Time-Reversibility, Causality and Compression-Complexity

Detection of the temporal reversibility of a given process is an interesting time series analysis scheme that enables the useful characterisation of processes and offers an insight into the underlying processes generating the time series. Reversibility detection measures have been widely employed in the study of ecological, epidemiological and physiological time series. Further, the time reversal of given data provides a promising tool for analysis of causality measures as well as studying the causal properties of processes. In this work, the recently proposed Compression-Complexity Causality (CCC) measure (by the authors) is shown to be free of the assumption that the "cause precedes the effect", making it a promising tool for causal analysis of reversible processes. CCC is a data-driven interventional measure of causality (second rung on the Ladder of Causation) that is based on Effort-to-Compress (ETC), a well-established robust method to characterize the complexity of time series for analysis and classification. For the detection of the temporal reversibility of processes, we propose a novel measure called the Compressive Potential based Asymmetry Measure. This asymmetry measure compares the probability of the occurrence of patterns at different scales between the forward-time and time-reversed process using ETC. We test the performance of the measure on a number of simulated processes and demonstrate its effectiveness in determining the asymmetry of real-world time series of sunspot numbers, digits of the transcedental number π and heart interbeat interval variability

Long-term solar variability in a hybrid Babcock-Leighton solar dynamo model

Le but de cette étude est d’élucider le comportement à long terme du cycle d’activité magnétique solaire, en particulier l’origine physique des épisodes prolongés d’activité fortement réduite ou amplifiée (Grand Minima et Maxima). Les principales questions abordées dans ce mémoire sont les suivantes: Les Grand Minima / Maxima relèvent-ils d’un processus stochastique? Sont-ils associés à des modes dynamo distincts? Est-ce que leur déclenchement peut être représenté par un processus de Poisson? Quels sont les mécanismes physiques à l’origine de ces événements irréguliers? Comment la dynamo sort-elle de ces modes extrêmes? Quel est le mécanisme qui favorise l’aggrégation des Grand Minima? Quel est le mécanisme responsable du changement de parité lors de ces événements extrêmes? Les réponses à ces questions sont recherchées via une approche de modélisation numérique basée sur un modèle hybride de la dynamo solaire Babcock Leighton. Les séries temporelles résultantes de l’activité solaire simulée et les statistiques de Grand Minima et Maxima sont comparées à leurs homologues déduits des reconstructions cosmogéniques de l’activité solaire passée basée sur les radionucléides cosmogéniques. On constate qu’avec différentes combinaisons de valeurs de paramètres dans des intervals raisonables, il est possible de reproduire un comportement solaire à long terme en accord avec les données des radionucléides cosmogéniques.The purpose of this study is to shed some light on the long-term behavior of the solar magnetic activity cycle, in particular the physical origins of the extended episodes of strongly suppressed or enhanced activity (so-called Grand Minima and Maxima). The primary questions that are tackled in this thesis are as follows: Is the occurrence of Grand Minima/Maxima a stochastic process? Are they associated with distinct dynamo modes? Is their triggering due to a Poisson-like processes? What are the physical mechanisms that cause these irregular events? How does the dynamo enter and exit from these extreme modes? What is the underlining mechanism that makes Grand Minima cluster? What is the mechanism which is responsible from parity change during these extreme events? Answers to these questions are sought via a modelling approach based on a hybrid Babcock Leighton solar dynamo model. The resulting simulated solar activity time series and the statistics of Grand Minima and Maxima are compared to their counterparts inferred from reconstructions of the past solar activity based on cosmogenic radionuclides. With different combination parameter values within a reasonable range, it is possible to reproduce solar-like long-term behavior in agreement with radionuclide data

The Sun's Supergranulation

Supergranulation is a fluid-dynamical phenomenon taking place in the solar photosphere, primarily detected in the form of a vigorous cellular flow pattern with a typical horizontal scale of approximately 30--35~megameters, a dynamical evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow component and a much weaker 20--30~m/s vertical component. Supergranulation was discovered more than sixty years ago, however, explaining its physical origin and most important observational characteristics has proven extremely challenging ever since, as a result of the intrinsic multiscale, nonlinear dynamical complexity of the problem concurring with strong observational and computational limitations. Key progress on this problem is now taking place with the advent of 21st-century supercomputing resources and the availability of global observations of the dynamics of the solar surface with high spatial and temporal resolutions. This article provides an exhaustive review of observational, numerical and theoretical research on supergranulation, and discusses the current status of our understanding of its origin and dynamics, most importantly in terms of large-scale nonlinear thermal convection, in the light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new theoretical, numerical and observational developments. All sections, including discussion, revised extensively. Also includes previously unpublished results on nonlinear dynamics of convection in large domains, and lagrangian transport at the solar surfac

