On the sum of the two largest signless Laplacian eigenvalues

Let $G$ be a simple connected graph and let $S_k(G)$ be the sum of the first $k$ largest signless Laplacian eigenvalues of $G$. It was conjectured by Ashraf, Omidi and Tayfeh-Rezaibe in 2013 that $S_k(G)\leq e(G)+\binom{k+1}{2}$ holds for $1\leq k\leq n-1$. They gave a proof for the conjecture when $k = 2$, but applied an incorrect key lemma. Therefore, the conjecture is still open when $k = 2$. In this paper, we prove that $S_2(G)<e(G)+3$ is true for any graphs which also confirm the conjecture when $k = 2$.Comment: 15 pages, 5 figure

Improving Model Generalization by On-manifold Adversarial Augmentation in the Frequency Domain

Deep neural networks (DNNs) may suffer from significantly degenerated performance when the training and test data are of different underlying distributions. Despite the importance of model generalization to out-of-distribution (OOD) data, the accuracy of state-of-the-art (SOTA) models on OOD data can plummet. Recent work has demonstrated that regular or off-manifold adversarial examples, as a special case of data augmentation, can be used to improve OOD generalization. Inspired by this, we theoretically prove that on-manifold adversarial examples can better benefit OOD generalization. Nevertheless, it is nontrivial to generate on-manifold adversarial examples because the real manifold is generally complex. To address this issue, we proposed a novel method of Augmenting data with Adversarial examples via a Wavelet module (AdvWavAug), an on-manifold adversarial data augmentation technique that is simple to implement. In particular, we project a benign image into a wavelet domain. With the assistance of the sparsity characteristic of wavelet transformation, we can modify an image on the estimated data manifold. We conduct adversarial augmentation based on AdvProp training framework. Extensive experiments on different models and different datasets, including ImageNet and its distorted versions, demonstrate that our method can improve model generalization, especially on OOD data. By integrating AdvWavAug into the training process, we have achieved SOTA results on some recent transformer-based models.Comment: Computer Vision and Image Understanding (CVIU) [under review

Mutation of SLC35D3 causes metabolic syndrome by impairing dopamine signaling in striatal D1 neurons

We thank Dr. Ya-Qin Feng from Shanxi Medical University, Dr. Tian-Yun Gao from Nanjing University and Dr. Yan-Hong Xue from Institute of Biophysics (CAS) for technical assistance in this study. We are very thankful to Drs. Richard T. Swank and Xiao-Jiang Li for their critical reading of this manuscript and invaluable advice. Funding: This work was partially supported by grants from National Basic Research Program of China (2013CB530605; 2014CB942803), from National Natural Science Foundation of China 1230046; 31071252; 81101182) and from Chinese Academy of Sciences (KSCX2-EW-R-05, KJZD-EW-L08). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Proof of a Conjecture on Trees with Large Energy *

Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. Based on a method of directly comparing the energies of the subdivision trees given in [1], together with using some computer-aided calculations and using some results provided by Andriantiana in [2], we prove that the conjecture proposed in [2] on the first 3n − 84 (when n is odd) and 3n − 87 (when n is even) largest energy trees is true