Thomas M. Bury

Tipping points are thresholds at which a system, often abruptly and irreversibly, transitions from a stable state to a contrasting one. Crossing such critical boundaries poses a risk to Earth system stability and may have catastrophic consequences. This is especially relevant, as current climate change is destabilizing Earth subsystems, potentially bringing them closer to tipping points. Thus, it is important to be able to detect approaching tipping points in the Earth’s system, which can be achieved through calibration on palaeo-records. Recently, new deep learning (DL) methods have been established that are able to confidently and quantitatively identify different types of critical transitions characterised by their abruptness and (ir)reversibility. Based on this, we develop a new (simplified) DL classifier focusing on the quantitative detection of catastrophic tipping points (fold bifurcations) in the Earth system. Our approach reduces computational demand and improves performance, especially for short timeseries. We first test the new classifier's performance on synthetic data and subsequently on different existing Cenozoic proxy records. Our DL results are compared to the results from previous studies applying generic early warning signals (EWS), which can detect approaching transitions qualitatively but cannot distinguish bifurcation types (abruptness and (ir)reversibility of the transition). Our DL classifier enables us to identify how abrupt and (ir)reversible an approaching transition is, which is important for tipping point risk assessment and mitigation. Results are generally consistent between generic EWS from previous studies and our DL approach and fit with what is known from the geological context. We note that some results are dependent on the length of the classifier used and the time interval investigated before the bifurcation. We implement an out-of-distribution (OOD) detection method to reduce the misclassification of non-catastrophic bifurcations as catastrophic tipping points. Combined with the binary DL classifier, this approach enables reliable, quantitative detection of catastrophic tipping points in Earth system records.

Tipping points are thresholds at which a system, often abruptly and irreversibly, transitions from a stable state to a contrasting one. Crossing such critical boundaries poses a risk to Earth system stability and may have catastrophic consequences. This is especially relevant, as current climate change is destabilizing Earth subsystems, potentially bringing them closer to tipping points. Thus, it is important to be able to detect approaching tipping points in the Earth’s system, which can be achieved through calibration on palaeo-records. Recently, new deep learning (DL) methods have been established that are able to confidently and quantitatively identify different types of critical transitions characterised by their abruptness and (ir)reversibility. Based on this, we develop a new (simplified) DL classifier focusing on the quantitative detection of catastrophic tipping points (fold bifurcations) in the Earth system. Our approach reduces computational demand and improves performance, especially for short timeseries. We first test the new classifier's performance on synthetic data and subsequently on different existing Cenozoic proxy records. Our DL results are compared to the results from previous studies applying generic early warning signals (EWS), which can detect approaching transitions qualitatively but cannot distinguish bifurcation types (abruptness and (ir)reversibility of the transition). Our DL classifier enables us to identify how abrupt and (ir)reversible an approaching transition is, which is important for tipping point risk assessment and mitigation. Results are generally consistent between generic EWS from previous studies and our DL approach and fit with what is known from the geological context. We note that some results are dependent on the length of the classifier used and the time interval investigated before the bifurcation. We implement an out-of-distribution (OOD) detection method to reduce the misclassification of non-catastrophic bifurcations as catastrophic tipping points. Combined with the binary DL classifier, this approach enables reliable, quantitative detection of catastrophic tipping points in Earth system records.

The transition from transient excitation to sustained reentry is a fundamental problem in the physics of excitable media. In cardiac tissue, reentry underlies many life-threatening cardiac arrhythmias, yet the pathway to initiation of reentry remains incompletely understood. Here, we formulate reentry initiation as a reinforcement-learning problem in which an agent applies sequences of spatial stimulation patterns while being rewarded for sustained activity and penalized according to the number of stimuli applied. Using cellular automata in one-, two-, and three-dimensional geometries, the agent discovered several mechanisms for generating unidirectional propagation and reentry. These included a previously described mechanism combining superthreshold and subthreshold stimulation, as well as two new mechanisms based entirely on subthreshold stimuli: a sequential mechanism involving stimuli delivered at different locations and times, and a spatial mechanism in which several individually subthreshold sites collectively initiated reentry. In geometries containing boundaries and branches, the learned protocols additionally exploited structural source-sink asymmetries. Optogenetic experiments in cardiac monolayers further demonstrated reproducible induction of unidirectional propagation using the learned spatial subthreshold patterns, while whole-heart experiments provided preliminary evidence that such patterns can shape early propagation in intact tissue. More broadly, we show that reinforcement learning provides a general framework for discovering mechanisms of reentry in arbitrary geometries and generating testable hypotheses about reentry initiation in excitable systems.