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Earth’s climate response to a changing Sun

For centuries, scientists have been fascinated by the role of the Sun in the Earth’s climate system. Recent discoveries, outlined in this book, have gradually unveiled a complex picture, in which our variable Sun a¬ffects the climate variability via a number of subtle pathways, the implications of which are only now becoming clear. This handbook provides the scientifically curious, from undergraduate students to policy makers with a complete and accessible panorama of our present understanding of the Sun-climate connection. 61 experts from di¬fferent communities have contributed to it, which reflects the highly multidisciplinary nature of this topic. The handbook is organised as a mosaic of short chapters, each of which addresses a specific aspect, and can be read independently. The reader will learn about the assumptions, the data, the models, and the unknowns behind each mechanism by which solar variability may impact climate variability. None of these mechanisms can adequately explain global warming observed since the 1950s. However, several of them do impact climate variability, in particular on a regional level. This handbook aims at addressing these issues in a factual way, and thereby challenge the reader to sharpen his/her critical thinking in a debate that is frequently distorted by unfounded claims

Causality analysis advancements and applications by subspace-based techniques.

Causality analysis remains a fundamental research question and the ultimate objective for many scientific studies. Alongside the increasing speed of data science and technological advancements, as well as the overwhelming existence of complex systems in social science and economics studies, causality analysis has become more complex than ever. The drawbacks of the existing empirical methods (parametric and limited nonparametric approaches) are gradually revealed through implementations. There are increasing number of proofs that the existing methods are limited and fail to catch up the rapid progress of the causality analysis study. Therefore, it is both crucial and time-sensitive to establish the advancements of causality analysis methods by embracing the advanced time series analysis techniques. Subspace-based techniques adopted in this thesis include Singular Value Decomposition (SVD), Singular Spectrum Analysis (SSA) and Convergent CrossMapping (CCM). These subspace-based techniques have been proved powerful nonparametric time series analysis techniques with promising performances on various fields, for instance, time series denoising, filtering, forecasting, signal extraction, image processing, etc. This thesis aims to expand the multivariate extension of subspace-based techniques on causality analysis and brings novel contributions to not only the theoretical advancements of causality analysis methods but also broadening the horizon of the corresponding applications in complex systems like climate change, economics and genetic science. This research project focuses on, but is not limited to the causality detection test. In particular, the thesis initially proposed four novel multivariate analysis methods based on the study of subspace-based techniques: the similarity measure based on eigenvalue distribution; the mutual association measure based on eigenvalue-based criterion; the causality detection method based on multivariate SSA forecasting accuracy; the hybrid causality detection approach by combining SSA and CCM. Moreover, this thesis also introduces CCM in details and expands its implementations in climate change, oil-tourism study, and gene regulatory role detection. The advantages of these methods are that they are nonparametric approaches, assumption free, only two key variables needed, no limitations to nonlinearity or complex dynamics, signal and noise together as a whole as the research object. Both simulations and a number of successful implementations are conducted for the critical evaluation of the proposed advancements with promising robust performances. Specifically, the novel similarity measure overcomes the difficulties of empirical similarity measures through identifying the comparable criterion, and it is proved robust among various types of series. The novel mutual association measure has no restriction on non- linearity, it performs well with various generated linear and nonlinear association patterns, as well as real data from oil-stock market and oil-tourism studies. SSA causality test, CCM causality and the SSA-CCM hybrid causality tests are comprehensively evaluated by comparing with empirical Granger approaches respectively and with two key variables considered, the results of applications significantly reflect their advantages on nonlinear dynamics and causality detection in complex systems. In general, this thesis contributes on offering novel solutions to the crucial question of causality analysis. However, causality analysis contains a broad range of integrated disciplines, and it has the characteristics of cross discipline, strong practicality and intimate connection with other academic fields. It is such a broad subject that no study can independently comprise all. Therefore, this research attempts to provide evidence of successful applications in a possibly wide range of subjects rather than one subject only so to initially evident on the applicability of these novel methods. The applications have covered studies of climate change, oil-stock market, oil-tourism relationship, gene regulatory role detection to date and more future works are in progress. These novel approaches are self-contained to address the corresponding advancements, therefore, they are not comparable between each other, but all contribute differently to the development of causality analysis in a broad sense. These newly proposed approaches offer the interested parties a different angle to resolve the causality analysis questions in a reduced form, data-oriented perspective. It is also expected to open up the research opportunities of nonparametric multivariate analysis through the advanced, inclusive subspace-based techniques that show strong adaptability and capability in the study of complex systems