Wensheng Tang

Wensheng Tang, Jingjing Zhang

We develop continuous-stage Runge-Kutta-Nyström (csRKN) methods for solving second order ordinary differential equations (ODEs) in this paper. The second order ODEs are commonly encountered in various fields and some of them can be reduced to the first order ODEs with the form of separable Hamiltonian systems. The symplecticity-preserving numerical algorithm is of interest for solving such special systems. We present a sufficient condition for a csRKN method to be symplecticity-preserving, and by using Legendre polynomial expansion we show a simple way to construct such symplectic RKN type method.

Wensheng Tang, Yajuan Sun, Jingjing Zhang

On the basis of the previous work by Tang \& Zhang (Appl. Math. Comput. 323, 2018, p. 204--219), in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.

Wensheng Tang

We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK) methods, can give us a new perspective on RK discretization and it may enlarge the application of RK approximation theory in modern mathematics and engineering fields. A highlighted advantage of investigation of csRK methods is that we do not need to study the tedious solution of multi-variable nonlinear algebraic equations stemming from order conditions. In this note, we will discuss and promote the recently-developed csRK theory. In particular, we will place emphasis on structure-preserving algorithms including symplectic methods, symmetric methods and energy-preserving methods which play a central role in the field of geometric numerical integration.

Yuandao Cai, Yuzhang Zhu, Liyou Gao et al.

Long-horizon language agents can make many plausible local tool calls yet fail to persist until a requested count is actually complete. We study this gap as Quantitative Goal Persistence (QGP): whether an agent keeps working until an external verifier confirms enough distinct valid items. PushBench turns this into a benchmark for repository-artifact collection and verifier-backed work units, so repeated work, duplicate submissions, false completion, and progress drift are measured directly rather than hidden behind a final success flag. In matched controller comparisons, a state-tracking retrieval controller reaches 69-78% success while eliminating duplicate submissions, and a backlog-tracking work-unit controller reaches 25-50% success in settings where standard and completion-gated controllers complete no task instances. Black-box frontier-agent evaluations with Claude Code (Sonnet 4.6) and Codex CLI (gpt-5.4) solve many 50-artifact tasks but drop to 3 out of 9 successes per condition at 100 artifacts. The results show that quantitative goals stress a different reliability requirement from local task competence: agents must maintain verified progress and stop only when the requested work is complete.

Wensheng Tang

We develop continuous-stage Runge-Kutta-NystrÖm (csRKN) methods in this paper. By leading weight function into the formalism of csRKN methods and modifying the original pattern of continuous-stage methods, we establish a new and larger framework for csRKN methods and it enables us to derive more effective RKN-type methods. Particularly, a variety of classical weighted orthogonal polynomials can be used in the construction of RKN-type methods. As an important application, new families of symmetric and symplectic integrators can be easily acquired in such framework. Numerical experiments have verified the effectiveness of the new integrators presented in this paper.

Yuandao Cai, Shuhao Fu, Wensheng Tang et al.

Concurrency testing is essential to improve the reliability and security of multi-threaded programs. Dynamic analysis tools, such as TSan, depend on high-quality test drivers that reach critical shared-memory interactions at runtime. However, current testing practices predominantly focus on sequential logic, leaving a gap in automated concurrent test generation. Recently, large language models (LLMs) have shown promise in generating sequential tests, but they struggle to produce effective concurrent tests without a deep understanding of concurrency semantics. This paper presents ConCovUp, a multi-agent framework that combines LLMs with program analysis. ConCovUp grounds test generation in static analysis to extract shared memory accesses and their calling contexts. To trigger hard-to-reach accesses, it introduces an LLM-driven backward tracing approach, leveraging the model's semantic reasoning to deduce concrete inputs that satisfy complex path constraints, and iteratively refines the generated tests via dynamic execution feedback. Our evaluation on nine real-world C/C++ libraries shows that ConCovUp improves average Shared Memory Access Pair Coverage (SMAP Coverage) from 36.6% to 68.1% over the general Claude Code agent baseline.

Yuandao Cai, Wensheng Tang, Cheng Wen et al.

Autonomous Large Language Model (LLM) agents are increasingly deployed to conduct complex tasks by interacting with external tools, APIs, and memory stores. However, processing untrusted external data exposes these agents to severe security threats, such as indirect prompt injection and unauthorized tool execution. Securing these systems requires effective information flow tracking. Yet, traditional taint analysis that is designed for program memory states fundamentally fails when applied to LLMs, where data propagation is governed by probabilistic natural language reasoning. In this paper, we present NeuroTaint, the first comprehensive taint tracking framework tailored for the unique information flow characteristics of LLM agents. Our key insight is that taint propagation in LLM agents must be understood not only as explicit content transfer, but also as semantic transformation, causal influence on decisions, and cross-session persistence through memory. NeuroTaint therefore audits execution traces offline to reconstruct provenance from untrusted sources to privileged sinks using semantic evidence, causal reasoning, and persistent context tracking, rather than relying on exact string matches or pre-defined source-sink paths alone. Extensive evaluation using TaintBench, our 400-scenario benchmark spanning 20 real-world agent frameworks, shows that NeuroTaint substantially outperforms FIDES, an information-flow-control (IFC)-style baseline for LLM agents, in source-sink propagation detection. We further show that NeuroTaint remains effective on established agent-security benchmarks, including InjecAgent and ToolEmu, while operating offline with modest additional auditing cost.

Wensheng Tang, Guangming Lang, Xuqiong Luo

Hamiltonian systems are one of the most important class of dynamical systems with a geometric structure called symplecticity and the numerical algorithms which can preserve such geometric structure are of interest. In this article we study the construction of symplectic (partitioned) Runge-Kutta methods with continuous stage, which provides a new and simple way to construct symplectic (partitioned) Runge-Kutta methods in classical sense. This line of construction of symplectic methods relies heavily on the expansion of orthogonal polynomials and the simplifying assumptions for (partitioned) Runge-Kutta type methods.