arXiv subjects
Publications and source records attributed to Xia Chen.
This paper is concerned with a wave equation in dimension $d\in \{1,2, 3\}$, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the space-time covariance of the Gaussian noise, allowing the existence and uniqueness of a mild Skorohod solution.
In this article, we study the stochastic wave equation in all dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that either the noise is white, or the covariance function of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the $p$-th moment of the solution either when the time is large or when $p$ is large. For the critical case, that is the case when $d=3$ and the noise is white, we obtain the exact transition time for the second moment to be finite.
Visual data in autonomous driving perception, such as camera image and LiDAR point cloud, can be interpreted as a mixture of two aspects: semantic feature and geometric structure. Semantics come from the appearance and context of objects to the sensor, while geometric structure is the actual 3D shape of point clouds. Most detectors on LiDAR point clouds focus only on analyzing the geometric structure of objects in real 3D space. Unlike previous works, we propose to learn both semantic feature and geometric structure via a unified multi-view framework. Our method exploits the nature of LiDAR scans -- 2D range images, and applies well-studied 2D convolutions to extract semantic features. By fusing semantic and geometric features, our method outperforms state-of-the-art approaches in all categories by a large margin. The methodology of combining semantic and geometric features provides a unique perspective of looking at the problems in real-world 3D point cloud detection.
Accurate 3D imaging is essential for machines to map and interact with the physical world. While numerous 3D imaging technologies exist, each addressing niche applications with varying degrees of success, none have achieved the breadth of applicability and impact that digital image sensors have achieved in the 2D imaging world. A large-scale two-dimensional array of coherent detector pixels operating as a light detection and ranging (LiDAR) system could serve as a universal 3D imaging platform. Such a system would offer high depth accuracy and immunity to interference from sunlight, as well as the ability to directly measure the velocity of moving objects. However, due to difficulties in providing electrical and photonic connections to every pixel, previous systems have been restricted to fewer than 20 pixels. Here, we demonstrate the first large-scale coherent detector array consisting of 512 ($32 \times 16$) pixels, and its operation in a 3D imaging system. Leveraging recent advances in the monolithic integration of photonic and electronic circuits, a dense array of optical heterodyne detectors is combined with an integrated electronic readout architecture, enabling straightforward scaling to arbitrarily large arrays. Meanwhile, two-axis solid-state beam steering eliminates any tradeoff between field of view and range. Operating at the quantum noise limit, our system achieves an accuracy of $3.1~\mathrm{mm}$ at a distance of 75 metres using only $4~\mathrm{mW}$ of light, an order of magnitude more accurate than existing solid-state systems at such ranges. Future reductions of pixel size using state-of-the-art components could yield resolutions in excess of 20 megapixels for arrays the size of a consumer camera sensor. This result paves the way for the development and proliferation of low cost, compact, and high performance 3D imaging cameras.
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: $\partial_{t} u_{t}(x) = \frac12 Δu_{t}(x) + u_{t}(x) \, \dot W_{t}(x)$, for $t\in\mathbb{R}_{+}$ and $x\in \mathbb{R}^{d}$, where $\dot W_{t}(x)$ is a Gaussian noise whose space time covariance function is singular. In this rough context, we shall give some information about the moments of $u_{t}(x)$ when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.
We construct a $K$-rough path above either a space-time or a spatial fractional Brownian motion, in any space dimension $d$. This allows us to provide an interpretation and a unique solution for the corresponding parabolic Anderson model, understood in the renormalized sense. We also consider the case of a spatial fractional noise.
We propose a simple, fast, and flexible framework to generate simultaneously semantic and instance masks for panoptic segmentation. Our method, called PanoNet, incorporates a clean and natural structure design that tackles the problem purely as a segmentation task without the time-consuming detection process. We also introduce position-sensitive embedding for instance grouping by accounting for both object's appearance and its spatial location. Overall, PanoNet yields high panoptic quality results of high-resolution Cityscapes images in real-time, significantly faster than all other methods with comparable performance. Our approach well satisfies the practical speed and memory requirement for many applications like autonomous driving and augmented reality.
High speed train system has proven to be a very flexible and attractive system that can be developed under various circumstances and in different contexts and cultures. As a result, high speed trains are widely deployed around the world. Providing more reliable and higher data rate communication services for high speed trains has become one of the most urgent challenges. With vast amounts of spectrum available, the millimeter wave (mmWave) system is able to provide transmission rates of several gigabits per second for high speed trains. At the same time, mmWave communication also suffers from high attenuation, thus higher energy efficiency should be considered. This paper proposes an energy efficient power control scheme of train-ground mmWave communication for high speed trains. Considering a beam switching method for efficient beam alignment, we first establish position prediction model, the realistic direction antenna model and receive power model. And then we allocate the transmission power rationally through the power minimization algorithm while ensuring the total amount of transmission data. Based on this, this paper also develops a hybrid optimization scheme and finds the limit of total energy consumption when the number of segments goes to infinity. Through simulation with various system parameters and taking velocity estimation error into account, we demonstrate the superior performance of our schemes.
