我们提出了一种从数据模拟动态系统的数值方法。我们使用最近引入的方法可扩展的概率近似（SPA）从欧几里德空间到凸多台的项目点，并表示在新的低维坐标中的系统的预计状态，表示其在多晶硅中的位置。然后，我们介绍特定的非线性变换，以构建多特渗透中动力学的模型，并转换回原始状态空间。为了克服投影到低维层的潜在信息损失，我们在局部延迟嵌入定理的意义上使用记忆。通过施工，我们的方法产生稳定的模型。我们说明了在各种示例上具有多个连接组件的甚至复制混沌动力学和吸引子的方法的能力。

We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.

Nucleolar organizer regions (NORs) are parts of the DNA that are involved in RNA transcription. Due to the silver affinity of associated proteins, argyrophilic NORs (AgNORs) can be visualized using silver-based staining. The average number of AgNORs per nucleus has been shown to be a prognostic factor for predicting the outcome of many tumors. Since manual detection of AgNORs is laborious, automation is of high interest. We present a deep learning-based pipeline for automatically determining the AgNOR-score from histopathological sections. An additional annotation experiment was conducted with six pathologists to provide an independent performance evaluation of our approach. Across all raters and images, we found a mean squared error of 0.054 between the AgNOR- scores of the experts and those of the model, indicating that our approach offers performance comparable to humans.

Mitotic activity is key for the assessment of malignancy in many tumors. Moreover, it has been demonstrated that the proportion of abnormal mitosis to normal mitosis is of prognostic significance. Atypical mitotic figures (MF) can be identified morphologically as having segregation abnormalities of the chromatids. In this work, we perform, for the first time, automatic subtyping of mitotic figures into normal and atypical categories according to characteristic morphological appearances of the different phases of mitosis. Using the publicly available MIDOG21 and TUPAC16 breast cancer mitosis datasets, two experts blindly subtyped mitotic figures into five morphological categories. Further, we set up a state-of-the-art object detection pipeline extending the anchor-free FCOS approach with a gated hierarchical subclassification branch. Our labeling experiment indicated that subtyping of mitotic figures is a challenging task and prone to inter-rater disagreement, which we found in 24.89% of MF. Using the more diverse MIDOG21 dataset for training and TUPAC16 for testing, we reached a mean overall average precision score of 0.552, a ROC AUC score of 0.833 for atypical/normal MF and a mean class-averaged ROC-AUC score of 0.977 for discriminating the different phases of cells undergoing mitosis.

Computer-aided systems in histopathology are often challenged by various sources of domain shift that impact the performance of these algorithms considerably. We investigated the potential of using self-supervised pre-training to overcome scanner-induced domain shifts for the downstream task of tumor segmentation. For this, we present the Barlow Triplets to learn scanner-invariant representations from a multi-scanner dataset with local image correspondences. We show that self-supervised pre-training successfully aligned different scanner representations, which, interestingly only results in a limited benefit for our downstream task. We thereby provide insights into the influence of scanner characteristics for downstream applications and contribute to a better understanding of why established self-supervised methods have not yet shown the same success on histopathology data as they have for natural images.

The pre-training of masked language models (MLMs) consumes massive computation to achieve good results on downstream NLP tasks, resulting in a large carbon footprint. In the vanilla MLM, the virtual tokens, [MASK]s, act as placeholders and gather the contextualized information from unmasked tokens to restore the corrupted information. It raises the question of whether we can append [MASK]s at a later layer, to reduce the sequence length for earlier layers and make the pre-training more efficient. We show: (1) [MASK]s can indeed be appended at a later layer, being disentangled from the word embedding; (2) The gathering of contextualized information from unmasked tokens can be conducted with a few layers. By further increasing the masking rate from 15% to 50%, we can pre-train RoBERTa-base and RoBERTa-large from scratch with only 78% and 68% of the original computational budget without any degradation on the GLUE benchmark. When pre-training with the original budget, our method outperforms RoBERTa for 6 out of 8 GLUE tasks, on average by 0.4%.

