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A survey is made of several aspects of the dynamics of networks, with special emphasis on unsupervised learning processes, non-Gaussian data analysis and pattern recognition in networks with complex nodes.

Recurrence Quantification Analysis (RQA) is a widely used method for capturing the dynamical structure embedded in time series data, relying on the analysis of recurrence patterns in the reconstructed phase space via recurrence plots (RPs).…

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

Recurrence Quantification Analysis (RQA) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. From recurrence plots different RQA variables…

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…

In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…

With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…

Air transport systems are highly dynamic at temporal scales from minutes to years. This dynamic behavior not only characterizes the evolution of the system but also affect the system's functioning. Understanding the evolutionary mechanisms…

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of…

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…

Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

Linearization of the dynamics of recurrent neural networks (RNNs) is often used to study their properties. The same RNN dynamics can be written in terms of the ``activations" (the net inputs to each unit, before its pointwise nonlinearity)…

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs,…

This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…