我们专注于一个在线2阶段问题，以以下情况进行：考虑一个应分配给大学的系统。在第一轮中，一些学生申请了一些学生，必须计算出第一个（稳定的）匹配$ m_1 $。但是，一些学生可能会决定离开系统（更改计划，去外国大学或不在系统中的某些机构）。然后，在第二轮（在这些删除之后）中，我们将计算第二个（最终）稳定的匹配$ m_2 $。由于不希望更改作业，因此目标是最大程度地减少两个稳定匹配$ m_1 $和$ m_2 $之间的离婚/修改数量。那么，我们应该如何选择$ m_1 $和$ m_2 $？我们表明，有一个{\ it Optival Online}算法可以解决此问题。特别是，由于具有优势属性，我们表明我们可以最佳地计算$ M_1 $，而无需知道会离开系统的学生。我们将结果概括为输入中的其他一些可能的修改（学生，开放位置）。我们还解决了更多阶段的情况，表明在有3个阶段后，就无法实现竞争性（在线）算法。

选民偏好共享某种共同结构的假设是绕开NP硬度的标准方法，导致社会选择问题。虽然在一般情况下，Kemeny排名问题是NP-HARD，但如果偏好是一维欧几里得人，众所周知，它变得容易。在本说明中，我们证明了kemeny排名问题仍然是$ k $ - 二维欧几里得的偏好，$ k \！\！\ ge \！2 $在norms $ \ ell_1 $，$ \ ell_1 $，$ \ ell_2 $和$ \ ell_ \ ell_ \ ell_ \ ell_ \ ell_ \ ell_ \ ell_ \ ell_通过证明任何具有相同平价的权重的加权锦标赛（分别加权双方锦标赛），这是可以诱导的，这是2-欧克里德式偏好符合2欧元$ \ ell_2 $的加权多数锦标赛（RESP）（RESP） 。$ \ ell_1，\ ell _ {\ infty} $），可在多项式时间计算。更普遍的是，这个关于加权锦标赛的结果本质上意味着，依赖于一般情况下（例如，Slater排名的NP-Hardness）的（加权）多数锦标赛的硬度结果仍然是正确的。

Neural style transfer is a deep learning technique that produces an unprecedentedly rich style transfer from a style image to a content image and is particularly impressive when it comes to transferring style from a painting to an image. It was originally achieved by solving an optimization problem to match the global style statistics of the style image while preserving the local geometric features of the content image. The two main drawbacks of this original approach is that it is computationally expensive and that the resolution of the output images is limited by high GPU memory requirements. Many solutions have been proposed to both accelerate neural style transfer and increase its resolution, but they all compromise the quality of the produced images. Indeed, transferring the style of a painting is a complex task involving features at different scales, from the color palette and compositional style to the fine brushstrokes and texture of the canvas. This paper provides a solution to solve the original global optimization for ultra-high resolution images, enabling multiscale style transfer at unprecedented image sizes. This is achieved by spatially localizing the computation of each forward and backward passes through the VGG network. Extensive qualitative and quantitative comparisons show that our method produces a style transfer of unmatched quality for such high resolution painting styles.

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.

State-of-the-art brain tumor segmentation is based on deep learning models applied to multi-modal MRIs. Currently, these models are trained on images after a preprocessing stage that involves registration, interpolation, brain extraction (BE, also known as skull-stripping) and manual correction by an expert. However, for clinical practice, this last step is tedious and time-consuming and, therefore, not always feasible, resulting in skull-stripping faults that can negatively impact the tumor segmentation quality. Still, the extent of this impact has never been measured for any of the many different BE methods available. In this work, we propose an automatic brain tumor segmentation pipeline and evaluate its performance with multiple BE methods. Our experiments show that the choice of a BE method can compromise up to 15.7% of the tumor segmentation performance. Moreover, we propose training and testing tumor segmentation models on non-skull-stripped images, effectively discarding the BE step from the pipeline. Our results show that this approach leads to a competitive performance at a fraction of the time. We conclude that, in contrast to the current paradigm, training tumor segmentation models on non-skull-stripped images can be the best option when high performance in clinical practice is desired.

