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.

In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

Parkinson’s disease (PD) is an irreversible neurodegenerative disorder clinically manifesting in uncontrolled motor symptoms. There are two primary hallmark features of Parkinson’s disease—an irreversible loss of dopaminergic neurons of the substantia nigra pars compacta and formation of intracellular insoluble aggregates called Lewy bodies mostly composed of alpha-synuclein. Using a clinical improvements-first approach, we identified several clinical trials involving consumption of a specific diet or nutritional supplementation that improved motor and nonmotor functions. Here, we aimed to investigate if and how pyrroloquinoline quinone (PQQ) compound disrupts preformed alpha-synuclein deposits using SH-SY5Y cells, widely used Parkinson’s disease cellular model. SH-SY5Y neuroblastoma cells, incubated in presence of potassium chloride (KCl) to induce alpha-synuclein protein aggregation, were treated with PQQ for up to 48 hr. Resulting aggregates were examined and quantified using confocal microscopy. Overall, nutritional compound PQQ reduced the average number and overall size of intracellular cytoplasmic alpha-synuclein aggregates in a PD cellular model.