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We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series.We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation).However, the highly nonlinear nature of ecological dynamics can give the appearance of randomness and stress traditional methods—such as model fitting or analysis of variance—to the point of breaking.The intractability of this problem from a classical linear standpoint can thus give the impression that algal blooms are fundamentally unpredictable.

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The combination of this modeling approach with an extensive dataset allows us to not only describe historical behavior and clarify existing hypotheses about the mechanisms, but also make out-of-sample predictions of recent algal blooms at La Jolla that were not included in the model development. However, tropical countries have much weaker annual climate cycles, and outbreaks show less seasonality and are more difficult to explain with environmental correlations.

We also find a hypothesized U-shaped relationship between absolute humidity and influenza that is predicted by theory and experiment, but hitherto has not been documented at the population level.

The balance between positive and negative effects of absolute humidity appears to be mediated by temperature, and the analysis reveals a key threshold around 75 degrees F.

By leveraging complexity, MVE is particularly effective for overcoming the limitations of short and noisy time series and should be highly relevant for many areas of science.

Objective: We propose a novel paradigm to predict acute attacks and exacerbations in chronic episodic disorders such as asthma, cardiac arrhythmias, migraine, epilepsy, and depression.

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