arXiv subjects

Jiahong Wu

Publications and source records attributed to Jiahong Wu.

At least 91 records · Page 5Linked to original sources

arXiv2020

Provenance-based Classification Policy based on Encrypted Search

As an important type of cloud data, digital provenance is arousing increasing attention on improving system performance. Currently, provenance has been employed to provide cues regarding access control and to estimate data quality. However, provenance itself might also be sensitive information. Therefore, provenance might be encrypted and stored in the Cloud. In this paper, we provide a mechanism to classify cloud documents by searching specific keywords from their encrypted provenance, and we prove our scheme achieves semantic security. In term of application of the proposed techniques, considering that files are classified to store separately in the cloud, in order to facilitate the regulation and security protection for the files, the classification policies can use provenance as conditions to determine the category of a document. Such as the easiest sample policy goes like: the documents have been reviewed twice can be classified as "public accessible", which can be accessed by the public.

cs.CR↗

arXiv2019

Unique weak solutions of the d-dimensional micropolar equation with fractional dissipation

This article examines the existence and uniqueness of weak solutions to the d-dimensional micropolar equations ($d=2$ or $d=3$) with general fractional dissipation $(-Δ)^αu$ and $(-Δ)^βw$. The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when $α\ge \frac12$ and $β\ge \frac12$, any initial data $(u_0, w_0)$ in the critical Besov space $u_0\in B^{1+\frac{d}{2}-2α}_{2,1}(\mathbb R^d)$ and $w_0\in B^{1+\frac{d}{2}-2β}_{2,1}(\mathbb R^d)$ yields a unique weak solution. For $α\ge 1$ and $β=0$, any initial data $u_0\in B^{1+\frac{d}{2}-2α}_{2,1}(\mathbb R^d)$ and $w_0\in B^{\frac{d}{2}}_{2,1}(\mathbb R^d)$ also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely $α=β=1$ have a unique weak solution for $(u_0, w_0)\in B^0_{2,1}$. The proof involves the construction of successive approximation sequences and extensive {\it a priori} estimates in Besov space settings.

math.AP↗

arXiv2019

Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium

This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic field. The stability problem on the MHD equations with partial or no dissipation has attracted considerable interests recently and there are substantial developments. The new stability result presented here is among the very few stability conclusions currently available for ideal or partially dissipated MHD equations. As a special consequence of the techniques introduced in this paper, we obtain the small data global well-posedness for the 3D incompressible Navier-Stokes equations without vertical dissipation.

math.AP↗

arXiv2019

Accurate Face Detection for High Performance

Face detection has witnessed significant progress due to the advances of deep convolutional neural networks (CNNs). Its central issue in recent years is how to improve the detection performance of tiny faces. To this end, many recent works propose some specific strategies, redesign the architecture and introduce new loss functions for tiny object detection. In this report, we start from the popular one-stage RetinaNet approach and apply some recent tricks to obtain a high performance face detector. Specifically, we apply the Intersection over Union (IoU) loss function for regression, employ the two-step classification and regression for detection, revisit the data augmentation based on data-anchor-sampling for training, utilize the max-out operation for classification and use the multi-scale testing strategy for inference. As a consequence, the proposed face detection method achieves state-of-the-art performance on the most popular and challenging face detection benchmark WIDER FACE dataset.

cs.CV↗

arXiv2019

Unique weak solutions of the non-resistive magnetohydrodynamic equations with fractional dissipation

This paper examines the uniqueness of weak solutions to the d-dimensional magnetohydrodynamic (MHD) equations with the fractional dissipation $(-Δ)^αu$ and without the magnetic diffusion. Important progress has been made on the standard Laplacian dissipation case $α=1$. This paper discovers that there are new phenomena with the case $α<1$. The approach for $α=1$ can not be directly extended to $α<1$. We establish that, for $α<1$, any initial data $(u_0, b_0)$ in the inhomogeneous Besov space $B^σ_{2,\infty}(\mathbb R^d)$ with $σ> 1+\frac{d}{2}-α$ leads to a unique local solution. For the case $α\ge 1$, $u_0$ in the homogeneous Besov space $\mathring B^{1+\frac{d}{2}-2α}_{2,1}(\mathbb R^d)$ and $b_0$ in $ \mathring B^{1+\frac{d}{2}-α}_{2,1}(\mathbb R^d)$ guarantees the existence and uniqueness. These regularity requirements appear to be optimal.

