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In the rapidly-evolving landscape of software development, the detection of vulnerabilities in source code has become paramount. Our study introduces a novel knowledge distillation (KD) technique aimed at enhancing vulnerability detection in software codebases. Using benchmark datasets such as SARD, SeVC, Devign, and D2A, we assess the prowess of the KD method when applied to different classifiers, specifically GPT2, CodeBERT, and LSTM. The empirical results revealed a marked improvement in the performance of these classifiers upon the implementation of the KD technique, particularly with the GPT-2 model demonstrating the most promising outcomes. This work underscores the potential of integrating transformer-based learning models, like GPT-2, with knowledge distillation for more efficient and accurate vulnerability detection.

We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method’s precision and effectiveness rely on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions.

The generalized fractional calculus operators introduced by Saigo and Maeda in 1996 will be examined and further explored in this paper. By combining an incomplete ℵ-function with a broad category of polynomials, we create generalized fractional calculus formulations. The findings are presented in a concise manner that are helpful in creating certain lists of fractional calculus operators. The derived outcomes are of a generic nature, may yield results in the form of various special functions and in the form of different polynomials as special instances of the primary findings.

This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. It is proved by using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequality that the hybrid finite difference scheme is almost second order accurate in the discrete maximum norm. Numerical experiments support these theoretical results and indicate that the estimates are sharp.

Dried grapes (or Raisins) are among the most frequently grown and consumed cereal crops worldwide. They are also an important source of nutrition and nourishment in a variety of countries including Türkiye, United States, Greece, etc. In addition to that raisins consist of 15% water, 79% carbs (including 4% fiber), 3% protein, and very little fat. In our study, there were a total of 900 raisin grains used, with 450 pieces from each type: Kecimen and Besni raisin. Seven morphological features were taken from these images after they went through several steps of pre-processing. Since machine learning algorithms can analyze large datasets quickly, automatic classification is made possible. With enough training and testing, machine learning models can attain a high degree of precision in classifying raisin grains. They are able to detect variations in size, shape, color, and texture that would be difficult for humans to detect consistently. Eleven machine learning and five different types of artificial intelligence have been used to classify these features. As part of this study, we look into different machine learning and deep learning methods: GaussianNB, Decision Tree, K-Nearest Neighbor, Random Forest, Support vector machine (SVM), XGBoost, LightGBM, and AdaBoost, Logistic Regression, Artificial Neural Network and Deep Learning Network. Study efficacy is evaluated using standard metrics like F1 score and ROC area under the curve (AUC). Using the caret, H2O, neuralnet, and keras packages, AdaBoost and LightGBM, two of the fourteen models, achieve an accuracy of 90.30% and 98.40%, respectively, and a ROC curve score of around 90%.

In this study, we obtain a sex prediction algorithm based on CNN in two ways - building a red Convolutional Neural Network (CNN) model from scratch and transfer learning. We built a model from scratch and compared it with fine-tuned EfficientNetB1. We use these models for gender determination using periocular images and compare the two models depending on the accuracy of the models. The CNN model proposed from scratch yields an accuracy of 94.46% while the fine-tuned EfficientNetB1 yields an accuracy of 97.94%. This paper is one of the first works in determining gender from periocular images in the visible spectrum using a CNN model built from scratch.

Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This set of equations includes the one-dimensional (1D) Oskolkov equation, the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation, the generalized hyperelastic rod wave (HERW) equation, and the Oskolkov Benjamin Bona Mahony Burgers (OBBMB) equation. We employ the new extended direct algebraic (NEDA) method to tackle these equations. The NEDA method serves as a powerful tool for our analysis, enabling us to obtain solutions grounded in various mathematical functions, such as hyperbolic, trigonometric, rational, exponential, and polynomial functions. As we delve into the physical implications of these solutions, we uncover complex structures with well-known characteristics. These include entities like dark, bright, singular, combined dark-bright solitons, dark-singular-combined solitons, solitary wave solutions, and others. It is worth highlighting that the solutions we unveil in this study are original and haven’t been documented in existing literature.

This study presents the problem of spreading a disease that is not fatal in a population by using the Morgan-voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modeled with a nonlinear system of ordinary differential equations, mathematically. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficients Morgan-Voyce polynomials and expanding approximate solutions. The Morgan-Voyce Polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operations derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to Homotopy perturbation method (HPM) and Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to the literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic.

The aim of this study is to forecast the revenue of a seller taking part in an online e-commerce marketplace by using hybrid intelligent methods to help the seller build a solid financial plan. For this purpose, three different approaches are applied in order to forecast the revenue, accurately. In the first approach, after applying simple preprocessing steps on the dataset, forecast models are developed with Random Forest (RF). In the second approach, Isolation Forest (IF) is used to detect outliers on the dataset, and minimum Redundancy Maximum Relevance (mRMR) is utilized to select the features correctly that affect the quality of revenue forecast. In the last approach, feature selection process is performed first and then the Density-Based Spatial Clustering and Application with Noise (DBSCAN) is used to cluster the dataset. After these processes are carried out, forecast models are developed with RF. The dataset used includes the daily revenue of a seller with several other features. Mean Absolute Percent Error (MAPE) is used for evaluating the performance of the forecast models. These results show that the average MAPE of the third approach is 17.40% lower than that of the first approach, and 10.15% lower than that of the second approach.

This work studies on the first equation of the Kadomtsev-Petviashvili (KP) hierarchy. The sine-Gordon expansion method (SGEM) and the rational SGEM (RSGEM) are applied to the governing model. RSGEM is the developed version of SGEM. New complex travelling wave solutions, logarithmic and complex function properties are obtained. Several simulations such as 2D, 3D and contour surfaces of the obtained results are plotted. Physical meanings of these solutions are also reported. Strain conditions are also extracted.