Matrix GARCH Model: Inference and Application

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the identification of conditional row and column covariance matrices. Moreover, we introduce a quasi maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices

Optical biopsy identification and grading of gliomas using label-free visible resonance Raman spectroscopy.

Glioma is one of the most refractory types of brain tumor. Accurate tumor boundary identification and complete resection of the tumor are essential for glioma removal during brain surgery. We present a method based on visible resonance Raman (VRR) spectroscopy to identify glioma margins and grades. A set of diagnostic spectral biomarkers features are presented based on tissue composition changes revealed by VRR. The Raman spectra include molecular vibrational fingerprints of carotenoids, tryptophan, amide I/II/III, proteins, and lipids. These basic in situ spectral biomarkers are used to identify the tissue from the interface between brain cancer and normal tissue and to evaluate glioma grades. The VRR spectra are also analyzed using principal component analysis for dimension reduction and feature detection and support vector machine for classification. The cross-validated sensitivity, specificity, and accuracy are found to be 100%, 96.3%, and 99.6% to distinguish glioma tissues from normal brain tissues, respectively. The area under the receiver operating characteristic curve for the classification is about 1.0. The accuracies to distinguish normal, low grade (grades I and II), and high grade (grades III and IV) gliomas are found to be 96.3%, 53.7%, and 84.1% for the three groups, respectively, along with a total accuracy of 75.1%. A set of criteria for differentiating normal human brain tissues from normal control tissues is proposed and used to identify brain cancer margins, yielding a diagnostic sensitivity of 100% and specificity of 71%. Our study demonstrates the potential of VRR as a label-free optical molecular histopathology method used for in situ boundary line judgment for brain surgery in the margins

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure

GANHead: Towards Generative Animatable Neural Head Avatars

To bring digital avatars into people's lives, it is highly demanded to efficiently generate complete, realistic, and animatable head avatars. This task is challenging, and it is difficult for existing methods to satisfy all the requirements at once. To achieve these goals, we propose GANHead (Generative Animatable Neural Head Avatar), a novel generative head model that takes advantages of both the fine-grained control over the explicit expression parameters and the realistic rendering results of implicit representations. Specifically, GANHead represents coarse geometry, fine-gained details and texture via three networks in canonical space to obtain the ability to generate complete and realistic head avatars. To achieve flexible animation, we define the deformation filed by standard linear blend skinning (LBS), with the learned continuous pose and expression bases and LBS weights. This allows the avatars to be directly animated by FLAME parameters and generalize well to unseen poses and expressions. Compared to state-of-the-art (SOTA) methods, GANHead achieves superior performance on head avatar generation and raw scan fitting.Comment: Camera-ready for CVPR 2023. Project page: https://wsj-sjtu.github.io/GANHead

A New ZrCuSiAs-Type Superconductor: ThFeAsN

We report the first nitrogen-containing iron-pnictide superconductor ThFeAsN, which is synthesized by a solid-state reaction in an evacuated container. The compound crystallizes in a ZrCuSiAs-type structure with the space group P4/nmm and lattice parameters a=4.0367(1) {\AA} and c=8.5262(2) {\AA} at 300 K. The electrical resistivity and dc magnetic susceptibility measurements indicate superconductivity at 30 K for the nominally undoped ThFeAsN.Comment: 6 pages, 4 figures, 1 tabl