Arc-Disjoint Paths and Trees in 2-Regular Digraphs

An out-(in-)branching B_s^+ (B_s^-) rooted at s in a digraph D is a connected spanning subdigraph of D in which every vertex x != s has precisely one arc entering (leaving) it and s has no arcs entering (leaving) it. We settle the complexity of the following two problems: 1) Given a 2-regular digraph $D$, decide if it contains two arc-disjoint branchings B^+_u, B^-_v. 2) Given a 2-regular digraph D, decide if it contains an out-branching B^+_u such that D remains connected after removing the arcs of B^+_u. Both problems are NP-complete for general digraphs. We prove that the first problem remains NP-complete for 2-regular digraphs, whereas the second problem turns out to be polynomial when we do not prescribe the root in advance. We also prove that, for 2-regular digraphs, the latter problem is in fact equivalent to deciding if $D$ contains two arc-disjoint out-branchings. We generalize this result to k-regular digraphs where we want to find a number of pairwise arc-disjoint spanning trees and out-branchings such that there are k in total, again without prescribing any roots.Comment: 9 pages, 7 figure

Identidad desde la violencia: la nueva división este-oeste en Timor Oriental

Este artículo hace un repaso histórico del origen de la distinción este-oeste en Timor Oriental, y describe cómo ha ido creciendo su relevancia en el país. El artículo comienza con una breve descripción de la distinción, tal y como ésta se expresaba antes de 2006, para después presentar los eventos de la crisis durante ese año. En la tercera parte, el artículo muestra cómo la nueva línea divisoria se manifiesta en los distintos sectores de la vida política y de la sociedad

Øst-Timors tilbageslag

I 1999 fremstod Øst-Timor som det perfekte la- boratorium for statsbygning under international ledelse. Men siden er meget gået galt

Meta-analysis for individual participant data with a continuous exposure: A case study

OBJECTIVE: Methods for meta-analysis of studies with individual participant data and continuous exposure variables are well described in the statistical literature but are not widely used in clinical and epidemiological research. The purpose of this case study is to make the methods more accessible. STUDY DESIGN AND SETTING: A two-stage process is demonstrated. Response curves are estimated separately for each study using fractional polynomials. The study-specific curves are then averaged pointwise over all studies at each value of the exposure. The averaging can be implemented using fixed effects or random effects methods. RESULTS: The methodology is illustrated using samples of real data with continuous outcome and exposure data and several covariates. The sample data set, segments of Stata and R code, and outputs are provided to enable replication of the results. CONCLUSION: These methods and tools can be adapted to other situations, including for time-to-event or categorical outcomes, different ways of modelling exposure-outcome curves, and different strategies for covariate adjustment

Early Menarche, Nulliparity, and the Risk for Premature and Early Natural Menopause

Study question: How the timing of menarche and parity link with premature and early natural 42 menopause? Summary answer: Early menarche (≤11 years) is a risk factor for both premature menopause (final 44 menstrual period, FMP <40 years) and early menopause (FMP 40-44 years), a risk that is amplified for nulliparous women. What is known already: Women with either premature or early menopause face increased risk of chronic conditions in later life and of early death. Findings from some studies suggest that early menarche and nulliparity are associated with early menopause, however overall the evidence is mixed. Much of the evidence for a direct relationship is hampered by a lack of comparability across studies, adjustment for confounding factors, and statistical power. Study design, size, duration: This pooled study comprises 51,450 postmenopausal women from nine observational studies in the UK, Scandinavia, Australia, and Japan that contribute to the International collaboration for a Life course Approach to reproductive health and Chronic disease Events (InterLACE). Participants/materials, setting, methods: Age at menarche (categorised as ≤11, 12, 13, 14, and 15 56 or more years) and parity (categorised as no children, one child, and two or more children) were exposure of interest. Age at FMP was confirmed by at least 12 months of cessation of menses where this was not the result of an intervention (such as surgical menopause due to bilateral oophorectomy or hysterectomy) and categorised as premature menopause (FMP before age 40), early menopause (FMP 40-44 years), 45-49 years, 50-51 years, 52-53 years, and 54 or more years. We used multivariate multinomial logistic regression models to estimate relative risk ratio (RRR) and 95% confidence intervals (95%CI) for associations between menarche, parity and age at FMP adjusting for within-study correlation. Main results and the role of chance: The median age at FMP was 50 years (interquartile range 48 to 53 years), with 2% of the women experiencing premature menopause and 7.6% early menopause. Women with early menarche (≤11 years, compared with 12-13 years) were at higher risk of premature menopause (RRR 1.80, 95% CI 1.53 to 2.12) and early menopause (1.31, 1.19 to 1.44). Nulliparity was associated with increased risk of premature menopause (2.26, 1.84 to 2.77) and early menopause (1.32, 1.09 to 1.59). Women having early menarche and nulliparity were at over five folds increased risk of premature menopause (5.64, 4.04 to 7.87) and two folds increased risk of early menopause (2.16, 1.48 to 3.15) compared with women who had menarche at ≥12 years and two or more children. Limitations, reasons for caution: Most of the studies (except the birth cohorts) relied on retrospectively reported age at menarche which may have led to some degree of recall bias. Wider implications of the findings: Our findings support early monitoring of women with early menarche, especially those who have no children, for preventive health interventions aimed at mitigating the risk of adverse health outcomes associated with early menopause

