Lun Zhang

Haiyong Wang, Lun Zhang, Daan Huybrechs

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{iωt})(x)=-int_{0}^{\infty}e^{iωt}\frac{f(t)}{t-x}dt,\qquad ω>0,\qquad x\geq 0,$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$, the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of $ω$ are derived for each fixed $x\geq 0$, which clarify the large $ω$ behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of $x$, we classify our discussion into three regimes, namely, $x=\mathcal{O}(1)$ or $x\gg1$, $0<x\ll 1$ and $x=0$. Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency $ω$ increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.

Haiyong Wang, Lun Zhang

In this paper, we are concerned with Jacobi polynomials $P_n^{(α,β)}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{(α,β)}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value of $\left|P_n^{(α,β)}(z)\right|$ over the Bernstein ellipse is attained at one of the endpoints of the major axis if $α+β\geq -1$. For the minimum value, we are able to show that for a large class of Gegenbauer polynomials (i.e., $α=β$), it is attained at two endpoints of the minor axis. These results particularly extend those previously known only for some special cases. Moreover, we obtain a more refined asymptotic estimate for Jacobi polynomials on the Bernstein ellipse.

Weian Guo, Zecheng Kang, Dongyang Li et al.

The significance of transportation efficiency, safety, and related services is increasing in urban vehicular networks. Within such networks, roadside units (RSUs) serve as intermediates in facilitating communication. Therefore, the deployment of RSUs is of utmost importance in ensuring the quality of communication services. However, the optimization objectives, such as time delay and deployment cost, are commonly developed from diverse perspectives. As a result, it is possible that conflicts may arise among the objectives. Furthermore, in urban environments, the presence of various obstacles, such as buildings, gardens, lakes, and other infrastructure, poses challenges for the deployment of RSUs. Hence, the deployment encounters significant difficulties due to the existence of multiple objectives, constraints imposed by obstacles, and the necessity to explore a large-scale optimization space. To address this issue, two versions of multi-objective optimization algorithms are proposed in this paper. By utilizing a multi-population strategy and an adaptive exploration technique, the methods efficiently explore a large-scale decision-variable space. In order to mitigate the issue of an overcrowded deployment of RSUs, a calibrating mechanism is adopted to adjust RSU density during the optimization procedures. The proposed methods also take care of data offloading between vehicles and RSUs by setting up an iterative best response sequence game (IBRSG). By comparing the proposed algorithms with several state-of-the-art algorithms, the results demonstrate that our strategies perform better in both high-density and low-density urban scenarios. The results also indicate that the proposed solutions substantially improve the efficiency of vehicular networks.

Weian Guo, Ruizhi Sha, Li Li et al.

To alleviate computational load on RSUs and cloud platforms, reduce communication bandwidth requirements, and provide a more stable vehicular network service, this paper proposes an optimized pinning control approach for heterogeneous multi-network vehicular ad-hoc networks (VANETs). In such networks, vehicles participate in multiple task-specific networks with asymmetric coupling and dynamic topologies. We first establish a rigorous theoretical foundation by proving the stability of pinning control strategies under both single and multi-network conditions, deriving sufficient stability conditions using Lyapunov theory and linear matrix inequalities (LMIs). Building on this theoretical groundwork, we propose an adaptive genetic algorithm tailored to select optimal pinning nodes, effectively balancing LMI constraints while prioritizing overlapping nodes to enhance control efficiency. Extensive simulations across various network scales demonstrate that our approach achieves rapid consensus with a reduced number of control nodes, particularly when leveraging network overlaps. This work provides a comprehensive solution for efficient control node selection in complex vehicular networks, offering practical implications for deploying large-scale intelligent transportation systems.

Bo Li, Caiming Xiong, Tianfu Wu et al.

