arXiv subjects
Publications and source records attributed to Ken Wang.
In this paper, we consider the Donaldson gauge functional and the twisted Aubin functionals on almost K\"ahler manifolds. As in K\"ahler geometry, we generalize the inequality between Aubin functionals.
In this paper, we introduce $\mathcal{D}^+_J$, a generalization of $\partial\bar{\partial}$ operator on higher dimensional almost K\"{a}hler manifolds. Using the $\mathcal{D}^+_J$ operator, we investigate the $\bar{\partial}$-problem in almost K\"{a}hler geometry and explore the generalized Monge-Amp\`{e}re equation on almost K\"{a}hler manifolds. We establish a uniqueness up to the addition of a constant and local existence theorem for this equation. At last, we find an elliptical system for $\mathcal{D}^+_J$ operator. As an application, we reorganize the result of Tosatti-Weinkove-Yau in \cite{TWY}.
We show the existence and uniqueness of solutions to a generalized Monge-Amp\`{e}re equation on closed almost K\"ahler surfaces, where the equation depends only on the underlying almost K\"ahler structure. As an application, we prove Donaldson's conjecture for tamed almost complex 4-manifolds.
Large-scale Pre-Training Vision-Language Model such as CLIP has demonstrated outstanding performance in zero-shot classification, e.g. achieving 76.3% top-1 accuracy on ImageNet without seeing any example, which leads to potential benefits to many tasks that have no labeled data. However, while applying CLIP to a downstream target domain, the presence of visual and text domain gaps and cross-modality misalignment can greatly impact the model performance. To address such challenges, we propose ReCLIP, the first source-free domain adaptation method for vision-language models, which does not require any source data or target labeled data. ReCLIP first learns a projection space to mitigate the misaligned visual-text embeddings and learns pseudo labels, and then deploys cross-modality self-training with the pseudo labels, to update visual and text encoders, refine labels and reduce domain gaps and misalignments iteratively. With extensive experiments, we demonstrate ReCLIP reduces the average error rate of CLIP from 30.17% to 25.06% on 22 image classification benchmarks. Code available at https://github.com/michiganleon/ReCLIP_WACV.
In this paper, by using weakly \widetilde{\mathcal{D}}^+_J (resp. \mathcal{D}^+_J )-closed technique firstly introduced by Tan, Wang, Zhou and Zhu, we will give a characterization of tamed and weakened tamed four-manifolds, and an almost Kaehler version of Nakai-Moishezon criterion for almost complex four-manifolds.
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent and diffusive waves is explored in detailed, and found to be comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems.