在这项研究中，我们检查了工程拓扑特征是否可以区分平衡和不平衡采样方案中的噪声特征不同的随机过程。我们将分类结果与基于统计和原始功能构建的相同分类任务的结果进行比较。我们得出的结论是，在时间序列的分类任务中，建立在工程拓扑功能上的不同机器学习模型比在标准统计和原始功能上构建的拓扑功能始终如一地表现更好。

在本文中，我们定义了一种新的非Archimedian度量标准结构，称为CopHenetic度量标准，对所有度的持久同源性等级。然后，我们将Zeroth持续同源与许多不同度量的核心度量和分层聚类算法一起，根据我们在不同的数据集上获得的实验结果，提供统计上可靠的相应拓扑信息。我们还观察到来自坐骨距离的所产生的集群在内部和外部评估措施（如轮廓分数和Rand指数）方面都能发光。此外，由于为所有同源度定义了CopHenetic度量，因此现在可以通过植根树显示所有度的持续同源类别的关系。

A large portion of today's world population suffer from vision impairments and wear prescription eyeglasses. However, eyeglasses causes additional bulk and discomfort when used with augmented and virtual reality headsets, thereby negatively impacting the viewer's visual experience. In this work, we remedy the usage of prescription eyeglasses in Virtual Reality (VR) headsets by shifting the optical complexity completely into software and propose a prescription-aware rendering approach for providing sharper and immersive VR imagery. To this end, we develop a differentiable display and visual perception model encapsulating display-specific parameters, color and visual acuity of human visual system and the user-specific refractive errors. Using this differentiable visual perception model, we optimize the rendered imagery in the display using stochastic gradient-descent solvers. This way, we provide prescription glasses-free sharper images for a person with vision impairments. We evaluate our approach on various displays, including desktops and VR headsets, and show significant quality and contrast improvements for users with vision impairments.

Giving machines the ability to imagine possible new objects or scenes from linguistic descriptions and produce their realistic renderings is arguably one of the most challenging problems in computer vision. Recent advances in deep generative models have led to new approaches that give promising results towards this goal. In this paper, we introduce a new method called DiCoMoGAN for manipulating videos with natural language, aiming to perform local and semantic edits on a video clip to alter the appearances of an object of interest. Our GAN architecture allows for better utilization of multiple observations by disentangling content and motion to enable controllable semantic edits. To this end, we introduce two tightly coupled networks: (i) a representation network for constructing a concise understanding of motion dynamics and temporally invariant content, and (ii) a translation network that exploits the extracted latent content representation to actuate the manipulation according to the target description. Our qualitative and quantitative evaluations demonstrate that DiCoMoGAN significantly outperforms existing frame-based methods, producing temporally coherent and semantically more meaningful results.

Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to information propagation bottlenecks, as information is repeatedly compressed at intermediary node representations, which causes loss of information, making it practically impossible to gather meaningful signals from distant nodes. To address this issue, we propose shortest path message passing neural networks, where the node representations of a graph are propagated to each node in the shortest path neighborhoods. In this setting, nodes can directly communicate between each other even if they are not neighbors, breaking the information bottleneck and hence leading to more adequately learned representations. Theoretically, our framework generalizes message passing neural networks, resulting in provably more expressive models, and we show that some recent state-of-the-art models are special instances of this framework. Empirically, we verify the capacity of a basic model of this framework on dedicated synthetic experiments, and on real-world graph classification and regression benchmarks, and obtain state-of-the-art results.

我们研究了图形表示学习的量子电路，并提出了等级的量子图电路（EQGCS），作为一类参数化量子电路，具有强大的关系感应偏压，用于学习图形结构数据。概念上，EQGCS作为量子图表表示学习的统一框架，允许我们定义几个有趣的子类，其中包含了现有的提案。就代表性权力而言，我们证明了感兴趣的子类是界限图域中的函数的普遍近似器，并提供实验证据。我们对量子图机学习方法的理论透视开启了许多方向以进行进一步的工作，可能导致具有超出古典方法的能力的模型。