Minimal half-spaces and external representation of tropical polyhedra

We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently represented internally (in terms of extreme points and rays) or externally (in terms of half-spaces containing it). A canonical external representation of a polyhedron turns out to be provided by the extreme elements of its tropical polar. We characterize these extreme elements, showing in particular that they are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures improved, references update

Node Vulnerability under Finite Perturbations in Complex Networks

A measure to quantify vulnerability under perturbations (attacks, failures, large fluctuations) in ensembles (networks) of coupled dynamical systems is proposed. Rather than addressing the issue of how the network properties change upon removal of elements of the graph (the strategy followed by most of the existing methods for studying the vulnerability of a network based on its topology), here a dynamical definition of vulnerability is introduced, referring to the robustness of a collective dynamical state to perturbing events occurring over a fixed topology. In particular, we study how the collective (synchronized) dynamics of a network of chaotic units is disrupted under the action of a finite size perturbation on one of its nodes. Illustrative examples are provided for three systems of identical chaotic oscillators coupled according to three distinct well-known network topologies. A quantitative comparison between the obtained vulnerability rankings and the classical connectivity/centrality rankings is made that yields conclusive results. Possible applications of the proposed strategy and conclusions are also discussed

International criteria for electrocardiographic interpretation in athletes: Consensus statement.

Sudden cardiac death (SCD) is the leading cause of mortality in athletes during sport. A variety of mostly hereditary, structural or electrical cardiac disorders are associated with SCD in young athletes, the majority of which can be identified or suggested by abnormalities on a resting 12-lead electrocardiogram (ECG). Whether used for diagnostic or screening purposes, physicians responsible for the cardiovascular care of athletes should be knowledgeable and competent in ECG interpretation in athletes. However, in most countries a shortage of physician expertise limits wider application of the ECG in the care of the athlete. A critical need exists for physician education in modern ECG interpretation that distinguishes normal physiological adaptations in athletes from distinctly abnormal findings suggestive of underlying pathology. Since the original 2010 European Society of Cardiology recommendations for ECG interpretation in athletes, ECG standards have evolved quickly, advanced by a growing body of scientific data and investigations that both examine proposed criteria sets and establish new evidence to guide refinements. On 26-27 February 2015, an international group of experts in sports cardiology, inherited cardiac disease, and sports medicine convened in Seattle, Washington (USA), to update contemporary standards for ECG interpretation in athletes. The objective of the meeting was to define and revise ECG interpretation standards based on new and emerging research and to develop a clear guide to the proper evaluation of ECG abnormalities in athletes. This statement represents an international consensus for ECG interpretation in athletes and provides expert opinion-based recommendations linking specific ECG abnormalities and the secondary evaluation for conditions associated with SCD

Spreading Patterns of the Influenza A (H1N1) Pandemic

We investigate the dynamics of the 2009 influenza A (H1N1/S-OIV) pandemic by analyzing data obtained from World Health Organization containing the total number of laboratory-confirmed cases of infections - by country - in a period of 69 days, from 26 April to 3 July, 2009. Specifically, we find evidence of exponential growth in the total number of confirmed cases and linear growth in the number of countries with confirmed cases. We also find that, i) at early stages, the cumulative distribution of cases among countries exhibits linear behavior on log-log scale, being well approximated by a power law decay; ii) for larger times, the cumulative distribution presents a systematic curvature on log-log scale, indicating a gradual change to lognormal behavior. Finally, we compare these empirical findings with the predictions of a simple stochastic model. Our results could help to select more realistic models of the dynamics of influenza-type pandemics

Gastric bypass versus best medical treatment for diabetic kidney disease: 5 years follow up of a single-centre open label randomised controlled trial