Tipping points are thresholds at which a system, often abruptly and irreversibly, transitions from a stable state to a contrasting one. Crossing such critical boundaries poses a risk to Earth system stability and may have catastrophic consequences. This is especially relevant, as current climate change is destabilizing Earth subsystems, potentially bringing them closer to tipping points. Thus, it is important to be able to detect approaching tipping points in the Earth’s system, which can be achieved through calibration on palaeo-records. Recently, new deep learning (DL) methods have been established that are able to confidently and quantitatively identify different types of critical transitions characterised by their abruptness and (ir)reversibility. Based on this, we develop a new (simplified) DL classifier focusing on the quantitative detection of catastrophic tipping points (fold bifurcations) in the Earth system. Our approach reduces computational demand and improves performance, especially for short timeseries. We first test the new classifier's performance on synthetic data and subsequently on different existing Cenozoic proxy records. Our DL results are compared to the results from previous studies applying generic early warning signals (EWS), which can detect approaching transitions qualitatively but cannot distinguish bifurcation types (abruptness and (ir)reversibility of the transition). Our DL classifier enables us to identify how abrupt and (ir)reversible an approaching transition is, which is important for tipping point risk assessment and mitigation. Results are generally consistent between generic EWS from previous studies and our DL approach and fit with what is known from the geological context. We note that some results are dependent on the length of the classifier used and the time interval investigated before the bifurcation. We implement an out-of-distribution (OOD) detection method to reduce the misclassification of non-catastrophic bifurcations as catastrophic tipping points. Combined with the binary DL classifier, this approach enables reliable, quantitative detection of catastrophic tipping points in Earth system records.

Tipping points are thresholds at which a system, often abruptly and irreversibly, transitions from a stable state to a contrasting one. Crossing such critical boundaries poses a risk to Earth system stability and may have catastrophic consequences. This is especially relevant, as current climate change is destabilizing Earth subsystems, potentially bringing them closer to tipping points. Thus, it is important to be able to detect approaching tipping points in the Earth’s system, which can be achieved through calibration on palaeo-records. Recently, new deep learning (DL) methods have been established that are able to confidently and quantitatively identify different types of critical transitions characterised by their abruptness and (ir)reversibility. Based on this, we develop a new (simplified) DL classifier focusing on the quantitative detection of catastrophic tipping points (fold bifurcations) in the Earth system. Our approach reduces computational demand and improves performance, especially for short timeseries. We first test the new classifier's performance on synthetic data and subsequently on different existing Cenozoic proxy records. Our DL results are compared to the results from previous studies applying generic early warning signals (EWS), which can detect approaching transitions qualitatively but cannot distinguish bifurcation types (abruptness and (ir)reversibility of the transition). Our DL classifier enables us to identify how abrupt and (ir)reversible an approaching transition is, which is important for tipping point risk assessment and mitigation. Results are generally consistent between generic EWS from previous studies and our DL approach and fit with what is known from the geological context. We note that some results are dependent on the length of the classifier used and the time interval investigated before the bifurcation. We implement an out-of-distribution (OOD) detection method to reduce the misclassification of non-catastrophic bifurcations as catastrophic tipping points. Combined with the binary DL classifier, this approach enables reliable, quantitative detection of catastrophic tipping points in Earth system records.

