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We discover a family of surfaces of general type with K 2 = 3 K^2=3 and p g = q = 0 p_g=q=0 as free C 13 C_{13} quotients of special linear cuts of the octonionic projective plane O P 2 \mathbb O \mathbb P^2 . A special member of the family has 3 3 singularities of type A 2 A_2 , and is a quotient of a fake projective plane. We use the techniques of earlier work of Borisov and Fatighenti to define this fake projective plane by explicit equations in its bicanonical embedding.

Pose estimation is the task of determining the 6D position of an object in a scene. Pose estimation aid the abilities and flexibility of robotic set-ups. However, the system must be configured towards the use case to perform adequately. This configuration is time-consuming and limits the usability of pose estimation and, thereby, robotic systems. Deep learning is a method to overcome this configuration procedure by learning parameters directly from the dataset. However, obtaining this training data can also be very time-consuming. The use of synthetic training data avoids this data collection problem, but a configuration of the training procedure is necessary to overcome the domain gap problem. Additionally, the pose estimation parameters also need to be configured. This configuration is jokingly known as grad student descent as parameters are manually adjusted until satisfactory results are obtained. This paper presents a method for automatic configuration using only synthetic data. This is accomplished by learning the domain randomization during network training, and then using the domain randomization to optimize the pose estimation parameters. The developed approach shows state-of-the-art performance of 82.0 % recall on the challenging OCCLUSION dataset, outperforming all previous methods with a large margin. These results prove the validity of automatic set-up of pose estimation using purely synthetic data., Comment: 8 pages, 4 figures, 6 tables

We present an approach to learn dense, continuous 2D-3D correspondence distributions over the surface of objects from data with no prior knowledge of visual ambiguities like symmetry. We also present a new method for 6D pose estimation of rigid objects using the learnt distributions to sample, score and refine pose hypotheses. The correspondence distributions are learnt with a contrastive loss, represented in object-specific latent spaces by an encoder-decoder query model and a small fully connected key model. Our method is unsupervised with respect to visual ambiguities, yet we show that the query- and key models learn to represent accurate multi-modal surface distributions. Our pose estimation method improves the state-of-the-art significantly on the comprehensive BOP Challenge, trained purely on synthetic data, even compared with methods trained on real data. The project site is at https://surfemb.github.io/ .

Since the introduction of modern deep learning methods for object pose estimation, test accuracy and efficiency has increased significantly. For training, however, large amounts of annotated training data are required for good performance. While the use of synthetic training data prevents the need for manual annotation, there is currently a large performance gap between methods trained on real and synthetic data. This paper introduces a new method, which bridges this gap. Most methods trained on synthetic data use 2D images, as domain randomization in 2D is more developed. To obtain precise poses, many of these methods perform a final refinement using 3D data. Our method integrates the 3D data into the network to increase the accuracy of the pose estimation. To allow for domain randomization in 3D, a sensor-based data augmentation has been developed. Additionally, we introduce the SparseEdge feature, which uses a wider search space during point cloud propagation to avoid relying on specific features without increasing run-time. Experiments on three large pose estimation benchmarks show that the presented method outperforms previous methods trained on synthetic data and achieves comparable results to existing methods trained on real data., Comment: 10 pages, 5 figures, 7 tables

In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula involves a new class of generalized Littlewood-Richardson coefficients, all of which surprisingly seem to be non-negative. We conjecture that each of these coefficients count the number of sequences of semistandard Young tableaux which satisfy certain conditions. In this paper I give a proof of this conjecture in the special case where the quiver variety can be described by at most four vector bundles. I also prove that the general conjecture follows from a simple combinatorial statement for which substantial computer verification has been obtained., Comment: 19 pages, rich supply of figures. This is half of my thesis, "Combinatorics of degeneracy loci"

This chapter presents a multi-contextual framework for engineering knowledge that serves to highlight how engineering knowledge is configured in diverse contexts. We argue that the insights from the sociology of knowledge research and design science research can help us understand the complexity of engineering knowledge production and the diversity of the makers and takers of engineering knowledge. We aim at looking beyond popular notions of evidence-based practice and knowledge transfer, which privilege academia as the main setting for knowledge production. This will, we argue, facilitate a more nuanced understanding of how engineering knowledge is formed and transformed as it is transferred between different contexts. We describe this as configuration and reconfiguration of engineering knowledge in particular contexts.