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As the era of sixth-generation (6G) communications approaches, there will be an unprecedented increase in the number of wireless internet-connected devices and a sharp rise in mobile data traffic. Faced with the scarcity of spectrum resources in traditional communication networks and challenges such as rapidly establishing communications after disasters, this study leverages unmanned aerial vehicles (UAVs) to promote an integrated multi-hop communication system combining free-space optical (FSO) communication, terahertz (THz) technology, and intelligent reflecting surface (IRS). This innovative amalgamation capitalizes on the flexibility of UAVs, the deployability of IRS, and the complementary strengths of FSO and THz communications. We have developed a comprehensive channel model that includes the effects of atmospheric turbulence, attenuation, pointing errors, and angle-of-arrival (AOA) fluctuations. Furthermore, we have derived probability density functions (PDFs) and cumulative distribution functions (CDFs) for various switching techniques. Employing advanced methods such as Gaussian–Laguerre quadrature and the central limit theorem (CLT), we have calculated key performance indicators including the average outage probability, bit error rate (BER), and channel capacity. The numerical results demonstrate that IRS significantly enhances the performance of the UAV-based hybrid FSO/THz system. The research indicates that optimizing the number of IRS elements can substantially increase throughput and reliability while minimizing switching costs. Additionally, the multi-hop approach specifically addresses the line-of-sight (LoS) dependency limitations inherent in FSO and THz systems by utilizing UAVs as dynamic relay points. This strategy effectively bridges longer distances, overcoming physical and atmospheric obstacles, and ensures stable communication links even under adverse conditions. This study underscores that the enhanced multi-hop FSO/THz link is highly effective for emergency communications after disasters, addressing the challenge of scarce spectrum resources. By strategically deploying UAVs as relay points in a multi-hop configuration, the system achieves greater flexibility and resilience, making it highly suitable for critical communication scenarios where traditional networks might fail. [ABSTRACT FROM AUTHOR]

In this article, we mainly studied the Gel'fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel'fand (N , δ) -widths of multivariate Sobolev space M W 2 r (T d) with mixed derivative equipped with the Gaussian measure in the S q -norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel'fand N-widths of univariate Sobolev space W 2 r (T) and multivariate Sobolev space M W 2 r (T d) with mixed derivative equipped with the Gaussian measure in the S q -norm. [ABSTRACT FROM AUTHOR]

Detecting road cracks is essential for inspecting and assessing the integrity of concrete pavement structures. Traditional image-based methods often require complex preprocessing to extract crack features, making them challenging when dealing with noisy concrete surfaces in diverse real-world scenarios, such as autonomous vehicle road detection. This study introduces an image-based crack detection approach that combines a Random Forest machine learning classifier with a deep convolutional neural network (CNN) to address these challenges. Three state-of-the-art models, namely MobileNet, InceptionV3, and Xception, were employed and trained using a dataset of 30,000 images to build an effective CNN. A systematic comparison of validation accuracy across various base learning rates identified a base learning rate of 0.001 as optimal, achieving a maximum validation accuracy of 99.97%. This optimal learning rate was then applied in the subsequent testing phase. The robustness and flexibility of the trained models were evaluated using 6,000 test photos, each with a resolution of 224 × 224 pixels, which were not part of the training or validation sets. The outstanding results, boasting a remarkable 99.95% accuracy, 99.95% precision, 99.94% recall, and a matching 99.94% F1 Score, unequivocally affirm the efficacy of the proposed technique in precisely identifying road fractures in photographs taken on real concrete surfaces. [ABSTRACT FROM AUTHOR]