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The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical data sets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on 2D Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially-resolved Earth systems.

Conditions such as insomnia, cardiac arrhythmia and jet-lag share a common feature: they are all related to the ability of biological systems to synchronize with the day-night cycle. When organisms lose resilience, this ability of synchronizing can become weaker till they eventually become desynchronized in a state of malfunctioning or sickness. It would be useful to measure this loss of resilience before the full desynchronization takes place. Several dynamical indicators of resilience (DIORs) have been proposed to account for the loss of resilience of a dynamical system. The performance of these indicators depends on the underlying mechanism of the critical transition, usually a saddle-node bifurcation. Before such bifurcation the recovery rate from perturbations of the system becomes slower, a mechanism known as critical slowing down. Here we show that, for a wide class of biological systems, desynchronization happens through another bifurcation, namely the saddle-node of cycles, for which critical slowing down cannot be directly detected. Such a bifurcation represents a system transitioning from synchronized (phase locked) to a desynchronized state, or vice versa. We show that after an appropriate transformation we can also detect this bifurcation using dynamical indicators of resilience. We test this method with data generated by models of sleep-wake cycles., Comment: 10 pages, 6 figures, 1 appendix

US funding agencies alone distribute a yearly total of roughly $65B dollars largely through the process of proposal peer review: scientists compete for project funding by submitting grant proposals which are evaluated by selected panels of peer reviewers. Similar funding systems are in place in most advanced democracies. However, in spite of its venerable history, proposal peer review is increasingly struggling to deal with the increasing mismatch between demand and supply of research funding., Comment: This working paper formed the basis of J. Bollen, Who would you share your funding with. Nature 560, 143 (2018)

Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most biological systems with two or more state variables such potentials do not exist. Here we use an analogy with art to provide an accessible explanation of why this happens. Additionally, we introduce a numerical method for decomposing differential equations into two terms: the gradient term that has an associated potential, and the non-gradient term that lacks it. In regions of the state space where the magnitude of the non-gradient term is small compared to the gradient part, we use the gradient term to approximate the potential as quasi-potential. The non-gradient to gradient ratio can be used to estimate the local error introduced by our approximation. Both the algorithm and a ready-to-use implementation in the form of an R package are provided.

Studies of affect labeling, i.e. putting your feelings into words, indicate that it can attenuate positive and negative emotions. Here we track the evolution of individual emotions for tens of thousands of Twitter users by analyzing the emotional content of their tweets before and after they explicitly report having a strong emotion. Our results reveal how emotions and their expression evolve at the temporal resolution of one minute. While the expression of positive emotions is preceded by a short but steep increase in positive valence and followed by short decay to normal levels, negative emotions build up more slowly, followed by a sharp reversal to previous levels, matching earlier findings of the attenuating effects of affect labeling. We estimate that positive and negative emotions last approximately 1.25 and 1.5 hours from onset to evanescence. A separate analysis for male and female subjects is suggestive of possible gender-specific differences in emotional dynamics.

Similarity of competitors has been proposed to facilitate coexistence of species because it slows down competitive exclusion, thus making it easier for equalizing mechanisms to maintain diverse communities. On the other hand, chaos can promote coexistence of species. Here we link these two previously unrelated findings, by analyzing the dynamics of food web models. We show that near-neutrality of competition of prey, in the presence of predators, increases the chance of developing chaotic dynamics. Moreover we confirm that this results in a higher biodiversity. Our results suggest that near-neutrality may promote biodiversity in two ways: through reducing the rates of competitive displacement and through promoting non-equilibrium dynamics., Comment: Added biodiversity measures, lacking in our previous analysis

In this paper, we characterize major depression (MD) as a complex dynamical system in which symptoms (e.g., insomnia and fatigue) are directly connected to one another in a network structure. We hypothesize that individuals can be characterized by their own network with unique architecture and resulting dynamics. With respect to architecture, we show that individuals vulnerable to developing MD are those with strong connections between symptoms: e.g., only one night of poor sleep suffices to make a particular person feel tired. Such vulnerable networks, when pushed by forces external to the system such as stress, are more likely to end up in a depressed state; whereas networks with weaker connections tend to remain in or return to a healthy state. We show this with a simulation in which we model the probability of a symptom becoming active as a logistic function of the activity of its neighboring symptoms. Additionally, we show that this model potentially explains some well-known empirical phenomena such as spontaneous recovery as well as accommodates existing theories about the various subtypes of MD. To our knowledge, we offer the first intra-individual, symptom-based, process model with the potential to explain the pathogenesis and maintenance of major depression., Comment: 8 figures

It has been widely debated whether Arctic sea-ice loss can reach a tipping point beyond which a large sea-ice area disappears abruptly. The theory of dynamical systems predicts a slowing down when a system destabilises towards a tipping point. In simple stochastic systems this can result in increasing variance and autocorrelation, potentially yielding an early warning of an abrupt change. Here we aim to establish whether the loss of Arctic sea ice would follow these conceptual predictions, and which trends in sea ice variability can be expected from pre-industrial conditions toward an Arctic that is ice-free during the whole year. To this end, we apply a model hierarchy consisting of two box models and one comprehensive Earth system model. We find a consistent and robust decrease of the ice volume's annual relaxation time before summer ice is lost because thinner ice can adjust more quickly to perturbations. Thereafter, the relaxation time increases, mainly because the system becomes dominated by the ocean water's large heat capacity when the ice-free season becomes longer. Both trends carry over to the autocorrelation of sea ice thickness in time series. These changes are robust to the nature and origin of climate variability in the models and hardly depend on the balance of feedbacks. Therefore, characteristic trends can be expected in the future. As these trends are not specific to the existence of abrupt ice loss, the prospects for early warnings seem very limited. This result also has implications for statistical indicators in other systems whose effective mass changes over time, affecting the trend of their relaxation time. However, the robust relation between state and variability would allow an estimate of sea-ice variability from only short observations. This could help one to estimate the likelihood and persistence of extreme events in the future., Comment: Discussion Paper, currently (Jan. 2016) under review in The Cryosphere

Background: Mathematical modeling approaches are becoming ever more established in clinical neuroscience. They provide insight that is key to understand complex interactions of network phenomena, in general, and interactions within the migraine generator network, in particular. Purpose: In this study, two recent modeling studies on migraine are set in the context of premonitory symptoms that are easy to confuse for trigger factors. This causality confusion is explained, if migraine attacks are initiated by a transition caused by a tipping point. Conclusion: We need to characterize the involved neuronal and autonomic subnetworks and their connections during all parts of the migraine cycle if we are ever to understand migraine. We predict that mathematical models have the potential to dismantle large and correlated fluctuations in such subnetworks as a dynamical network biomarker of migraine., Comment: 4 pages, 1 figure

Recent studies show that the microbial communities inhabiting the human intestine can have profound impact on our well-being and health. However, we have limited understanding of the mechanisms that control this complex ecosystem. Based on a deep phylogenetic analysis of the intestinal microbiota in a thousand western adults we identified groups of bacteria that tend to be either nearly absent, or abundant in most individuals. The abundances of these bimodally distributed bacteria vary independently, and their contrasting alternative states are associated with host factors such as ageing and overweight. We propose that such bimodal groups represent independent tipping elements of the intestinal microbiota. These reflect the overall state of the intestinal ecosystem whose critical transitions can have profound health implications and diagnostic potential., Comment: 29 pages; 9 figures; 4 tables; preprint