Group-equivariant convolutional neural networks (G-CNN) heavily rely on parameter sharing to increase CNN's data efficiency and performance. However, the parameter-sharing strategy greatly increases the computational burden for each added parameter, which hampers its application to deep neural network models. In this paper, we address these problems by proposing a non-parameter-sharing approach for group equivariant neural networks. The proposed methods adaptively aggregate a diverse range of filters by a weighted sum of stochastically augmented decomposed filters. We give theoretical proof about how the group equivariance can be achieved by our methods. Our method applies to both continuous and discrete groups, where the augmentation is implemented using Monte Carlo sampling and bootstrap resampling, respectively. Our methods also serve as an efficient extension of standard CNN. The experiments show that our method outperforms parameter-sharing group equivariant networks and enhances the performance of standard CNNs in image classification and denoising tasks, by using suitable filter bases to build efficient lightweight networks.

Many applications in MRI such as accelerated receive and transmit sequences require the synthesis of nonuniform 3-D gradient trajectories. Several methods have been proposed to design these gradient trajectories in a time-optimal manner, subject to hardware specific gradient magnitude and slew rate constraints. In this work a novel method is derived that designs time-optimal trajectories, solely based on a set of arbitrarily chosen control points in k-space. In particular, no path constraint is required for the k-space trajectory. It is shown that the above problem can be formulated as a constrained optimization problem. The fact that the objective function is derived in an analytic manner allows for designing time-optimal 3-D gradient trajectories within only few seconds without any significant numerical instabilities. The utilization of the shape of the trajectory--serving as a degree of freedom--results in significantly accelerated trajectories compared to current standard methods. This is proven in an extensive evaluation of the proposed method and in comparison with what can be considered the current Gold Standard method. The proposed Gradient Basis Function method provides significant benefits over current standard methods in terms of the duration of the trajectory (in average 9.2% acceleration), computation time (acceleration by at least 25% up to factors of 100), and robustness (no significant numerical instabilities).

UNLABELLED: We present a method for automatic test case generation for protein-protein docking. A consensus-type approach is proposed processing the whole PDB and classifying protein structures into complexes and unbound proteins by combining information from three different approaches (current PDB-at-a-glance classification, search of complexes by sequence identical unbound structures and chain naming). Out of this classification test cases are generated automatically. All calculations were run on the database. The information stored is available via a web interface. The user can choose several criteria for generating his own subset out of our test cases, e.g. for testing docking algorithms. AVAILABILITY: http://bibiserv.techfak.uni-bielefeld.de/agt-sdp/ CONTACT: [email protected].