Renormalized solutions of a nonlinear parabolic equation with double degeneracy

In this paper, we consider the initial-boundary value problem of a nonlinear parabolic equation with double degeneracy, and establish the existence and uniqueness theorems of renormalized solutions which are stronger than $BV$ solutions

MEASUREMENT OF SPANNING TREE PERFORMANCE BETWEEN DIFFERENT PROTOCOLS : Bachelor's Thesis

Network is becoming more and more important in daily life, the performance of the network is most critical issue. In this article, we will talk about the spanning tree protocol which is used to prevent bridge loops, broadcast radiation and provide the protection of convergence in order to provide the nice performance of the network. You can see from this article about what it is the spanning tree, how it works, and what kind of enhanced protocols are used. I will test and measure the original protocol and enhanced protocols, and show the results of the performance of convergence time. We will see which protocol have nice performance. After that we can decide which protocol is suit for our network and provide the best performance.STP has two main functions: one is in the use of spanning tree algorithm to prevent bridge loops and the broadcast radiation. The second is in the Ethernet network topology change, through the spanning tree protocol to achieve the purpose of protection of convergence

Semi-Supervised Learning for Mars Imagery Classification and Segmentation

With the progress of Mars exploration, numerous Mars image data are collected and need to be analyzed. However, due to the imbalance and distortion of Martian data, the performance of existing computer vision models is unsatisfactory. In this paper, we introduce a semi-supervised framework for machine vision on Mars and try to resolve two specific tasks: classification and segmentation. Contrastive learning is a powerful representation learning technique. However, there is too much information overlap between Martian data samples, leading to a contradiction between contrastive learning and Martian data. Our key idea is to reconcile this contradiction with the help of annotations and further take advantage of unlabeled data to improve performance. For classification, we propose to ignore inner-class pairs on labeled data as well as neglect negative pairs on unlabeled data, forming supervised inter-class contrastive learning and unsupervised similarity learning. For segmentation, we extend supervised inter-class contrastive learning into an element-wise mode and use online pseudo labels for supervision on unlabeled areas. Experimental results show that our learning strategies can improve the classification and segmentation models by a large margin and outperform state-of-the-art approaches.Comment: Accepted by ACM Trans. on Multimedia Computing Communications and Applications (TOMM

S5^{5}Mars: Semi-Supervised Learning for Mars Semantic Segmentation

Deep learning has become a powerful tool for Mars exploration. Mars terrain semantic segmentation is an important Martian vision task, which is the base of rover autonomous planning and safe driving. However, there is a lack of sufficient detailed and high-confidence data annotations, which are exactly required by most deep learning methods to obtain a good model. To address this problem, we propose our solution from the perspective of joint data and method design. We first present a newdataset S5Mars for Semi-SuperviSed learning on Mars Semantic Segmentation, which contains 6K high-resolution images and is sparsely annotated based on confidence, ensuring the high quality of labels. Then to learn from this sparse data, we propose a semi-supervised learning (SSL) framework for Mars image semantic segmentation, to learn representations from limited labeled data. Different from the existing SSL methods which are mostly targeted at the Earth image data, our method takes into account Mars data characteristics. Specifically, we first investigate the impact of current widely used natural image augmentations on Mars images. Based on the analysis, we then proposed two novel and effective augmentations for SSL of Mars segmentation, AugIN and SAM-Mix, which serve as strong augmentations to boost the model performance. Meanwhile, to fully leverage the unlabeled data, we introduce a soft-to-hard consistency learning strategy, learning from different targets based on prediction confidence. Experimental results show that our method can outperform state-of-the-art SSL approaches remarkably. Our proposed dataset is available at https://jhang2020.github.io/S5Mars.github.io/

Path Generation for Wheeled Robots Autonomous Navigation on Vegetated Terrain

Wheeled robot navigation has been widely used in urban environments, but little research has been conducted on its navigation in wild vegetation. External sensors (LiDAR, camera etc.) are often used to construct point cloud map of the surrounding environment, however, the supporting rigid ground used for travelling cannot be detected due to the occlusion of vegetation. This often causes unsafe or not smooth path during planning process. To address the drawback, we propose the PE-RRT* algorithm, which effectively combines a novel support plane estimation method and sampling algorithm to generate real-time feasible and safe path in vegetation environments. In order to accurately estimate the support plane, we combine external perception and proprioception, and use Multivariate Gaussian Processe Regression (MV-GPR) to estimate the terrain at the sampling nodes. We build a physical experimental platform and conduct experiments in different outdoor environments. Experimental results show that our method has high safety, robustness and generalization

To See is to Believe: Prompting GPT-4V for Better Visual Instruction Tuning

Existing visual instruction tuning methods typically prompt large language models with textual descriptions to generate instruction-following data. Despite the promising performance achieved, these descriptions are derived from image annotations, which are oftentimes coarse-grained. Furthermore, the instructions might even contradict the visual content without observing the entire visual context. To address this challenge, we introduce a fine-grained visual instruction dataset, LVIS-Instruct4V, which contains 220K visually aligned and context-aware instructions produced by prompting the powerful GPT-4V with images from LVIS. Through experimental validation and case studies, we demonstrate that high-quality visual instructional data could improve the performance of LLaVA-1.5, a state-of-the-art large multimodal model, across a wide spectrum of benchmarks by clear margins. Notably, by simply replacing the LLaVA-Instruct with our LVIS-Instruct4V, we achieve better results than LLaVA on most challenging LMM benchmarks, e.g., LLaVA$^w$ (76.7 vs. 70.7) and MM-Vet (40.2 vs. 35.4). We release our data and model at https://github.com/X2FD/LVIS-INSTRUCT4V.Comment: techical report; work in progres

Linear stability for a free boundary problem modeling the growth of tumor cord with time delay

This paper was concerned with a free boundary problem modeling the growth of tumor cord with a time delay in cell proliferation, in which the cell location was incorporated, the domain was bounded in $\mathbb{R}^2$, and its boundary included two disjoint closed curves, one fixed and the other moving and a priori unknown. A parameter $\mu$ represents the aggressiveness of the tumor. We proved that there exists a unique radially symmetric stationary solution for sufficiently small time delay, and this stationary solution is linearly stable under the nonradially symmetric perturbations for any $\mu > 0$. Moreover, adding the time delay in the model leads to a larger stationary tumor. If the tumor aggressiveness parameter is bigger, the time delay has a greater effect on the size of the stationary tumor, but it has no effect on the stability of the stationary solution

Conditional DETR for Fast Training Convergence

The recently-developed DETR approach applies the transformer encoder and decoder architecture to object detection and achieves promising performance. In this paper, we handle the critical issue, slow training convergence, and present a conditional cross-attention mechanism for fast DETR training. Our approach is motivated by that the cross-attention in DETR relies highly on the content embeddings for localizing the four extremities and predicting the box, which increases the need for high-quality content embeddings and thus the training difficulty. Our approach, named conditional DETR, learns a conditional spatial query from the decoder embedding for decoder multi-head cross-attention. The benefit is that through the conditional spatial query, each cross-attention head is able to attend to a band containing a distinct region, e.g., one object extremity or a region inside the object box. This narrows down the spatial range for localizing the distinct regions for object classification and box regression, thus relaxing the dependence on the content embeddings and easing the training. Empirical results show that conditional DETR converges 6.7x faster for the backbones R50 and R101 and 10x faster for stronger backbones DC5-R50 and DC5-R101. Code is available at https://github.com/Atten4Vis/ConditionalDETR.Comment: Accepted by ICCV 2021. The first two authors share first authorship, and the order was determined by rolling dic