Wenji Xi

Zhicheng Du, Changyue Liu, Wenji Xi et al.

Reported retrieval scores for training-free shape descriptors conflate local signal design, normalization, aggregation, codebook fitting, and metric choices, making isolated component evaluation difficult. This paper reframes descriptor evaluation as a {\em protocol audit}. We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses, converts them to distance-like fields, and summarizes each vertex by low-order moments across seeds and scales. DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects. On the registered FAUST benchmark split (FAUST-Reg) and the TOSCA shape collection, aggregation-matched experiments show that an independent Geometric Moment Shape Descriptor baseline built on Heat Kernel Signature features (GMSD-HKS) obtains the highest scores in this implementation ($0.621/0.820$ and $0.865/0.963$ mean average precision (mAP)/top-1), Wave Kernel Signature (WKS) remains a strong classical signal, and DGM is useful mainly when sparse solves, non-spectral deployment, or symmetry-informative seed frames are priorities. The broader finding is methodological: the input field and aggregation protocol can dominate the moment formula. The paper contributes a reproducible protocol-cascade analysis, a cross-shape alignment diagnostic for functional-map compatibility, and concrete recommendations for designing and reporting training-free shape descriptors.

Zhicheng Du, Wenji Xi, Zhuo Deng et al.

Let $G_n$ be the coprime graph on $\{1,\ldots,n\}$. We prove that the mixed vertex-coloring coprime Ramsey number satisfies \[ \Rcop(k_1,\ldots,k_c)=p_{\sum_{i=1}^c(k_i-1)}, \] where $p_m$ is the $m$-th prime. The proof is elementary: the prime clique $\{1\}\cup\{p\le n:p\text{ prime}\}$ gives the upper bound by pigeonhole, while a prime-bin partition gives the matching lower bound by coloring each composite with a bin containing one of its prime divisors. We reserve $\Rcop$ for this vertex-coloring parameter; the edge-coloring parameter on the same host graph is denoted $\Redge$. The same certificate viewpoint yields three extensions: a support-disjointness generalization, a polynomial-time certificate-extraction primitive, and an exact reduction of the edge-coloring variant to classical Ramsey numbers: $\Redge(k_1,\ldots,k_c)=p_{\Rcl(k_1,\ldots,k_c)-1}$. These two formulas are rank transfers from the same clique-label certificate. We also prove that the balanced two-color diagonal threshold equals the unrestricted threshold $p_{2k-2}$ for all $k\ge2$, via a deterministic prime-bin split requiring only the weak inequality $2p_m<p_{2m}<3p_m$; for fixed $c$, a Hall argument plus a standard Selberg--Delange estimate gives eventual multicolor balanced certificates.

Yu Zheng, Kezhi Wang, Wenji Xi et al.

Modeling indoor radio propagation is crucial for wireless network planning and optimization. However, existing approaches often rely on labor-intensive manual modeling of geometry and material properties, resulting in limited scalability and efficiency. To overcome these challenges, this paper presents SenseRay-3D, a generalizable and physics-informed end-to-end framework that predicts three-dimensional (3D) path-loss heatmaps directly from RGB-D scans, thereby eliminating the need for explicit geometry reconstruction or material annotation. The proposed framework builds a sensing-driven voxelized scene representation that jointly encodes occupancy, electromagnetic material characteristics, and transmitter-receiver geometry, which is processed by a SwinUNETR-based neural network to infer environmental path-loss relative to free-space path-loss. A comprehensive synthetic indoor propagation dataset is further developed to validate the framework and to serve as a standardized benchmark for future research. Experimental results show that SenseRay-3D achieves a mean absolute error of 4.27 dB on unseen environments and supports real-time inference at 217 ms per sample, demonstrating its scalability, efficiency, and physical consistency. SenseRay-3D paves a new path for sense-driven, generalizable, and physics-consistent modeling of indoor propagation, marking a major leap beyond our pioneering EM DeepRay framework.