A signed graph offers richer information than an unsigned graph, since it describes both collaborative and competitive relationships in social networks. In this paper, we study the opinion dynamics on a signed graph, based on the Friedkin-Johnsen model. We first interpret the equilibrium opinion in terms of a defined random walk on an augmented signed graph, by representing the equilibrium opinion of every node as a combination of all nodes’ internal opinions, with the coefficient of the internal opinion for each node being the difference of two absorbing probabilities. We then quantify some relevant social phenomena and express them in terms of the $\ell _{2}$ norms of vectors. We also design a nearly-linear time signed Laplacian solver for assessing these quantities, by establishing a connection between the absorbing probability of random walks on a signed graph and that on an associated unsigned graph. We further study the opinion optimization problem by changing the initial opinions of a fixed number of nodes, which can be optimally solved in cubic time. We provide a nearly-linear time algorithm with error guarantee to approximately solve the problem. Finally, we execute extensive experiments on sixteen real-life signed networks, which show that both of our algorithms are effective and efficient, and are scalable to massive graphs with over 20 million nodes.

Jointly optimising both the body and brain of a robot is known to be a challenging task, especially when attempting to evolve designs in simulation that will subsequently be built in the real world. To address this, it is increasingly common to combine evolution with a learning algorithm that can either improve the inherited controllers of new offspring to fine tune them to the new body design or learn them from scratch. In this paper an approach is proposed in which a robot is specified indirectly by two compositional pattern producing networks (CPPN) encoded in a single genome, one which encodes the brain and the other the body. The body part of the genome is evolved using an evolutionary algorithm (EA), with an individual learning algorithm (also an EA) applied to the inherited controller to improve it. The goal of this paper is to determine how to utilise the results of learning process most effectively to improve task performance of the robot. Specifically, three variants are investigated: (1) evolution of the body+controller only; (2) a learning algorithm is applied to the inherited controller with the learned fitness assigned to the genome; (3) learning is applied and the genome is updated with the learned controller, as well as being assigned the learned fitness. Experiments are performed in three different scenarios chosen to favour different bodies and locomotion patterns. It is shown that better performance can be obtained using learning but only if the learned controller is inherited by the offspring.

In this letter, we propose a novel reinforcement learning (RL) based path generation (RL-PG) approach for mobile robot navigation without a prior exploration of an unknown environment. Multiple predictive path points are dynamically generated by a deep Markov model optimized using an RL approach for the robot to track. To ensure safety when tracking the predictive points, the robot's motion is fine-tuned by a motion fine-tuning module. Such an approach, using a deep Markov model with RL algorithm for planning, focuses on the relationship between adjacent path points. We analyze the benefits of our proposed approach and show it is more effective and has higher success rates than the RL-based approach DWA-RL (Patel et al. 2021) and a traditional navigation approach APF (Chen et al. 2021). We deploy our model on both simulation and physical platforms and demonstrate our model performs robot navigation effectively and safely.

In this paper, we study the opinion maximization problem for the leader-follower DeGroot model of opinion dynamics in a social network modelled by a directed graph with n nodes, where a small number of nodes are competing leader nodes with binary opposing opinions 0 or 1, and the rest are follower nodes. We address the problem of maximizing the overall opinion by adding k ⇐ n new edges, where each edge is incident to a 1-leader and a follower. We prove that the objective function is monotone and submodular, and then propose a deterministic greedy algorithm with an approximation ratio (1-1 over e) and O(n³) running time. We then develop a fast sampling algorithm based on l-truncated absorbing random walks and sample-materialization techniques, which has sublinear time complexity O(kn^1/2 log^3/2 n/ε³) for any error parameter ε > 0. We provide extensive experiments on real networks to evaluate the performance of our algorithms. The results show that for undirected graphs our fast sampling algorithm outperforms the state-of-the-art method in terms of efficiency and effectiveness. While for directed graphs our fast sampling algorithm is as effective as our deterministic greedy algorithm, both of which are much better than the baseline strategies. Moreover, our fast algorithm is scalable to large directed graphs with over 41 million nodes.