Reinforcement learning is a machine learning approach based on behavioral psychology. It is focused on learning agents that can acquire knowledge and learn to carry out new tasks by interacting with the environment. However, a problem occurs when reinforcement learning is used in critical contexts where the users of the system need to have more information and reliability for the actions executed by an agent. In this regard, explainable reinforcement learning seeks to provide to an agent in training with methods in order to explain its behavior in such a way that users with no experience in machine learning could understand the agent's behavior. One of these is the memory-based explainable reinforcement learning method that is used to compute probabilities of success for each state-action pair using an episodic memory. In this work, we propose to make use of the memory-based explainable reinforcement learning method in a hierarchical environment composed of sub-tasks that need to be first addressed to solve a more complex task. The end goal is to verify if it is possible to provide to the agent the ability to explain its actions in the global task as well as in the sub-tasks. The results obtained showed that it is possible to use the memory-based method in hierarchical environments with high-level tasks and compute the probabilities of success to be used as a basis for explaining the agent's behavior.

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean \textit{k}-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.

Natural language inference has trended toward studying contexts beyond the sentence level. An important application area is law: past cases often do not foretell how they apply to new situations and implications must be inferred. This paper introduces LawngNLI, constructed from U.S. legal opinions with automatic labels with high human-validated accuracy. Premises are long and multigranular. Experiments show two use cases. First, LawngNLI can benchmark for in-domain generalization from short to long contexts. It has remained unclear if large-scale long-premise NLI datasets actually need to be constructed: near-top performance on long premises could be achievable by fine-tuning using short premises. Without multigranularity, benchmarks cannot distinguish lack of fine-tuning on long premises versus domain shift between short and long datasets. In contrast, our long and short premises share the same examples and domain. Models fine-tuned using several past NLI datasets and/or our short premises fall short of top performance on our long premises. So for at least certain domains (such as ours), large-scale long-premise datasets are needed. Second, LawngNLI can benchmark for implication-based retrieval. Queries are entailed or contradicted by target documents, allowing users to move between arguments and evidence. Leading retrieval models perform reasonably zero shot on a LawngNLI-derived retrieval task. We compare different systems for re-ranking, including lexical overlap and cross-encoders fine-tuned using a modified LawngNLI or past NLI datasets. LawngNLI can train and test systems for implication-based case retrieval and argumentation.

In recent years, unmanned aerial vehicle (UAV) related technology has expanded knowledge in the area, bringing to light new problems and challenges that require solutions. Furthermore, because the technology allows processes usually carried out by people to be automated, it is in great demand in industrial sectors. The automation of these vehicles has been addressed in the literature, applying different machine learning strategies. Reinforcement learning (RL) is an automation framework that is frequently used to train autonomous agents. RL is a machine learning paradigm wherein an agent interacts with an environment to solve a given task. However, learning autonomously can be time consuming, computationally expensive, and may not be practical in highly-complex scenarios. Interactive reinforcement learning allows an external trainer to provide advice to an agent while it is learning a task. In this study, we set out to teach an RL agent to control a drone using reward-shaping and policy-shaping techniques simultaneously. Two simulated scenarios were proposed for the training; one without obstacles and one with obstacles. We also studied the influence of each technique. The results show that an agent trained simultaneously with both techniques obtains a lower reward than an agent trained using only a policy-based approach. Nevertheless, the agent achieves lower execution times and less dispersion during training.

We define the bicategory of Graph Convolutional Neural Networks $\mathbf{GCNN}_n$ for an arbitrary graph with $n$ nodes. We show it can be factored through the already existing categorical constructions for deep learning called $\mathbf{Para}$ and $\mathbf{Lens}$ with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor $\mathbf{GCNN}_n \to \mathbf{Para}(\mathsf{CoKl}(\mathbb{R}^{n \times n} \times -))$. We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.