Hierarchy Composition GAN for High-fidelity Image Synthesis

Despite the rapid progress of generative adversarial networks (GANs) in image synthesis in recent years, the existing image synthesis approaches work in either geometry domain or appearance domain alone which often introduces various synthesis artifacts. This paper presents an innovative Hierarchical Composition GAN (HIC-GAN) that incorporates image synthesis in geometry and appearance domains into an end-to-end trainable network and achieves superior synthesis realism in both domains simultaneously. We design an innovative hierarchical composition mechanism that is capable of learning realistic composition geometry and handling occlusions while multiple foreground objects are involved in image composition. In addition, we introduce a novel attention mask mechanism that guides to adapt the appearance of foreground objects which also helps to provide better training reference for learning in geometry domain. Extensive experiments on scene text image synthesis, portrait editing and indoor rendering tasks show that the proposed HIC-GAN achieves superior synthesis performance qualitatively and quantitatively.Comment: 11 pages, 8 figure

The limit set of iterations of entire functions on wandering domains

We first establish any continuum without interiors can be a limit set of iterations of an entire function on an oscillating wandering domain, and hence arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every bounded connected regular open set, whose closure has a connected complement, is an oscillating or an escaping wandering domain of some entire function. A natural question is: What kind of domains can be realized as a periodic domain of some entire function? In this paper, we construct a sequence of entire functions whose invariant Fatou components can be approached to a regular domain

A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces

In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space $\mathbb{P}^k$. This is a generalization of Cartan's Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersects $O(k^3)$ many totally geodesic hypersurfaces

Spectral Unsupervised Domain Adaptation for Visual Recognition

Unsupervised domain adaptation (UDA) aims to learn a well-performed model in an unlabeled target domain by leveraging labeled data from one or multiple related source domains. It remains a great challenge due to 1) the lack of annotations in the target domain and 2) the rich discrepancy between the distributions of source and target data. We propose Spectral UDA (SUDA), an efficient yet effective UDA technique that works in the spectral space and is generic across different visual recognition tasks in detection, classification and segmentation. SUDA addresses UDA challenges from two perspectives. First, it mitigates inter-domain discrepancies by a spectrum transformer (ST) that maps source and target images into spectral space and learns to enhance domain-invariant spectra while suppressing domain-variant spectra simultaneously. To this end, we design novel adversarial multi-head spectrum attention that leverages contextual information to identify domain-variant and domain-invariant spectra effectively. Second, it mitigates the lack of annotations in target domain by introducing multi-view spectral learning which aims to learn comprehensive yet confident target representations by maximizing the mutual information among multiple ST augmentations capturing different spectral views of each target sample. Extensive experiments over different visual tasks (e.g., detection, classification and segmentation) show that SUDA achieves superior accuracy and it is also complementary with state-of-the-art UDA methods with consistent performance boosts but little extra computation

Quantum color screening in external magnetic field

We calculate color screening mass in a thermalized and magnetized QCD matter in the frame of loop resummation theory at finite temperature and magnetic field. Different from the normal Debye screening in classical electrodynamics, the color screening mass in an external magnetic field is characterized by the quantized quark transverse energy $\epsilon_n^2=2n|qB|$, similar to the Landau energy levels derived in quantum mechanics. Our calculation without constriction to the temperature and magnetic field strengths comes back to the well-known results in the limits of weak and strong magnetic field.Comment: 9 pages, 1 figur