arXiv subjects
Publications and source records attributed to Yaojun Wang.
For $d\geqslant3$, let $p^*=\frac{2d}{d-2}$. We prove that the Born-Jordan distribution maps $L^{2,p^*}(\mathbb R^d)\times L^{2,p^*}(\mathbb R^d)$ boundedly into $L^{p^*}(\mathbb R^{2d})$. The Lorentz index $p^*$ cannot be increased in either variable. In particular, this gives the endpoint $L^2\times L^2\to L^{p^*}$ estimate, settling the critical boundedness problem raised by Stra, Svela, and Trapasso \cite{SST26}.
In this paper we prove the sharp weak estimates for the Riesz potentials $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\leq \gamma_{n,s} v_n^{\frac{n-s}{n}}\frac{\Gamma(s/2)\Gamma((n+2-s)/2)}{\Gamma(n/2)}\|f\|_{L^1},~~ \text{when}~~0<s<\min\{n,2\}$$ and $$ \|I_sf\|_{L^{\frac{n}{n-s},\infty}} \leq \gamma_{n,s}v_n^{\frac{n-s}{n}}\|f\|_{L^1}, ~~\text{when}~~2\leq s<n,$$ where $\gamma_{n,s}=2^{-s}\pi^{-\frac{n}{2}}\frac{\Gamma(\frac{n-s}{2})}{\Gamma(\frac{s}{2})}$ and $v_n$ is the volume of the unit ball. The isoperimetric inequality for the Riesz capacity and the Newtonian isocapacitary inequality play a crucial role in our approach.
Let $\mathbb{G}$ be a stratified Lie group and $\mathcal L$ be its sub-Laplacian. We prove that the full horizontal Riesz transform $\nabla_{H} \mathcal L^{-1/2}$ is of weak type $(1,1)$ on real-valued functions, with constant at most $2$. In particular, the constant is independent of the horizontal dimension, the homogeneous dimension, the step, and the underlying group structure of $\mathbb{G}$. Our result provides a noncommutative generalization of the dimension-free Euclidean theorem of Ouyang, Spector, and Stockdale arXiv:2608.18068, with the same universal constant. Our proof relies upon a fractional obstacle problem adapted to stratified Lie groups by using the functional calculus of $\mathcal L$ instead of the Fourier transform. As a consequence, by interpolation we obtain uniform $L^p$ bounds for the full horizontal Riesz transform $\nabla_{H} \mathcal L^{-1/2}$ for $p \in (1,2]$. By contrast, for every $p > 2$, we construct a sequence of stratified Lie groups with fixed horizontal dimension $5$ and steps tending to infinity for which the $L^p$ norms of the horizontal Riesz transforms diverge.
Greenhouse reinforcement learning can test climate-control ideas at a speed and scale that is difficult to achieve with crop experiments alone. For smart-greenhouse control, however, a single simulator return is not enough: a grower or control engineer also needs to know when the policy heats, enriches CO2, vents, manages humidity, deploys screens, or uses lamps.We propose a reproducible calibration-first reward audit framework that keeps named greenhouse-control reward components comparable across simulator training, facility-adapted rollouts, logged Autonomous Greenhouse Challenge records, and actuator-rule distillation. In GreenLight-Gym, the framework decomposes the scalar reward into conditional temperature, CO2, humidity and vapor-pressure-deficit, screen, and actuation-proxy terms; adapts GreenLight to the second Autonomous Greenhouse Challenge logged climate traces; and scores the same components on logged greenhouse data.
We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers $\mathcal{L}_{s}(0<s<1)$ of the sublaplacian on H-type groups. From these inequalities we derive a sharp log-Sobolev inequality by considering a limiting case and a sharp Sobolev trace inequality. The later extends to this context the result of Frank, Gonz\'alez, Monticelli and Tan (Adv. Math, 2015).
Recently, there has been growing interest in investigating the effects of self-representation on user experience and perception in virtual environments. However, few studies investigated the effects of levels of body representation (full-body, lower-body and viewpoint) on locomotion experience in terms of spatial awareness, self-presence and spatial presence during virtual locomotion. Understanding such effects is essential for building new virtual locomotion systems with better locomotion experience. In the present study, we first built a walking-in-place (WIP) virtual locomotion system that can represent users using avatars at three levels (full-body, lower-body and viewpoint) and is capable of rendering walking animations during in-place walking of a user. We then conducted a virtual locomotion experiment using three levels of representation to investigate the effects of body representation on spatial awareness, self-presence and spatial presence during virtual locomotion. Experimental results showed that the full-body representation provided better virtual locomotion experience in these three factors compared to that of the lower-body representation and the viewpoint representation. The lower-body representation also provided better experience than the viewpoint representation. These results suggest that self-representation of users in virtual environments using a full-body avatar is critical for providing better locomotion experience. Using full-body avatars for self-representation of users should be considered when building new virtual locomotion systems and applications.
Body actions and head gestures are natural interfaces for interaction in virtual environments. Existing methods for in-place body action recognition often require hardware more than a head-mounted display (HMD), making body action interfaces difficult to be introduced to ordinary virtual reality (VR) users as they usually only possess an HMD. In addition, there lacks a unified solution to recognize in-place body actions and head gestures. This potentially hinders the exploration of the use of in-place body actions and head gestures for novel interaction experiences in virtual environments. We present a unified two-stream 1-D convolutional neural network (CNN) for recognition of body actions when a user performs walking-in-place (WIP) and for recognition of head gestures when a user stands still wearing only an HMD. Compared to previous approaches, our method does not require specialized hardware and/or additional tracking devices other than an HMD and can recognize a significantly larger number of body actions and head gestures than other existing methods. In total, ten in-place body actions and eight head gestures can be recognized with the proposed method, which makes this method a readily available body action interface (head gestures included) for interaction with virtual environments. We demonstrate one utility of the interface through a virtual locomotion task. Results show that the present body action interface is reliable in detecting body actions for the VR locomotion task but is physically demanding compared to a touch controller interface. The present body action interface is promising for new VR experiences and applications, especially for VR fitness applications where workouts are intended.
Generating forward-backward self-representation leg animation in virtual environments for walking-in-place (WIP) techniques is an underexplored research topic. A challenging aspect of the problem is to find an appropriate mapping from tracked vertical foot motion to natural cyclical movements of real walking. In this work, we present a kinematic approach based on animation rigging to generating real-time leg animation. Our method works by tracking vertical in-place foot movements of a user with a Kinect v2 sensor and mapping tracked foot height to inverse kinematics (IK) targets. These IK targets were aligned with an avatar's feet to guide the virtual feet to perform cyclic walking motions. We conducted a user study to evaluate our approach. Results showed that the proposed method produced compelling forward-backward leg animation during walking. We show that the proposed technique can be easily integrated into existing WIP techniques.
Prestack seismic data carries much useful information that can help us find more complex atypical reservoirs. Therefore, we are increasingly inclined to use prestack seismic data for seis- mic facies recognition. However, due to the inclusion of ex- cessive redundancy, effective feature extraction from prestack seismic data becomes critical. In this paper, we consider seis- mic facies recognition based on prestack data as an image clus- tering problem in computer vision (CV) by thinking of each prestack seismic gather as a picture. We propose a convo- lutional autoencoder (CAE) network for deep feature learn- ing from prestack seismic data, which is more effective than principal component analysis (PCA) in redundancy removing and valid information extraction. Then, using conventional classification or clustering techniques (e.g. K-means or self- organizing maps) on the extracted features, we can achieve seismic facies recognition. We applied our method to the prestack data from physical model and LZB region. The re- sult shows that our approach is superior to the conventionals.