The Existence of Hamilton Cycle in n-Balanced k-Partite Graphs

Let $G_{k,n}$ be the $n$-balanced $k$-partite graph, whose vertex set can be partitioned into $k$ parts, each has $n$ vertices. In this paper, we prove that if $k \geq 2,n \geq 1$, for the edge set $E(G)$ of $G_{k,n}$ $$|E(G)| \geq\left\{\begin{array}{cc} 1 & \text { if } k=2, n=1 n^{2} C_{k}^{2}-(k-1) n+2 & \text { other } \end{array}\right.$$ then $G_{k,n}$ is hamiltonian. And the result may be the best

EventRPG: Event Data Augmentation with Relevance Propagation Guidance

Event camera, a novel bio-inspired vision sensor, has drawn a lot of attention for its low latency, low power consumption, and high dynamic range. Currently, overfitting remains a critical problem in event-based classification tasks for Spiking Neural Network (SNN) due to its relatively weak spatial representation capability. Data augmentation is a simple but efficient method to alleviate overfitting and improve the generalization ability of neural networks, and saliency-based augmentation methods are proven to be effective in the image processing field. However, there is no approach available for extracting saliency maps from SNNs. Therefore, for the first time, we present Spiking Layer-Time-wise Relevance Propagation rule (SLTRP) and Spiking Layer-wise Relevance Propagation rule (SLRP) in order for SNN to generate stable and accurate CAMs and saliency maps. Based on this, we propose EventRPG, which leverages relevance propagation on the spiking neural network for more efficient augmentation. Our proposed method has been evaluated on several SNN structures, achieving state-of-the-art performance in object recognition tasks including N-Caltech101, CIFAR10-DVS, with accuracies of 85.62% and 85.55%, as well as action recognition task SL-Animals with an accuracy of 91.59%. Our code is available at https://github.com/myuansun/EventRPG.Comment: Accepted by ICLR 202

ZSTAD: Zero-Shot Temporal Activity Detection

An integral part of video analysis and surveillance is temporal activity detection, which means to simultaneously recognize and localize activities in long untrimmed videos. Currently, the most effective methods of temporal activity detection are based on deep learning, and they typically perform very well with large scale annotated videos for training. However, these methods are limited in real applications due to the unavailable videos about certain activity classes and the time-consuming data annotation. To solve this challenging problem, we propose a novel task setting called zero-shot temporal activity detection (ZSTAD), where activities that have never been seen in training can still be detected. We design an end-to-end deep network based on R-C3D as the architecture for this solution. The proposed network is optimized with an innovative loss function that considers the embeddings of activity labels and their super-classes while learning the common semantics of seen and unseen activities. Experiments on both the THUMOS14 and the Charades datasets show promising performance in terms of detecting unseen activities

On the decay of strength in Guilin red clay with cracks

In order to research the effect of cracks in red clay on shear strength through dry-wet cycle test, the experimenters used imaging software and a mathematical model to determine fractal dimension and crack ratio of surface cracks in red clay in Guilin, China. After each dry-wet cycle, direct shear tests were carried out on the sample, and such variables as matrix suction on the crack propagation process of red clay were analyzed. The mechanics model was established and obtained the critical condition of soil cracks. The results show that with the increase in the number of dry-wet cycles the shear strength of the samples would decrease. But the rule of shear strength of sample 3 is slightly different from samples 1 and 2. The shear strength of red clay has a good correlation with fractal dimension and crack ratio, which could be an identification index of the strength of red clay