Phase resetting of cardiac oscillators underlies some complex arrhythmias. Here we use optogenetic stimulation to construct phase response curves (PRC) for spheroids of human induced pluripotent stem cell derived cardiomyocytes (iPSC-CM) and a computational cardiomyocyte model to identify ionic mechanisms shaping the PRC. The clinical utility of the human PRCs is demonstrated by adding a patient-based conduction delay to the same equations to explain complex multi-day Holter ECG dynamics and cardiac arrhythmias. Periodic stimulation of these patient-based models and the computational model of human iPSC-CM reveal similar bifurcation patterns and entrainment zones. Cell therapy by injecting iPSC-CM into diseased hearts can induce ectopic foci-based engraftment arrhythmias. The PRC analysis offers a potential strategy to entrain these foci in a parameter space that avoids such arrhythmias.

Objective: Frequent premature ventricular complexes (PVCs) can lead to adverse health conditions such as cardiomyopathy. The linear correlation between PVC frequency and heart rate (as positive, negative, or neutral) on a 24-hour Holter recording has been proposed as a way to classify patients and guide treatment with beta-blockers. Our objective was to evaluate the robustness of this classification to measurement methodology, different 24-hour periods, and nonlinear dependencies of PVCs on heart rate. Materials and Methods: We analyzed 82 multi-day Holter recordings (1-7 days) collected from 48 patients with frequent PVCs (burden 1%-44%). For each record, linear correlation between PVC frequency and heart rate was computed for different 24-hour periods and using different length intervals to determine PVC frequency. Results: Using a 1-hour interval, the correlation between PVC frequency and heart rate was consistently positive, negative, or neutral on different days in only 36.6% of patients. Using shorter time intervals, the correlation was consistent in 56.1% of patients. Shorter time intervals revealed nonlinear and piecewise linear relationships between PVC frequency and heart rate in many patients. Discussion: The variability of the correlation between PVC frequency and heart rate across different 24-hour periods and interval durations suggests that the relationship is neither strictly linear nor stationary. A better understanding of the mechanism driving the PVCs, combined with computational and biological models that represent these mechanisms, may provide insight into the observed nonlinear behavior and guide more robust classification strategies. Conclusion: Linear correlation as a tool to classify patients with frequent PVCs should be used with caution. It is sensitive to the specific 24-hour period analyzed and the methodology used to segment the data. More sophisticated classification approaches that can capture nonlinear and time-varying dependencies should be developed and considered in clinical practice.

Cardiovascular disease is the leading cause of death, demanding new tools to improve mechanistic understanding and overcome limitations of stem cell and animal-based research. We introduce T-World, a highly general virtual model of human ventricular cardiomyocyte suitable for multiscale studies. T-World shows comprehensive agreement with human physiology, from electrical activation to contraction, and is the first to replicate all key cellular mechanisms driving life-threatening arrhythmias. Extensively validated on unseen data, it demonstrates strong predictivity across applications and scales. Using T-World we revealed a likely sex-specific arrhythmia risk in females related to restitution properties, identified arrhythmia drivers in type 2 diabetes, and describe unexpected pro-arrhythmic role of NaV1.8 in heart failure. T-World demonstrates strong performance in predicting drug-induced arrhythmia risk and opens new opportunities for predicting and explaining drug efficacy, demonstrated by unpicking effects of mexiletine in Long QT syndrome 2. T-World is available as open-source code and an online app.

Complex systems can undergo critical transitions, where slowly changing environmental conditions trigger a sudden shift to a new, potentially catastrophic state. Early warning signals for these events are crucial for decision-making in fields such as ecology, biology and climate science. Generic early warning signals motivated by dynamical systems theory have had mixed success on real noisy data. More recent studies found that deep learning classifiers trained on synthetic data could improve performance. However, neither of these methods take advantage of historical, system-specific data. Here, we introduce an approach that trains machine learning classifiers directly on surrogate data of past transitions, namely surrogate data-based machine learning (SDML). The approach provides early warning signals in empirical and experimental data from geology, climatology, sociology, and cardiology with higher sensitivity and specificity than two widely used generic early warning signals -- variance and lag-1 autocorrelation. Since the approach is trained directly on surrogates of historical data, it is not bound by the restricting assumption of a local bifurcation like previous methods. This system-specific approach can contribute to improved early warning signals to help humans better prepare for or avoid undesirable critical transitions.