Ling Qin

Zhijun Zeng, Zhitong Chen, Ling Qin et al.

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization of the Caputo memory term and the nonlocal fractional Laplacian by Monte Carlo simulation of the associated fractional dynamics. Each Picard update is approximated by stochastic label generation and realized through supervised neural-network regression, thereby avoiding residual minimization involving fractional differential operators. The fractional trajectories are generated by coupling a discretized beta-stable subordinator with a walk-on-spheres-type simulation of the rotationally symmetric alpha-stable Lévy process. Numerical experiments on two-dimensional and high-dimensional test problems ddemonstrate stable Picard convergence and accurate approximation, with tests reported up to dimension d=100.

Shunyu An, Miao Wang, Yongchao Li et al.

This paper proposes Co-TAP (T: Triple, A: Agent, P: Protocol), a three-layer agent interaction protocol designed to address the challenges faced by multi-agent systems across the three core dimensions of Interoperability, Interaction and Collaboration, and Knowledge Sharing. We have designed and proposed a layered solution composed of three core protocols: the Human-Agent Interaction Protocol (HAI), the Unified Agent Protocol (UAP), and the Memory-Extraction-Knowledge Protocol (MEK). HAI focuses on the interaction layer, standardizing the flow of information between users, interfaces, and agents by defining a standardized, event-driven communication paradigm. This ensures the real-time performance, reliability, and synergy of interactions. As the core of the infrastructure layer, UAP is designed to break down communication barriers among heterogeneous agents through unified service discovery and protocol conversion mechanisms, thereby enabling seamless interconnection and interoperability of the underlying network. MEK, in turn, operates at the cognitive layer. By establishing a standardized ''Memory (M) - Extraction (E) - Knowledge (K)'' cognitive chain, it empowers agents with the ability to learn from individual experiences and form shareable knowledge, thereby laying the foundation for the realization of true collective intelligence. We believe this protocol framework will provide a solid engineering foundation and theoretical guidance for building the next generation of efficient, scalable, and intelligent multi-agent applications.