Heterogeneous network embedding (HNE) is a challenging task due to the diverse node types and/or diverse relationships between nodes. Existing HNE methods are typically unsupervised. To maximize the profit of utilizing the rare and valuable supervised information in HNEs, we develop a novel Active Heterogeneous Network Embedding (ActiveHNE) framework, which includes two components: Discriminative Heterogeneous Network Embedding (DHNE) and Active Query in Heterogeneous Networks (AQHN). In DHNE, we introduce a novel semi-supervised heterogeneous network embedding method based on graph convolutional neural network. In AQHN, we first introduce three active selection strategies based on uncertainty and representativeness, and then derive a batch selection method that assembles these strategies using a multi-armed bandit mechanism. ActiveHNE aims at improving the performance of HNE by feeding the most valuable supervision obtained by AQHN into DHNE. Experiments on public datasets demonstrate the effectiveness of ActiveHNE and its advantage on reducing the query cost.
We introduce a prediction driven method for visual tracking and segmentation in videos. Instead of solely relying on matching with appearance cues for tracking, we build a predictive model which guides finding more accurate tracking regions efficiently. With the proposed prediction mechanism, we improve the model robustness against distractions and occlusions during tracking. We demonstrate significant improvements over state-of-the-art methods not only on visual tracking tasks (VOT 2016 and VOT 2018) but also on video segmentation datasets (DAVIS 2016 and DAVIS 2017).
In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $\dot{W}$ in space. We consider the case $H<\frac{1}{2}$ and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form $\frac{1}{2} Δ+ \dot{W}$.
A novel technique is presented for realising programmable silicon photonic circuits. Once the proposed photonic circuit is programmed, its routing is retained without the need for additional power consumption. This technology enables a uniform multi-purpose design of photonic chips for a range of different applications and performance requirements, as it can be programmed for each specific application after chip fabrication. Therefore the cost per chip can be dramatically reduced because of the increase in production volume, and rapid prototyping of new photonic circuits is enabled. Essential building blocks for programmable circuits, erasable directional couplers (DCs) were designed and fabricated, utilising ion implanted waveguides. We demonstrate permanent switching between the drop port and through port of the DCs using a localised post-fabrication laser annealing process. Proof-of-principle demonstrators in the form of generic 1X4 and 2X2 programmable switching circuits were then fabricated and subsequently programmed, to define their function.
As the next generation cellular system, 5G network is required to provide a large variety of services for different kinds of terminals, from traditional voice and data services over mobile phones to small packet transmission over massive machine-type terminals. Although orthogonal-subcarrier based waveform has been widely used nowadays in many practical systems, it can hardly meet the future requirements in the coming 5G networks. Therefore, more flexible waveforms have been proposed to address the unprecedented challenges. In this article, we will provide comprehensive analysis and comparison for the typical waveform candidates. To obtain insightful analysis, we will not only introduce the basic principles of the waveforms but also reveal the underlying characteristics of each waveform. Moreover, a comprehensive comparison in terms of different performance metrics will be also presented in this article, which provide an overall understanding of the new waveforms.
The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance structure of a fractional Brownian motion with Hurst parameter greater than 1/4 and less than 1/2 in the space variable.
In this paper, we consider fractional parabolic equation of the form $ \frac{\partial u}{\partial t}=-(-Δ)^{\fracα{2}}u+u\dot W(t,x)$, where $-(-Δ)^{\fracα{2}}$ with $α\in(0,2]$ is a fractional Laplacian and $\dot W$ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by $α$-stable process. As a byproduct, we obtain the critical values for $θ$ and $η$ such that $\mathbb{E}\exp\left(θ\left(\int_0^1 \int_0^1 |r-s|^{-β_0}γ(X_r-X_s)drds\right)^η\right)$ is finite, where $X$ is $d$-dimensional symmetric $α$-stable process and $γ(x)$ is $|x|^{-β}$ or $\prod_{j=1}^d|x_j|^{-β_j}$.
Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for the parabolic Anderson equation \[\cases{\displaystyle {\frac{\partial u}{\partial t}}(t,x)={\frac{1}{2}}Δu(t,x)+V(t,x)u(t,x),\cr u(0,x)=u_0(x),}\] where the homogeneous generalized Gaussian noise $V(t,x)$ is, among other forms, white or fractional white in time and space. Associated with the Cole-Hopf solution to the KPZ equation, in particular, the precise asymptotic form \[\lim_{R\to\infty}(\log R)^{-2/3}\log\max_{|x|\le R}u(t,x)={\frac{3}{4}}\root 3\of {\frac{2t}{3}}\qquad a.s.\] is obtained for the parabolic Anderson model $\partial_tu={\frac{1}{2}}\partial_{xx}^2u+\dot{W}u$ with the $(1+1)$-white noise $\dot{W}(t,x)$. In addition, some links between time and space asymptotics for the parabolic Anderson equation are also pursued.
In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is applied to obtain the Hölder continuity and moment formula of the solution.
Motivated by the study of the directed polymer model with mobile Poissonian traps or catalysts and the stochastic parabolic Anderson model with time dependent potential, we investigate the asymptotic behavior of \[\mathbb{E}\otimes\mathbb{E}_0\exp\left\{\pmθ\int^t_0\bar{V}(s,B_s)ds\right\}\qquad (t\to\infty)\] where $þ>0$ is a constant, $\overline{V}$ is the renormalized Poisson potential of the form \[\overline{V}(s,x)=\int_{\mathbb{R}^d}\frac{1}{|y-x|^p}\left(ω_s(dy)-dy\right),\] and $ω_s$ is the measure-valued process consisting of independent Brownian particles whose initial positions form a Poisson random measure on $\mathbb{R}^d$ with Lebesgue measure as its intensity. Different scaling limits are obtained according to the parameter $p$ and dimension $d$. For the logarithm of the negative exponential moment, the range of $\frac{d}{2} 2)$, the exponential moments become infinite for all $t>0$.