Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network ensemble, and allows to solve the dynamical evolution of the whole network ensemble all at once. Our results accurately reproduce those obtained by extensive numerical simulations showing a large improvement with respect to the usual heterogeneous mean-field formulation. Moreover, by means of the annealed formulation we derive a new heterogeneous mean-field formulation that correctly reproduces the epidemic dynamics.Comment: 5 pages, 3 Figures. Final version published in Physical Review E (Rapid Comm.

How Big Is Too Big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighboring agents. Several critical constellations determine whether this cascade affects the system in part or as a whole which, in the second case, leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold θ i determining their capacity to handle a load αθ i with 1−α being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(θ), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big” shock is not the problem, as the systemic risk only varies slightly for changes in the number of initially failing agents, the safety margin and the threshold distribution, which further gives hints on how to reduce systemic ris

Dynamical organization towards consensus in the Axelrod model on complex networks

We analyze the dynamics toward cultural consensus in the Axelrod model on scale-free networks. By looking at the microscopic dynamics of the model, we are able to show how culture traits spread across different cultural features. We compare the diffusion at the level of cultural features to the growth of cultural consensus at the global level, finding important differences between these two processes. In particular, we show that even when most of the cultural features have reached macroscopic consensus, there are still no signals of globalization. Finally, we analyze the topology of consensus clusters both for global culture and at the feature level of representation.Comment: 8 pages, 7 figures. Final version published in Physical Review

Multiple Score Comparison: a network meta-analysis approach to comparison and external validation of prognostic scores

BACKGROUND Prediction models and prognostic scores have been increasingly popular in both clinical practice and clinical research settings, for example to aid in risk-based decision making or control for confounding. In many medical fields, a large number of prognostic scores are available, but practitioners may find it difficult to choose between them due to lack of external validation as well as lack of comparisons between them. METHODS Borrowing methodology from network meta-analysis, we describe an approach to Multiple Score Comparison meta-analysis (MSC) which permits concurrent external validation and comparisons of prognostic scores using individual patient data (IPD) arising from a large-scale international collaboration. We describe the challenges in adapting network meta-analysis to the MSC setting, for instance the need to explicitly include correlations between the scores on a cohort level, and how to deal with many multi-score studies. We propose first using IPD to make cohort-level aggregate discrimination or calibration scores, comparing all to a common comparator. Then, standard network meta-analysis techniques can be applied, taking care to consider correlation structures in cohorts with multiple scores. Transitivity, consistency and heterogeneity are also examined. RESULTS We provide a clinical application, comparing prognostic scores for 3-year mortality in patients with chronic obstructive pulmonary disease using data from a large-scale collaborative initiative. We focus on the discriminative properties of the prognostic scores. Our results show clear differences in performance, with ADO and eBODE showing higher discrimination with respect to mortality than other considered scores. The assumptions of transitivity and local and global consistency were not violated. Heterogeneity was small. CONCLUSIONS We applied a network meta-analytic methodology to externally validate and concurrently compare the prognostic properties of clinical scores. Our large-scale external validation indicates that the scores with the best discriminative properties to predict 3 year mortality in patients with COPD are ADO and eBODE

How big is too big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure

Association Between Preexisting Versus Newly Identified Atrial Fibrillation and Outcomes of Patients With Acute Pulmonary Embolism

Background Atrial fibrillation (AF) may exist before or occur early in the course of pulmonary embolism (PE). We determined the PE outcomes based on the presence and timing of AF. Methods and Results Using the data from a multicenter PE registry, we identified 3 groups: (1) those with preexisting AF, (2) patients with new AF within 2 days from acute PE (incident AF), and (3) patients without AF. We assessed the 90-day and 1-year risk of mortality and stroke in patients with AF, compared with those without AF (reference group). Among 16 497 patients with PE, 792 had preexisting AF. These patients had increased odds of 90-day all-cause (odds ratio [OR], 2.81; 95% CI, 2.33-3.38) and PE-related mortality (OR, 2.38; 95% CI, 1.37-4.14) and increased 1-year hazard for ischemic stroke (hazard ratio, 5.48; 95% CI, 3.10-9.69) compared with those without AF. After multivariable adjustment, preexisting AF was associated with significantly increased odds of all-cause mortality (OR, 1.91; 95% CI, 1.57-2.32) but not PE-related mortality (OR, 1.50; 95% CI, 0.85-2.66). Among 16 497 patients with PE, 445 developed new incident AF within 2 days of acute PE. Incident AF was associated with increased odds of 90-day all-cause (OR, 2.28; 95% CI, 1.75-2.97) and PE-related (OR, 3.64; 95% CI, 2.01-6.59) mortality but not stroke. Findings were similar in multivariable analyses. Conclusions In patients with acute symptomatic PE, both preexisting AF and incident AF predict adverse clinical outcomes. The type of adverse outcomes may differ depending on the timing of AF onset.info:eu-repo/semantics/publishedVersio

