Kun Wang

Kun Wang, Jizu Huang

In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of $u'(t)$ with the kernel $(t_n-t)^{-α}$. In the fast algorithm, the interval $[0,t_{n-1}]$ is split into nonuniform subintervals. The number of the subintervals is in the order of $\log n$ at the $n$-th time step. The fractional kernel function is approximated by a polynomial function of $K$-th degree with a uniform absolute error on each subinterval. We save $K+1$ integrals on each subinterval, which can be written as a convolution of $u'(t)$ with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from $O(n)$ to $O((K+1)\log n)$ at the $n$-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples.

Zhenhong Zhou, Zherui Li, Jie Zhang et al.

Large Language Model-based Multi-Agent Systems (LLM-MASs) have demonstrated remarkable real-world capabilities, effectively collaborating to complete complex tasks. While these systems are designed with safety mechanisms, such as rejecting harmful instructions through alignment, their security remains largely unexplored. This gap leaves LLM-MASs vulnerable to targeted disruptions. In this paper, we introduce Contagious Recursive Blocking Attacks (Corba), a novel and simple yet highly effective attack that disrupts interactions between agents within an LLM-MAS. Corba leverages two key properties: its contagious nature allows it to propagate across arbitrary network topologies, while its recursive property enables sustained depletion of computational resources. Notably, these blocking attacks often involve seemingly benign instructions, making them particularly challenging to mitigate using conventional alignment methods. We evaluate Corba on two widely-used LLM-MASs, namely, AutoGen and Camel across various topologies and commercial models. Additionally, we conduct more extensive experiments in open-ended interactive LLM-MASs, demonstrating the effectiveness of Corba in complex topology structures and open-source models. Our code is available at: https://github.com/zhrli324/Corba.

Sibo Cheng, Marc Bocquet, Weiping Ding et al.

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field.