Trajectory or path planning is a fundamental issue in a wide variety of applications. In this article, we show that it is possible to solve path planning on a maze for multiple start point and endpoint highly efficiently with a novel configuration of multilayer networks that use only weighted pooling operations, for which no network training is needed. These networks create solutions, which are identical to those from classical algorithms such as breadth-first search (BFS), Dijkstra's algorithm, or TD(0). Different from competing approaches, very large mazes containing almost one billion nodes with dense obstacle configuration and several thousand importance-weighted path endpoints can this way be solved quickly in a single pass on parallel hardware.

Path planning is important for robot action execution, since a path or a motion trajectory for a particular action has to be defined first before the action can be executed. Most of the current approaches are iterative methods where the trajectory is generated by predicting the next state based on the current state. Here we propose a novel method by utilising a fully convolutional neural network, which allows generation of complete paths even for several agents with one network prediction iteration. We demonstrate that our method is able to successfully generate optimal or close to optimal paths (less than 10% longer) in more than 99% of the cases for single path predictions in 2D and 3D environments. Furthermore, we show that the network is - without specific training on such cases - able to create (close to) optimal paths in 96% of the cases for two and in 84% of the cases for three simultaneously generated paths.

Neural networks in the brain are dominated by sometimes more than 60% feedback connections, which most often have small synaptic weights. Different from this, little is known how to introduce feedback into artificial neural networks. Here we use transfer entropy in the feed-forward paths of deep networks to identify feedback candidates between the convolutional layers and determine their final synaptic weights using genetic programming. This adds about 70% more connections to these layers all with very small weights. Nonetheless performance improves substantially on different standard benchmark tasks and in different networks. To verify that this effect is generic we use 36000 configurations of small (2-10 hidden layer) conventional neural networks in a non-linear classification task and select the best performing feed-forward nets. Then we show that feedback reduces total entropy in these networks always leading to performance increase. This method may, thus, supplement standard techniques (e.g. error backprop) adding a new quality to network learning.

Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control theory and is based on a second order dynamic system. We evaluate our method and compare it to state-of-the-art movement generation methods in both simulations and a real robot experiment. We show that the new method is very compact in its representation and can reproduce demonstrated trajectories with zero error. Moreover, it has most of the properties of the state-of-the-art trajectory generation methods such as robustness to perturbations and generalisation to new boundary position and velocity conditions. We believe that, due to these features, our method has great potential for various robotic applications, especially, where high accuracy is required, for example, in industrial and medical robotics.

BACKGROUND: The identification of functionally or structurally important non-conserved residue sites in protein MSAs is an important challenge for understanding the structural basis and molecular mechanism of protein functions. Despite the rich literature on compensatory mutations as well as sequence conservation analysis for the detection of those important residues, previous methods often rely on classical information-theoretic measures. However, these measures usually do not take into account dis/similarities of amino acids which are likely to be crucial for those residues. In this study, we present a new method, the Quantum Coupled Mutation Finder (QCMF) that incorporates significant dis/similar amino acid pair signals in the prediction of functionally or structurally important sites. RESULTS: The result of this study is twofold. First, using the essential sites of two human proteins, namely epidermal growth factor receptor (EGFR) and glucokinase (GCK), we tested the QCMF-method. The QCMF includes two metrics based on quantum Jensen-Shannon divergence to measure both sequence conservation and compensatory mutations. We found that the QCMF reaches an improved performance in identifying essential sites from MSAs of both proteins with a significantly higher Matthews correlation coefficient (MCC) value in comparison to previous methods. Second, using a data set of 153 proteins, we made a pairwise comparison between QCMF and three conventional methods. This comparison study strongly suggests that QCMF complements the conventional methods for the identification of correlated mutations in MSAs. CONCLUSIONS: QCMF utilizes the notion of entanglement, which is a major resource of quantum information, to model significant dissimilar and similar amino acid pair signals in the detection of functionally or structurally important sites. Our results suggest that on the one hand QCMF significantly outperforms the previous method, which mainly focuses on dissimilar amino acid signals, to detect essential sites in proteins. On the other hand, it is complementary to the existing methods for the identification of correlated mutations. The method of QCMF is computationally intensive. To ensure a feasible computation time of the QCMF's algorithm, we leveraged Compute Unified Device Architecture (CUDA).The QCMF server is freely accessible at http://qcmf.informatik.uni-goettingen.de/.