Bei Zhang

Jikun Zhao, Wenhao Zhu, Bei Zhang et al.

In this paper, we introduce a new framework for designing stabilization-free virtual element methods (VEMs) based on an finite element interpolation-based strategy, where we can simultaneously eliminate the stabilization terms in the discretizations of diffusion and reaction terms. The core idea is to construct a computable, polynomial-preserving, and norm-equivalent interpolation operator from the virtual element space to a (local) finite element space. Leveraging the properties of this operator, we design two types of stabilization-free schemes. The first scheme requires the interpolation to preserve the polynomial consistency related to the bilinear forms, thereby maintaining both consistency and stability as in the standard VEM. The second scheme relaxes this consistency requirement. While it may not satisfy the standard polynomial consistency, the second scheme retains optimal convergence with simpler construction, fewer degrees of freedom and, more importantly, applicable to more complex problems such as those involving nonlinearities or variable coefficients. We construct concrete interpolation operators for both conforming and nonconforming virtual elements in two and three dimensions. These operators are then employed to realize stabilization-free schemes for conforming and nonconforming VEMs. Numerical experiments confirm the optimal convergence rates of the proposed methods. The presented framework can be extended to design stabilization-free schemes for other polytopal discretization methods, such as the hybrid high-order method and the weak Galerkin method.

Kexin Luo, Yue Mao, Bei Zhang et al.

Inspired by the concept of the male gaze (Mulvey, 1975) in literature and media studies, this paper proposes a framework for analyzing gender bias in terms of female objectification: the extent to which a text portrays female individuals as objects of visual pleasure. Our framework measures female objectification along two axes. First, we compute an agency bias score that indicates whether male entities are more likely to appear in the text as grammatical agents than female entities. Next, by analyzing the word embedding space induced by a text (Caliskan et al., 2017), we compute an appearance bias score that indicates whether female entities are more closely associated with appearance-related words than male entities. Applying our framework to 19th and 20th century novels reveals evidence of female objectification in literature: we find that novels written from a male perspective systematically objectify female characters, while novels written from a female perspective do not exhibit statistically significant objectification of any gender.