Generalized Theorems for Nonlinear State Space Reconstruction

Takens' theorem (1981) shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR) from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags) can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences

Global and regional cardiac function in lifelong endurance athletes with and without myocardial fibrosis

The aim of the present study was to compare cardiac structure as well as global and regional cardiac function in athletes with and without myocardial fibrosis (MF). Cardiac magnetic resonance imaging with late gadolinium enhancement was used to detect MF and global cardiac structure in nine lifelong veteran endurance athletes (58 ± 5 years, 43 ± 5 years of training). Transthoracic echocardiography using tissue-Doppler and myocardial strain imaging assessed global and regional (18 segments) longitudinal left ventricular function. MF was present in four athletes (range 1–8 g) and not present in five athletes. MF was located near the insertion points of the right ventricular free wall on the left ventricle in three athletes and in the epicardial lateral wall in one athlete. Athletes with MF demonstrated a larger end diastolic volume (205 ± 24 vs 173 ± 18 ml) and posterior wall thickness (11 ± 1 vs 9 ± 1 mm) compared to those without MF. The presence of MF did not mediate global tissue velocities or global longitudinal strain and strain rate; however, regional analysis of longitudinal strain demonstrated reduced function in some fibrotic regions. Furthermore, base to apex gradient was affected in three out of four athletes with MF. Lifelong veteran endurance athletes with MF demonstrate larger cardiac dimensions and normal global cardiac function. Fibrotic areas may demonstrate some co-localised regional cardiac dysfunction, evidenced by an affected cardiac strain and base to apex gradient. These data emphasize the heterogeneous phenotype of MF in athletes

Non-linearity in stock–recruitment relationships of Atlantic cod: insights from a multi-model approach

The stock–recruitment relationship is the basis of any stock prediction and thus fundamental for fishery management. Traditional parametric stock–recruitment models often poorly fit empirical data, nevertheless they are still the rule in fish stock assessment procedures. We here apply a multi-model approach to predict recruitment of 20 Atlantic cod (Gadus morhua) stocks as a function of adult biomass and environmental variables. We compare the traditional Ricker model with two non-parametric approaches: (i) the stochastic cusp model from catastrophe theory and (ii) multivariate simplex projections, based on attractor state-space reconstruction. We show that the performance of each model is contingent on the historical dynamics of individual stocks, and that stocks which experienced abrupt and state-dependent dynamics are best modelled using non-parametric approaches. These dynamics are pervasive in Western stocks highlighting a geographical distinction between cod stocks, which have implications for their recovery potential. Furthermore, the addition of environmental variables always improved the models’ predictive power indicating that they should be considered in stock assessment and management routines. Using our multi-model approach, we demonstrate that we should be more flexible when modelling recruitment and tailor our approaches to the dynamical properties of each individual stock.https://academic.oup.com/icesjms/article/77/4/1492/5522545Published versio

Susceptible host availability modulates climate effects on dengue dynamics

Experiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context-dependent effects of population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way.R35GM133439 - NIH HHS; DBI-1667584 - National Science Foundation; DEB-1655203 - National Science Foundation; 00028335 - Lenfest Foundation; Stanford University: Bing Fellowship in Honor of Paul Ehrlich, Stanford Data Science Scholars program, Lindsay Family E-IPER Fellowship, Illich-Sadowsky Interdisciplinary Graduate Fellowship, Terman Fellowship, King Center for Global Development seed grant; SERDP 15 RC-2509 - U.S. Department of Defense; University of California San Diego: McQuown Chair in Natural Sciences; DBI-1611767 - National Science Foundation; RAPID DEB-1640780 - National Science Foundation; R35GM133439 - NIH HHS; Hellman Foundation: Hellman Faculty Fellowship; Stanford Woods Institute for the Environment: Environmental Ventures Program; DEB-1518681 - National Science Foundation; R35 GM133439 - NIGMS NIH HHS; DEB-2011147 - National Science Foundationhttps://www.biorxiv.org/content/biorxiv/early/2020/10/19/2019.12.20.883363.full.pdfAccepted manuscrip