Mild Solution of Semilinear SPDEs with Young Drifts

In this paper, we study a semilinear SPDE with a linear Young drift $du_{t}=Lu_{t}dt+f\left(t, u_{t}\right)dt+\left(G_{t}u_{t}+g_{t}\right)d\eta_{t}+h\left(t, u_{t}\right)dW_{t}$, where $L$ is the generator of an analytical semigroup, $\eta$ is an $\alpha$-H\"older continuous path with $\alpha \in \left(1/2, 1\right)$ and $W$ is a Brownian motion. After establishing through two different approaches the Young convolution integrals for stochastic integrands, we introduce the corresponding definition of mild solutions and continuous mild solutions, and give via a fixed-point argument the existence and uniqueness of the (continuous) mild solution under suitable conditions.Comment: 17 page

Exploring Disentangled Content Information for Face Forgery Detection

Convolutional neural network based face forgery detection methods have achieved remarkable results during training, but struggled to maintain comparable performance during testing. We observe that the detector is prone to focus more on content information than artifact traces, suggesting that the detector is sensitive to the intrinsic bias of the dataset, which leads to severe overfitting. Motivated by this key observation, we design an easily embeddable disentanglement framework for content information removal, and further propose a Content Consistency Constraint (C2C) and a Global Representation Contrastive Constraint (GRCC) to enhance the independence of disentangled features. Furthermore, we cleverly construct two unbalanced datasets to investigate the impact of the content bias. Extensive visualizations and experiments demonstrate that our framework can not only ignore the interference of content information, but also guide the detector to mine suspicious artifact traces and achieve competitive performance

DH-AUG: DH Forward Kinematics Model Driven Augmentation for 3D Human Pose Estimation

Due to the lack of diversity of datasets, the generalization ability of the pose estimator is poor. To solve this problem, we propose a pose augmentation solution via DH forward kinematics model, which we call DH-AUG. We observe that the previous work is all based on single-frame pose augmentation, if it is directly applied to video pose estimator, there will be several previously ignored problems: (i) angle ambiguity in bone rotation (multiple solutions); (ii) the generated skeleton video lacks movement continuity. To solve these problems, we propose a special generator based on DH forward kinematics model, which is called DH-generator. Extensive experiments demonstrate that DH-AUG can greatly increase the generalization ability of the video pose estimator. In addition, when applied to a single-frame 3D pose estimator, our method outperforms the previous best pose augmentation method. The source code has been released at https://github.com/hlz0606/DH-AUG-DH-Forward-Kinematics-Model-Driven-Augmentation-for-3D-Human-Pose-Estimation

LSTM Pose Machines

We observed that recent state-of-the-art results on single image human pose estimation were achieved by multi-stage Convolution Neural Networks (CNN). Notwithstanding the superior performance on static images, the application of these models on videos is not only computationally intensive, it also suffers from performance degeneration and flicking. Such suboptimal results are mainly attributed to the inability of imposing sequential geometric consistency, handling severe image quality degradation (e.g. motion blur and occlusion) as well as the inability of capturing the temporal correlation among video frames. In this paper, we proposed a novel recurrent network to tackle these problems. We showed that if we were to impose the weight sharing scheme to the multi-stage CNN, it could be re-written as a Recurrent Neural Network (RNN). This property decouples the relationship among multiple network stages and results in significantly faster speed in invoking the network for videos. It also enables the adoption of Long Short-Term Memory (LSTM) units between video frames. We found such memory augmented RNN is very effective in imposing geometric consistency among frames. It also well handles input quality degradation in videos while successfully stabilizes the sequential outputs. The experiments showed that our approach significantly outperformed current state-of-the-art methods on two large-scale video pose estimation benchmarks. We also explored the memory cells inside the LSTM and provided insights on why such mechanism would benefit the prediction for video-based pose estimations.Comment: Poster in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 201

Inertia of partial transpose of positive semidefinite matrices

We show that the partial transpose of $9\times 9$ positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in "LINEAR AND MULTILINEAR ALGEBRA, Changchun Feng et al, 2022". We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of $12\times 12$ positive semidefinite matrices.Comment: 20 pages, comments are welcom

Electric Field-Induced Magnetization Reversal of Multiferroic Nanomagnet

Using the inverse piezoelectric effect and inverse magnetostrictive effect in a multiferroic heterojunction, an electric field is able to control the magnetization switching of a uniaxial nanomagnet. Compared with traditional spintronic devices based on magnetic field, multiferroic nanomagnet devices have the advantages of ultra-low consumption and high radiation resistance, showing great application potential in modern high-integrated circuits and military electronic systems. However, the difficulties of electric field control of complete magnetization reversal of the nanomagnet and nanomagnet arrays in a nanomagnetic logic gate still restrict the developments of multiferroic nanomagnet device. In this chapter, the uniaxial nanomagnets in multiferroic heterojunctions are mainly discussed. The two core problems of the electric field control of nanomagnets and nanomagnetic logic gate are well solved