Nonlinear time series analysis of palaeoclimate proxy records

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability.In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These includeapproaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling.Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5~million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series.We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate.Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.

TRAKR - A reservoir-based tool for fast and accurate classification of neural time-series patterns

Neuroscience has seen a dramatic increase in the types of recording modalities and complexity of neural time-series data collected from them. The brain is a highly recurrent system producing rich, complex dynamics that result in different behaviors. Correctly distinguishing such nonlinear neural time series in real-time, especially those with non-obvious links to behavior, could be useful for a wide variety of applications. These include detecting anomalous clinical events such as seizures in epilepsy, and identifying optimal control spaces for brain machine interfaces. It remains challenging to correctly distinguish nonlinear time-series patterns because of the high intrinsic dimensionality of such data, making accurate inference of state changes (for intervention or control) difficult. Simple distance metrics, which can be computed quickly do not yield accurate classifications. On the other end of the spectrum of classification methods, ensembles of classifiers or deep supervised tools offer higher accuracy but are slow, data-intensive, and computationally expensive. We introduce a reservoir-based tool, state tracker (TRAKR), which offers the high accuracy of ensembles or deep supervised methods while preserving the computational benefits of simple distance metrics. After one-shot training, TRAKR can accurately, and in real time, detect deviations in test patterns. By forcing the weighted dynamics of the reservoir to fit a desired pattern directly, we avoid many rounds of expensive optimization. Then, keeping the output weights frozen, we use the error signal generated by the reservoir in response to a particular test pattern as a classification boundary. We show that, using this approach, TRAKR accurately detects changes in synthetic time series. We then compare our tool to several others, showing that it achieves highest classification performance on a benchmark dataset, sequential MNIST, even when corrupted by noise. Additionally, we apply TRAKR to electrocorticography (ECoG) data from the macaque orbitofrontal cortex (OFC), a higher-order brain region involved in encoding the value of expected outcomes. We show that TRAKR can classify different behaviorally relevant epochs in the neural time series more accurately and efficiently than conventional approaches. Therefore, TRAKR can be used as a fast and accurate tool to distinguish patterns in complex nonlinear time-series data, such as neural recordings.

Nonlinear time-series forecasts for decision support: short-term demand for ICU beds in Santiago, Chile during the 2021 COVID-19 pandemic

In Chile, due to the explosive increase of new COVID-19 cases during the first part of 2021, the ability of health services to accommodate new incoming cases was jeopardized. It has become necessary to be able to manage intensive care unit (ICU) capacity, and for this purpose, monitoring both the evolution of new cases and the demand of ICU beds, has become urgent. This paper presents short-term forecast models for the number of new cases and the number of COVID-19 patients admitted to ICUs in the Metropolitan Region in Chile.

On the effect of COVID-19 pandemic in the excess of human mortality. The case of Brazil and Spain

Excess of deaths is a technique used in epidemiology to assess the deaths caused by an unexpected event. For the present COVID–19 pandemic, we discuss the performance of some linear and nonlinear time series forecasting techniques widely used for modeling the actual pandemic and provide estimates for this metric from January 2020 to April 2021. We apply the results obtained to evaluate the evolution of the present pandemic in Brazil and Spain, which allows in particular to compare how well (or bad) these countries have managed the pandemic. For Brazil, our calculations refute the claim made by some officials that the present pandemic is “a little flu”. Some studies suggest that the virus could be lying dormant across the world before been detected for the first time. In that regard, our results show that there is no evidence of deaths by the virus in 2019.