In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

In the last decade, ground-level ozone exposure has led to a significant increase in environmental and health risks. Thus, it is essential to measure and monitor atmospheric ozone concentration levels. Specifically, recent improvements in machine learning (ML) processes, based on statistical modeling, have provided a better approach to solving these risks. In this study, we compare Naive Bayes, K-Nearest Neighbors, Decision Tree, Stochastic Gradient Descent, and Extreme Gradient Boosting (XGBoost) algorithms and their ensemble technique to classify ground-level ozone concentration in the El Paso-Juarez area. As El Paso-Juarez is a non-attainment city, the concentrations of several air pollutants and meteorological parameters were analyzed. We found that the ensemble (soft voting classifier) of algorithms used in this paper provide high classification accuracy (94.55%) for the ozone dataset. Furthermore, variables that are highly responsible for the high ozone concentration such as Nitrogen Oxide (NOx), Wind Speed and Gust, and Solar radiation have been discovered.

In this work, an analytic approach for solving higher order ordinary differential equations (ODEs) is developed. The techniques offer analytic flexibility in many research areas such as physics, engineering, and applied sciences and are effective for solving complex ODEs.