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Yingmo Zhang

Publications and source records attributed to Yingmo Zhang.

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Well--posedness for the continuum Calogero--Moser equations by parabolic regularization

We prove that the focusing and defocusing continuum Calogero--Moser equations are globally well-posed in $H^s_+(\mathbb R)$ for every integer $s\geq 3$. In the focusing case, this requires the initial data to satisfy the mass condition $$\|q_0\|_{L^2}^2<2\pi.$$ Our proof is based on a parabolic regularization of the equation, uniform \textit{a--priori} estimates for the regularized solutions, and a Bona--Smith type approximation argument.

math.AP

Scattering for the quintic generalized Benjamin-Bona-Mahony equation

We consider the quintic generalized Benjamin-Bona-Mahony equation $$ u_t-u_{xxt} + \partial_x\big(u + u^{5}\big)= 0,\qquad (t,x)\in \mathbb{R}_+ \times \mathbb{R}. $$ Using the space-time resonance method, we prove that sufficiently small and smooth solutions scatter to the linear flow. While the higher nonlinearity simplifies the treatment of nonresonant interactions compared to the quartic model in \cite{Morgan}, resonance analysis is more intricate. The resonance analysis occurs in a higher-dimensional geometric setting, and certain null or vanishing conditions present in the quartic case fail at specific resonance points. As a result, refined computations and precise estimates near the resonant set are required to close the bootstrap argument.

math.AP

SAFEFLOW: A Principled Protocol for Trustworthy and Transactional Autonomous Agent Systems

Recent advances in large language models (LLMs) and vision-language models (VLMs) have enabled powerful autonomous agents capable of complex reasoning and multi-modal tool use. Despite their growing capabilities, today's agent frameworks remain fragile, lacking principled mechanisms for secure information flow, reliability, and multi-agent coordination. In this work, we introduce SAFEFLOW, a new protocol-level framework for building trustworthy LLM/VLM-based agents. SAFEFLOW enforces fine-grained information flow control (IFC), precisely tracking provenance, integrity, and confidentiality of all the data exchanged between agents, tools, users, and environments. By constraining LLM reasoning to respect these security labels, SAFEFLOW prevents untrusted or adversarial inputs from contaminating high-integrity decisions. To ensure robustness in concurrent multi-agent settings, SAFEFLOW introduces transactional execution, conflict resolution, and secure scheduling over shared state, preserving global consistency across agents. We further introduce mechanisms, including write-ahead logging, rollback, and secure caches, that further enhance resilience against runtime errors and policy violations. To validate the performances, we built SAFEFLOWBENCH, a comprehensive benchmark suite designed to evaluate agent reliability under adversarial, noisy, and concurrent operational conditions. Extensive experiments demonstrate that agents built with SAFEFLOW maintain impressive task performance and security guarantees even in hostile environments, substantially outperforming state-of-the-art. Together, SAFEFLOW and SAFEFLOWBENCH lay the groundwork for principled, robust, and secure agent ecosystems, advancing the frontier of reliable autonomy.

cs.AI