神经机器翻译（NMT）是一个开放的词汇问题。结果，处理在培训期间没有出现的单词（又称唱歌外（OOV）单词）长期以来一直是NMT系统的基本挑战。解决此问题的主要方法是字节对编码（BPE），将包括OOV单词在内的单词分为子字段中。在自动评估指标方面，BPE为广泛的翻译任务取得了令人印象深刻的结果。尽管通常假定使用BPE，但NMT系统能够处理OOV单词，但BPE在翻译OOV单词中的有效性尚未明确测量。在本文中，我们研究了BPE在多大程度上成功地翻译了单词级别的OOV单词。我们根据单词类型，段数，交叉注意权重和训练数据中段NGram的段频率分析OOV单词的翻译质量。我们的实验表明，尽管仔细的BPE设置似乎在整个数据集中翻译OOV单词时相当有用，但很大一部分的OOV单词被错误地翻译而成。此外，我们强调了BPE在为特殊案例（例如命名本性和涉及的语言彼此接近的语言）翻译OOV单词中的有效性稍高。

拖延是任务的非理性延迟，是在线学习中的普遍情况。潜在的负面后果包括更高的辍学风险，增加压力和情绪减少。由于学习管理系统和学习分析的增加，可以检测到这种行为的指标，从而预测未来的拖延和其他扩张行为。但是，关注此类预测的研究很少。此外，几乎不存在涉及不同类型的预测指标和预测性能之间的比较的研究。在这项研究中，我们旨在通过分析多个机器学习算法的性能来填补这些研究空白，以预测具有两类预测指标的高等教育环境中在线作业的延迟或及时提交：基于主观的，基于问卷的变量和目标，客观，客观，客观，目标，客观，客观，客观，客观，从学习管理系统中提取的基于日志数据的指标。结果表明，具有客观预测变量的模型始终优于主观预测指标的模型，并且两种变量类型的组合表现稍好一些。对于这三个选项中的每一个，一种不同的方法盛行（主观，贝叶斯多层次模型的梯度增强机器，共同预测指标的随机森林）。我们得出的结论是，在学习管理系统中实施此类模型之前，应仔细注意预测变量和算法。

由于形态的相似性，皮肤肿瘤的组织学切片分化为个体亚型可能具有挑战性。最近，基于深度学习的方法证明了它们在这方面支持病理学家的潜力。但是，这些监督算法中的许多都需要大量的注释数据才能进行稳健开发。我们提供了一个公开可用的数据集，该数据集是七个不同的犬皮肤肿瘤的350张全滑图像，其中有13种组织学类别的12,424个多边形注释，包括7种皮肤肿瘤亚型。在评估者间实验中，我们显示了提供的标签的高稠度，尤其是对于肿瘤注释。我们通过训练深层神经网络来进一步验证数据集，以完成组织分割和肿瘤亚型分类的任务。我们的肿瘤尤其是0.7047的类平均Jaccard系数为0.7047，尤其是0.9044。对于分类，我们达到了0.9857的幻灯片级准确性。由于犬皮肤肿瘤对人肿瘤具有各种组织学同源性，因此该数据集的附加值不限于兽医病理学，而是扩展到更一般的应用领域。

注释数据，尤其是在医疗领域，需要专家知识和很多努力。这限制了可用医疗数据集的实验量和/或有用性。因此，发展策略以增加注释的数量，同时降低所需的域知识是感兴趣的。可能的策略是使用游戏，即即将注释任务转换为游戏。我们提出了一种方法来游戏从病理整体幻灯片图像中注释肺部流体细胞的任务。由于该域是未知的非专家注释器所知，我们将用视网网架构检测到的细胞图像到花卉图像域。使用Compygan架构执行此域传输，用于不同的小区类型。在这种更科的域名中，非专家注释器可以（t）要求在俏皮的环境中注释不同种类的花朵。为了提供概念证据，该工作表明，通过评估在真实单元图像上培训的图像分类网络并在由Cyclegan网络生成的小区图像上测试的图像分类网络可以进行域传输。分类网络分别达到原始肺液体细胞和转化肺部流体细胞的精度​​为97.48％和95.16％。通过这项研究，我们为使用自行车队进行了未来的游戏研究的基础。