The recent advancements across multiple research areas have collectively pushed the boundaries of what is possible in various technological applications, from language processing and neural networks to privacy-preserving machine learning and synthetic biology. In sentiment analysis and code-mixed language processing, large language models (LLMs) are being innovatively leveraged for tasks such as sarcasm detection and translation of code-mixed texts, addressing the complexities introduced by code-mixing. Notably, the development of specialized corpora and methodologies, along with the integration of LLMs through prompting strategies, has shown promising results in classifying sarcasm and sentiment polarity in code-mixed contexts. Additionally, advancements in neural networks and multimedia processing have explored alternative network architectures for positional encoding and optimized video and image compression techniques, particularly in the context of neural radiance fields (NeRF) and volumetric video. These innovations enhance high-frequency reconstruction and reduce storage requirements while maintaining high fidelity in the reconstructed content. In the realm of language model watermarking and model security, robust watermarking techniques are being developed to withstand paraphrasing attacks and semantic perturbations, enhancing the security of proprietary models and contributing to ethical and legal compliance. Federated learning (FL) and differential privacy (DP) have seen significant progress in addressing data heterogeneity, computational efficiency, and fairness, with innovations like low-rank adaptation (LoRA) integration and novel frameworks such as Wasserstein Fair Federated Learning (WassFFed) and EPIC. These developments underscore the shift towards more decentralized and privacy-aware optimization frameworks. Synthetic biology and related fields are leveraging advanced mathematical tools like differential geometry and port-Hamiltonian neural networks to analyze and optimize complex biological and energy systems, enhancing system stability, efficiency, and resilience. Perception and tracking algorithms are advancing robotics, augmented reality, and IoT systems through novel querying languages and frameworks for multi-modal dynamic environments, improving pattern matching and runtime monitoring. Lastly, satellite-based AI and IoT security are integrating blockchain technology and federated learning to enhance security and efficiency in satellite communications, addressing the unique challenges posed by LEO satellite networks and resource-constrained IoT devices.