Time Series Of Fluctuations Research Articles

Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind.

The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different turbulent plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD), and fully developed turbulent magnetic fluctuations of the solar wind taken from the Wind spacecraft. The entropy and complexity values are presented as coordinates on the CH plane for comparison among the different plasma environments and other fluctuation models. The solar wind is found to have the highest permutation entropy and lowest statistical complexity of the three data sets analyzed. Both laboratory data sets have larger values of statistical complexity, suggesting that these systems have fewer degrees of freedom in their fluctuations, with SSX magnetic fluctuations having slightly less complexity than the LAPD edge I(sat). The CH plane coordinates are compared to the shape and distribution of a spectral decomposition of the wave forms. These results suggest that fully developed turbulence (solar wind) occupies the lower-right region of the CH plane, and that other plasma systems considered to be turbulent have less permutation entropy and more statistical complexity. This paper presents use of this statistical analysis tool on solar wind plasma, as well as on an MHD turbulent experimental plasma.

Lagrangian Measurement of Waves and Near Surface Turbulence from Acoustic Instruments

We demonstrate high-resolution measurements of upper ocean flow and turbulence using a Lagrangian drifter. A spherical buoy as a quasi-wave following drifter mitigate the contaminations induced by wave orbital velocities and motion-induced disturbances. The platform, with dimensions of 1.13 m diameter and 4.30 m overall length, is modified to include an Acoustic Doppler Velocimeter to measure time series of velocity fluctuations, a GPS logger, two GoPro video cameras to estimate both platform orientation and sea surface topography evolution, and a 5-beam Acoustic Doppler Current Profiler to collect near the surface velocity profiles. Results are reported from a 2-hour test deployment in November 2014, off Karmøy, Norway. This flexible measuring system is designed for a wide range of air-sea interaction studies, including the effect of wave breaking on the upper ocean variability. Such process understanding is of interest for the estimation of loads on fixed and floating offshore structures, and for efficient and optimal design of offshore platforms.

Laboratory Study on the Characteristics of Deep-water Breaking Waves

In this paper, deep-water breaking waves are generated by the method of energy focusing in a wave flume and the intensity of wave breaking is toned by changing input wave steepness. In the experiment, the time series of surface elevation fluctuation along the flume are obtained utilizing 22 wave probes which are mounted along the mid-stream of the flume. The characteristics of wave surface are analyzed. The spectrum are computed for surface elevations by a fast Fourier transform (FFT). It is concluded that the energy keeps stable in low frequencies part and spreads toward the higher frequencies of the first harmonic band as the wave approaching the breaking zone. After the breaking, the spectrum restores almost its initial shape, but the spectrum energy is lost in the high-frequency end of the first harmonic band, which is more appreciable when the wave breaking happens and is stronger. As the energy is spread to higher frequencies for non-breaking wave, the “spectrally weighted wave frequency” fs becomes bigger and the “spectrally weighted group velocity” Cgs become smaller after the wave focusing. When the wave breaking occurs, the loss in energy is obvious leading to fs decreasing and Cgs increasing after wave breaking, which is more appreciable for plunging wave.

The Multiscale Conformation Evolution of the Financial Time Series

Fluctuations of the nonlinear time series are driven by the traverses of multiscale conformations from one state to another. Aiming to characterize the evolution of multiscale conformations with changes in time and frequency domains, we present an algorithm that combines the wavelet transform and the complex network. Based on defining the multiscale conformation using a set of fluctuation states from different frequency components at each time point rather than the single observable value, we construct the conformational evolution complex network. To illustrate, using data of Shanghai’s composition index with daily frequency from 1991 to 2014 as an example, we find that a few major conformations are the main contributors of evolution progress, the whole conformational evolution network has a clustering effect, and there is a turning point when the size of the chain of multiscale conformations is 14. This work presents a refined perspective into underlying fluctuation features of financial markets.

