Nonlinear time-series analysis of Hyperion's lightcurves

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.Comment: 34 pages, 12 figures, 4 tables; v2 after referee report; matches the version accepted in Astrophysics and Space Scienc

Multi-epoch, multi-frequency VLBI study of the parsec-scale jet in the blazar 3C 66A

We present the observational results of the Gamma-ray blazar, 3C 66A, at 2.3, 8.4, and 22 GHz at 4 epochs during 2004-05 with the VLBA. The resulting images show an overall core-jet structure extending roughly to the south with two intermediate breaks occurring in the region near the core. By model-fitting to the visibility data, the northmost component, which is also the brightest, is identified as the core according to its relatively flat spectrum and its compactness. As combined with some previous results to investigate the proper motions of the jet components, it is found the kinematics of 3C 66A is quite complicated with components of inward and outward, subluminal and superluminal motions all detected in the radio structure. The superluminal motions indicate strong Doppler boosting exists in the jet. The apparent inward motions of the innermost components last for at least 10 years and could not be caused by new-born components. The possible reason could be non-stationarity of the core due to opacity change.Comment: 24 pages, 4 figure

Active visual search in non-stationary scenes: coping with temporal variability and uncertainty

Objective. State-of-the-art experiments for studying neural processes underlying visual cognition often constrain sensory inputs (e.g., static images) and our behavior (e.g., fixed eye-gaze, long eye fixations), isolating or simplifying the interaction of neural processes. Motivated by the non-stationarity of our natural visual environment, we investigated the electroencephalography (EEG) correlates of visual recognition while participants overtly performed visual search in non-stationary scenes. We hypothesized that visual effects (such as those typically used in human–computer interfaces) may increase temporal uncertainty (with reference to fixation onset) of cognition-related EEG activity in an active search task and therefore require novel techniques for single-trial detection. Approach. We addressed fixation-related EEG activity in an active search task with respect to stimulus-appearance styles and dynamics. Alongside popping-up stimuli, our experimental study embraces two composite appearance styles based on fading-in, enlarging, and motion effects. Additionally, we explored whether the knowledge obtained in the pop-up experimental setting can be exploited to boost the EEG-based intention-decoding performance when facing transitional changes of visual content. Main results. The results confirmed our initial hypothesis that the dynamic of visual content can increase temporal uncertainty of the cognition-related EEG activity in active search with respect to fixation onset. This temporal uncertainty challenges the pivotal aim to keep the decoding performance constant irrespective of visual effects. Importantly, the proposed approach for EEG decoding based on knowledge transfer between the different experimental settings gave a promising performance. Significance. Our study demonstrates that the non-stationarity of visual scenes is an important factor in the evolution of cognitive processes, as well as in the dynamic of ocular behavior (i.e., dwell time and fixation duration) in an active search task. In addition, our method to improve single-trial detection performance in this adverse scenario is an important step in making brain–computer interfacing technology available for human–computer interaction applications.EC/FP7/611570/EU/Symbiotic Mind Computer Interaction for Information Seeking/MindSeeBMBF, 01GQ0850, Bernstein Fokus Neurotechnologie - Nichtinvasive Neurotechnologie für Mensch-Maschine Interaktio

25 Years of Self-Organized Criticality: Numerical Detection Methods

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines - the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.Comment: Space Science Review series on SO

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field