arXiv subjects

Qifan Shen

Publications and source records attributed to Qifan Shen.

4 recordsLinked to original sources

arXiv2026

Representation characterization of equivariant geometric bordism

Let $G_k=(\mathbb Z_2)^k$. We establish a representation characterization determining when finitely many faithful $G_k$-representations can serve as the fixed-point data of a smooth closed $G_k$-manifold. By partitioning representations via multiplicities of nonzero weights $ρ$ and isomorphic restrictions to $\ker ρ$, we formulate an evenness condition; realizability is equivalent to this condition, yielding a finite local restatement of the tom Dieck--Kosniowski--Stong integrality criterion. As an application, we prove that $\dim_{\mathbb Z_2}\mathcal Z_4(G_3)=32$ and exhibit 32 basis elements represented by $G_3$-actions on $\mathbb RP^2\times\mathbb RP^2$, $\mathbb RP^4$ and $\mathbb RP(γ\oplusγ\oplusγ\oplus\underline{\mathbb R})$, obtained from three basic actions by precomposition with automorphisms of $G_3$.

math.AT↗

arXiv2026

mmWave-Diffusion:A Novel Framework for Respiration Sensing Using Observation-Anchored Conditional Diffusion Model

Millimeter-wave (mmWave) radar enables contactless respiratory sensing,yet fine-grained monitoring is often degraded by nonstationary interference from body micromotions.To achieve micromotion interference removal,we propose mmWave-Diffusion,an observation-anchored conditional diffusion framework that directly models the residual between radar phase observations and the respiratory ground truth,and initializes sampling within an observation-consistent neighborhood rather than from Gaussian noise-thereby aligning the generative process with the measurement physics and reducing inference overhead. The accompanying Radar Diffusion Transformer (RDT) is explicitly conditioned on phase observations, enforces strict one-to-one temporal alignment via patch-level dual positional encodings, and injects local physical priors through banded-mask multi-head cross-attention, enabling robust denoising and interference removal in just 20 reverse steps. Evaluated on 13.25 hours of synchronized radar-respiration data, mmWave-Diffusion achieves state-of-the-art waveform reconstruction and respiratory-rate estimation with strong generalization. Code repository:https://github.com/goodluckyongw/mmWave-Diffusion.

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arXiv2022

Lower bound for Buchstaber invariants of real universal complexes

In this article, we prove that Buchstaber invariant of 4-dimensional real universal complex is no less than 24 as a follow-up to the work of Ayzenberg and Sun. Moreover, a lower bound for Buchstaber invariants of $n$-dimensional real universal complexes is given as an improvement of result of Erokhovets.

math.AT↗

arXiv2022

On string quasitoric manifolds and their orbit polytopes

This article mainly aims to give combinatorial characterizations and topological descriptions of quasitoric manifolds with string property. We provide a necessary and sufficient condition for a simple polytope in dimension 2 and 3 to be realizable as the orbit polytope of a string quasitoric manifold. In particular, a complete description of string quasitoric manifolds over prisms is obtained. On the other hand, we characterize string quasitoric manifolds over $n$-dimensional simple polytopes with no more than $2n+2$ facets. Further results are available when the orbit polytope is the connected sum of a cube and another simple polytope. In addtion, a real analogue concerning small cover is briefly discussed.

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