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Zhuo Peng

Publications and source records attributed to Zhuo Peng.

3 recordsLinked to original sources

On an invariant curvature cone along 4-dimensional Ricci flow

In this paper, we study 4-dimensional complete noncompact manifolds (M,g) satisfying Rm(g) $\in\mathfrak{C}_{\eta,\mu}$ via Ricci flow. Under the additional assumption of maximal volume growth, we prove topological and geometric gap theorems. We also study 4-dimensional complete manifolds satisfying a lower bound with respect to $\mathfrak{C}_{\eta,\mu}$ and obtain regularity results for Gromov-Hausdorff limits of complete volume non-collapsed manifolds satisfying such curvature lower bounds.

math.DG

A note on a diffeomorphism criterion via long-time Ricci flow

In this note, we give a diffeomorphism (to $\mathbb{R}^n$) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in [Manifolds with small curvature concentration, Ann. PDE, 2024] by Chan, Lee and the first named author and [Removing scalar curvature assumption for Ricci flow smoothing, Bull. Lond. Math. Soc., 2025] by A. Martens about manifolds with small curvature concentration can be improved to diffeomorphism in dimension $4$.

math.DG

OS-MAP: How Far Can Computer-Using Agents Go in Breadth and Depth?

Computer-using agents have shown strong potential to boost human productivity and enable new application forms across platforms. While recent advances have led to usable applications, existing benchmarks fail to account for the internal task heterogeneity and the corresponding agent capabilities, as well as their alignment with actual user demands-hindering both targeted capability development and the reliable transition of research progress into practical deployment. To bridge the gap, we present OS-MAP, a benchmark for daily computer-using automation that organizes its 416 realistic tasks across 15 applications along two key dimensions: a five-level taxonomy of automation and a generalization scope derived from a real-world user demand hierarchy. To enable fine-grained analysis of required capabilities and alignment with real-world scenarios, OS-MAP evaluates agents along two dimensions: automation level across a five-level taxonomy, and generalization scope across a demand hierarchy. This design captures varying levels of required agent autonomy and generalization, forming a performance-generalization evaluation matrix for structured and comprehensive assessment. Experiments show that even State-of-the-Art agents with VLM backbones struggle with higher-level tasks involving perception, reasoning, and coordination-highlighting the need for a deeper understanding of current strengths and limitations to drive the future progress in computer-using agents research and deployment. All code, environments, baselines, and data are publicly available at https://github.com/OS-Copilot/OS-Map.

cs.AI