arXiv subjects
Publications and source records attributed to Yongjie Shi.
In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequality, we obtain sharp logarithmic Sobolev inequalities on integer lattices.
In this paper, we extend a lower bound estimate for Steklov eigenvalues by Perrin \cite{Pe} on unit-weighted graphs to general weighted graphs and characterise its rigidity.
In this paper, we obtain some comparisons of the Dirichlet, Neumann and Laplacian eigenvalues on graphs. We also discuss their rigidities and some of their applications including some Lichnerowicz-type, Fiedler-type and Friedman-type estimates for Dirichlet eigenvalues and Neumann eigenvalues. The comparisons on Neumann eigenvalues can be translated to comparisons on Steklov eigenvalues in our setting. So, some of the results can be viewed as extensions for parts of the works of \cite{HHW} by Hua-Huang-Wang, and parts of our previous works \cite{SY,SY2}.
Temporal modeling is crucial for video super-resolution. Most of the video super-resolution methods adopt the optical flow or deformable convolution for explicitly motion compensation. However, such temporal modeling techniques increase the model complexity and might fail in case of occlusion or complex motion, resulting in serious distortion and artifacts. In this paper, we propose to explore the role of explicit temporal difference modeling in both LR and HR space. Instead of directly feeding consecutive frames into a VSR model, we propose to compute the temporal difference between frames and divide those pixels into two subsets according to the level of difference. They are separately processed with two branches of different receptive fields in order to better extract complementary information. To further enhance the super-resolution result, not only spatial residual features are extracted, but the difference between consecutive frames in high-frequency domain is also computed. It allows the model to exploit intermediate SR results in both future and past to refine the current SR output. The difference at different time steps could be cached such that information from further distance in time could be propagated to the current frame for refinement. Experiments on several video super-resolution benchmark datasets demonstrate the effectiveness of the proposed method and its favorable performance against state-of-the-art methods.
Recently unsupervised domain adaptation for the semantic segmentation task has become more and more popular due to high-cost of pixel-level annotation on real-world images. However, most domain adaptation methods are only restricted to single-source-single-target pair, and can not be directly extended to multiple target domains. In this work, we propose a collaborative learning framework to achieve unsupervised multi-target domain adaptation. An unsupervised domain adaptation expert model is first trained for each source-target pair and is further encouraged to collaborate with each other through a bridge built between different target domains. These expert models are further improved by adding the regularization of making the consistent pixel-wise prediction for each sample with the same structured context. To obtain a single model that works across multiple target domains, we propose to simultaneously learn a student model which is trained to not only imitate the output of each expert on the corresponding target domain, but also to pull different expert close to each other with regularization on their weights. Extensive experiments demonstrate that the proposed method can effectively exploit rich structured information contained in both labeled source domain and multiple unlabeled target domains. Not only does it perform well across multiple target domains but also performs favorably against state-of-the-art unsupervised domain adaptation methods specially trained on a single source-target pair
In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity. As applications of the comparison of eigenvalues, we obtain Lichnerowicz-type estimates and some combinatorial estimates for Steklov eigenvalues on graphs.
Data-driven based approaches, in spite of great success in many tasks, have poor generalization when applied to unseen image domains, and require expensive cost of annotation especially for dense pixel prediction tasks such as semantic segmentation. Recently, both unsupervised domain adaptation (UDA) from large amounts of synthetic data and semi-supervised learning (SSL) with small set of labeled data have been studied to alleviate this issue. However, there is still a large gap on performance compared to their supervised counterparts. We focus on a more practical setting of semi-supervised domain adaptation (SSDA) where both a small set of labeled target data and large amounts of labeled source data are available. To address the task of SSDA, a novel framework based on dual-level domain mixing is proposed. The proposed framework consists of three stages. First, two kinds of data mixing methods are proposed to reduce domain gap in both region-level and sample-level respectively. We can obtain two complementary domain-mixed teachers based on dual-level mixed data from holistic and partial views respectively. Then, a student model is learned by distilling knowledge from these two teachers. Finally, pseudo labels of unlabeled data are generated in a self-training manner for another few rounds of teachers training. Extensive experimental results have demonstrated the effectiveness of our proposed framework on synthetic-to-real semantic segmentation benchmarks.
In this paper, we obtain a Lichnerowicz-type estimate for the first Steklov eigenvalues on graphs and discuss its rigidity.
In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.
In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Trace and inverse trace of Steklov eigenvalues. J. Differential Equations 261 (2016), no. 3, 2026--2040.). Namely, we show that equality of the estimate holds if and only if the manifold is a direct product of a round ball and a closed manifold. The key ingredient in the proof is a decomposition theorem for flat and totally geodesic Riemannian submersions which may be of independent interests.
In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-Wang\cite{HHW} and Hassannezhad-Miclo \cite{HM}. Then, some Raulot-Savo-type estimates on the eigenvalues of the DtN maps introduced are derived.
Let $f:M^m\to N^n$ be a smooth map between two differential manifolds with $N$ connected, $f(M)$ closed and $f(M)\neq N$. In this short note, we show that either all the points of $M$ are critical points of $f$ or the dimension the collection of all critical points of $f$ is not less than $n-1$. Some consequences of this result for surjectivity of mappings are also presented.
In this paper, we present an interesting application of Baire's category theorem.
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.