A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Generalized Structural Kinetic Modeling: A Survey and Guide

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

Whole-brain modelling identifies distinct but convergent paths to unconsciousness in anaesthesia and disorders of consciousness

The human brain entertains rich spatiotemporal dynamics, which are drastically reconfigured when consciousness is lost due to anaesthesia or disorders of consciousness (DOC). Here, we sought to identify the neurobiological mechanisms that explain how transient pharmacological intervention and chronic neuroanatomical injury can lead to common reconfigurations of neural activity. We developed and systematically perturbed a neurobiologically realistic model of whole-brain haemodynamic signals. By incorporating PET data about the cortical distribution of GABA receptors, our computational model reveals a key role of spatially-specific local inhibition for reproducing the functional MRI activity observed during anaesthesia with the GABA-ergic agent propofol. Additionally, incorporating diffusion MRI data obtained from DOC patients reveals that the dynamics that characterise loss of consciousness can also emerge from randomised neuroanatomical connectivity. Our results generalise between anaesthesia and DOC datasets, demonstrating how increased inhibition and connectome perturbation represent distinct neurobiological paths towards the characteristic activity of the unconscious brain.