Large-scale external validation and comparison of prognostic models: an application to chronic obstructive pulmonary disease

Background: External validations and comparisons of prognostic models or scores are a prerequisite for their use in routine clinical care but are lacking in most medical fields including chronic obstructive pulmonary disease (COPD). Our aim was to externally validate and concurrently compare prognostic scores for 3-year all-cause mortality in mostly multimorbid patients with COPD. Methods: We relied on 24 cohort studies of the COPD Cohorts Collaborative International Assessment consortium, corresponding to primary, secondary, and tertiary care in Europe, the Americas, and Japan. These studies include globally 15,762 patients with COPD (1871 deaths and 42,203 person years of follow-up). We used network meta-analysis adapted to multiple score comparison (MSC), following a frequentist two-stage approach; thus, we were able to compare all scores in a single analytical framework accounting for correlations among scores within cohorts. We assessed transitivity, heterogeneity, and inconsistency and provided a performance ranking of the prognostic scores. Results: Depending on data availability, between two and nine prognostic scores could be calculated for each cohort. The BODE score (body mass index, airflow obstruction, dyspnea, and exercise capacity) had a median area under the curve (AUC) of 0.679 [1st quartile-3rd quartile = 0.655-0.733] across cohorts. The ADO score (age, dyspnea, and airflow obstruction) showed the best performance for predicting mortality (difference AUC(ADO) - AUC(BODE) = 0.015 [95% confidence interval (CI) = - 0.002 to 0.032]; p = 0.08) followed by the updated BODE (AUCBODE updated - AUCBODE = 0.008 [95% CI = -0.005 to +0.022]; p = 0.23). The assumption of transitivity was not violated. Heterogeneity across direct comparisons was small, and we did not identify any local or global inconsistency. Conclusions: Our analyses showed best discriminatory performance for the ADO and updated BODE scores in patients with COPD. A limitation to be addressed in future studies is the extension of MSC network meta-analysis to measures of calibration. MSC network meta-analysis can be applied to prognostic scores in any medical field to identify the best scores, possibly paving the way for stratified medicine, public health, and research

Prediction models for exacerbations in patients with COPD

Personalised medicine aims to tailor medical decisions to the individual patient. A possible approach is to stratify patients according to the risk of adverse outcomes such as exacerbations in chronic obstructive pulmonary disease (COPD). Risk-stratified approaches are particularly attractive for drugs like inhaled corticosteroids or phosphodiesterase-4 inhibitors that reduce exacerbations but are associated with harms. However, it is currently not clear which models are best to predict exacerbations in patients with COPD. Therefore, our aim was to identify and critically appraise studies on models that predict exacerbations in COPD patients. Out of 1382 studies, 25 studies with 27 prediction models were included. The prediction models showed great heterogeneity in terms of number and type of predictors, time horizon, statistical methods and measures of prediction model performance. Only two out of 25 studies validated the developed model, and only one out of 27 models provided estimates of individual exacerbation risk, only three out of 27 prediction models used high-quality statistical approaches for model development and evaluation. Overall, none of the existing models fulfilled the requirements for risk-stratified treatment to personalise COPD care. A more harmonised approach to develop and validate high- quality prediction models is needed to move personalised COPD medicine forward

Crystal structure of the emptied clathrate form (delta(e) form) of syndiotactic polystyrene

The crystal structure of the emptied clathrate form (delta(e) form) of syndiotactic polystyrene, obtained by removing the guest molecules from different clathrate delta forms, is presented. Chains in s(2/1)2 helical conformation are packed in the monoclinic unit cell with axes a = 17.4 Angstrom, b = 11.85 Angstrom, c = 7.70 Angstrom, and gamma = 117 degrees according to the space group PS1/a. The crystalline density of the emptied clathrate form (0.977 g/cm(3)) is lower than that of the amorphous phase (1.055 g/cm(3)). The differences between the structures of the emptied clathrate form and clathrate delta forms are discussed by the analysis of X-ray diffraction patterns and packing energy calculations