Semantic Graph Convolutional Networks for 3D Human Pose Regression

In this paper, we study the problem of learning Graph Convolutional Networks (GCNs) for regression. Current architectures of GCNs are limited to the small receptive field of convolution filters and shared transformation matrix for each node. To address these limitations, we propose Semantic Graph Convolutional Networks (SemGCN), a novel neural network architecture that operates on regression tasks with graph-structured data. SemGCN learns to capture semantic information such as local and global node relationships, which is not explicitly represented in the graph. These semantic relationships can be learned through end-to-end training from the ground truth without additional supervision or hand-crafted rules. We further investigate applying SemGCN to 3D human pose regression. Our formulation is intuitive and sufficient since both 2D and 3D human poses can be represented as a structured graph encoding the relationships between joints in the skeleton of a human body. We carry out comprehensive studies to validate our method. The results prove that SemGCN outperforms state of the art while using 90% fewer parameters.Comment: In CVPR 2019 (13 pages including supplementary material). The code can be found at https://github.com/garyzhao/SemGC

Wormholes and the Thermodynamic Arrow of Time

In classical thermodynamics, heat cannot spontaneously pass from a colder system to a hotter system, which is called the thermodynamic arrow of time. However, if the initial states are entangled, the direction of the thermodynamic arrow of time may not be guaranteed. Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space. We make the temperature difference between the two sides by changing the Hamiltonian. We turn on proper interaction between the two sides and calculate the changes in energy and entropy. The energy transfer, as well as the thermodynamic arrow of time, are mainly determined by the competition between two channels: thermal diffusion and anomalous heat flow. The former is not related to the wormhole and obeys the thermodynamic arrow of time; the latter is related to the wormhole and reverses the thermodynamic arrow of time, i.e. transfer energy from the colder side to the hotter side at the cost of entanglement consumption. Finally, we find that the thermal diffusion wins the competition, and the whole thermodynamic arrow of time has not been reversed.Comment: 37 pages, 21 figures; v2: minor corrections and updated figure

Testing the number of common factors by bootstrapped sample covariance matrix in high-dimensional factor models

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under the high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits via proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by order statistics of bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. According to the simulations and a real data example, the proposed methods are the only ones performing reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions.Comment: 95 pages, 9 figures, 4 table

GG: A domain involved in phage LTF apparatus and implicated in human MEB and non-syndromic hearing loss diseases

AbstractHere, we report the identification of a novel domain – GG (domain in KIAA1199, FAM3, POMGnT1 and Tmem2 proteins, with two well-conserved glycine residues), present in eukaryotic FAM3 superfamily (FAM3A, FAM3B, FAM3C and FAM3D), POMGnT1 (protein O-linked mannose β-1,2-N-acetylglucosaminyltransferase), TEM2 proteins as well as phage gp35 proteins. GG domain has been revealed to be implicated in muscle–eye–brain disease and non-syndromic hearing loss. The presence of GG domain in Bacteriophage gp35 hinge connector of long tail fiber might reflect the horizontal gene transfer from organisms. And we proposed that GG domain might function as important structural element in phage LTF