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Mingyang Xia

Publications and source records attributed to Mingyang Xia.

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On the Absence of Anosov Factors for DA Local Diffeomorphisms

We give a class of local diffeomorphisms which are homotopic to toral hyperbolic endomorphisms, but which are not topologically semi-conjugate, within the homotopic class of the identity, to any Anosov local diffeomorphism. In particular, we show that for a non-invertible partially hyperbolic $C^1$-smooth local diffeomorphism with expanding directions on the $2$-torus, if it is semi-conjugate to an Anosov local diffeomorphism, then it is also an Anosov local diffeomorphism.

math.DS

NeuroAgent: LLM Agents for Multimodal Neuroimaging Analysis and Research

Multimodal neuroimaging analysis often involves complex, modality-specific preprocessing workflows that require careful configuration, quality control, and coordination across heterogeneous toolchains. Beyond preprocessing, downstream statistical analysis and disease classification commonly require task-specific code, evaluation protocols, and data-format conventions, creating additional barriers between raw acquisitions and reproducible scientific analysis. We present NeuroAgent, an LLM-driven agentic framework that automates key preprocessing and analysis steps for heterogeneous neuroimaging data, including sMRI, fMRI, dMRI, and PET, and supports interactive downstream analysis through natural-language queries. NeuroAgent employs a hierarchical multi-agent architecture with a feedback-driven Generate-Execute-Validate engine: agents autonomously generate executable preprocessing code, detect and recover from runtime errors, and validate output integrity. We evaluate the system on 1,470 subjects pooled across all ADNI phases (CN=1,000, AD=470), where all subjects have sMRI and tabular data, with subsets also having Tau-PET (n=469), fMRI (n=278), and DTI ($n=620$). Pipeline ablation studies across multiple LLM backends show that capable models reach up to 100% intent-parsing accuracy, with the strongest backend (Qwen3.5-27B) reaching 84.8% end-to-end preprocessing step correctness. Automated recovery limits manual intervention to edge cases where human review is required via the Human-In-The-Loop interface. For Alzheimer's Disease classification using automatically preprocessed multimodal data, our agent ensemble achieves an AUC of 0.9518 with four modalities, outperforming all single-modality baselines. These results show that NeuroAgent can reduce the manual effort required for neuroimaging preprocessing and enable end-to-end automated analysis pipelines for neuroimaging research.

cs.AI

Robust Transitivity of Partially Hyperbolic Diffeomorphisms with Interval Central Leaves

For a boundary-preserving partially hyperbolic diffeomorphism with interval central leaves, we completely characterize the $C^k$-robust transitivity $(k\geq 2)$ by boundary interconnection. As an application, if the boundary SRB measures admit negative central Lyapunov exponents, then boundary interconnection also completely characterizes the phenomenon of robustly intermingled basins for boundary SRB measures.

math.DS

Semi-conjugacy rigidity for endomorphisms derived from Anosov on the 2-torus

Let $f$ be a non-invertible partially hyperbolic endomorphism on $\TT^2$ which is derived from a non-expanding Anosov endomorphism. Differing from the case of diffeomorphisms derived from Anosov automorphisms, there is no a priori semi-conjugacy between $f$ and its linearization on $\TT^2$. We show that $f$ is semi-conjugate to its linearization if and only if $f$ admits a partially hyperbolic splitting with two $Df$-invariant subbundles. Moreover, if we assume that $f$ has an unstable subbundle, then the semi-conjugacy is exactly a topological conjugacy, and the center Lyapunov exponents of the periodic points of $f$ coincide with its linearization. In particular, $f$ is an Anosov endomorphism and the conjugacy is smooth along the stable foliation. For the case that $f$ has a stable subbundle, there is still some rigidity in its stable Lyapunov exponents. However, we also give examples which admit a partially hyperbolic splitting with center subbundle but the semi-conjugacy is indeed non-injective. Finally, we present some applications under the volume-preserving assumption.

math.DS

On the density of Birkhoff sums for Anosov diffeomorphisms

Let f be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides of zero, then the set of Birkhoff sums of all periodic points is dense in the whole set of real numbers.

math.DS