BACKGROUND: We compared the albuminuria-lowering effects of Roux-en-Y gastric bypass (RYGB) to best medical treatment in patients with diabetic kidney disease and obesity to determine which treatment is better. METHODS: A 5 year, open-label, single-centre, randomised trial studied patients with diabetic kidney disease and class I obesity after 1:1 randomization to best medical treatment (n = 49) or RYGB (n = 51). The primary outcome was the proportion of patients achieving remission of microalbuminuria after 5 years. Secondary outcomes included improvements in diabetic kidney disease, glycemic control, quality of life, and safety. For efficacy outcomes, we performed an intention-to-treat (ITT) analysis. This study was registered with ClinicalTrials.gov, NCT01821508. FINDINGS: 88% of patients (44 per arm) completed 5-year follow-up. Remission of albuminuria occurred in 59.6% (95% CI = 45.5–73.8) after best medical treatment and 69.7% (95% CI = 59.6–79.8) after RYGB (risk difference: 10%, 95% CI, −7 to 27, P = 0.25). Patients after RYGB were twice as likely to achieve an HbA1c ≤ 6.5% (60.2% versus 25.4%, risk difference, 34.9%; 95% CI = 15.8–53.9, P < 0.001). Quality of life after five years measured by the 36-Item Short Form Survey questionnaire (standardized to a 0-to-100 scale) was higher in the RYGB group than in the best medical treatment group for several domains. The mean differences were 13.5 (95% CI, 5.5–21.6, P = 0.001) for general health, 19.7 (95% CI, 9.1–30.3, P < 0.001) for pain, 6.1 (95% CI, −4.8 to 17.0, P = 0.27) for social functioning, 8.3 (95% CI, 0.23 to 16.3, P = 0.04) for emotional well-being, 12.2 (95% CI, 3.9–20.4, P = 0.004) for vitality, 16.8 (95% CI, −0.75 to 34.4, P = 0.06) for mental health, 21.8 (95% CI, 4.8–38.7, P = 0.01) for physical health and 11.1 (95% CI, 2.24–19.9, P = 0.01) for physical functioning. Serious adverse events were experienced in 7/46 (15.2%) after best medical treatment and 11/46 patients (24%) after RYGB (P = 0.80). INTERPRETATION: Albuminuria remission was not statistically different between best medical treatment and RYGB after 5 years in participants with diabetic kidney disease and class 1 obesity, with 6–7 in ten patients achieving remission of microalbuminuria (uACR <30 mg/g) in both groups. RYGB was superior in improving glycemia, diastolic blood pressure, lipids, body weight, and quality of life. FUNDING: The study was supported by research grants from Johnson & Johnson Brasil, Oswaldo Cruz German Hospital, and by grant 12/YI/B2480 from Science Foundation Ireland (Dr le Roux) and grant 2015-02733 from the Swedish Medical Research Council (Dr le Roux). Dr Pereira was funded by the Chevening Scholarship Programme (Foreign and Commonwealth Office, UK)

Evaluation of two formulations of adjuvanted RTS, S malaria vaccine in children aged 3 to 5 years living in a malaria-endemic region of Mozambique: a Phase I/IIb randomized double-blind bridging trial

