Quaternions are a number system extended to four dimensions. It is used to describe the movement of physical objects in 3D space. This concept is widely applied in fields such as computer vision, robotics, and game design. However, the mathematics involved can be unintuitive, and the notation is often confusing for beginners. In this demonstration, I will use skateboarding, a popular sport among young people, to illustrate Quaternion concepts through a series of interactive computer simulations. I will show how skateboarding tricks like spins, flips, and shuvits can be elegantly represented and modeled using Quaternions and explain why some tricks are more complex than others. This tool is valuable for students interested in 3D graphics, game development, robotics, or computer vision, where Quaternions are foundational concepts. Additionally, it benefits visual and kinesthetic learners by grounding complex mathematical ideas in the familiar and engaging context of skateboarding. It is suitable for middle or high school students or undergraduate students in formal and informal learning settings.

Clinically, the pathological images are intuitive for cancer diagnosis and have been considered as the ‘gold standard’. There are two challenges for applying deep learning into the pathological images analysis: the ultra-large size and the noisy annotations. A pathological image usually contains billions of pixels, which is unsuitable for normal classification models. Furthermore, the ultra-large size and mixed cancerous cells compel the doctor to draw rough boundaries of lesion area according to the cancerous level, which brings two kinds of noisy labels: space noise (annotating inaccurate scope of cancerous area) and level noise (annotating inaccurate cancerous level). Based on the above findings, we propose the space and level cooperation framework, comprising a space-aware branch and a level-aware branch, for pathological cancer grading with noisy annotations. The space-aware branch first turns the ultra-large image into a Multilayer Superpixel (MS) graph, significantly reducing the size and preserving the global features. Then, a global-to-local rectifying strategy is adopted to solve the space noise. The level-aware branch adopts different grouped kernels and a novel grading loss function to handle level noise. Mean-while, two branches cooperate through complementing missing features of each other for handling the above two challenges. Extensive experiments demonstrate that with noisy annotations, the proposed framework achieves SOTA performance on our HCC dataset and two public datasets.

Detection and segmentation of nuclei are fundamental analysis operations in pathology images, the assessments derived from which serve as the gold standard for cancer diagnosis. Manual segmenting nuclei is expensive and time-consuming. What’s more, accurate segmentation detection of nuclei can be challenging due to the large appearance variation, conjoined and overlapping nuclei, and serious degeneration of histological structures. Supervised methods highly rely on massive annotated samples. The existing two unsupervised methods are prone to failure on degenerated samples. This paper proposes a Mutual-Complementing Framework (MCF) for nuclei detection and segmentation in pathology images. Two branches of MCF are trained in the mutual-complementing manner, where the detection branch complements the pseudo mask of the segmentation branch, while the progressive trained segmentation branch complements the missing nucleus templates through calculating the mask residual between the predicted mask and detected result. In the detection branch, two response map fusion strategies and gradient direction based postprocessing are devised to obtain the optimal detection response. Furthermore, the confidence loss combined with the synthetic samples and self-finetuning is adopted to train the segmentation network with only high confidence areas. Extensive experiments demonstrate that MCF achieves comparable performance with only a few nucleus patches as supervision. Especially, MCF possesses good robustness (only dropping by about 6%) on degenerated samples, which are critical and common cases in clinical diagnosis.

Point cloud compression is critical to deploy 3D applications like autonomous driving. However, LiDAR point clouds contain many disconnected regions, where redundant bits for unoccupied 3D space and weak correlations between points make it a troublesome problem to achieve efficient compression. This paper aims to aggregate LiDAR point clouds to get compact representations with full consideration of the point distribution characteristics. Specifically, we propose a novel Layer-wise Geometry Aggregation (LGA) framework for LiDAR point cloud lossless geometry compression, which adaptively partitions point clouds into three layers based on the content properties, including a ground layer, an object layer, and a noise layer. The aggregation algorithms are delicately designed for each layer. Firstly, the ground layer is fitted to a Gaussian Mixture Model, which can uniformly represent ground points using much fewer model parameters than adopting the original 3D coordinates. Then, the object layer is tightly packed to reduce the space between objects effectively, and a dense layout for points can benefit compression efficiency. Finally, in the noise layer, the difference between neighbor points is reduced by reordering using Morton Code, and the reduced residuals can help saving bit consumption. Experimental results demonstrate that the proposed LGA significantly outperforms competitive methods without prior knowledge by 12.05~23.37% compression ratio gains. Furthermore, the enhanced LGA with prior knowledge shows consistent performance gains than the latest reference software. Additional results also validate the robustness and stability of our proposed scheme with acceptable time complexity.

The dynamic nature of the Grid environment brings challenges to the services provisioning technique. A major aspect of Grid is to match demands for services with resources. Since resources and demands are fluctuating, Grid services provisioning need to be adjusted accordingly in responding to changes. In this paper, we propose a novel approach, Grid services migration, to enabling services provisioning on demand. The major motivation is to achieve the desired Quality of Service (QoS) such as performance, reliability, and etc. of Grid services on resources assembled dynamically responding to dynamic demand. In this paper, the technical characteristics of Grid services migration and its taxonomy are introduced. The Grid service migration algorithms are also presented. The Grid services migration framework with MAPE (Monitor, Analyze, Plan, and Execute) loop is proposed based on Open Grid Services Architecture (OGSA) and the prototype named Services Ecosystem, a resilient infrastructure for services provisioning on demand in Grid is developed. Demonstrations and experiments are conducted and results are presented to illustrate the capabilities of Grid services migration.