In this paper, we consider the Bayesian estimation of the parameters and reliability function for a Cosine inverse log compound Rayleigh distribution under squared error and squared logarithmic loss functions. We use Lindley’s approximation to compute the Bayesian estimates. This method is evaluated using mean square error through simulation study with varying sample size.

The healthcare system in Libya faces significant challenges due to political instability, fragmented infrastructure, and inconsistent medical practices. Clinical Practice Guidelines (CPGs) serve as essential tools for standardising care, ensuring evidence- based treatment, and optimising healthcare resources. In Libya, the lack of structured guidelines has contributed to disparities in disease management, affecting patient outcomes and overall healthcare efficiency. This commentary explores the critical need for CPGs in Libya, highlighting their potential to improve healthcare delivery, minimise variability in treatment, and enhance patient safety. While implementation poses challenges, including centralisation, limited research capacity, and resource constraints, integrating CPGs through a phased implementation framework could be a transformative step toward a more resilient and equitable healthcare system. By fostering collaboration among policymakers, healthcare professionals, and international organisations, Libya can lay the foundation for a systematic approach to disease management, ultimately improving the quality of care for its population. Healthcare reform in Libya is urgently needed, and strategic investments in CPG development and dissemination could drive the necessary transformation in Libyan healthcare.

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.

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 ).

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.