When to switch? Index policies for resource scheduling in emergency response

This paper considers the scheduling of limited resources to a large number of jobs (e.g., medical treatment) with uncertain lifetimes and service times, in the aftermath of a mass casualty incident. Jobs are subject to triage at time zero, and placed into a number of classes. Our goal is to maximise the expected number of job completions. We propose an effective yet simple index policy based on Whittle’s restless bandits approach. The problem concerned features a finite and uncertain time horizon that is dependent upon the service policy, which also determines the decision epochs. Moreover, the number of job classes still competing for service diminishes over time. To the best of our knowledge, this is the first application of Whittle’s index policies to such problems. Two versions of Lagrangian relaxation are proposed in order to decompose the problem. The first is a direct extension of the standard Whittle’s restless bandits approach, while in the second the total number of job classes still competing for service is taken into account; the latter is shown to generalise the former. We prove the indexability of all job classes in the Markovian case, and develop closed-form indices. Extensive numerical experiments show that the second proposal outperforms the first one (that fails to capture the dynamics in the number of surviving job classes, or bandits) and produces more robust and consistent results as compared to alternative heuristics suggested from the literature, even in non-Markovian settings

Summary plot for SHAP values of features in the Catboost model.

Summary plot for SHAP values of features in the Catboost model.</p

The predictive values of different machine learning prediction models.

The predictive values of different machine learning prediction models.</p

The screen process of the participants.

BackgroundTo construct several prediction models for the risk of stroke in coronary artery disease (CAD) patients receiving coronary revascularization based on machine learning methods.MethodsIn total, 5757 CAD patients receiving coronary revascularization admitted to ICU in Medical Information Mart for Intensive Care IV (MIMIC-IV) were included in this cohort study. All the data were randomly split into the training set (n = 4029) and testing set (n = 1728) at 7:3. Pearson correlation analysis and least absolute shrinkage and selection operator (LASSO) regression model were applied for feature screening. Variables with Pearson correlation coefficientResultsThe Catboost model presented the best predictive performance with the AUC of 0.831 (95%CI: 0.811–0.851) in the training set, and 0.760 (95%CI: 0.722–0.798) in the testing set. The AUC of the logistic regression model was 0.789 (95%CI: 0.764–0.814) in the training set and 0.731 (95%CI: 0.686–0.776) in the testing set. The results of Delong test revealed that the predictive value of the Catboost model was significantly higher than the logistic regression model (PConclusionThe Catboost model was the optimal model for predicting the risk of stroke in CAD patients receiving coronary revascularization, which might provide a tool to quickly identify CAD patients who were at high risk of postoperative stroke.</div

The number and percentage of missing values.

BackgroundTo construct several prediction models for the risk of stroke in coronary artery disease (CAD) patients receiving coronary revascularization based on machine learning methods.MethodsIn total, 5757 CAD patients receiving coronary revascularization admitted to ICU in Medical Information Mart for Intensive Care IV (MIMIC-IV) were included in this cohort study. All the data were randomly split into the training set (n = 4029) and testing set (n = 1728) at 7:3. Pearson correlation analysis and least absolute shrinkage and selection operator (LASSO) regression model were applied for feature screening. Variables with Pearson correlation coefficientResultsThe Catboost model presented the best predictive performance with the AUC of 0.831 (95%CI: 0.811–0.851) in the training set, and 0.760 (95%CI: 0.722–0.798) in the testing set. The AUC of the logistic regression model was 0.789 (95%CI: 0.764–0.814) in the training set and 0.731 (95%CI: 0.686–0.776) in the testing set. The results of Delong test revealed that the predictive value of the Catboost model was significantly higher than the logistic regression model (PConclusionThe Catboost model was the optimal model for predicting the risk of stroke in CAD patients receiving coronary revascularization, which might provide a tool to quickly identify CAD patients who were at high risk of postoperative stroke.</div

Additional file 1 of Fine-scale geographic difference of the endangered Big-headed Turtle (Platysternon megacephalum) fecal microbiota, and comparison with the syntopic Beale’s Eyed Turtle (Sacalia bealei)

Additional file 1: Figure S2. Rarefaction curves of samples for Platysternon. Figure S2. The alpha diversity analysis of Platysternon at three sites. Figure S3. Comparison of bacterial community at the phylum level. (A) Bar plots of community abundance. Taxa with abundances  2%. The phyla significantly different between sites are indicated (**, P  2 are shown. (B) Cladogram of taxa showing significant difference between sites. Red, blue, and green dots represent the core bacterial populations in Sites X, Y, and Z, respectively. Figure S7. The alpha diversity analysis of Platysternon and Sacalia at Site X. Figure S8. The relative abundance of different functional pathways of the gut microbiota. The heat map shows the predicted pathways of KEGG level 1. The value shows the percentage of pathway abundance

Parameter settings for 8 machine learning models.

BackgroundTo construct several prediction models for the risk of stroke in coronary artery disease (CAD) patients receiving coronary revascularization based on machine learning methods.MethodsIn total, 5757 CAD patients receiving coronary revascularization admitted to ICU in Medical Information Mart for Intensive Care IV (MIMIC-IV) were included in this cohort study. All the data were randomly split into the training set (n = 4029) and testing set (n = 1728) at 7:3. Pearson correlation analysis and least absolute shrinkage and selection operator (LASSO) regression model were applied for feature screening. Variables with Pearson correlation coefficientResultsThe Catboost model presented the best predictive performance with the AUC of 0.831 (95%CI: 0.811–0.851) in the training set, and 0.760 (95%CI: 0.722–0.798) in the testing set. The AUC of the logistic regression model was 0.789 (95%CI: 0.764–0.814) in the training set and 0.731 (95%CI: 0.686–0.776) in the testing set. The results of Delong test revealed that the predictive value of the Catboost model was significantly higher than the logistic regression model (PConclusionThe Catboost model was the optimal model for predicting the risk of stroke in CAD patients receiving coronary revascularization, which might provide a tool to quickly identify CAD patients who were at high risk of postoperative stroke.</div

Comparisons of the characteristics of participants with and without postoperative stroke in the training set.

Comparisons of the characteristics of participants with and without postoperative stroke in the training set.</p

Absolut summary plot showing the importance of each feature in the Catboost model.

Absolut summary plot showing the importance of each feature in the Catboost model.</p

The ROC curves of machine learning models in the training set.

The ROC curves of machine learning models in the training set.</p