Matching rules for collective behaviors on complex networks: optimal configurations for vibration frequencies of networked harmonic oscillators

Notes on resonant and synchronized states in complex networks

Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial role in shaping the local and global evolution of the two phenomena. This article further explores this relationship within a compact mathematical framework and provides new contributions on certain pivotal issues, including a closed bound for the average synchronization time in arbitrary topologies; new evidences of the effect of the coupling strength on this time; exact closed expressions for the resonance frequencies in terms of the eigenvalues of the Laplacian matrix; a measure of the effectiveness of an influencer node's impact on the network; and, finally, a discussion on the existence of a resonant synchronized state. Some properties of the solution of the linear swing equation are also discussed within the same setting. Numerical experiments conducted on two distinct real networks-a social network and a power grid-illustrate the significance of these results and shed light on intriguing aspects of how these processes can be interpreted within networks of this kind.

Inferring synchronizability of networked heterogeneous oscillators with machine learning

In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Whereas methods have been proposed to address this question in the literature, the methods are all based on accurate models describing the system dynamics, which, however, are normally unavailable in realistic situations. Here, we show that this question can be addressed by the model-free technique of a feed-forward neural network (FNN) in machine learning. Specifically, we measure the synchronization performance of a number of allocation schemes and use the measured data to train a machine. It is found that the trained machine is able to not only infer the synchronization performance of any new allocation scheme, but also find from a huge amount of candidates the optimal allocation scheme for synchronization.

Application of Machine Learning Techniques to Predict Binding Affinity for Drug Targets: A Study of Cyclin-Dependent Kinase 2

BACKGROUND

The elucidation of the structure of cyclin-dependent kinase 2 (CDK2) made it possible to develop targeted scoring functions for virtual screening aimed to identify new inhibitors for this enzyme. CDK2 is a protein target for the development of drugs intended to modulate cellcycle progression and control. Such drugs have potential anticancer activities.

OBJECTIVE

Our goal here is to review recent applications of machine learning methods to predict ligand- binding affinity for protein targets. To assess the predictive performance of classical scoring functions and targeted scoring functions, we focused our analysis on CDK2 structures.

METHODS

We have experimental structural data for hundreds of binary complexes of CDK2 with different ligands, many of them with inhibition constant information. We investigate here computational methods to calculate the binding affinity of CDK2 through classical scoring functions and machine- learning models.

RESULTS

Analysis of the predictive performance of classical scoring functions available in docking programs such as Molegro Virtual Docker, AutoDock4, and Autodock Vina indicated that these methods failed to predict binding affinity with significant correlation with experimental data. Targeted scoring functions developed through supervised machine learning techniques showed a significant correlation with experimental data.

CONCLUSION

Here, we described the application of supervised machine learning techniques to generate a scoring function to predict binding affinity. Machine learning models showed superior predictive performance when compared with classical scoring functions. Analysis of the computational models obtained through machine learning could capture essential structural features responsible for binding affinity against CDK2.

Periodic coupling inhibits second-order consensus on networks

Consensus algorithms on networks have received increasing attention in recent years for various applications, ranging from distributed decision making to multivehicle coordination. In particular, second-order consensus models take into account the Newtonian dynamics of interacting physical agents. For this model class, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations. We treat the model in its spectral decomposition and find analytically that, for certain intermediate coupling frequencies, parametric resonance is induced on a network level-at odds with the expected emergence of consensus for very short and long coupling time scales. Our formalism precisely predicts those resonance frequencies and links them to the Laplacian spectrum of the static backbone network. The excitation of the system is furthermore quantified within the theory of parametric resonance, which we extend to the domain of networks with time-periodic couplings.