The aim of this study is to evaluate students’ achievements in mathematics using three machine learning regression methods: classification and regression trees (CART), CART ensembles and bagging (CART-EB) and multivariate adaptive regression splines (MARS). A novel ensemble methodology is proposed based on the combination of CART and CART-EB models in a new ensemble to regress the actual data using MARS. Results of a final exam test, control and home assignments, and other learning activities to assess students’ knowledge and competencies in applied mathematics are examined. The exam test combines problems on elements of mathematical analysis, statistics and a small practical project. The project is the new competence-oriented element, which requires students to formulate problems themselves, to choose different solutions and to use or not use specialized software. Initially, empirical data are statistically modeled using six CART and six CART-EB competing models. The models achieve a goodness-of-fit up to 96% to actual data. The impact of the examined factors on the students’ success at the final exam is determined. Using the best of these models and proposed novel ensemble procedure, final MARS models are built that outperform the other models for predicting the achievements of students in applied mathematics.

In animal husbandry, it is of great interest to determine and control the key factors that affect the production characteristics of animals, such as milk yield. In this study, simplified selective tree-based ensembles were used for modeling and forecasting the 305-day average milk yield of Holstein-Friesian cows, depending on 12 external traits and the farm as an environmental factor. The preprocessing of the initial independent variables included their transformation into rotated principal components. The resulting dataset was divided into learning (75%) and holdout test (25%) subsamples. Initially, three diverse base models were generated using Classifiction and Regression Trees (CART) ensembles and bagging and arcing algorithms. These models were processed using the developed simplified selective algorithm based on the index of agreement. An average reduction of 30% in the number of trees of selective ensembles was obtained. Finally, by separately stacking the predictions from the non-selective and selective base models, two linear hybrid models were built. The hybrid model of the selective ensembles showed a 13.6% reduction in the test set prediction error compared to the hybrid model of the non-selective ensembles. The identified key factors determining milk yield include the farm, udder width, chest width, and stature of the animals. The proposed approach can be applied to improve the management of dairy farms.

In this study, a novel general multi-step ahead strategy is developed for forecasting time series of air pollutants. The values of the predictors at future moments are gathered from official weather forecast sites as independent ex-ante data. They are updated with new forecasted values every day. Each new sample is used to build- a separate single model that simultaneously predicts future pollution levels. The sought forecasts were estimated by averaging the actual predictions of the single models. The strategy was applied to three pollutants—PM₁₀, SO₂, and NO₂—in the city of Pernik, Bulgaria. Random forest (RF) and arcing (Arc-x4) machine learning algorithms were applied to the modeling. Although there are many highly changing day-to-day predictors, the proposed averaging strategy shows a promising alternative to single models. In most cases, the root mean squared errors (RMSE) of the averaging models (aRF and aAR) for the last 10 horizons are lower than those of the single models. In particular, for PM₁₀, the aRF’s RMSE is 13.1 vs. 13.8 micrograms per cubic meter for the single model; for the NO₂ model, the aRF exhibits 21.5 vs. 23.8; for SO_2, the aAR has 17.3 vs. 17.4; for NO₂, the aAR’s RMSE is 22.7 vs. 27.5, respectively. Fractional bias is within the same limits of (−0.65, 0.7) for all constructed models.

Many anticancer drugs cannot recognize selectively tumor tissues, and cause destruction to normal ones. Although it is very toxic, cisplatin is still one of the most applied chemotherapeutics used for treatment of sarcomas, carcinomas, etc. It causes severe side effects as a result of the lack of selectivity of the drug to tumor tissue and acquired or intrinsic resistance occurs. Wheat germ agglutinin (WGA) is a lectin that specifically recognizes transformed cells: prostate cancer cells, pancreatic cells etc., and is uptaken into the tumor cells for which it appears to be a suitable target for anticancer agents. A fluorescence spectroscopy method was used to study the interaction of WGA with four metal-based anticancer drugs: cisplatin, Pt porphyrin and two gold porphyrins. The affinity constant (k_D) for binding of cisplatin with WGA was k_D = 6.67 ± 2.5 μM. The hyperbolic curve indicated the presence of a single cisplatin binding site. The affinity of Au and Pt porphyrin to WGA (k_D = 0.08–0.49 μM) is almost two orders of magnitude higher than that for cisplatin. We found that Pt porphyrin could displace fluorescent dye ANS showing an increase in the fluorescence intensity with a concomitant blue shift of the emission maximum suggesting that the compounds accommodate the same binding site. Current research characterizes the metalloanticancer binding capacity of WGA. Our results indicate that four metal-based anticancer agents have high affinity for WGA. Since WGA recognizes transformed cells, the obtained data show that this protein might have putative usage as a drug delivery molecule in cancer.

We show how one can use polynomial techniques to compute all possible distance distributions of binary orthogonal arrays (OAs) of relatively small lengths and strengths. Then we exploit certain connections between OAs and their derived OAs. Having all distance distributions of OAs under consideration, we are able to test them aimed at classification results.