math.AP↗

arXiv2018

A Large-scale Attribute Dataset for Zero-shot Learning

Zero-Shot Learning (ZSL) has attracted huge research attention over the past few years; it aims to learn the new concepts that have never been seen before. In classical ZSL algorithms, attributes are introduced as the intermediate semantic representation to realize the knowledge transfer from seen classes to unseen classes. Previous ZSL algorithms are tested on several benchmark datasets annotated with attributes. However, these datasets are defective in terms of the image distribution and attribute diversity. In addition, we argue that the "co-occurrence bias problem" of existing datasets, which is caused by the biased co-occurrence of objects, significantly hinders models from correctly learning the concept. To overcome these problems, we propose a Large-scale Attribute Dataset (LAD). Our dataset has 78,017 images of 5 super-classes, 230 classes. The image number of LAD is larger than the sum of the four most popular attribute datasets. 359 attributes of visual, semantic and subjective properties are defined and annotated in instance-level. We analyze our dataset by conducting both supervised learning and zero-shot learning tasks. Seven state-of-the-art ZSL algorithms are tested on this new dataset. The experimental results reveal the challenge of implementing zero-shot learning on our dataset.

cs.CV↗

arXiv2017

AI Challenger : A Large-scale Dataset for Going Deeper in Image Understanding

Significant progress has been achieved in Computer Vision by leveraging large-scale image datasets. However, large-scale datasets for complex Computer Vision tasks beyond classification are still limited. This paper proposed a large-scale dataset named AIC (AI Challenger) with three sub-datasets, human keypoint detection (HKD), large-scale attribute dataset (LAD) and image Chinese captioning (ICC). In this dataset, we annotate class labels (LAD), keypoint coordinate (HKD), bounding box (HKD and LAD), attribute (LAD) and caption (ICC). These rich annotations bridge the semantic gap between low-level images and high-level concepts. The proposed dataset is an effective benchmark to evaluate and improve different computational methods. In addition, for related tasks, others can also use our dataset as a new resource to pre-train their models.

cs.CV↗

arXiv2017

Global regularity for the 2D MHD equations with partial hyperresistivity

This paper establishes the global existence and regularity for a system of the two-dimensional (2D) magnetohydrodynamic (MHD) equations with only directional hyperresistivity. More precisely, the equation of $b_1$ (the horizontal component of the magnetic field) involves only vertical hyperdiffusion (given by $Λ_2^{2β} b_1$) while the equation of $b_2$ (the vertical component) has only horizontal hyperdiffusion (given by $Λ_1^{2β} b_2$), where $Λ_1$ and $Λ_2$ are directional Fourier multiplier operators with the symbols being $|ξ_1|$ and $|ξ_2|$, respectively. We prove that, for $β>1$, this system always possesses a unique global-in-time classical solution when the initial data is sufficiently smooth. The model concerned here is rooted in the MHD equations with only magnetic diffusion, which play a significant role in the study of magnetic reconnection and magnetic turbulence. In certain physical regimes and under suitable scaling, the magnetic diffusion becomes partial (given by part of the Laplacian operator). There have been considerable recent developments on the fundamental issue of whether classical solutions of these equations remain smooth for all time. The papers of Cao-Wu-Yuan \cite{CaoWuYuan} and of Jiu-Zhao \cite{JiuZhao2} obtained the global regularity when the magnetic diffusion is given by the full fractional Laplacian $(-Δ)^β$ with $β>1$. The main result presented in this paper requires only directional fractional diffusion and yet we prove the regularization in all directions. The proof makes use of a key observation on the structure of the nonlinearity in the MHD equations and technical tools on Fourier multiplier operators such as the Hörmander-Mikhlin multiplier theorem. The result presented here appears to be the sharpest for the 2D MHD equations with partial magnetic diffusion.

math.AP↗

arXiv2017

Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion

This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also obtained. These results are achieved through a new approach of diagonalizing a system of coupled linearized equations. The standard method of diagonalization via the eigenvalues and eigenvectors of the matrix symbol is very difficult to implement here. This new process allows us to obtain an integral representation of the full system through explicit kernels. In addition, in order to overcome various difficulties such as the anisotropicity and criticality, we fully exploit the structure of the integral representation and employ extremely delicate Fourier analysis and associated estimates.

math.AP↗

arXiv2016

On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation

This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness of solutions by imposing natural boundary conditions and minimal regularity assumptions on the initial data. Besides, the global solution is shown to possess higher regularity when the initial datum is more regular. To obtain these results, we overcome two main difficulties, one due to the lack of full dissipation and one due to the boundary conditions. In addition to the global regularity problem, we also examine the large-time behavior of solutions and obtain explicit decay rates.

