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Study of equivalence classes of links up to n-moves plays an important role in the theory of invariants based on the skein relation and, in particular, skein modules. In this paper, we consider Nakanishi's 4-move conjecture [12]. The modification of the conjecture to 2-component link (homotopically trivial links) is a question proposed by Kawauchi [10]. We define a new invariant of links which is preserved by 4-moves and analyze its potential strength. In particular, we show that our invariant allows us to obtain results of [8, 9, 13] concerning 4-moves.

We study equivalence classes of knots and links of 2 components modulo 4-move. We show that all knots up to 12 crossings and knots in the family 6* reduce by 4-moves to the trivial knot. We also prove that links of 2 components with 11 crossings, and links 6* a1.a2.a3.a4.a5.a6 such that ai is a 2-algebraic tangle with no trivial components reduce to either the trivial link or to the Hopf link. For alternating links of 2-components with 12 we show that L reduces by 4-moves to either trivial link or to the Hopf link whenever L is different than 9*.2 : .2 : .2 (or its mirror image). We suggest the alternating link 9*.2 : .2 : .2 with 12 crossings as a potential example to answer the Problem 1.1(iii) in negative.

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.