arXiv subjects

Yuan Shan

Publications and source records attributed to Yuan Shan.

4 recordsLinked to original sources

arXiv2026

Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator

We study the mosaic Almost Mathieu operator, a quasiperiodic model that naturally admits a singular strip-Jacobi representation. By establishing a duality framework and extending the correspondence between the integrated density of states and the fibered rotation number to this setting, we obtain an effective reduction to $SL(2,\mathbb{R})$ cocycles. As a consequence, combining Aubry duality, reducibility theory, and the Moser--P\"oschel argument, we prove that the spectrum is a Cantor set for all noncritical parameters.

math-ph↗

arXiv2026

Age-Dependent Heterogeneity in the Association Between Physical Activity and Mental Distress: A Causal Machine Learning Analysis of 3.2 Million U.S. Adults

Physical activity (PA) is widely recognized as protective against mental distress, yet whether this benefit varies systematically across population subgroups remains poorly understood. Using pooled data from ten consecutive annual waves of the U.S. Behavioral Risk Factor Surveillance System (2015-2024; n = 3,242,218), we investigate heterogeneity in the association between leisure-time PA and frequent mental distress (FMD, >=14 days/month) across age groups. Survey-weighted logistic regression reveals a striking age gradient: the adjusted odds ratio for PA ranges from 0.89 among young adults (18-24) to 0.50 among adults aged 55-64, with the protective association strengthening monotonically with age. Temporal analysis across all ten years shows that the young-adult PA effect has been eroding over the past decade, with the 18-24 OR reaching 1.01 (null) in both 2018 and 2024 -- paralleling the deepening youth mental health crisis. Causal Forest via Double Machine Learning independently identifies age as the dominant driver of treatment effect heterogeneity (feature importance = 0.39, 2.5x the next predictor). E-value sensitivity analysis, propensity score overlap checks, placebo tests, and imputation comparisons confirm the robustness of the findings. These results suggest that the well-documented exercise--mental health link may not generalize to the youngest adult population, whose distress appears increasingly driven by stressors that PA alone cannot mitigate.

cs.LG↗

arXiv2025

Meow: End-to-End Outline Writing for Automatic Academic Survey

As academic paper publication numbers grow exponentially, conducting in-depth surveys with LLMs automatically has become an inevitable trend. Outline writing, which aims to systematically organize related works, is critical for automated survey generation. Yet existing automatic survey methods treat outline writing as mere workflow steps in the overall pipeline. Such template-based workflows produce outlines that lack in-depth understanding of the survey topic and fine-grained styles. To address these limitations, we propose Meow, the first metadata-driven outline writing framework that produces organized and faithful outlines efficiently. Specifically, we first formulate outline writing as an end-to-end task that generates hierarchical structured outlines from paper metadata. We then curate a high-quality dataset of surveys from arXiv, bioRxiv, and medRxiv, and establish systematic evaluation metrics for outline quality assessment. Finally, we employ a two-stage training approach combining supervised fine-tuning and reinforcement learning. Our 8B reasoning model demonstrates strong performance with high structural fidelity and stylistic coherence.

cs.CL↗

arXiv2011

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations(II)

Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this index theory we construct a new reduced functional to investigate multiple solutions for asymptotically linear operator equations by Morse theory. The functional is defined on an infinite dimensional Hilbert space, is twice differentiable and has a finite Morse index. Investigating critical points of this functional by Morse theory gives us a unified way to deal with nontrivial solutions of both asymptotically second order Hamiltonian systems and asymptotically first order Hamiltonian systems.

math.CA↗