arXiv subjects
Publications and source records attributed to Yanhong Zhu.
Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple hypergraphs with prime square order.
The flexible endoscope is a minimally invasive tool in clinical settings, but most of them rely on exogenous staining for diagnosis to provide qualitative information. Here, we demonstrated a flexible endoscopic microscopy (FEM) with diffracted gradient light for quantitative phase imaging of unlabeled thick samples. Our instrument features a small form factor fiber bundle as the endoscope probe, cellular-level lateral and axial resolutions, and direct phase measurement via simple field modulation. By testing pathologic slices, thick opaque mammalian tissue ex vivo and wound healing in vivo, FEM identifies normal and tumor glandular structures, secreta, and tomographic skin layers. With the advantages of direct morphological and phase measurement, high resolution, and thin fiber tip, the label-free FEM could be an attractive tool for various clinical applications.
A subset $R$ of the vertex set of a graph $Γ$ is said to be $(κ,τ)$-regular if $R$ induces a $κ$-regular subgraph and every vertex outside $R$ is adjacent to exactly $τ$ vertices in $R$. In particular, if $R$ is a $(κ,τ)$-regular set of some Cayley graph on a finite group $G$, then $R$ is called a $(κ,τ)$-regular set of $G$. Let $H$ be a non-trivial normal subgroup of $G$, and $κ$ and $τ$ a pair of integers satisfying $0\leqκ\leq|H|-1$, $1\leqτ\leq|H|$ and $\gcd(2,|H|-1)\midκ$. It is proved that (i) if $τ$ is even, then $H$ is a $(κ,τ)$-regular set of $G$; (ii) if $τ$ is odd, then $H$ is a $(κ,τ)$-regular set of $G$ if and only if it is a $(0,1)$-regular set of $G$.