In this paper, a new continuous probability distribution has been proposed. The proposed distribution is considered as one of the extended distributions of Rayleigh distribution, which is well known in probability Theory and its applications. The distribution under consideration is titled "Exponential Log-compound Rayleigh distribution". proposed. The statistical properties of distribution parameters estimating using Maximum likelihood technique and Fisher information matrix are investigated theoretically. The evaluating of distribution performance is demonstrated on both simulated data and real data. Based on the values of bias, MSE and Fisher information matrix of the parameters estimates, the proposed distribution is considered to be working well.

Early and precise diagnosis of brain tumors is essential for successful treatment planning and improved patient outcomes. This paper introduces a novel hybrid deep model that incorporates DenseNet121, a convolutional neural network (CNN), and the Swin Transformer, a vision transformer model, by feature-level fusion to classify brain tumors from magnetic resonance imaging (MRI) scans. The suggested method provides a more discriminative and better representation by uniting the global context capability of the Transformer model with the local feature extraction capability of the CNN model. The suggested method was trained and assessed on a publicly available brain MRI dataset of four classes: glioma, meningioma, pituitary tumor, and no tumor. Experimental results indicate that the proposed approach outperforms many baseline models including VGG16, MobileNetV2, and AlexNet with an accuracy of 99.39%, precision of 99.36%, recall of 99.34%, and F1-score of 99.35%. Grad-CAM was utilized to visualize class-discriminative regions in the MRI scans to enhance interpretability, hence validating the model's emphasis on tumor-relevant regions. These outcomes prove the efficacy of coupling Transformer and CNN architectures in obtaining accurate and interpretable brain tumor classification from MRI scans.

 Fuzzy Neural Networks (FNNs) enhance conventional Artificial Neural Networks (ANNs) by incorporating fuzzy membership functions, which enable the handling of uncertainty, ambiguity, and imprecise information. While Fuzzy Backpropagation Neural Networks (FBNNs) improve classification performance across noisy datasets, the effectiveness of fuzzification heavily depends on the proper tuning of membership function parameters—typically optimized manually. This paper presents a novel Artificial Immune System framework for optimizing Fuzzy Backpropagation Neural Networks used in the classification of biological image data. The approach integrates a fuzzy min–max fuzzification layer with a feed-forward backpropagation network and applies an optimization version of an Artificial Immune Network model, derived from opt-aiNet, to tune trapezoidal membership functions. Experimental results confirm that the proposed immune-driven optimization is an effective technique for enhancing FBNN robustness and generalization.

The aim of this paper is to represent a bitopological representation (𝑉,𝜏𝑆1,𝜏𝑆2) of divisor graph 𝐺=(𝑉,𝐸) defining in a finite commutative rings in which every vertex 𝑣 is adjacent with a vertex 𝑢 if and only if 𝑔.𝑐.𝑑(𝑢,𝑣)=1. Then some properties of this bitopological space were investigated.

This paper introduces a finite topological space 𝜏𝑝 on the group of units modulo a prime 𝑝, defined by its basis of conjugate residue pairs {𝛼, 𝑝 − 𝛼} for all units 𝛼 ∈ 𝑈𝑝. We investigate the fundamental topological concepts such as point-set topology, separation axioms, and characterise the structure and behaviour of this topology. Additionally, we examine a function 𝑓 from 𝜏𝑝 to the topology of quadratic residues 𝜏𝑄, mapping each unit to its square modulo 𝑝. We analyse the continuity, openness of 𝑓, and explore its implications for separation properties. Furthermore, we define a quotient topology on 𝑈𝑝 based on the equivalence relation 𝑥 ∼ 𝑦 if and only if 𝑥2 ≡ 𝑦2 𝑚𝑜𝑑 𝑝, showing that the resulting quotient space is homeomorphic to (𝑄𝑝 , 𝜏𝑄 ).

Abstract— Crime prediction has gained increasing attention due to the growing availability of historical crime data and the need for data-driven decision-making in public safety. This study presents a comparative analysis of Long Short-Term Memory (LSTM) architectures for predicting the exact occurrence time of crimes based on temporal patterns. Three LSTM-based models are evaluated: Vanilla LSTM, Stacked LSTM, and Bidirectional LSTM.

The proposed approach integrates time-based features and lag features to capture temporal dependencies within crime data. Model performance is assessed using standard regression metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). Experimental results indicate that deeper LSTM architectures combined with temporal lag information improve prediction accuracy compared to the baseline model.

This study demonstrates the effectiveness of LSTM-based models for crime occurrence prediction and provides insights into selecting suitable deep learning architectures for time-series crime analysis, supporting the development of more reliable tools for proactive crime prevention.