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Monocular 3D face reconstruction plays a crucial role in avatar generation, with significant demand in web-related applications such as generating virtual financial advisors in FinTech. Current reconstruction methods predominantly rely on deep learning techniques and employ 2D self-supervision as a means to guide model learning. However, these methods encounter challenges in capturing the comprehensive 3D structural information of the face due to the utilization of 2D images for model training purposes. To overcome this limitation and enhance the reconstruction of 3D structural features, we propose an innovative approach that integrates existing 2D features with 3D features to guide the model learning process. Specifically, we introduce the 3D-ID Loss, which leverages the high-dimensional structure features extracted from a Spectral-Based Graph Convolution Encoder applied to the facial mesh. This approach surpasses the sole reliance on the 3D information provided by the facial mesh vertices coordinates. Our model is trained using 2D-3D data pairs from a combination of datasets and achieves state-of-the-art performance on the NoW benchmark., Comment: 4 pages, 3 figures. Accepted to WWW 2024

This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange finite elements, setting the foundation for further analysis. The discussion then extends to $H(\rm{div})$-conforming and $H(\rm{curl})$-conforming finite element spaces, adopting variable frames across differing sub-simplices. The imposition of tangential or normal continuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice., Comment: 23 pages, 6 figures

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly-regular simplicial meshes. This can be a significant limitation for many popular methods based on polytopal meshes in the case of inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces, and potentially worsened by geometric singularities, making many popular methods based on broken spaces, non-conforming or polytopal meshes particularly challenging to apply. In this article, we present a virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. There are two key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely $\mathbf{H}^{\theta}$ regularity, $\theta\in(1/2,1]$; (ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method.

Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local $H(\textrm{div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization., Comment: 26 pages, 8 figures

Security is one of the biggest concern in power system operation. Recently, the emerging cyber security threats to operational functions of power systems arouse high public attention, and cybersecurity vulnerability thus become an emerging topic to evaluate compromised operational performance under cyber attack. In this paper, vulnerability of cyber security of load frequency control (LFC) system, which is the key component in energy manage system (EMS), is assessed by exploiting the system response to attacks on LFC variables/parameters. Two types of attacks: 1) injection attack and 2) scale attack are considered for evaluation. Two evaluation criteria reflecting the damage on system stability and power generation are used to quantify system loss under cyber attacks. Through a sensitivity-based method and attack tree models, the vulnerability of different LFC components is ranked. In addition, a post-intrusion cyber attack detection scheme is proposed. Classification-based schemes using typical classification algorithms are studied and compared to identify different attack scenarios., Comment: 9 pages, 13 figures

In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging nodes as polygon vertices without additional processing. Besides, to effectively simulate the phase separation behavior in strong segregation systems, an adaptive method on polygonal mesh equipped with a new marking strategy is developed. This new marking strategy will indicate the times of marked elements to be refined and coarsened, making full use of the information contained in the current numerical results. Using the halfedge data structure, we can apply the adaptive method to the arbitrary polygonal mesh. Numerical results demonstrate that the developed method is efficient in simulating polymers' phase behavior in complex geometric domains. The accuracy is consistent with theoretical results. The adaptive method can greatly reduce computational costs to obtain prescribed numerical accuracy for strong segregation systems., Comment: 17 pages, 11 figures