Complex systems methods characterizing nonlinear processes in the near-Earth electromagnetic environment: recent advances and open challenges

Learning from successful applications of methods originating in statistical mechanics, complex systems science, or information theory in one scientific field (e.g., atmospheric physics or climatology) can provide important insights or conceptual ideas for other areas (e.g., space sciences) or even stimulate new research questions and approaches. For instance, quantification and attribution of dynamical complexity in output time series of nonlinear dynamical systems is a key challenge across scientific disciplines. Especially in the field of space physics, an early and accurate detection of characteristic dissimilarity between normal and abnormal states (e.g., pre-storm activity vs. magnetic storms) has the potential to vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. This review provides a systematic overview on existing nonlinear dynamical systems-based methodologies along with key results of their previous applications in a space physics context, which particularly illustrates how complementary modern complex systems approaches have recently shaped our understanding of nonlinear magnetospheric variability. The rising number of corresponding studies demonstrates that the multiplicity of nonlinear time series analysis methods developed during the last decades offers great potentials for uncovering relevant yet complex processes interlinking different geospace subsystems, variables and spatiotemporal scales

Reduced Complexity Models in the Identifi cation of Dynamical Networks: links with sparsi cation problems.

In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that ``better'' satisfies the constraints according to the criterion of approximation

Econometrics as Sorcery

The paper deals with the problem of identifying the internal dependencies and similarities among a large number of random processes. Linear models are considered to describe the relations among the time series and the energy associated to the corresponding modeling error is the criterion adopted to quantify their similarities. Such an approach is interpreted in terms of graph theory suggesting a natural way to group processes together when one provides the best model to explain the other. Moreover, the clustering technique introduced in this paper will turn out to be the dynamical generalization of other multivariate procedures described in literature.

Model identification of a network as compressing sensing

In many applications, it is of interest to derive information about the topology and the internal connections of multiple dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network with no a-priori knowledge on its topology. It is assumed that the network nodes are passively observed and data are collected in the form of time series. The underlying structure is then determined by the non-zero entries of a “sparse Wiener filter”. We cast the problem as the optimization of a quadratic cost function, where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model