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Institute
Goal-Conditioned Reinforcement Learning (GCRL) is a popular framework for training agents to solve multiple tasks in a single environment. It is cru- cial to train an agent on a diverse set of goals to ensure that it can learn to generalize to unseen downstream goals. Therefore, current algorithms try to learn to reach goals while simultaneously exploring the environment for new ones (Aubret et al., 2021; Mendonca et al., 2021). This creates a form of the prominent exploration-exploitation dilemma. To relieve the pres- sure of a single agent having to optimize for two competing objectives at once, this thesis proposes the novel algorithm family Goal-Conditioned Re- inforcement Learning with Prior Intrinsic Exploration (GC-π), which sep- arates exploration and goal learning into distinct phases. In the first ex- ploration phase, an intrinsically motivated agent explores the environment and collects a rich dataset of states and actions. This dataset is then used to learn a representation space, which acts as the distance metric for the goal- conditioned reward signal. In the final phase, a goal-conditioned policy is trained with the help of the representation space, and its training goals are randomly sampled from the dataset collected during the exploration phase. Multiple variations of these three phases have been extensively evaluated in the classic AntMaze MuJoCo environment (Nachum et al., 2018). The fi- nal results show that the proposed algorithms are able to fully explore the environment and solve all downstream goals while using every dimension of the state space for the goal space. This makes the approach more flexible compared to previous GCRL work, which only ever uses a small subset of the dimensions for the goals (S. Li et al., 2021a; Pong et al., 2020).
Nowadays, digitalization has an immense impact on the landscape of jobs. This technological revolution creates new industries and professions, promises greater efficiency and improves the quality of working life. However, emerging technologies such as robotics and artificial intelligence (AI) are reducing human intervention, thus advancing automation and eliminating thousands of jobs and whole occupational images. To prepare employees for the changing demands of work, adequate and timely training of the workforce and real-time support of workers in new positions is necessary. Therefore, it is investigated whether user-oriented technologies, such as augmented reality (AR) and virtual reality (VR) can be applied “on-the-job” for such training and support—also known as intelligence augmentation (IA). To address this problem, this work synthesizes results of a systematic literature review as well as a practically oriented search on augmented reality and virtual reality use cases within the IA context. A total of 150 papers and use cases are analyzed to identify suitable areas of application in which it is possible to enhance employees' capabilities. The results of both, theoretical and practical work, show that VR is primarily used to train employees without prior knowledge, whereas AR is used to expand the scope of competence of individuals in their field of expertise while on the job. Based on these results, a framework is derived which provides practitioners with guidelines as to how AR or VR can support workers at their job so that they can keep up with anticipated skill demands. Furthermore, it shows for which application areas AR or VR can provide workers with sufficient training to learn new job tasks. By that, this research provides practical recommendations in order to accompany the imminent distortions caused by AI and similar technologies and to alleviate associated negative effects on the German labor market.
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has a fixed sign on one side, then it will be symmetric in the perpendicular direction. Moreover, the solution will be monotonic in the part where it is of fixed sign. In addition, we present also a class of examples in which our result can be applied.
Motivated by Gröbner basis theory for finite point configurations, we define and study the class of standard complexes associated to a matroid. Standard complexes are certain subcomplexes of the independence complex that are invariant under matroid duality. For the lexicographic term order, the standard complexes satisfy a deletion-contraction-type recurrence. We explicitly determine the lexicographic standard complexes for lattice path matroids using classical bijective combinatorics.
For an abeloid variety A over a complete algebraically closed field extension K of Qp, we construct a p-adic Corlette–Simpson correspondence, namely an equivalence between finite-dimensional continuous K-linear representations of the Tate module and a certain subcategory of the Higgs bundles on A. To do so, our central object of study is the category of vector bundles for the v-topology on the diamond associated to A. We prove that any pro-finite-étale v-vector bundle can be built from pro-finite-étale v-line bundles and unipotent v-bundles. To describe the latter, we extend the theory of universal vector extensions to the v-topology and use this to generalise a result of Brion by relating unipotent v-bundles on abeloids to representations of vector groups.
Nodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) can show variable histological growth patterns and present remarkable overlap with T-cell/histiocyte-rich large B-cell lymphoma (THRLBCL). Previous studies suggest that NLPHL histological variants represent progression forms of NLPHL and THRLBCL transformation in aggressive disease. Since molecular studies of both lymphomas are limited due to the low number of tumor cells, the present study aimed to learn if a better understanding of these lymphomas is possible via detailed measurements of nuclear and cell size features in 2D and 3D sections. Whereas no significant differences were visible in 2D analyses, a slightly increased nuclear volume and a significantly enlarged cell size were noted in 3D measurements of the tumor cells of THRLBCL in comparison to typical NLPHL cases. Interestingly, not only was the size of the tumor cells increased in THRLBCL but also the nuclear volume of concomitant T cells in the reactive infiltrate when compared with typical NLPHL. Particularly CD8+ T cells had frequent contacts to tumor cells of THRLBCL. However, the nuclear volume of B cells was comparable in all cases. These results clearly demonstrate that 3D tissue analyses are superior to conventional 2D analyses of histological sections. Furthermore, the results point to a strong activation of T cells in THRLBCL, representing a cytotoxic response against the tumor cells with unclear effectiveness, resulting in enhanced swelling of the tumor cell bodies and limiting proliferative potential. Further molecular studies combining 3D tissue analyses and molecular data will help to gain profound insight into these ill-defined cellular processes.
Through the glasses of didactic reduction, we consider a (periodic) tessellation Δ of either Euclidean or hyperbolic 𝑛-space 𝑀. By a piecewise isometric rearrangement of Δ we mean the process of cutting 𝑀 along corank-1 tile-faces into finitely many convex polyhedral pieces, and rearranging the pieces to a new tight covering of the tessellation Δ. Such a rearrangement defines a permutation of the (centers of the) tiles of Δ, and we are interested in the group of 𝑃𝐼(Δ) all piecewise isometric rearrangements of Δ. In this paper, we offer (a) an illustration of piecewise isometric rearrangements in the visually attractive hyperbolic plane, (b) an explanation on how this is related to Richard Thompson's groups, (c) a section on the structure of the group pei(ℤ𝑛) of all piecewise Euclidean rearrangements of the standard cubically tessellated ℝ𝑛, and (d) results on the finiteness properties of some subgroups of pei(ℤ𝑛).