Flat λ\lambda-Connections, Mochizuki Correspondence and Twistor Spaces

In this paper, we first collect some basic results for $\lambda$-flat bundles, and then get an estimate for the norm of $\lambda$-flat sections, which leads to some vanishing theorem. Mochizuki correspondence provides a homeomorphism between the moduli space of (poly-)stable $\lambda$-flat bundles and that of (poly-)stable Higgs bundles, and provides a dynamical system on the later moduli space (the Dolbeault moduli space). We investigate such dynamical system, in particular, we discuss the corresponding first variation and asymptotic behavior. We generalize the Deligne's twistor construction for any element $\gamma$ of the outer automorphism group of the fundamental group of Riemann surface to obtain the $\gamma$-twistor space, and we apply the twistor theory to study a Lagrangian submanifold of the de Rham moduli space. As an application, we prove a Torelli-type theorem for the twistor spaces, and meanwhile, we prove that the oper stratum in the oper stratification of the de Rham moduli space is the unique closed stratum of minimal dimension, which partially confirms a conjecture by Simpson.Comment: Simpson pointed out a mistake on the Moishezon property for the twistor space in the last version, we delete it and add a section on the study of oper stratification of the de Rham moduli space as an applicatio

The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized K\"ahler Manifolds

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to both $I_+$ and $I_-$, namely $\mathcal{E}$ is $(\alpha,\sigma,\tau)$-polystable if and only if $\mathcal{E}$ admits an $(\alpha,\sigma,\tau)$-Hermitian--Einstein metric.Comment: To appear in The Journal of Geometric Analysi

Moduli Spaces of Parabolic Bundles over P1\mathbb{P}^1 with Five Marked Points

This paper considers the moduli spaces (stacks) of parabolic bundles (parabolic logarithmic flat bundles with given spectrum, parabolic regular Higgs bundles) with rank $2$ and degree $1$ over $\mathbb{P}^1$ with five marked points. The foliation and stratification structures on these moduli spaces (stacks) are investigated. In paricular, we confirm Simpson's conjecture for moduli space of parabolic logarithmic flat bundles with certain non-special weight system

Poly[diaqua­(μ-oxalato)(μ-2-oxidopyridinium-3-carboxyl­ato)lanthanum(III)]

In the title complex, [La(C6H4NO3)(C2O4)(H2O)2]n, the LaIII ion is coordinated by eight O atoms from two 2-oxido­pyridinium-3-carboxyl­ate ligands, two oxalate ligands and two water mol­ecules in a distorted bicapped square-anti­prismatic geometry. The carboxyl­ate groups link adjacent LaIII ions, forming two-dimensional layers that are further linked by N—H⋯O and O—H⋯O hydrogen bonds

Faithful completion of images of scenic landmarks using internet images

Abstract—Previous works on image completion typically aim to produce visually plausible results rather than factually correct ones. In this paper, we propose an approach to faithfully complete the missing regions of an image. We assume that the input image is taken at a well-known landmark, so similar images taken at the same location can be easily found on the Internet. We first download thousands of images from the Internet using a text label provided by the user. Next, we apply two-step filtering to reduce them to a small set of candidate images for use as source images for completion. For each candidate image, a co-matching algorithm is used to find correspondences of both points and lines between the candidate image and the input image. These are used to find an optimal warp relating the two images. A completion result is obtained by blending the warped candidate image into the missing region of the input image. The completion results are ranked according to combination score, which considers both warping and blending energy, and the highest ranked ones are shown to the user. Experiments and results demonstrate that our method can faithfully complete images

Efficient, edge-aware, combined color quantization and dithering

Abstract—In this paper we present a novel algorithm to simultaneously accomplish color quantization and dithering of images. This is achieved by minimizing a perception-based cost function which considers pixel-wise differences between filtered versions of the quantized image and the input image. We use edge aware filters in defining the cost function to avoid mixing colors on opposite sides of an edge. The importance of each pixel is weighted according to its saliency. To rapidly minimize the cost function, we use a modified multi-scale iterative conditional mode (ICM) algorithm which updates one pixel a time while keeping other pixels unchanged. As ICM is a local method, careful initialization is required to prevent termination at a local minimum far from the global one. To address this problem, we initialize ICM with a palette generated by a modified median-cut method. Compared to previous approaches, our method can produce high quality results with fewer visual artifacts but also requires significantly less computational effort. Index Terms—Color quantization, dithering, optimization-based image processing. I