arXiv subjects

Lijuan Wang

Publications and source records attributed to Lijuan Wang.

159 records · Page 9Linked to original sources

arXiv2020

Constrained approximate null controllability of coupled heat equation with periodic impulse controls

This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices $\{Q_k\}_{k=1}^\hbar$. The conclusions are given in two cases. In the case that the controls act globally into the system, we prove that the system is global constrained approximate null controllable under a spectral condition of $P$ together with a rank condition of $P$ and $\{Q_k\}_{k=1}^\hbar$; While in the case that the controls act locally into the system, we prove the global constrained approximate null controllability under a stronger condition for $P$ and the same rank condition as the above case. Moreover, we prove that the above mentioned spectral condition of $P$ is necessary for global constrained approximate null controllability of the control problem considered in this paper.

math.OC↗

arXiv2020

Cross-Domain Complementary Learning Using Pose for Multi-Person Part Segmentation

Supervised deep learning with pixel-wise training labels has great successes on multi-person part segmentation. However, data labeling at pixel-level is very expensive. To solve the problem, people have been exploring to use synthetic data to avoid the data labeling. Although it is easy to generate labels for synthetic data, the results are much worse compared to those using real data and manual labeling. The degradation of the performance is mainly due to the domain gap, i.e., the discrepancy of the pixel value statistics between real and synthetic data. In this paper, we observe that real and synthetic humans both have a skeleton (pose) representation. We found that the skeletons can effectively bridge the synthetic and real domains during the training. Our proposed approach takes advantage of the rich and realistic variations of the real data and the easily obtainable labels of the synthetic data to learn multi-person part segmentation on real images without any human-annotated labels. Through experiments, we show that without any human labeling, our method performs comparably to several state-of-the-art approaches which require human labeling on Pascal-Person-Parts and COCO-DensePose datasets. On the other hand, if part labels are also available in the real-images during training, our method outperforms the supervised state-of-the-art methods by a large margin. We further demonstrate the generalizability of our method on predicting novel keypoints in real images where no real data labels are available for the novel keypoints detection. Code and pre-trained models are available at https://github.com/kevinlin311tw/CDCL-human-part-segmentation

cs.CV↗

arXiv2020

Rethinking Classification and Localization for Object Detection

Two head structures (i.e. fully connected head and convolution head) have been widely used in R-CNN based detectors for classification and localization tasks. However, there is a lack of understanding of how does these two head structures work for these two tasks. To address this issue, we perform a thorough analysis and find an interesting fact that the two head structures have opposite preferences towards the two tasks. Specifically, the fully connected head (fc-head) is more suitable for the classification task, while the convolution head (conv-head) is more suitable for the localization task. Furthermore, we examine the output feature maps of both heads and find that fc-head has more spatial sensitivity than conv-head. Thus, fc-head has more capability to distinguish a complete object from part of an object, but is not robust to regress the whole object. Based upon these findings, we propose a Double-Head method, which has a fully connected head focusing on classification and a convolution head for bounding box regression. Without bells and whistles, our method gains +3.5 and +2.8 AP on MS COCO dataset from Feature Pyramid Network (FPN) baselines with ResNet-50 and ResNet-101 backbones, respectively.

cs.CV↗

arXiv2020

Learning Nonparametric Human Mesh Reconstruction from a Single Image without Ground Truth Meshes

Nonparametric approaches have shown promising results on reconstructing 3D human mesh from a single monocular image. Unlike previous approaches that use a parametric human model like skinned multi-person linear model (SMPL), and attempt to regress the model parameters, nonparametric approaches relax the heavy reliance on the parametric space. However, existing nonparametric methods require ground truth meshes as their regression target for each vertex, and obtaining ground truth mesh labels is very expensive. In this paper, we propose a novel approach to learn human mesh reconstruction without any ground truth meshes. This is made possible by introducing two new terms into the loss function of a graph convolutional neural network (Graph CNN). The first term is the Laplacian prior that acts as a regularizer on the reconstructed mesh. The second term is the part segmentation loss that forces the projected region of the reconstructed mesh to match the part segmentation. Experimental results on multiple public datasets show that without using 3D ground truth meshes, the proposed approach outperforms the previous state-of-the-art approaches that require ground truth meshes for training.

cs.CV↗

arXiv2019

Observability inequalities for the heat equation with bounded potentials on the whole space

In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy localized in a subdomain, which is equidistributed over the whole space. The proof of this inequality is mainly adapted from the parabolic frequency function method, which plays an important role in proving the unique continuation property for solutions of parabolic equations. As an immediate application, we show that the null controllability holds for the heat equation with bounded potentials on the whole space.

math.AP↗

arXiv2019

Large Scale Incremental Learning

Modern machine learning suffers from catastrophic forgetting when learning new classes incrementally. The performance dramatically degrades due to the missing data of old classes. Incremental learning methods have been proposed to retain the knowledge acquired from the old classes, by using knowledge distilling and keeping a few exemplars from the old classes. However, these methods struggle to scale up to a large number of classes. We believe this is because of the combination of two factors: (a) the data imbalance between the old and new classes, and (b) the increasing number of visually similar classes. Distinguishing between an increasing number of visually similar classes is particularly challenging, when the training data is unbalanced. We propose a simple and effective method to address this data imbalance issue. We found that the last fully connected layer has a strong bias towards the new classes, and this bias can be corrected by a linear model. With two bias parameters, our method performs remarkably well on two large datasets: ImageNet (1000 classes) and MS-Celeb-1M (10000 classes), outperforming the state-of-the-art algorithms by 11.1% and 13.2% respectively.

