Arif Gursoy

In this study, we present a comparative analysis of gradient descent-based optimizers frequently used in Convolutional Neural Networks (CNNs), including SGD, mSGD, RMSprop, Adadelta, Nadam, Adamax, Adam, and the recent EVE optimizer. To explore the interaction between optimization strategies and activation functions, we systematically evaluate all combinations of these optimizers with four activation functions—ReLU, LeakyReLU, Tanh, and GELU—across three benchmark image classification datasets: CIFAR-10, Fashion-MNIST (F-MNIST), and Labeled Faces in the Wild (LFW). Each configuration was assessed using multiple evaluation metrics, including accuracy, precision, recall, F1-score, mean absolute error (MAE), and mean squared error (MSE). All experiments were performed using k-fold cross-validation to ensure statistical robustness. Additionally, two-way ANOVA was employed to validate the significance of differences across optimizer–activation combinations. This study aims to highlight the importance of jointly selecting optimizers and activation functions to enhance training dynamics and generalization in CNNs. We also consider the role of critical hyperparameters, such as learning rate and regularization methods, in influencing optimization stability. This work provides valuable insights into the optimizer–activation interplay and offers practical guidance for improving architectural and hyperparameter configurations in CNN-based deep learning models.

In this study, we introduce the Sheffer stroke L-algebra and prove some fundamental theorems, propositions and lemmas of Sheffer Stroke L-algebras. The notions of filter and ultrafilter for Sheffer stroke L-algebra are studied. We give subalgebra and normal subset definitions of a Sheffer stroke L-algebras. Moreover, a homomorphism between Sheffer stroke L-algebras is introduced and isomorphism theorems are presented. Finally, we give three new algorithms for Sheffer stroke L-algebras. Thus, it is contributed to researchers on different application areas by presenting an algorithmic approach on this subject, for the first time in the literature.

In this paper, we investigate the Sombor index of the zero-divisor graph of ℤ _n which is denoted by Γ(ℤ _n ) for n ∈ { p ^α , pq, p ² q, pqr } where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Γ(ℤ _n ). Finally, we give Sombor index of product of rings of integers modulo n .

The idea that data lies in a non-linear space has brought up the concept of manifold learning as a part of machine learning and such notion is one of the most important research fields of today. The main idea here is to design the data as a submanifold model embedded in a high-dimensional manifold. On the other hand, graph theory is one of the most important research areas of applied mathematics and computer science. As a result, many researchers investigate new methods for machine learning on graphs. From the above information, it is seen that the theory of submanifolds and graph theory have become two important concepts in machine learning and nowadays, the geometric deep learning research area using these two concepts has emerged. By combining these two fields, this article aims to present the relationships between submanifolds of complex manifolds with the help of graphs. In this paper, we build some directed networks by identifying with submanifolds of almost Hermitian manifolds. Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.

The idea that data lies on a non-linear space has brought up the concept of manifold learning as a part of machine learning.

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formalism comprise synchronically bilateral and trilateral diagrammatical appearance and a naive algorithmic nature. And also, there is no need specific knowledge or exclusive ability to understand as well as to use it. Consequently, we give an effective algorithm used to determine whether a syllogistic reasoning valid or not by using SLCD.