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Abstract. Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N -fold torus). This result has been used to explain the existence of the N − 3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk ∆ with the hyperbolic metric. We show that in this metric the original Kuramoto phase model (with order parameter Z 1 equal to the centroid of the oscillator configuration of points on the unit circle) is a gradient flow and the model with order parameter iZ 1 (corresponding to cosine phase coupling) is a completely integrable Hamiltonian flow. We give necessary and sufficient conditions for general Kuramoto phase models to be gradient or Hamiltonian flows in this metric. This allows us to identify several new infinite families of hyperbolic gradient or Hamiltonian Kuramoto oscillator networks which therefore have simple dynamics with respect to this geometry. We prove that for the Z 1 model, a generic 2D reduced group orbit has a unique fixed point corresponding to the hyperbolic barycenter of the oscillator configuration, and therefore the dynamics are equivalent on different generic reduced group orbits. This is not always the case for more general hyperbolic gradient or Hamiltonian flows; the reduced group orbits may have multiple fixed points, which also may bifurcate as the reduced group orbits vary.

Background Technological and research advances have produced large volumes of biomedical data. When represented as a network (graph), these data become useful for modeling entities and interactions in biological and similar complex systems. In the field of network biology and network medicine, there is a particular interest in predicting results from drug–drug, drug–disease, and protein–protein interactions to advance the speed of drug discovery. Existing data and modern computational methods allow to identify potentially beneficial and harmful interactions, and therefore, narrow drug trials ahead of actual clinical trials. Such automated data-driven investigation relies on machine learning techniques. However, traditional machine learning approaches require extensive preprocessing of the data that makes them impractical for large datasets. This study presents wide range of machine learning methods for predicting outcomes from biomedical interactions and evaluates the performance of the traditional methods with more recent network-based approaches. Results We applied a wide range of 32 different network-based machine learning models to five commonly available biomedical datasets, and evaluated their performance based on three important evaluations metrics namely AUROC, AUPR, and F1-score. We achieved this by converting link prediction problem as binary classification problem. In order to achieve this we have considered the existing links as positive example and randomly sampled negative examples from non-existant set. After experimental evaluation we found that Prone, ACT and $$LRW_5$$ L R W 5 are the top 3 best performers on all five datasets. Conclusions This work presents a comparative evaluation of network-based machine learning algorithms for predicting network links, with applications in the prediction of drug-target and drug–drug interactions, and applied well known network-based machine learning methods. Our work is helpful in guiding researchers in the appropriate selection of machine learning methods for pharmaceutical tasks.

Emerging mobile edge techniques and applications such as Augmented Reality (AR)/Virtual Reality (VR), Internet of Things (IoT), and vehicle networking, result in an explosive growth of power and computing resource consumptions. In the meantime, the volume of data generated at the edge networks is also increasing rapidly. Under this circumstance, building energy-efficient and privacy-protected communications is imperative for 5G and beyond wireless communication systems. The recent emerging distributed learning methods such as federated learning (FL) perform well in improving resource efficiency while protecting user privacy with low communication overhead. Specifically, FL enables edge devices to learn a shared network model by aggregating local updates while keeping all the training processes on local devices. This paper investigates distributed power allocation for edge users in decentralized wireless networks with aim to maximize energy/spectrum efficiency while preventing privacy leakage based on a FL framework. Due to the dynamics and complexity of wireless networks, we adopt an on-line Actor-Critic (AC) architecture as the local training model, and FL performs cooperation for edge users by sharing the gradients and weightages generated in the Actor network. Moreover, in order to resolve the over-fitting problem caused by data leakages in Non-independent and identically distributed (Non-i.i.d) data environment, we propose a federated augmentation mechanism with Wasserstein Generative Adversarial Networks (WGANs) algorithm for data augmentation. Federated augmentation empowers each device to replenish the data buffer using a generative model of WGANs until accomplishing an i.i.d training dataset, which significantly reduces the communication overhead in distributed learning compared to direct data sample exchange method. Numerical results reveal that the proposed federated learning based cooperation and augmentation (FL-CA) algorithm possesses a good convergence property, high robustness and achieves better accuracy of power allocation strategy than other three benchmark algorithms. INDEX TERMS Federated learning, power allocation, wireless networks, federated cooperation, federated augmentation.

The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. In this paper, we propose a link prediction algorithm based on ant colony optimization. By exploiting the swarm intelligence, the algorithm employs artificial ants to travel on a logical graph. Pheromone and heuristic information are assigned in the edges of the logical graph. Each ant chooses its path according to the value of the pheromone and heuristic information on the edges. The paths the ants traveled are evaluated, and the pheromone information on each edge is updated according to the quality of the path it located. The pheromone on each edge is used as the final score of the similarity between the nodes. Experimental results on a number of real networks show that the algorithm improves the prediction accuracy while maintaining low time complexity. We also extend the method to solve the link prediction problem in networks with node attributes, and the extended method also can detect the missing or incomplete attributes of data. Our experimental results show that it can obtain higher quality results on the networks with node attributes than other algorithms.