BACKGROUND: Previous trials of the RTS, S malaria candidate vaccine have shown that this vaccine is safe, tolerated and immunogenic. The development plan for this vaccine aims at administering it in the first year of life through the Expanded Program on Immunization (EPI). The objective was to evaluate the safety and reactogenicity of RTS, S/AS02D (0.5 ml dose), a pediatric formulation of GlaxoSmithKline Biologicals' current malaria candidate vaccine RTS, S/AS02A (0.25 ml dose). A 0.5 ml dose of AS02D is composed of the same active ingredients in the same quantities as in a 0.25 ml dose of AS02A and has been developed to be easily introduced into routine EPI practices. METHODS: We performed a phase I/IIb randomized double-blind bridging study in a malaria-endemic region of Mozambique, to compare the safety and immunogenicity of both candidate vaccines with the aim of replacing RTS, S/AS02A with RTS, S/AS02D as the candidate pediatric vaccine. 200 Mozambican children aged 3 to 5 years were randomized 1:1 to receive one of the 2 vaccines according to a 0, 1, 2 month schedule. RESULTS: Both vaccines were safe and had similar reactogenicity profiles. All subjects with paired pre and post-vaccination samples showed a vaccine response with respect to anti-circumsporozoite (CS) antibodies irrespective of initial anti-CS serostatus. Geometric mean titers (GMTs) were 191 EU/ml (95% CI 150–242) in recipients of RTS, S/AS02D compared to 180 EU/ml (95% CI 146–221) in recipients of RTS, S/AS02A. For the anti-hepatitis B surface antigen (HBsAg), all subjects were seroprotected at day 90, and the GMTs were 23978 mIU/ml (95% CI 17896–32127) in RTS, S/AS02D recipients and 17410 mIU/ml (95% CI 13322–22752) in RTS, S/AS02A recipients. There was a decrease in anti-CS GMTs between months 3 and 14 in both groups (191 vs 22 EU/mL in RTS, S/AS02D group and 180 vs 29 EU/mL in RTS, S/AS02A group). CONCLUSION: Our data show that the RTS, S/AS02D is safe, well tolerated, and demonstrates non-inferiority (defined as upper limit of the 95% confidence interval of the anti-CS GMT ratio of RTS, S/AS02A to RTS, S/AS02D below 3.0) of the antibody responses to circumsporozoite and HBsAg induced by the RTS, S/AS02D as compared to the RTS, S/AS02A

Development and validation of an interpretable machine learning-based calculator for predicting 5-year weight trajectories after bariatric surgery: a multinational retrospective cohort SOPHIA study

Background Weight loss trajectories after bariatric surgery vary widely between individuals, and predicting weight loss before the operation remains challenging. We aimed to develop a model using machine learning to provide individual preoperative prediction of 5-year weight loss trajectories after surgery. Methods In this multinational retrospective observational study we enrolled adult participants (aged $\ge$18 years) from ten prospective cohorts (including ABOS [NCT01129297], BAREVAL [NCT02310178], the Swedish Obese Subjects study, and a large cohort from the Dutch Obesity Clinic [Nederlandse Obesitas Kliniek]) and two randomised trials (SleevePass [NCT00793143] and SM-BOSS [NCT00356213]) in Europe, the Americas, and Asia, with a 5 year followup after Roux-en-Y gastric bypass, sleeve gastrectomy, or gastric band. Patients with a previous history of bariatric surgery or large delays between scheduled and actual visits were excluded. The training cohort comprised patients from two centres in France (ABOS and BAREVAL). The primary outcome was BMI at 5 years. A model was developed using least absolute shrinkage and selection operator to select variables and the classification and regression trees algorithm to build interpretable regression trees. The performances of the model were assessed through the median absolute deviation (MAD) and root mean squared error (RMSE) of BMI. Findings10 231 patients from 12 centres in ten countries were included in the analysis, corresponding to 30 602 patient-years. Among participants in all 12 cohorts, 7701 (75$\bullet$3%) were female, 2530 (24$\bullet$7%) were male. Among 434 baseline attributes available in the training cohort, seven variables were selected: height, weight, intervention type, age, diabetes status, diabetes duration, and smoking status. At 5 years, across external testing cohorts the overall mean MAD BMI was 2$\bullet$8 kg/m${}^2$ (95% CI 2$\bullet$6-3$\bullet$0) and mean RMSE BMI was 4$\bullet$7 kg/m${}^2$ (4$\bullet$4-5$\bullet$0), and the mean difference between predicted and observed BMI was-0$\bullet$3 kg/m${}^2$ (SD 4$\bullet$7). This model is incorporated in an easy to use and interpretable web-based prediction tool to help inform clinical decision before surgery. InterpretationWe developed a machine learning-based model, which is internationally validated, for predicting individual 5-year weight loss trajectories after three common bariatric interventions.Comment: The Lancet Digital Health, 202

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

SummaryBackground The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6–58·8) of global deaths and 41·2% (39·8–42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Funding Bill & Melinda Gates Foundation