Identifying causal relations from time series is the first step to understanding the behavior of complex systems. Although many methods have been proposed, few papers have applied multiple methods together to detect causal relations based on time series generated from coupled nonlinear systems with some unobserved parts. Here we propose the combined use of three methods and a majority vote to infer causality under such circumstances. Two of these methods are proposed here for the first time, and all of the three methods can be applied even if the underlying dynamics is nonlinear and there are hidden common causes. We test our methods with coupled logistic maps, coupled Rössler models, and coupled Lorenz models. In addition, we show from ice core data how the causal relations among the temperature, the CH4 level, and the CO2 level in the atmosphere changed in the last 800,000 years, a conclusion also supported by irregularly sampled data analysis. Moreover, these methods show how three regions of the brain interact with each other during the visually cued, two-choice arm reaching task. Especially, we demonstrate that this is due to bottom up influences at the beginning of the task, while there exist mutual influences between the posterior medial prefrontal cortex and the presupplementary motor area. Based on our results, we conclude that identifying causality with an appropriate ensemble of multiple methods ensures the validity of the obtained results more firmly.
The mechanism of CO oxidation reaction on oxygen-precovered Pt(111) surfaces has been studied by using time-resolved near-edge x-ray absorption fine structure spectroscopy. The whole reaction process is composed of two distinct paths: (1) a reaction of isolated oxygen atoms with adsorbed CO, and (2) a reaction of island-periphery oxygen atoms after the CO saturation. CO coadsorption plays a role to induce the dynamic change in spatial distribution of O atoms, which switches over the two reaction paths. These mechanisms were confirmed by kinetic Monte Carlo simulations. The effect of coadsorbed water in the reaction mechanism was also examined.
We studied the mechanism of the N + NO reaction on Rh(111) surfaces by means of near edge X-ray absorption fine structure (NEXAFS) spectroscopy. Atomic nitrogen layers on Rh(111) were titrated with NO at various temperatures. Below 350 K, the chemisorbed NO monomer does not react with N, while the NO dimer formed in the second layer acts as an extrinsic precursor to the reaction: N(a) + (NO) 2 (a) f N 2 O(g) + NO(a). Because of a dominant role of the precursor-mediated mechanism, the reaction proceeds slower with an increase in temperature. Above 350 K, the reaction switches to a different path: N(a) + NO(a) f N 2 (g) + O(a).
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