The InterLACE study: design, data harmonization and characteristics across 20 studies on women's health

The International Collaboration for a Life Course Approach to Reproductive Health and Chronic Disease Events (InterLACE) project is a global research collaboration that aims to advance understanding of women's reproductive health in relation to chronic disease risk by pooling individual participant data from several cohort and cross-sectional studies. The aim of this paper is to describe the characteristics of contributing studies and to present the distribution of demographic and reproductive factors and chronic disease outcomes in InterLACE

Interaction Testing and Polygenic Risk Scoring to Estimate the Association of Common Genetic Variants with Treatment Resistance in Schizophrenia

Importance: About 20% to 30% of people with schizophrenia have psychotic symptoms that do not respond adequately to first-line antipsychotic treatment. This clinical presentation, chronic and highly disabling, is known as treatment-resistant schizophrenia (TRS). The causes of treatment resistance and their relationships with causes underlying schizophrenia are largely unknown. Adequately powered genetic studies of TRS are scarce because of the difficulty in collecting data from well-characterized TRS cohorts. Objective: To examine the genetic architecture of TRS through the reassessment of genetic data from schizophrenia studies and its validation in carefully ascertained clinical samples. Design, Setting, and Participants: Two case-control genome-wide association studies (GWASs) of schizophrenia were performed in which the case samples were defined as individuals with TRS (n = 10501) and individuals with non-TRS (n = 20325). The differences in effect sizes for allelic associations were then determined between both studies, the reasoning being such differences reflect treatment resistance instead of schizophrenia. Genotype data were retrieved from the CLOZUK and Psychiatric Genomics Consortium (PGC) schizophrenia studies. The output was validated using polygenic risk score (PRS) profiling of 2 independent schizophrenia cohorts with TRS and non-TRS: a prevalence sample with 817 individuals (Cardiff Cognition in Schizophrenia [CardiffCOGS]) and an incidence sample with 563 individuals (Genetics Workstream of the Schizophrenia Treatment Resistance and Therapeutic Advances [STRATA-G]). Main Outcomes and Measures: GWAS of treatment resistance in schizophrenia. The results of the GWAS were compared with complex polygenic traits through a genetic correlation approach and were used for PRS analysis on the independent validation cohorts using the same TRS definition. Results: The study included a total of 85490 participants (48635 [56.9%] male) in its GWAS stage and 1380 participants (859 [62.2%] male) in its PRS validation stage. Treatment resistance in schizophrenia emerged as a polygenic trait with detectable heritability (1% to 4%), and several traits related to intelligence and cognition were found to be genetically correlated with it (genetic correlation, 0.41-0.69). PRS analysis in the CardiffCOGS prevalence sample showed a positive association between TRS and a history of taking clozapine (r2 = 2.03%; P =.001), which was replicated in the STRATA-G incidence sample (r2 = 1.09%; P =.04). Conclusions and Relevance: In this GWAS, common genetic variants were differentially associated with TRS, and these associations may have been obscured through the amalgamation of large GWAS samples in previous studies of broadly defined schizophrenia. Findings of this study suggest the validity of meta-analytic approaches for studies on patient outcomes, including treatment resistance