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

Nitroxyl improves cellular heart function by directly enhancing cardiac sarcoplasmic reticulum Ca2+ cycling.

Heart failure remains a leading cause of morbidity and mortality worldwide. Although depressed pump function is common, development of effective therapies to stimulate contraction has proven difficult. This is thought to be attributable to their frequent reliance on cAMP stimulation to increase activator Ca(2+). A potential alternative is nitroxyl (HNO), the 1-electron reduction product of nitric oxide (NO) that improves contraction and relaxation in normal and failing hearts in vivo. The mechanism for myocyte effects remains unknown. Here, we show that this activity results from a direct interaction of HNO with the sarcoplasmic reticulum Ca(2+) pump and the ryanodine receptor 2, leading to increased Ca(2+) uptake and release from the sarcoplasmic reticulum. HNO increases the open probability of isolated ryanodine-sensitive Ca(2+)-release channels and accelerates Ca(2+) reuptake into isolated sarcoplasmic reticulum by stimulating ATP-dependent Ca(2+) transport. Contraction improves with no net rise in diastolic calcium. These changes are not induced by NO, are fully reversible by addition of reducing agents (redox sensitive), and independent of both cAMP/protein kinase A and cGMP/protein kinase G signaling. Rather, the data support HNO/thiolate interactions that enhance the activity of intracellular Ca(2+) cycling proteins. These findings suggest HNO donors are attractive candidates for the pharmacological treatment of heart failure