Carpe Diem: A Novel Approach to Select Representative Days for Long-Term Power System Models with High Shares of Renewable Energy Sources

In order to explore scenarios on the future of power systems, a variety of numerical models have been developed. As the share of variable renewable energy sources, particularly wind and solar, is projected to significantly increase, accounting for their temporal and spatial variability becomes ever more important in developing sound long-term scenarios. Computational restrictions prevent many long-term power system models being developed with an hourly resolution; instead they use time slices that aggregate periods with similar load and renewable electricity generation levels. There is to date no reproducible and validated method to derive and select time slices for power system models with multiple fluctuating time series. In this paper, we present a novel and effective method that is easily applied to input data for all kinds of power system models. We utilize this procedure in the long-term power system model LIMES-EU and show that a small number of representative days developed in this way are sufficient to reflect the characteristic fluctuations of the input data. Alongside a validation of the method, we discuss the conditions under which seasonal differentiation, and the use of representative weeks instead of days, is necessary.

Evaluation of river–aquifer interaction in the north part of Dezful–Andimeshk district, SW of Iran

The river and groundwater are significant components of hydrological cycle, and the interaction between these two water resources attracted a great attention recently. Over the years, several methods have been used for the study of the water exchanges between these resources. In this research, a combined approach including hydraulic head measurements, hydrochemistry, and water balance calculations is applied to the assessment of the river–aquifer interactions. The study area is located in the north part of the Dezful–Andimeshk district in the southwest of Iran. The Dez River is the major surface water body that interacts with groundwater in this area. The Dez dam has been constructed on this river in the northern part of the study area. In this study, a series of water measurements including river water stages and discharge monitoring at Dez dam site and Dezful hydrometric station, groundwater table measurement in the piezometric network, and chemical analysis of river and groundwater were carried out for the evaluation of river–aquifer interaction. In order to monitor river and groundwater in the study area, a monitoring network including a hydrometric station (near the Dezful city), 38 piezometers, and 23 water quality monitoring wells have been established by the Khuzestan Water and Power Authority (KWPA). Data of the monitoring network were used for the evaluation of temporal variation of river and groundwater interaction in this research. The discharge measurements of the Dez dam site and Dezful hydrometric station in a 47-year period (1964–2011) shows that the water volume is decreased between these two stations. In addition, examining the time series of river stage and groundwater fluctuations in the study area shows that the groundwater table and river water stage variations have similar patterns. This similar pattern is an observant indication of groundwater and surface water interactions that is confirmed by the interpretation of groundwater potentiometric map of the study area. Following these conclusions, the hydrochemical measurements also were used for the assessment of the Dez River and groundwater connectivity. The surveys showed the similar patterns in the temporal variation trends of chemical characteristics (especially chloride ion) of the Dez River and groundwater as a base for connectivity of these resources. For better assessment of the river–aquifer interaction, 69 groundwater samples were collected from the abstraction wells in August 2012. The physicochemical analysis results show the river influences the groundwater quality. That is, the amounts of electrical conductivity (EC), temperature, and anions such as chloride, sulfate, and nitrate show a notable decrease in river-adjacent wells. Finally, for the quantifying of river–aquifer exchange rate, a simple water balance was formulated. This water budget also confirmed the Dez River role in the hydrologic balance of the study area, and according to calculation, the water infiltration from the riverbed was estimated to be more than 8 % of the aquifer recharge. This research shows the losing nature of the Dez River and its influence on the underlying groundwater quality in the study area.

Mouse activity across time scales: fractal scenarios.

In this work we devise a classification of mouse activity patterns based on accelerometer data using Detrended Fluctuation Analysis. We use two characteristic mouse behavioural states as benchmarks in this study: waking in free activity and slow-wave sleep (SWS). In both situations we find roughly the same pattern: for short time intervals we observe high correlation in activity - a typical 1/f complex pattern - while for large time intervals there is anti-correlation. High correlation of short intervals ( to : waking state and to : SWS) is related to highly coordinated muscle activity. In the waking state we associate high correlation both to muscle activity and to mouse stereotyped movements (grooming, waking, etc.). On the other side, the observed anti-correlation over large time scales ( to : waking state and to : SWS) during SWS appears related to a feedback autonomic response. The transition from correlated regime at short scales to an anti-correlated regime at large scales during SWS is given by the respiratory cycle interval, while during the waking state this transition occurs at the time scale corresponding to the duration of the stereotyped mouse movements. Furthermore, we find that the waking state is characterized by longer time scales than SWS and by a softer transition from correlation to anti-correlation. Moreover, this soft transition in the waking state encompass a behavioural time scale window that gives rise to a multifractal pattern. We believe that the observed multifractality in mouse activity is formed by the integration of several stereotyped movements each one with a characteristic time correlation. Finally, we compare scaling properties of body acceleration fluctuation time series during sleep and wake periods for healthy mice. Interestingly, differences between sleep and wake in the scaling exponents are comparable to previous works regarding human heartbeat. Complementarily, the nature of these sleep-wake dynamics could lead to a better understanding of neuroautonomic regulation mechanisms.

