arXiv subjects

Chao Deng

Publications and source records attributed to Chao Deng.

97 records · Page 6Linked to original sources

arXiv2018

Single-shot thermal ghost imaging using wavelength-division multiplexing

Ghost imaging (GI) is a potential imaging technique that reconstructs the target scene from its correlated measurements with a sequential of patterns. Restricted by the multi-shot principle, GI usually requires long acquisition time and is limited in observation of dynamic scenes. To handle this problem, this paper proposes a single-shot thermal ghost imaging scheme via wavelength-division multiplexing technique. Specifically, we generate thousands of patterns simultaneously by modulating a broadband light source with a wavelength dependent diffuser. These patterns carry the scene's spatial information and then the correlated measurements are coupled into a spectrometer for the final reconstruction. This technique accelerates the ghost imaging speed significantly and promotes the applications in dynamic ghost imaging.

physics.optics↗

arXiv2016

Variational Autoencoders for Semi-supervised Text Classification

Although semi-supervised variational autoencoder (SemiVAE) works in image classification task, it fails in text classification task if using vanilla LSTM as its decoder. From a perspective of reinforcement learning, it is verified that the decoder's capability to distinguish between different categorical labels is essential. Therefore, Semi-supervised Sequential Variational Autoencoder (SSVAE) is proposed, which increases the capability by feeding label into its decoder RNN at each time-step. Two specific decoder structures are investigated and both of them are verified to be effective. Besides, in order to reduce the computational complexity in training, a novel optimization method is proposed, which estimates the gradient of the unlabeled objective function by sampling, along with two variance reduction techniques. Experimental results on Large Movie Review Dataset (IMDB) and AG's News corpus show that the proposed approach significantly improves the classification accuracy compared with pure-supervised classifiers, and achieves competitive performance against previous advanced methods. State-of-the-art results can be obtained by integrating other pretraining-based methods.

cs.CL↗

arXiv2013

Well-posedness and ill-posedness of the 3D generalized Navier-Stokes equations in Triebel-Lizorkin spaces

In this paper, we study the Cauchy problem of the 3-dimensional (3D) generalized incompressible Navier-Stokes equations (gNS) in Triebel-Lizorkin space $\dot{F}^{-α,r}_{q_α}(\mathbb{R}^3)$ with $(α,r)\in(1,5/4)\times[2,\infty]$ and $q_α=\frac{3}{α-1}$. Our work establishes a {\it dichotomy} of well-posedness and ill-posedness depending on $r=2$ or $r>2$. Specifically, by combining the new endpoint bilinear estimates in $L^{q_α}_x L^2_T$ with the characterization of Triebel-Lizorkin space via fractional semigroup, we prove the well-posedness of the gNS in $\dot{F}^{-α,r}_{q_α}(\mathbb{R}^3)$ for $r=2$. On the other hand, for any $r>2$, we show that the solution to the gNS can develop {\it norm inflation} in the sense that arbitrarily small initial data in the spaces $\dot{F}^{-α,r}_{q_α}(\mathbb{R}^3)$ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In particular, such dichotomy of Triebel-Lizorkin spaces is also true for the classical N-S equations, i.e.\,\,$α=1$. Thus the Triebel-Lizorkin space framework naturally provides better connection between the well-known Koch-Tataru's $BMO^{-1}$ well-posed work and Bourgain-Pavlović's $\dot{B}_\infty^{-1,\infty}$ ill-posed work.

math.AP↗

arXiv2012

Well-posedness of a Parabolic-hyperbolic Keller-Segel System in the Sobolev Space Framework

We study the global strong solutions to a 3-dimensional parabolic-hyperbolic Keller-Segel model with initial data close to a stable equilibrium with perturbations belonging to $L^2(\mathbb R^3)\times H^1(\mathbb{R}^3)$. We obtain global well-posedness and decay property. Furthermore, if the mean value of initial cell density is smaller than a suitabale constant, then the chemical concentration decays exponentially to zero as $t$ goes to infinity. Proofs of the main results are based on an application of Fourier analysis method to uniform estimates for a linearized parabolic-hyperbolic system and also based on the smoothing effect of the cell density as well as the damping effect of the chemical concentration.

math.AP↗

arXiv2012

Global Well-posedness of the Parabolic-parabolic Keller-Segel Model in $L^{1}(R^2)\times{L}^{\infty}(R^2)$ and $H^1_b(R^2)\times{H}^1(R^2)$

In this paper, we study global well-posedness of the two-dimensional Keller-Segel model in Lebesgue space and Sobolev space. Recall that in the paper "Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space, J. Differential Equations, {252}(2012), 1213--1228", Kozono, Sugiyama & Wachi studied global well-posedness of $n$($\ge3$) dimensional Keller-Segel system and posted a question about the even local in time existence for the Keller-Segel system with $L^1(R^2)\times{L}^\infty(R^2)$ initial data. Here we give an affirmative answer to this question: in fact, we show the global in time existence and uniqueness for $L^1(R^2)\times{L}^{\infty}(R^2)$ initial data. Furthermore, we prove that for any $H^1_b(R^2) \times {H}^1(R^2)$ initial data with $H^1_b(R^2):=H^1(R^2)\cap{L}^\infty(R^2)$, there also exists a unique global mild solution to the parabolic-parabolic Keller-Segel model. The estimates of ${\sup_{t>0}}t^{1-\frac{n}{p}}\|u\|_{L^p}$ for $(n,p)=(2,\infty)$ and the introduced special half norm, i.e. $\sup_{t>0}t^{1/2}(1+t)^{-1/2}\|\nabla{v}\|_{L^\infty}$, are crucial in our proof.

math.AP↗

arXiv2011

Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index $s=-1$

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,θ_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,ε}_{p,\infty}$ if $r\in[1,\infty]$, $ε>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,ε}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $ε>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.

math.AP↗

arXiv2011

Random-data Cauchy Problem for the Periodic Navier-Stokes Equations with Initial Data in Negative-order Sobolev Spaces

In this paper we study existence of solutions of the initial-boundary value problems of the Navier-Stokes equations with a periodic boundary value condition for initial data in the Sobolev spaces $\mathcal{H}^{s}(\mathbb{T}^N)$ with a negative order $-1<s<0$, where $N=2, 3$. By using the randomization approach of N. Burq and N. Tzvetkov, we prove that for almost all $ω\inΩ$, where $Ω$ is the sample space of a probability space $(Ω,\mathcal{A},p)$, for the randomized initial data $\vec{f}^ω\in\mathcal{H}_σ^{s}(\mathbb{T}^N)$ with $-1<s<0$, such a problem has a unique local solution.

math.AP↗