arXiv subjects

Yi-Yang Zhang

Publications and source records attributed to Yi-Yang Zhang.

3 recordsLinked to original sources

arXiv2026

Quasi-admissible, raisable nilpotent orbits and covering Barbasch-Vogan duality

For simply-connected Lie groups of type E over $ p $-adic local field $ F $, we determine the degree of the cover required for a given $ F $-split nilpotent orbit to be quasi-admissible or raisable, respectively. Combining this result with the previously computed data for other types by Gao-Liu-Tsai, we prove that all $ F $-split nilpotent orbits whose geometry type contained in the image of the covering Barbasch-Vogan duality map $ d_{\mathrm{BV},G}^{(n)} $ of almost-simple Lie groups $ G $ in each Cartan type are always $ \overline{G}^{(n)} $-quasi-admissible.

math.RT↗

arXiv2026

MotionDuet: Dual-Conditioned 3D Human Motion Generation with Video-Regularized Text Learning

3D Human motion generation is pivotal across film, animation, gaming, and embodied intelligence. Traditional 3D motion synthesis relies on costly motion capture, while recent work shows that 2D videos provide rich, temporally coherent observations of human behavior. Existing approaches, however, either map high-level text descriptions to motion or rely solely on video conditioning, leaving a gap between generated dynamics and real-world motion statistics. We introduce MotionDuet, a multimodal framework that aligns motion generation with the distribution of video-derived representations. In this dual-conditioning paradigm, video cues extracted from a pretrained model (e.g., VideoMAE) ground low-level motion dynamics, while textual prompts provide semantic intent. To bridge the distribution gap across modalities, we propose Dual-stream Unified Encoding and Transformation (DUET) and a Distribution-Aware Structural Harmonization (DASH) loss. DUET fuses video-informed cues into the motion latent space via unified encoding and dynamic attention, while DASH aligns motion trajectories with both distributional and structural statistics of video features. An auto-guidance mechanism further balances textual and visual signals by leveraging a weakened copy of the model, enhancing controllability without sacrificing diversity. Extensive experiments demonstrate that MotionDuet generates realistic and controllable human motions, surpassing strong state-of-the-art baselines.

cs.GR↗

arXiv2026

Local level sets of the Takagi-van der Waerden function

In this paper, we investigate the Takagi-van der Waerden function, $$ T_r(x) = \sum_{n=0}^{\infty} \frac{ϕ(r^n x)}{r^n} ,\quad x\in [0,1], \quad r \in \mathbb{Z}^+, $$ where $ϕ(x)={\rm dist}(x,\mathbb{Z})$ represents the distance from $x$ to the nearest integer. %We prove that for every even integer $r \geq 2$, the expected number of local level sets contained in the level set $L_r(y)$ is $1 + 1/r$, if $y$ is a random variable uniformly distributed over the range of $T_r$. Lagarias and Maddock [Level sets of the Takagi function: local level sets, \emph{Monatsh. Math.}, {\bf 166} (2012), No. 2, 201--238] introduced the notion of local level sets for the classical Takagi function $T_2$. They proved that if $y$ is a random variable uniformly distributed over the range of $T_2$, then the expected number of local level sets contained in the level set $L_2(y)$ equals $3/2$. We extend the study by defining an analogous concept of local level sets for all even integers $r$. Then we prove that, for every even integer $r\geq 2$, if $y$ is a random variable uniformly distributed, then the expected number of local level sets contained in the level set $L_r(y)$ equals $1 + 1/r$.

math.CA↗