Chinese traditional painting is one of the most historical artworks in the world. It is very popular in Eastern and Southeast Asia due to being aesthetically appealing. Compared with western artistic painting, it is usually more visually abstract and textureless. Recently, neural network based style transfer methods have shown promising and appealing results which are mainly focused on western painting. It remains a challenging problem to preserve abstraction in neural style transfer. In this paper, we present a Neural Abstract Style Transfer method for Chinese traditional painting. It learns to preserve abstraction and other style jointly end-to-end via a novel MXDoG-guided filter (Modified version of the eXtended Difference-of-Gaussians) and three fully differentiable loss terms. To the best of our knowledge, there is little work study on neural style transfer of Chinese traditional painting. To promote research on this direction, we collect a new dataset with diverse photo-realistic images and Chinese traditional paintings. In experiments, the proposed method shows more appealing stylized results in transferring the style of Chinese traditional painting than state-of-the-art neural style transfer methods.

Bo Li, Tianfu Wu, Lun Zhang et al.

Region-based convolutional neural networks (R-CNN)~\cite{fast_rcnn,faster_rcnn,mask_rcnn} have largely dominated object detection. Operators defined on RoIs (Region of Interests) play an important role in R-CNNs such as RoIPooling~\cite{fast_rcnn} and RoIAlign~\cite{mask_rcnn}. They all only utilize information inside RoIs for RoI prediction, even with their recent deformable extensions~\cite{deformable_cnn}. Although surrounding context is well-known for its importance in object detection, it has yet been integrated in R-CNNs in a flexible and effective way. Inspired by the auto-context work~\cite{auto_context} and the multi-class object layout work~\cite{nms_context}, this paper presents a generic context-mining RoI operator (i.e., \textit{RoICtxMining}) seamlessly integrated in R-CNNs, and the resulting object detection system is termed \textbf{Auto-Context R-CNN} which is trained end-to-end. The proposed RoICtxMining operator is a simple yet effective two-layer extension of the RoIPooling or RoIAlign operator. Centered at an object-RoI, it creates a $3\times 3$ layout to mine contextual information adaptively in the $8$ surrounding context regions on-the-fly. Within each of the $8$ context regions, a context-RoI is mined in term of discriminative power and its RoIPooling / RoIAlign features are concatenated with the object-RoI for final prediction. \textit{The proposed Auto-Context R-CNN is robust to occlusion and small objects, and shows promising vulnerability for adversarial attacks without being adversarially-trained.} In experiments, it is evaluated using RoIPooling as the backbone and shows competitive results on Pascal VOC, Microsoft COCO, and KITTI datasets (including $6.9\%$ mAP improvements over the R-FCN~\cite{rfcn} method on COCO \textit{test-dev} dataset and the first place on both KITTI pedestrian and cyclist detection as of this submission).

Bo Li, Tianfu Wu, Shuai Shao et al.

Jointly integrating aspect ratio and context has been extensively studied and shown performance improvement in traditional object detection systems such as the DPMs. It, however, has been largely ignored in deep neural network based detection systems. This paper presents a method of integrating a mixture of object models and region-based convolutional networks for accurate object detection. Each mixture component accounts for both object aspect ratio and multi-scale contextual information explicitly: (i) it exploits a mixture of tiling configurations in the RoI pooling to remedy the warping artifacts caused by a single type RoI pooling (e.g., with equally-sized 7 x 7 cells), and to respect the underlying object shapes more; (ii) it "looks from both the inside and the outside of a RoI" by incorporating contextual information at two scales: global context pooled from the whole image and local context pooled from the surrounding of a RoI. To facilitate accurate detection, this paper proposes a multi-stage detection scheme for integrating the mixture of object models, which utilizes the detection results of the model at the previous stage as the proposals for the current in both training and testing. The proposed method is called the aspect ratio and context aware region-based convolutional network (ARC-R-CNN). In experiments, ARC-R-CNN shows very competitive results with Faster R-CNN [41] and R-FCN [10] on two datasets: the PASCAL VOC and the Microsoft COCO. It obtains significantly better mAP performance using high IoU thresholds on both datasets.