Dan Mønster

Superstructure formation and the structural phase diagram of YBa2Cu3O6+x

Abstract The structural ordering properties of oxygen in YBa2Cu3O6+x have been studied by neutron and high-energy synchrotron X-ray diffraction and by computer simulations based on an extension of the Asymmetric Next Nearest Neighbour Interaction (ASYNNNI) model. The observed structural phases are the tetragonal disordered and five orthorhombic ordered phases that result from Cu–O chains formation along the b-axis and ordering with different periodicity na along the a-axis: ortho-I (a), ortho-II (2a), ortho-III (3a), ortho-V (5a) and ortho-VIII (8a). Only the tetragonal and the ortho-I structure have long range order. The structural phase diagram of the superstructure ordering has been established from the experimental data, and it is concluded that the short-range superstructure ordering results from the formation of finite size domains that freeze before long range order is established. By an extension of the 2D ASYNNNI lattice gas model to include Coulomb interactions between oxygen atoms on chains that are 2a apart, we account for the observed structural phases, and confirm that the superstructures freeze into finite size domains at low temperatures.

Multidimensional Recurrence Quantification Analysis (MdRQA) for the analysis of multidimensional time-series: A software implementation in MATLAB and its application to group-level data in joint action

We introduce Multidimensional Recurrence Quantification Analysis (MdRQA) as a tool to analyze multidimensional time-series data. We show how MdRQA can be used to capture the dynamics of high-dimensional signals, and how MdRQA can be used to assess coupling between two or more variables. In particular, we describe applications of the method in research on joint and collective action, as it provides a coherent analysis framework to systematically investigate dynamics at different group levels—from individual dynamics, to dyadic dynamics, up to global group-level of arbitrary size. The Appendix in Supplementary Material contains a software implementation in MATLAB to calculate MdRQA measures.

Causal inference from noisy time-series data — Testing the Convergent Cross-Mapping algorithm in the presence of noise and external influence

Abstract Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of detailed models. This has implications for the understanding of complex information systems, as well as complex systems more generally. This article assesses the strengths and weaknesses of the CCM algorithm by varying coupling strength and noise levels in a model system consisting of two coupled logistic maps. As expected, it is found that CCM fails to accurately infer coupling strength and even causality direction in strongly coupled synchronized time-series, but surprisingly also in the presence of intermediate coupling. It is further found that the presence of noise reduces the level of cross-mapping fidelity, where the converged value of the CCM correlation decreases roughly linearly as a function of the noise, while the convergence rate of the CCM correlation shows little sensitivity to noise. The article proposes controlled noise injections in intermediate-to-strongly coupled systems could enable more accurate causal inferences. Initial investigation of an external driving signal indicates robustness of CCM toward this potentially confounding influence. Given the inherent noisy nature of real-world systems, the findings enable a more accurate evaluation of CCM applicability and the article advances suggestions on how to overcome the method’s weaknesses.

Inferring Causality from Noisy Time Series Data - A Test of Convergent Cross-Mapping

Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We find that CCM fails to infer accurate coupling strength and even causality direction in synchronized time-series and in the presence of intermediate coupling. We find that the presence of noise deterministically reduces the level of cross-mapping fidelity, while the convergence rate exhibits higher levels of robustness. Finally, we propose that controlled noise injections in intermediate-to-strongly coupled systems could enable more accurate causal inferences. Given the inherent noisy nature of real-world systems, our findings enable a more accurate evaluation of CCM applicability and advance suggestions on how to overcome its weaknesses.

Calculation of average mutual information (AMI) and false-nearest neighbors (FNN) for the estimation of embedding parameters of multidimensional time-series in Matlab

Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series involve the inspection of the Average Mutual Information (AMI) function and the False Nearest Neighbor (FNN) function. In some contexts, however, such as phase-space reconstruction for Multidimensional Recurrence Quantification Analysis (MdRQA), the empirical time series that need to be embedded already possess a dimensionality higher than one. In the current article, we present extensions of the AMI and FNN functions for higher dimensional time series and their application to data from the Lorenz system coded in Matlab.

Monte Carlo Study of Oxygen Ordering in YBa2Cu306+x

We have performed Monte Carlo simulations of the oxygen ordering phenomena in the CuO x planes of YBa2Cu3O6+x using a lattice gas model and have found very good agreement with the experimental results.