Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems

By using Morse theory, the critical point theory, and the character of 1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2(−1)=(,()),∈ℤ(1,) subject to (0)=0=Δ(), where is a positive integer, ℤ(1,)={1,2,…,},Δ is the forward difference operator defined by Δ()=(+1)−(), and ∶ℤ(1,)×ℝ→ℝ is continuous. In argument, Morse inequalities play an important role

CNN-based Real-time Dense Face Reconstruction with Inverse-rendered Photo-realistic Face Images

With the powerfulness of convolution neural networks (CNN), CNN based face reconstruction has recently shown promising performance in reconstructing detailed face shape from 2D face images. The success of CNN-based methods relies on a large number of labeled data. The state-of-the-art synthesizes such data using a coarse morphable face model, which however has difficulty to generate detailed photo-realistic images of faces (with wrinkles). This paper presents a novel face data generation method. Specifically, we render a large number of photo-realistic face images with different attributes based on inverse rendering. Furthermore, we construct a fine-detailed face image dataset by transferring different scales of details from one image to another. We also construct a large number of video-type adjacent frame pairs by simulating the distribution of real video data. With these nicely constructed datasets, we propose a coarse-to-fine learning framework consisting of three convolutional networks. The networks are trained for real-time detailed 3D face reconstruction from monocular video as well as from a single image. Extensive experimental results demonstrate that our framework can produce high-quality reconstruction but with much less computation time compared to the state-of-the-art. Moreover, our method is robust to pose, expression and lighting due to the diversity of data.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence, 201

Suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs

AbstractAs one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs, the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper. We determine all the suborbits of a point-stabilizer in the orthogonal group on the last subconstituent, and calculate the length of each suborbit. Moreover, we discuss the quasi-strongly regular graphs and the association schemes based on the last subconstituent, respectively

Porous amorphous Ge/C composites with excellent electrochemical properties

Porous amorphous germanium/carbon (Ge/C) composites, which were synthesized through the reduction/carbonization of germanium oxide/oleic acid precursors, could exhibit a high-capacity, high-rate and long-life performance due to the synergistic effect of the porous structure and carbon

DLFuzz: Differential Fuzzing Testing of Deep Learning Systems

Deep learning (DL) systems are increasingly applied to safety-critical domains such as autonomous driving cars. It is of significant importance to ensure the reliability and robustness of DL systems. Existing testing methodologies always fail to include rare inputs in the testing dataset and exhibit low neuron coverage. In this paper, we propose DLFuzz, the frst differential fuzzing testing framework to guide DL systems exposing incorrect behaviors. DLFuzz keeps minutely mutating the input to maximize the neuron coverage and the prediction difference between the original input and the mutated input, without manual labeling effort or cross-referencing oracles from other DL systems with the same functionality. We present empirical evaluations on two well-known datasets to demonstrate its efficiency. Compared with DeepXplore, the state-of-the-art DL whitebox testing framework, DLFuzz does not require extra efforts to find similar functional DL systems for cross-referencing check, but could generate 338.59% more adversarial inputs with 89.82% smaller perturbations, averagely obtain 2.86% higher neuron coverage, and save 20.11% time consumption.Comment: This paper is to appear in ESEC/FSE'2018 (NIER track

CLIPood: Generalizing CLIP to Out-of-Distributions

Out-of-distribution (OOD) generalization, where the model needs to handle distribution shifts from training, is a major challenge of machine learning. Contrastive language-image pre-training (CLIP) models have shown impressive zero-shot ability, but the further adaptation of CLIP on downstream tasks undesirably degrades OOD performances. This paper aims at generalizing CLIP to out-of-distribution test data on downstream tasks. We propose CLIPood, a fine-tuning method that can adapt CLIP models to OOD situations where both domain shifts and open classes may occur on the unseen test data. To exploit the semantic relations between classes from the text modality, CLIPood introduces a new training objective, margin metric softmax (MMS), with class adaptive margins for fine-tuning. To incorporate both pre-trained zero-shot model and fine-tuned task-adaptive model, CLIPood leverages a new optimization strategy, Beta moving average (BMA), to maintain a temporal ensemble weighted by Beta distribution. Experiments on diverse datasets with different OOD scenarios show that CLIPood consistently outperforms existing generalization techniques.Comment: Accepted by ICML 202

Free-standing sulfur-polypyrrole cathode in conjunction with polypyrrole-coated separator for flexible Li-S batteries

A free-standing sulfur-polypyrrole cathode and a polypyrrole coated separator were designed for flexible Li-S batteries. The free-standing sulfur-polypyrrole cathode was prepared by directly pasting a sulfur-coated polypyrrole (S@PPy) nanofiber composite on a flexible and conductive polypyrrole (PPy) film. Compared with carbonaceous matrixes, PPy has a strong interaction with polysulfides to mitigate the dissolution of polysulfides due to its unique chain structure and the lone pair electrons in the nitrogen atoms in PPy. In addition, the as-prepared PPy film not only shows excellent mechanical elasticity, but also possesses a rough surface, which can accommodate volume expansion, enhance the adhesion of active materials, and further trap the dissolved polysulfides. Due to the synergistic effect provided by the PPy film, the free-standing sulfur-polypyrrole cathode shows better electrochemical performance than the traditional cathode with S@PPy composite coated on Al foil. In order to further improve the cycling stability of Li-S batteries, a PPy coated separator was prepared, which acts as a fishing net to capture polysulfides and alleviate the shuttle effect, leading to a stable cycling performance. Moreover, the PPy layer coated on commercial separator is much lighter than many other free-standing interlayers reported previously. Considering the flexibility of the free-standing sulfur cathode and PPy coated separator, a soft-packaged flexible Li-S battery based on them has been designed and fabricated to power a device consisting of 24 light emitting diode (LED) lights. After repeated bending, the flexible Li-S battery can still maintain good performance, indicating the excellent mechanical flexibility of the designed Li-S battery