 0.0221), and a high degree of genetic correlation between it and overall psychiatric diagnosis (rg = 0.4298). We also found evidence supporting a genetic causality for overall infection on overall psychiatric diagnosis. Our genome-wide association study for infection load identified 138 suggestive associations. Our study provides further evidence for genetic links between susceptibility to infection and psychiatric disorders, and suggests that a higher infection load may have a cumulative association with psychiatric disorders, beyond what has been described for individual infections.

We prove a new sufficient pair degree condition for tight Hamiltonian cycles in $3$-uniform hypergraphs that (asymptotically) improves the best known pair degree condition due to Rödl, Ruciński, and Szemerédi. For graphs, Chvátal characterised all those sequences of integers for which every pointwise larger (or equal) degree sequence guarantees the existence of a Hamiltonian cycle. A step towards Chvátal’s theorem was taken by Pósa, who improved on Dirac’s tight minimum degree condition for Hamiltonian cycles by showing that a certain weaker condition on the degree sequence of a graph already yields a Hamiltonian cycle.

In this work, we take a similar step towards a full characterisation of all pair degree matrices that ensure the existence of tight Hamiltonian cycles in $3$-uniform hypergraphs by proving a $3$-uniform analogue of Pósa’s result. In particular, our result strengthens the asymptotic version of the result by Rödl, Ruciński, and Szemerédi.

We study a fully funded, collective defined contribution (DC) pension system with multiple overlapping generations. We investigate whether the welfare of participants can be improved by intergenerational risk sharing (IRS) implemented with a realistic investment strategy (e.g., no borrowing) and without an outside entity (e.g., shareholders) that helps finance the pension fund. To implement IRS, the pension system uses an automatic adjustment rule for the indexation of individual accounts, which adapts to the notional funding ratio of the pension system. The pension system has two parameters that determine the investment strategy and the strength of the adjustment rule, which are optimized by expected utility maximization using Bayesian optimization. The volatility of the retirement benefits and that of the funding ratio are analyzed, and it is shown that the trade-off between them can be controlled by the optimal adjustment parameter to attain IRS. Compared with the optimal individual DC benchmark using the life cycle strategy, the studied pension system with IRS is shown to improve the welfare of risk-averse participants, when the financial market is volatile.

In this paper, we discuss the estimation of conditional quantiles of aggregate claim amounts for non-life insurance embedding the problem in a quantile regression framework using the neural network approach. As the first step, we consider the quantile regression neural networks (QRNN) procedure to compute quantiles for the insurance ratemaking framework. As the second step, we propose a new quantile regression combined actuarial neural network (Quantile-CANN) combining the traditional quantile regression approach with a QRNN. In both cases, we adopt a two-part model scheme where we fit a logistic regression to estimate the probability of positive claims and the QRNN model or the Quantile-CANN for the positive outcomes. Through a case study based on a health insurance dataset, we highlight the overall better performances of the proposed models with respect to the classical quantile regression one. We then use the estimated quantiles to calculate a loaded premium following the quantile premium principle, showing that the proposed models provide a better risk differentiation.

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.

We extend the notion of universal graphs to a geometric setting. A geometric graph is universal for a class $\mathcal H$ of planar graphs if it contains an embedding, that is, a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that is universal for $n$-vertex forests; this generalises a well-known result by Chung and Graham, which states that there exists an (abstract) graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that contains every $n$-vertex forest as a subgraph. The upper bound of $O\!\left(n \log n\right)$ edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega _h(n^{2-1/h})$, for every positive integer $h$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that is universal for $n$-vertex caterpillars.

Since the discovery of Legionnaires’ disease (LD), limited progress has been made in understanding the epidemiology of sporadic cases of LD. Outbreaks have confirmed that air conditioning and potable water systems can be sources of community-acquired LD. However, studying the association between water quality and LD incidence has been challenging due to the heterogeneity of water systems across large geographic areas. Furthermore, although seasonal trends in incidence have been linked to increased rainfall and temperatures, the large geographic units have posed similar difficulties. To address this issue, a retrospective ecological study was conducted in Washington, DC, from 2001 to 2019. The study identified aseasonal pattern of LD incidence, with the majority of cases occurring between June and December, peaking in August, October, and November. Increased temperature was found to be associated with LD incidence. In surface water, higher concentrations of manganese, iron, and strontium were positively associated with LD, while aluminum and orthophosphate showed a negative association. Intreatment plant water, higher concentrations of total organic carbon, aluminum, barium, and chlorine were positively associated with LD, while strontium, zinc, and orthophosphate showed a negative association. The results for orthophosphates and turbidity were inconclusive, indicating the need for further research.

We establish new results on the strictly stationary solution to an iterated function system. When the driving sequence is stationary and ergodic, though not independent, the strictly stationary solution may admit no moment but we show an exponential control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasi-maximum likelihood estimator of GARCH(p,q) models with non-independent innovations.