Graphical models with heavy-tailed factors can be used to model extremal dependence or causality between extreme events. In a Bayesian network, variables are recursively defined in terms of their parents according to a directed acyclic graph (DAG). We focus on max-linear graphical models with respect to a special type of graph, which we call a tree of transitive tournaments. The latter is a block graph combining in a tree-like structure a finite number of transitive tournaments, each of which is a DAG in which every two nodes are connected. We study the limit of the joint tails of the max-linear model conditionally on the event that a given variable exceeds a high threshold. Under a suitable condition, the limiting distribution involves the factorization into independent increments along the shortest trail between two variables, thereby imitating the behaviour of a Markov random field.

We are also interested in the identifiability of the model parameters in the case when some variables are latent and only a subvector is observed. It turns out that the parameters are identifiable under a criterion on the nodes carrying the latent variables which is easy and quick to check.

The present study investigated the psychopathological processes of post-traumatic stress disorder (PTSD) following the network approach to psychopathology. The directed acyclic graph model was employed to analyse a large longitudinal data-set of Chinese children and adolescents exposed to a destructive earthquake. It was found that intrusion symptoms were first activated by trauma exposure, and subsequently activated other PTSD symptoms. The data are consistent with the idea that symptoms may form a self-sustaining dynamic network by interacting with each other to promote or maintain the chronicity of PTSD. The findings advance the current understanding about the psychopathological processes of PTSD, and inform further research and clinical practices on post-traumatic psychopathology.

This study aimed to identify patterns of anthropometric trajectories throughout life and to analyse their association with the occurrence of sarcopenia in people from the Longitudinal Study of Adult Health (ELSA-Brasil). It is a cross-sectional study involving 9670 public servants, aged 38–79 years, who answered the call for new data collection and exams, conducted approximately 4 years after the study baseline (2012–2014). Data sequence analysis was used to identify patterns of anthropometric trajectory. A theoretical model was elaborated based on the directed acyclic graph (DAG) to select the variables of minimum adjustment in the analysis of the causal effect between trajectory and sarcopenia. Poisson regression with robust variance was adopted for data analysis. The patterns of change in the anthropometric trajectory were classified in stable weight (T1); change to normal weight (T2); change to excess weight (T3); weight fluctuation (T4) and change to low weight (T5). The prevalence of sarcopenia in men and women who changed the anthropometric path for the low weight was twice as large when compared to participants with a stable weight trajectory. A protective effect of the excess weight trajectory was observed for the occurrence of sarcopenia in them. The results pointed to the need for health policies that encourage the proper management of body components in order to prevent and control obesity, as well as to preserve the quantity and quality of skeletal muscle mass throughout life, especially in older adults.

Metabolically healthy obesity (MHO) might be an alternative valuable target in obesity treatment. We aimed to assess whether alternative Mediterranean (aMED) diet and Dietary Approaches to Stop Hypertension (DASH) diet were favourably associated with obesity and MHO phenotype in a Chinese multi-ethnic population. We conducted this cross-sectional analysis using the baseline data of the China Multi-Ethnic Cohort study that enrolled 99 556 participants from seven diverse ethnic groups. Participants with self-reported cardiometabolic diseases were excluded to eliminate possible reverse causality. Marginal structural logistic models were used to estimate the associations, with confounders determined by directed acyclic graph (DAG). Among 65 699 included participants, 11·2 % were with obesity. MHO phenotype was present in 5·7 % of total population and 52·7 % of population with obesity. Compared with the lowest quintile, the highest quintile of DASH diet score had 23 % decreased odds of obesity (OR = 0·77, 95 % CI 0·71, 0·83, P trend < 0·001) and 27 % increased odds of MHO (OR = 1·27, 95 % CI 1·10, 1·48, P trend = 0·001) in population with obesity. However, aMED diet showed no obvious favourable associations. Further adjusting for BMI did not change the associations between diet scores and MHO. Results were robust to various sensitivity analyses. In conclusion, DASH diet rather than aMED diet is associated with reduced risk of obesity and presents BMI-independent metabolic benefits in this large population-based study. Recommendation for adhering to DASH diet may benefit the prevention of obesity and related metabolic disorders in Chinese population.

A shared ledger is a record of transactions that can be updated by any member of a group of users. The notion of independent and consistent record-keeping in a shared ledger is important for blockchain and more generally for distributed ledger technologies. In this paper we analyze a stochastic model for the shared ledger known as the tangle, which was devised as the basis for the IOTA cryptocurrency. The model is a random directed acyclic graph, and its growth is described by a non-Markovian stochastic process. We first prove ergodicity of the stochastic process, and then derive a delay differential equation for the fluid model which describes the tangle at high arrival rate. We prove convergence in probability of the tangle process to the fluid model, and also prove global stability of the fluid model. The convergence proof relies on martingale techniques.

Non-alcoholic fatty liver disease (NAFLD) is the hepatic manifestation of the metabolic syndrome. Recent evidence has suggested the protective effects of honey consumption against the metabolic syndrome, but the association between honey intake and NAFLD is still unclear. We investigated how the consumption frequency of honey was associated with NAFLD in the general population. This was a cross-sectional study of 21 979 adults aged 20–90 years. NAFLD was diagnosed based on the ultrasound-diagnosed fatty liver without significant alcohol intake and other liver diseases. Diet information, including consumption frequency of honey, was assessed by a validated 100-item FFQ. OR with 95 % CI were calculated by the binary logistic regression model, adjusting for confounding factors identified by the directed acyclic graph. Overall, 6513 adults (29·6 %) had NAFLD. Compared with participants consuming ≤1 time/week of honey, the multivariable OR of NAFLD were 0·86 (95 % CI 0·77, 0·97) for 2–6 times/week and 1·10 (95 % CI 0·95, 1·27) for ≥1 times/d (Pfor trend = 0·90). The results were generally similar in subgroups of BMI at a cut-point of 24·0 kg/m2 (Pfor interaction = 0·10). In this large-scale study, consuming honey 2–6 times/week was inversely associated with NAFLD, whereas consuming honey ≥1 times/d had no association with NAFLD. These results need replication in other large-scale prospective studies.

Low gestational weight gain (GWG) is a known risk factor of low birthweight. Although studies have previously examined the associations between GWG and birthweight, the period-specific effects of low GWG in each trimester remain unclear. This study aimed to quantify the trimester-specific direct effects of low GWG in Japanese women on birthweight. Using perinatal data from a cohort study, we analyzed pregnant women delivered at an obstetrics/gynecology hospital between October 2006 and May 2010. We focused on women with a pre-pregnancy body mass index (BMI) below 25 kg/m2. The exposure was low GWG. The gestation period was subdivided into trimesters, and the direct effects of low trimester-specific GWG on birthweight were estimated using marginal structural models. These models were guided by a direct acyclic graph that incorporated potential confounders, including pre-pregnancy BMI, age, smoking during pregnancy, height, and parity. We analyzed 563 women and their families. The mean cumulative GWG by the end of the first, second, and third trimesters was 0.9, 6.2, and 10.7 kg, respectively. Approximately 14.0% of the women gained total weight below the range recommended by Japanese Ministry of Health, Labour and Welfare. The direct effects of low GWG on birthweight were 65.9 g (95% confidence interval: 11.4, 120.5), −195.4 g (−263.4, −127.4), and −188.8 g (−292.0, −85.5) for the first, second, and third trimesters, respectively. Insufficient weight gain in the second and third trimesters had a negative impact on birthweight after adjusting for pre-pregnancy BMI and other covariates.

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.