Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions

We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.Comment: 22 pages, 2 tables; v2: ref added, minor typos fixe

Fast Preprocessing for Robust Face Sketch Synthesis

Exemplar-based face sketch synthesis methods usually meet the challenging problem that input photos are captured in different lighting conditions from training photos. The critical step causing the failure is the search of similar patch candidates for an input photo patch. Conventional illumination invariant patch distances are adopted rather than directly relying on pixel intensity difference, but they will fail when local contrast within a patch changes. In this paper, we propose a fast preprocessing method named Bidirectional Luminance Remapping (BLR), which interactively adjust the lighting of training and input photos. Our method can be directly integrated into state-of-the-art exemplar-based methods to improve their robustness with ignorable computational cost.Comment: IJCAI 2017. Project page: http://www.cs.cityu.edu.hk/~yibisong/ijcai17_sketch/index.htm

Learning to Hallucinate Face Images via Component Generation and Enhancement

We propose a two-stage method for face hallucination. First, we generate facial components of the input image using CNNs. These components represent the basic facial structures. Second, we synthesize fine-grained facial structures from high resolution training images. The details of these structures are transferred into facial components for enhancement. Therefore, we generate facial components to approximate ground truth global appearance in the first stage and enhance them through recovering details in the second stage. The experiments demonstrate that our method performs favorably against state-of-the-art methodsComment: IJCAI 2017. Project page: http://www.cs.cityu.edu.hk/~yibisong/ijcai17_sr/index.htm

Stylizing Face Images via Multiple Exemplars

We address the problem of transferring the style of a headshot photo to face images. Existing methods using a single exemplar lead to inaccurate results when the exemplar does not contain sufficient stylized facial components for a given photo. In this work, we propose an algorithm to stylize face images using multiple exemplars containing different subjects in the same style. Patch correspondences between an input photo and multiple exemplars are established using a Markov Random Field (MRF), which enables accurate local energy transfer via Laplacian stacks. As image patches from multiple exemplars are used, the boundaries of facial components on the target image are inevitably inconsistent. The artifacts are removed by a post-processing step using an edge-preserving filter. Experimental results show that the proposed algorithm consistently produces visually pleasing results.Comment: In CVIU 2017. Project Page: http://www.cs.cityu.edu.hk/~yibisong/cviu17/index.htm

Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs

Let $G_k$ be a connected reductive algebraic group over an algebraically closed field $k$ of characteristic $\neq 2$. Let $K_k \subset G_k$ be a quasi-split symmetric subgroup of $G_k$ with respect to an involution $\theta_k$ of $G_k$. The classification of such involutions is independent of the characteristic of $k$ (provided not $2$). We first construct a closed subgroup scheme \mathbf{G}^\imath of the Chevalley group scheme $\mathbf{G}$ over $\mathbb{Z}$. The pair (\mathbf{G}, \mathbf{G}^\imath) parameterizes symmetric pairs of the given type over any algebraically closed field of characteristic $\neq 2$, that is, the geometric fibre of \mathbf{G}^\imath becomes the reductive group $K_k \subset G_k$ over any algebraically closed field $k$ of characteristic $\neq 2$. As a consequence, we show the coordinate ring of the group $K_k$ is spanned by the dual $\imath$canonical basis of the corresponding $\imath$quantum group. We then construct a quantum Frobenius splitting for the quasi-split $\imath$quantum group at roots of $1$. This generalizes Lusztig's quantum Frobenius splitting for quantum groups at roots of $1$. Over a field of positive characteristic, our quantum Frobenius splitting induces a Frobenius splitting of the algebraic group $K_k$. Finally, we construct Frobenius splittings of the flag variety $G_k / B_k$ that compatibly split certain $K_k$-orbit closures over positive characteristics. We deduce cohomological vanishings of line bundles as well as normalities. Results apply to characteristic $0$ as well, thanks to the existence of the scheme \mathbf{G}^\imath. Our construction of splittings is based on the quantum Frobenius splitting of the corresponding $\imath$quantum group.Comment: 65 page