cs.CV↗

arXiv2018

Minimal time impulse control of the heat equation

The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution of the heat equation from a given initial state to a given target set as soon as possible. We will first study the existence and uniqueness of optimal solution for this problem. In the formulation of this problem, there are two parameters: one is the upper bound of the control constraint and the other one is the moment of impulse time. Then, we will establish the continuity of the minimal time function of this problem with respect to the above mentioned two parameters. Moreover, the convergence of the optimal control is also discussed.

math.OC↗

arXiv2018

Minimal time control of exact synchronization for parabolic systems

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The purpose of such a problem is to find a control (from a constraint set) synchronizing components of the corresponding solution vector for the controlled system in the shortest time. In this paper, we build up a necessary and sufficient condition for the optimal time and the optimal control; we also obtain how the existence of optimal controls depends on the above mentioned two parameters.

math.OC↗

arXiv2018

A Game Problem for Heat Equation

In this paper, we consider a two-person game problem governed by a linear heat equation. The existence of Nash equilibrium for this problem is considered. Moreover, the bang-bang property of Nash equilibrium is discussed.

math.OC↗

arXiv2018

Incremental Classifier Learning with Generative Adversarial Networks

In this paper, we address the incremental classifier learning problem, which suffers from catastrophic forgetting. The main reason for catastrophic forgetting is that the past data are not available during learning. Typical approaches keep some exemplars for the past classes and use distillation regularization to retain the classification capability on the past classes and balance the past and new classes. However, there are four main problems with these approaches. First, the loss function is not efficient for classification. Second, there is unbalance problem between the past and new classes. Third, the size of pre-decided exemplars is usually limited and they might not be distinguishable from unseen new classes. Forth, the exemplars may not be allowed to be kept for a long time due to privacy regulations. To address these problems, we propose (a) a new loss function to combine the cross-entropy loss and distillation loss, (b) a simple way to estimate and remove the unbalance between the old and new classes , and (c) using Generative Adversarial Networks (GANs) to generate historical data and select representative exemplars during generation. We believe that the data generated by GANs have much less privacy issues than real images because GANs do not directly copy any real image patches. We evaluate the proposed method on CIFAR-100, Flower-102, and MS-Celeb-1M-Base datasets and extensive experiments demonstrate the effectiveness of our method.

cs.CV↗

arXiv2015

Bang-bang property of time optimal controls for some semilinear heat equation

In this paper, we derive a bang-bang property of a kind of time optimal control problem for some semilinear heat equation on bounded $C^2$ domains (of the Euclidean space), with homogeneous Dirichlet boundary condition and controls distributed on an open and non-empty subset of the domain where the equation evolves.

math.OC↗

arXiv2015

Impulse and sampled-data optimal control of heat equations, and error estimates

We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique optimal solution, which can be characterized by an optimality system derived from the Pontryagin maximum principle. We define two approximations of this optimal control problem. The first one is an impulse approximation, and consists of considering a system of linear heat equations with impulse control. The second one is obtained by the sample-and-hold procedure applied to the control, resulting into a sampled-data approximation of the controlled heat equation. We prove that both problems have a unique optimal solution, and we establish precise error estimates for the optimal controls and optimal states of the initial problem with respect to its impulse and sampled-data approximations.

math.OC↗

arXiv2014

Mediation analysis with missing data through multiple imputation and bootstrap

A method using multiple imputation and bootstrap for dealing with missing data in mediation analysis is introduced and implemented in SAS. Through simulation studies, it is shown that the method performs well for both MCAR and MAR data without and with auxiliary variables. It is also shown that the method works equally well for MNAR data if auxiliary variables related to missingness are included. The application of the method is demonstrated through the analysis of a subset of data from the National Longitudinal Survey of Youth.

stat.ME↗

arXiv2010

Heterogeneous confinement in laterally coupled InGaAs/GaAs quantum dot molecules under lateral electric fields

We study the electronic and optical properties of laterally coupled InGaAs/GaAs quantum dot molecules under lateral electric field. We find that electrons perceive the double-dot structure as a compound single object, while the holes discern two well separated dots. Through a combination of predictive atomistic modeling, detailed morphology studies, and single object micro-photoluminescence measurements, we show that this peculiar confinement results in an unusual heterogeneous behavior of electrons and holes with profound consequences on optical properties.

cond-mat.mes-hall↗

arXiv2006

{\it In-situ} Laser Microprocessing at the Quantum Level

One of the biggest challenges of nanotechnology is the fabrication of nano-objects with perfectly controlled properties. Here we employ a focused laser beam both to characterize and to {\it in-situ} modify single semiconductor structures by heating them from cryogenic to high temperatures. The heat treatment allows us to blue-shift, in a broad range and with resolution-limited accuracy, the quantized energy levels of light and charge carriers confined in optical microcavities and self-assembled quantum dots (QDs). We demonstrate the approach by tuning an optical mode into resonance with the emission of a single QD and by bringing different QDs in mutual resonance. This processing method may open the way to a full control of nanostructures at the quantum level.

cond-mat.mtrl-sci↗