One of the most significant issues in wireless sensor networks (WSNs) is security, which must be addressed to keep WSNs safe from malicious attacks. An intrusion detection system (IDS) is essential in analyzing network traffic and detecting abnormal events. However, these IDSs suffer from several drawbacks that affect their effectiveness and flexibility in accuracy, so they must overcome these drawbacks to improve the performance of IDS. These drawbacks include difficulties in determining the appropriate dataset, the problem of feature selection, and the issue of the imbalanced dataset and choosing the appropriate algorithms for the classification process in WSN. In this paper, a model for an anomaly‐based IDS in WSNs is proposed. This model applied mutual information (MI) for feature selection and the synthetic minority oversampling technique (SMOTE) for solving the imbalanced dataset problem. It used different machine learning (ML) algorithms, random forest (RF), decision tree (DT), support vector machine (SVM), and K‐nearest neighbors (KNNs) to analyze network traffic and binary classification or multiclass classification. To implement and evaluate the performance of the proposed model, the standard dataset NSL‐KDD is used. Python language is used to implement the proposed model in the Anaconda platform, and many evaluation metrics are also utilized to evaluate the performance of the proposed method. Experimental results show that the proposed model can detect intrusions using different ML algorithms with high accuracy. The results of the proposed model for different ML algorithms outperform the state‐of‐the‐art algorithms, and the maximum enhancement reached 15% in the accuracy metric.

Topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph, it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. In the other side, titania nanotube is a well-known semiconductor and has numerous technological applications such as biomedical devices, dye-sensitized solar cells, and etc. In this paper, the second Hyper-Zagreb index and their coindex of Titania nanotubes have been computed. Furthermore, strong correlation coefficients between second Hyper-Zagreb index and some physicochemical properties such as Density (DENS), Molar volume (MV), Acentric factor (Acenfac) and Entropy (S) have been Appeared.

Cheminformatics is a modern field of chemistry information science and mathematics that is very much helpful in keeping the data and getting information about chemicals. A new two-dimensional carbon known as diphenylene was identified and synthesized. It is considered one of the materials that have many applications in most fields such as catalysis. The number of spanning trees of a graph G, also known as the complexity of a graph G, denoted by τ(G), is an important, well-studied quantity in graph theory, and appears in a number of applications. In this paper, we introduce a new chemical compound that is a chain of diphenylene where any two diphenylene intersect by one edge. We derive two formulas for the number of spanning trees in a chain of diphenylene planar graphs that have connected intersection of one edge but where the diphenylenes have same sizes.

This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified $$\left( \frac{G^{'}}{G^2}\right)$$G ′ G 2 -expansion method, $$\left( \frac{1}{G^{'}}\right)$$1 G ′ -expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of $$\beta$$β . In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models.