The cohomology rings of real permutohedral varieties

We establish explicit descriptions of the cohomology ring of real permutohedral varieties. In particular, the multiplicative structure is given in terms of alternating permutations

THE BETTI NUMBERS OF REAL TORIC VARIETIES ASSOCIATED TO WEYL CHAMBERS OF TYPES E7 AND E8

We compute the rational Betti numbers of the real toric varieties associated to Weyl Chambers of types E7 and E8, completing the computations for all types of root systems

Prediction and Interpretation of Water Quality Recovery after a Disturbance in a Water Treatment System Using Artificial Intelligence

In this study, an ensemble machine learning model was developed to predict the recovery rate of water quality in a water treatment plant after a disturbance. XGBoost, one of the most popular ensemble machine learning models, was used as the main framework of the model. Water quality and operational data observed in a pilot plant were used to train and test the model. Disturbance was determined when the observed turbidity was higher than the given turbidity criteria. Therefore, the recovery rate of water quality at a time t was defined during the falling limb of the turbidity recovery period. It was considered as a relative ratio of the differences between the peak and observed turbidities at time t to the difference between the peak turbidity and turbidity criteria. The root mean square error–observation standard deviation ratio of the XGBoost model improved from 0.730 to 0.373 by pretreatment, removing the observation for the rising limb of the disturbance from the training data. Moreover, Shapley value analysis, a novel explainable artificial intelligence method, was used to provide a reasonable interpretation of the model’s performance