Partial cross mapping eliminates indirect causal influences

Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data

The effects of graded levels of calorie restriction XV : phase space attractors reveal distinct behavioral phenotypes

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Locating unstable periodic orbits: when adaptation integrates into delayed feedback control

Finding unstable periodic orbits (UPOs) is always a challenging demand in biophysics and computational biology, which needs efficient algorithms. To meet this need, an approach to locating unstable periodic orbits in chaotic dynamical system is presented. The uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted UPO periods a priori. This approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays

Adaptive identification of time delays in nonlinear dynamical models

This paper develops an adaptive synchronization strategy to identify both discrete and distributed time delays in nonlinear dynamical models. In contrast with adaptive techniques for parameter estimation in the literature, the adaptive strategy developed here for time-delay identification invites more precise results that have physical and dynamical importance. It is analytically and numerically found that distributed time delays in a model with an asymptotically stable steady state can be adaptively identified, and which is different from the case of discrete time-delays identification. Other aspects of the strategy developed here, for time-delay identification, are illustrated by several representative dynamical models. Aside from illustrations for toy models and their generated data, the strategy developed is used with experimental data, to identify a time delay, called transcriptional delay, in a model describing the transcription of messenger RNAs (mRNAs) for Notch signaling molecules

Adhesion Effect on the Hyperfine Frequency Shift of an Alkali Metal Vapor Cell with Paraffin Coating Using Peak-Force Tapping AFM

We have investigated the adhesion effect on the hyperfine frequency shift of an alkali metal vapor cell with paraffin coating using the peak-force tapping AFM (atomic force microscopy) technique by developing a uniform and high-quality paraffin coating method. We observed a relatively uniform temperature field on the substrate can be obtained theoretically and experimentally with the closed-type previse temperature-controlled evaporation method. The roughness and adhesion of the coating surface as low as 0.8 nm and 20 pN were successfully obtained, respectively. Furthermore, the adhesion information dependence of the topography was investigated from the force spectroscopy, which indicates that the adhesion force jumped on the edge of the particles and stepped but remained constant above the particles and steps regardless of their height for paraffin coating. Finally, we can evaluate the relaxation and the hyperfine frequency shift of an alkali metal vapor cell through accurately calculating the surface adsorption energy of the paraffin coating from peak-force tapping information. This finding is crucial for improving the sensitivity of the atomic sensors through directly analyzing the adhesion effect of the paraffin coating films instead of measuring the relaxation times