It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group-equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various areas of machine learning. Recently, Barron spaces have been used to prove bounds on the generalisation error for neural networks. Unfortunately, Barron spaces cannot be understood in terms of RKHS due to the strong nonlinear coupling of the weights. We show that this can be solved by using the more general Reproducing Kernel Banach spaces (RKBS). This class of integral RKBS can be understood as an infinite union of RKHS spaces. As the RKBS is not a Hilbert space, it is not its own dual space. However, we show that its dual space is again an RKBS where the roles of the data and parameters are interchanged, forming an adjoint pair of RKBSs including a reproducing property in the dual space. This allows us to construct the saddle point problem for neural networks, which can be used in the whole field of primal-dual optimisation.

这项工作提出了一种随机变化深内核学习方法，用于从高维噪声数据中发现低维动力学模型的数据驱动。该框架由一个编码器组成，该编码器将高维测量值压缩为低维状态变量，以及用于状态变量的潜在动力学模型，该模型可以预测随时间时间的系统演化。提出的模型的培训是以无监督的方式进行的，即不依赖标记的数据。我们的学习方法是根据摆锤的运动进行评估的，这是通过高维嘈杂的RGB图像测量的非线性模型识别和对照的良好研究基线。结果表明，该方法可以有效地确定测量，学习紧凑的状态表示和潜在的动力学模型，并识别和量化建模不确定性。

这篇综述解决了在深度强化学习（DRL）背景下学习测量数据的抽象表示的问题。尽管数据通常是模棱两可，高维且复杂的解释，但许多动态系统可以通过一组低维状态变量有效地描述。从数据中发现这些状态变量是提高数据效率，稳健性和DRL方法的概括，应对维度的诅咒以及将可解释性和见解带入Black-Box DRL的关键方面。这篇综述通过描述用于学习世界的学习代表的主要深度学习工具，提供对方法和原则的系统观点，总结应用程序，基准和评估策略，并讨论开放的方式，从而提供了DRL中无监督的代表性学习的全面概述，挑战和未来的方向。

个性化的3D血管模型对于心血管疾病患者的诊断，预后和治疗计划很有价值。传统上，这样的模型是用明确表示（例如网格和体素掩码）构建的，或隐式表示，例如径向基函数或原子（管状）形状。在这里，我们建议在可区分的隐式神经表示（INR）中以其签名距离函数（SDF）的零级集表示表面。这使我们能够用隐性，连续，轻巧且易于与深度学习算法集成的表示复杂的血管结构对复杂的血管结构进行建模。我们在这里通过三个实际示例证明了这种方法的潜力。首先，我们从CT图像中获得了腹主动脉瘤（AAA）的精确和水密表面，并显示出从表面上的200点出现的可靠拟合。其次，我们同时将嵌套的容器壁贴在一个没有交叉点的单个INR中。第三，我们展示了如何将3D模型的单个动脉模型平滑地混合到单个水密表面。我们的结果表明，INR是一种灵活的表示，具有微小互动注释和操纵复杂血管结构的潜力。

颈动脉壳壁厚测量是监测动脉粥样硬化患者的重要步骤。这需要精确分割血管壁，即动脉的内腔和外壁之间的区域，在黑血磁共振（MR）图像中。对于语义分割的常用卷积神经网络（CNNS）是本任务的次优，因为它们的使用不保证连续的环形分割。相反，在这项工作中，我们将船舶壁分段作为极坐标系中的多任务回归问题。对于每个轴向图像切片中的每种颈动脉，我们的目的是同时发现两个非交叉的嵌套轮廓，在一起叠加血管壁。应用于此问题的CNNS使电感偏压能够保证环形血管壁。此外，我们确定了一个特定于问题的培训数据增强技术，其大大影响了分割性能。我们将我们的方法应用于内部和外部颈动脉壁的分割，并在公共挑战中实现排名级定量结果，即血管墙壁的中值骰子相似系数为0.813，中位Hausdorff距离为0.552 mm和0.776 mm对于内腔和外墙。此外，我们展示了如何通过传统的语义分割方法来改善方法。这些结果表明，可以高精度地自动获得颈动脉壁的解剖学似合子分割是可行的。

计算流体动力学（CFD）是一种有价值的工具，用于动脉中血流动力学的个性化，非侵入性评估，但其复杂性和耗时的大自然在实践中禁止大规模使用。最近，已经研究了利用深度学习进行CFD参数的快速估计，如表面网格上的壁剪切应力（WSS）。然而，现有方法通常取决于表面网格的手工制作的重新参数化以匹配卷积神经网络架构。在这项工作中，我们建议使用Mesh卷积神经网络，该网状神经网络直接在CFD中使用的相同的有限元表面网格操作。我们在使用从CFD模拟中获得的地面真理培训并在两种合成冠状动脉模型的两种数据集上培训和评估我们的方法。我们表明我们灵活的深度学习模型可以准确地预测该表面网上的3D WSS矢量。我们的方法在少于5分钟内处理新网格，始终如一地实现$ \ LEQ $ 1.6 [％]的标准化平均值误差，并且在保持测试集中的90.5 [％]中位近似精度为90.5 [％]的峰值，比较以前发表的工作。这证明了CFD代理建模的可行性，使用网状卷积神经网络进行动脉模型中的血流动力学参数估计。

Deep-learning of artificial neural networks (ANNs) is creating highly functional tools that are, unfortunately, as hard to interpret as their natural counterparts. While it is possible to identify functional modules in natural brains using technologies such as fMRI, we do not have at our disposal similarly robust methods for artificial neural networks. Ideally, understanding which parts of an artificial neural network perform what function might help us to address a number of vexing problems in ANN research, such as catastrophic forgetting and overfitting. Furthermore, revealing a network's modularity could improve our trust in them by making these black boxes more transparent. Here we introduce a new information-theoretic concept that proves useful in understanding and analyzing a network's functional modularity: the relay information $I_R$. The relay information measures how much information groups of neurons that participate in a particular function (modules) relay from inputs to outputs. Combined with a greedy search algorithm, relay information can be used to {\em identify} computational modules in neural networks. We also show that the functionality of modules correlates with the amount of relay information they carry.

Cashews are grown by over 3 million smallholders in more than 40 countries worldwide as a principal source of income. As the third largest cashew producer in Africa, Benin has nearly 200,000 smallholder cashew growers contributing 15% of the country's national export earnings. However, a lack of information on where and how cashew trees grow across the country hinders decision-making that could support increased cashew production and poverty alleviation. By leveraging 2.4-m Planet Basemaps and 0.5-m aerial imagery, newly developed deep learning algorithms, and large-scale ground truth datasets, we successfully produced the first national map of cashew in Benin and characterized the expansion of cashew plantations between 2015 and 2021. In particular, we developed a SpatioTemporal Classification with Attention (STCA) model to map the distribution of cashew plantations, which can fully capture texture information from discriminative time steps during a growing season. We further developed a Clustering Augmented Self-supervised Temporal Classification (CASTC) model to distinguish high-density versus low-density cashew plantations by automatic feature extraction and optimized clustering. Results show that the STCA model has an overall accuracy of 80% and the CASTC model achieved an overall accuracy of 77.9%. We found that the cashew area in Benin has doubled from 2015 to 2021 with 60% of new plantation development coming from cropland or fallow land, while encroachment of cashew plantations into protected areas has increased by 70%. Only half of cashew plantations were high-density in 2021, suggesting high potential for intensification. Our study illustrates the power of combining high-resolution remote sensing imagery and state-of-the-art deep learning algorithms to better understand tree crops in the heterogeneous smallholder landscape.