[Al(H2O)6][Cr(OH)6Mo6O18]·10H2O

The title compound, [Al(H2O)6][Cr(OH)6Mo6O18]·10H2O, hexa­aqua­aluminium hexa­hydroxidoocta­deca­oxido­molybdo­chromate(III) deca­hydrate, crystallizes isotypically with its gallium analogue [Ga(H2O)6][Cr(OH)6Mo6O18].10H2O. In the structure of the title compound, both the [Al(H2O)6]3+ cation and the Anderson-type [Cr(OH)6Mo6O18]3− anion lie on centres of inversion. The anion is composed of seven edge-sharing octa­hedra, six of which are MoO6 octa­hedra that are arranged hexa­gonally around the central Cr(OH)6 octa­hedron. The anions are linked to each other by O—H⋯O hydrogen bonds into infinite chains along [100]. These chains are further connected with the [Al(H2O)6]3+ cations through O—H⋯O hydrogen bonds into sheets parallel to (01). O—H⋯O hydrogen bonds involving all the lattice water mol­ecules finally link the sheets into a three-dimensional network

MVF-Net: Multi-View 3D Face Morphable Model Regression

We address the problem of recovering the 3D geometry of a human face from a set of facial images in multiple views. While recent studies have shown impressive progress in 3D Morphable Model (3DMM) based facial reconstruction, the settings are mostly restricted to a single view. There is an inherent drawback in the single-view setting: the lack of reliable 3D constraints can cause unresolvable ambiguities. We in this paper explore 3DMM-based shape recovery in a different setting, where a set of multi-view facial images are given as input. A novel approach is proposed to regress 3DMM parameters from multi-view inputs with an end-to-end trainable Convolutional Neural Network (CNN). Multiview geometric constraints are incorporated into the network by establishing dense correspondences between different views leveraging a novel self-supervised view alignment loss. The main ingredient of the view alignment loss is a differentiable dense optical flow estimator that can backpropagate the alignment errors between an input view and a synthetic rendering from another input view, which is projected to the target view through the 3D shape to be inferred. Through minimizing the view alignment loss, better 3D shapes can be recovered such that the synthetic projections from one view to another can better align with the observed image. Extensive experiments demonstrate the superiority of the proposed method over other 3DMM methods.Comment: 2019 Conference on Computer Vision and Pattern Recognitio

On Khintchine exponents and Lyapunov exponents of continued fractions

Assume that $x\in [0,1)$ admits its continued fraction expansion $x=[a_1(x), a_2(x),...]$. The Khintchine exponent $\gamma(x)$ of $x$ is defined by $\gamma(x):=\lim\limits_{n\to \infty}\frac{1}{n}\sum_{j=1}^n \log a_j(x)$ when the limit exists. Khintchine spectrum $\dim E_\xi$ is fully studied, where $E_{\xi}:=\{x\in [0,1):\gamma(x)=\xi\} (\xi \geq 0)$ and $\dim$ denotes the Hausdorff dimension. In particular, we prove the remarkable fact that the Khintchine spectrum $\dim E_{\xi}$, as function of $\xi \in [0, +\infty)$, is neither concave nor convex. This is a new phenomenon from the usual point of view of multifractal analysis. Fast Khintchine exponents defined by $\gamma^{\phi}(x):=\lim\limits_{n\to\infty}\frac{1}{\phi(n)} \sum_{j=1}^n \log a_j(x)$ are also studied, where $\phi (n)$ tends to the infinity faster than $n$ does. Under some regular conditions on $\phi$, it is proved that the fast Khintchine spectrum $\dim (\{x\in [0,1]: \gamma^{\phi}(x)= \xi \})$ is a constant function. Our method also works for other spectra like the Lyapunov spectrum and the fast Lyapunov spectrum.Comment: 37 pages, 5 figures, accepted by Ergodic Theory and Dyanmical System

Self-supervised Learning of Detailed 3D Face Reconstruction

In this paper, we present an end-to-end learning framework for detailed 3D face reconstruction from a single image. Our approach uses a 3DMM-based coarse model and a displacement map in UV-space to represent a 3D face. Unlike previous work addressing the problem, our learning framework does not require supervision of surrogate ground-truth 3D models computed with traditional approaches. Instead, we utilize the input image itself as supervision during learning. In the first stage, we combine a photometric loss and a facial perceptual loss between the input face and the rendered face, to regress a 3DMM-based coarse model. In the second stage, both the input image and the regressed texture of the coarse model are unwrapped into UV-space, and then sent through an image-toimage translation network to predict a displacement map in UVspace. The displacement map and the coarse model are used to render a final detailed face, which again can be compared with the original input image to serve as a photometric loss for the second stage. The advantage of learning displacement map in UV-space is that face alignment can be explicitly done during the unwrapping, thus facial details are easier to learn from large amount of data. Extensive experiments demonstrate the superiority of the proposed method over previous work.Comment: Accepted by IEEE Transactions on Image Processing (TIP

Gemcitabine enhances cell invasion via activating HAb18G/CD147-EGFR-pSTAT3 signaling

Pancreatic cancer, one of the most lethal cancers, has very poor 5-year survival partly due to gemcitabine resistance. Recently, it was reported that chemotherapeutic agents may act as stressors to induce adaptive responses and to promote chemoresistance in cancer cells. During long-term drug treatment, the minority of cancer cells survive and acquire an epithelial-mesenchymal transition phenotype with increased chemo-resistance and metastasis. However, the short-term response of most cancer cells remains unclear. This study aimed to investigate the short-term response of pancreatic cancer cells to gemcitabine stress and to explore the corresponding mechanism. Our results showed that gemcitabine treatment for 24 hours enhanced pancreatic cancer cell invasion. In gemcitabine-treated cells, HAb18G/CD147 was up-regulated; and HAb18G/CD147 down-regulation or inhibition attenuated gemcitabine-enhanced invasion. Mechanistically, HAb18G/CD147 promoted gemcitabine-enhanced invasion by activating the EGFR (epidermal growth factor receptor)-STAT3 (signal transducer and activator of transcription 3) signaling pathway. Inhibition of EGFR-STAT3 signaling counteracted gemcitabine-enhanced invasion, and which relied on HAb18G/CD147 levels. In pancreatic cancer tissues, EGFR was highly expressed and positively correlated with HAb18G/CD147. These data indicate that pancreatic cancer cells enhance cell invasion via activating HAb18G/CD147-EGFR-pSTAT3 signaling. Our findings suggest that inhibiting HAb18G/CD147 is a potential strategy for overcoming drug stress-associated resistance in pancreatic cancer