math.AP↗

arXiv2015

Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane

This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these equations defined in the upper half-plane. Under suitable growth conditions on the flux function, we are able to establish the global well-posedness in a Sobolev class. When the initial- and boundary-data become more regular, the corresponding solutions are shown to be classical. In addition, the continuous dependence on the data is also obtained.

math.AP↗

arXiv2015

Blowup in Stagnation-point Form Solutions of the Inviscid 2d Boussinesq Equations

The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth nontrivial initial velocities in stagnation-point form solutions of this system is established. On an infinite strip $Ω=\{(x,y)\in[0,1]\times\mathbb{R}^+\}$, we consider velocities of the form $u=(f(t,x),-yf_x(t,x))$, with scalar temperature\, $θ=yρ(t,x)$. Assuming $f_x(0,x)$ attains its global maximum only at points $x_i^*$ located on the boundary of $[0,1]$, general criteria for finite-time blowup of the vorticity $-yf_{xx}(t,x_i^*)$ and the time integral of $f_x(t,x_i^*)$ are presented. Briefly, for blowup to occur it is sufficient that $ρ(0,x)\geq0$ and $f(t,x_i^*)=ρ(0,x_i^*)=0$, while $-yf_{xx}(0,x_i^*)\neq0$. To illustrate how vorticity may suppress blowup, we also construct a family of global exact solutions. A local-existence result and additional regularity criteria in terms of the time integral of $\left\|f_x(t,\cdot)\right\|_{L^\infty([0,1])}$ are also provided.

math.AP↗

arXiv2015

A global regularity result for the 2D Boussinesq equations with critical dissipation

This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by $Λ^αu$ in the velocity equation and by $Λ^βθ$ in the temperature equation, where $Λ=\sqrt{-Δ}$ denotes the Zygmund operator. We establish the global existence and smoothness of classical solutions when $(α,β)$ is in the critical range: $α>\frac{\sqrt{1777}-23}{24} =0.798103..$, $β>0$ and $α+ β=1$. This result improves the previous work of Jiu, Miao, Wu and Zhang \cite{JMWZ} which obtained the global regularity for $α> \frac{23-\sqrt{145}}{12} \approx 0.9132$, $β>0$ and $α+ β=1$.

math.AP↗

arXiv2015

Local well-posedness for the Hall-MHD equations with fractional magnetic diffusion

The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from kinetic models, are useful in describing many physical phenomena in geophysics and astrophysics. This paper studies the local well-posedness of classical solutions to the Hall-MHD equations with the magnetic diffusion given by a fractional Laplacian operator, $(-Δ)^α$. Due to the presence of the Hall term in the Hall-MHD equations, standard energy estimates appear to indicate that we need $α\ge 1$ in order to obtain the local well-posedness. This paper breaks the barrier and shows that the fractional Hall-MHD equations are locally well-posed for any $α>\frac12$. The approach here fully exploits the smoothing effects of the dissipation and establishes the local bounds for the Sobolev norms through the Besov space techniques. The method presented here may be applicable to similar situations involving other partial differential equations.

math.AP↗

arXiv2014

Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at least for short time. We show that they have real analytic Lagrangian paths. More precisely, we show that as long as a solution of any of these equations is in a class of regularity that assures Hölder continuous gradients of velocity, the corresponding Lagrangian paths are real analytic functions of time. The method of proof is conceptually straightforward and general, and we address the combinatorial issues head-on.

math.AP↗

arXiv2014

An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.

math.AP↗

arXiv2013

Global small solution to the 2D MHD system with a velocity damping term

This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also given.

math.AP↗

arXiv2013

Small global solutions to the damped two-dimensional Boussinesq equations

The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in a satisfactory status. In contrast, the global regularity problem concerning the 2D inviscid Boussinesq equations remains widely open. In an attempt to understand this problem, we examine the damped 2D Boussinesq equations and study how damping affects the regularity of solutions. Since the damping effect is insufficient in overcoming the difficulty due to the "vortex stretching", we seek unique global small solutions and the efforts have been mainly devoted to minimizing the smallness assumption. By positioning the solutions in a suitable functional setting (more precisely the homogeneous Besov space $\mathring{B}^1_{\infty,1}$), we are able to obtain a unique global solution under a minimal smallness assumption.

math.AP↗