In a limestone quarry mine, fragmentation is a crucial outcome of blasting operations. The optimization of blasting operations greatly benefits from the prediction of rock fragmentation. The main factors that affect fragmentation are rock mass characteristics, blast geometry, and explosive properties. This paper is a step towards the implementation of machine learning and deep learning algorithms for predicting the extent of fragmentation (in percentage) in opencast mining. Various parameters can affect fragmentation. But, in this paper initially, ten parameters (spacing, drill hole diameter, burden, average bench height, powder factor, number of holes, charge per delay, uniaxial compressive strength, specific drilling, and stemming) are collected to train the model. However, due to a weak correlation with rock fragmentation, drill diameter, Average bench height, compressive strength, stemming, and charge per delay are eliminated to reduce model complexity. A total of 219 data sets having five input features i.e., the number of holes, spacing, burden, specific drilling, and powder factor are used to develop the models. To predict rock fragmentation due to blasting in limestone quarry mines, both machine learning models (Random Forest Regression (Bagging), Support Vector Regression, and XG Boost Regression (Boosting)), as well as a deep learning model (Neural Network Regression), are applied to develop a model that can optimize the prediction of fragmentation. The Artificial neural network model optimization showed that the model with architecture 64-32-16-1 can perform well giving MSE (mean squared error) values of 41.32 and 28.59 on training and test data respectively. The R2 value for both training and test is 0.83. Random Forest regression is also performing well compared to SVR and XG boost with the MSE value 12.37 and 9.89 on training and testing data respectively. Here, the R2 value for both sets are 94%. Based on the permutation importance and Shapely plot values, the powder factor has the highest impact, and the burden has the lowest impact on fragmentation.

One of the most significant developments in the sports world over the last two decades has been the use of mathematical methods in conjunction with the massive amounts of data now available to analyze performances, identify trends and patterns, and forecast results. Football analytics has advanced significantly in recent years and continues to evolve as it becomes a more recognized and integral part of the game. Football analytics is also used to forecast game outcomes, allowing bettors to make educated guesses. This article describes mathematical concepts related to football analytics that enable a better betting strategies. We explain how the pitch is partitioned into different zones and we define possession sequences. Furthermore, we explain what an expected goals model is and which expected goals model we use in this research. Furthermore, we define two general characteristics of a player evaluation method, each corresponding to one of the equations of the Dawson model. Based on these characteristics, we describe the developments of several general approaches for evaluating players in the context of the Dawson model.