Threshold-activated transport stabilizes chaotic populations to steady states

Machine learning approach to detect dynamical states from recurrence measures

We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms: Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing, we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyperchaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her, from the data of their light curves. We also indicate how the algorithms can be trained to classify data from discrete systems.

Emerging landscape of molecular interaction networks: Opportunities, challenges and prospects

Network biology finds application in interpreting molecular interaction networks and providing insightful inferences using graph theoretical analysis of biological systems. The integration of computational bio-modelling approaches with different hybrid network-based techniques provides additional information about the behaviour of complex systems. With increasing advances in high-throughput technologies in biological research, attempts have been made to incorporate this information into network structures, which has led to a continuous update of network biology approaches over time. The newly minted centrality measures accommodate the details of omics data and regulatory network structure information. The unification of graph network properties with classical mathematical and computational modelling approaches and technologically advanced approaches like machine-learning- and artificial intelligence-based algorithms leverages the potential application of these techniques. These computational advances prove beneficial and serve various applications such as essential gene prediction, identification of drug–disease interaction and gene prioritization. Hence, in this review, we have provided a comprehensive overview of the emerging landscape of molecular interaction networks using graph theoretical approaches. With the aim to provide information on the wide range of applications of network biology approaches in understanding the interaction and regulation of genes, proteins, enzymes and metabolites at different molecular levels, we have reviewed the methods that utilize network topological properties, emerging hybrid network-based approaches and applications that integrate machine learning techniques to analyse molecular interaction networks. Further, we have discussed the applications of these approaches in biomedical research with a note on future prospects.

Identifying nodal properties that are crucial for the dynamical robustness of multistable networks

We investigate the collective dynamics of bistable elements connected in different network topologies and estimate the network response to localized perturbations on different classes of nodes by introducing a variant of the concept of multinode basin stability. We show that perturbations on nodes with high closeness and betweeness centrality drastically reduces the capacity of the system to return to the original state. This effect is most pronounced for a star network, where perturbation of the single hub node can destroy the collective state, while the system manages to recover even when a majority of the peripheral nodes are strongly perturbed. This demonstrates the extreme effect of the centrality of the perturbed node on the stability of the network. Further, we exploit the difference in centrality distributions in random scale-free networks with m=1 and m=2 to probe which property most influences the collective dynamics in heterogeneous networks. Significantly, we find clear evidence that the betweeness centrality of the perturbed node is more crucial for dynamical robustness than closeness centrality or degree of the node. This allows us to decide which nodes to safeguard in order to maintain the collective state of a network against targeted localized attacks.