An empirical method for approximating stream baseflow time series using groundwater table fluctuations

Developing reliable methods to estimate stream baseflow has been a subject of interest due to its importance in catchment response and sustainable watershed management. However, to date, in the absence of complex numerical models, baseflow is most commonly estimated using statistically derived empirical approaches that do not directly incorporate physically-meaningful information. On the other hand, Artificial Intelligence (AI) tools such as Genetic Programming (GP) offer unique capabilities to reduce the complexities of hydrological systems without losing relevant physical information. This study presents a simple-to-use empirical equation to estimate baseflow time series using GP so that minimal data is required and physical information is preserved. A groundwater numerical model was first adopted to simulate baseflow for a small semi-urban catchment (0.043 km2) located in Singapore. GP was then used to derive an empirical equation relating baseflow time series to time series of groundwater table fluctuations, which are relatively easily measured and are physically related to baseflow generation. The equation was then generalized for approximating baseflow in other catchments and validated for a larger vegetation-dominated basin located in the US (24 km2). Overall, this study used GP to propose a simple-to-use equation to predict baseflow time series based on only three parameters: minimum daily baseflow of the entire period, area of the catchment and groundwater table fluctuations. It serves as an alternative approach for baseflow estimation in un-gauged systems when only groundwater table and soil information is available, and is thus complementary to other methods that require discharge measurements.

Fractal-like correlations of the fluctuating inter-spike membrane potential of a Helix aspersa pacemaker neuron

We analyzed the voltage fluctuations of the membrane potential manifested along the inter-spike segment of a pacemaker neuron. Time series of intracellular inter-spike voltage fluctuations were obtained in the current-clamp configuration from the F1 neuron of 12 Helix aspersa specimens. To assess the dynamic or stochastic nature of the voltage fluctuations these series were analyzed by Detrended Fluctuation Analysis (DFA), providing the scaling exponent α. The median α result obtained for the inter-spike segments was 0.971 ([0.963, 0.995] lower and upper quartiles). Our results indicate a critical-like dynamic behavior in the inter-spike membrane potential that, far from being random, shows long-term correlations probably linked to the dynamics of the mechanisms involved in the regulation of the membrane potential, thereby endorsing the occurrence of critical-like phenomena at a single-neuron level.

Monitoring, analysis, and correction of magnetic field fluctuations in echo planar imaging time series.

To assess the utility of concurrent magnetic field monitoring for observing and correcting for variations in k-space trajectories and global background fields that occur in single-shot echo planar imaging (EPI) time series as typically used in functional MRI (fMRI). Field monitoring was performed using an array of NMR field probes operated concurrently with series of single-shot EPI acquisitions from a static phantom. The observed fluctuations in field evolution were analyzed in terms of their temporal and spatial behavior at the field level as well as at the level of reconstructed image series. The potential to correct for such fluctuations was assessed by accounting for them upon image reconstruction. An indication of the number and relative magnitude of underlying effects was obtained via principal component analysis. Trajectory and global field variations were found to induce substantial image fluctuations. Global field fluctuations induced standard deviations in image intensity up to 31%. Fluctuations in the trajectory induced ghosting artifacts with standard deviations up to 2%. Concurrent magnetic field monitoring reduced the fluctuations in the EPI time series to a maximum of 1.2%. Concurrent magnetic field monitoring holds the potential to improve the net sensitivity of fMRI by reducing signal fluctuations unrelated to brain activity.

Linguistic Summarization of Europe Brent Spot Price Time Series Along with the Interpretations from the Perspective of Turkey

Compared to the predictive models for forecasting crude oil price, the descriptive models are also important for discovering the relations among factors that have influence on crude oil price. In this paper, linguistic summarization of time series, a descriptive technique, is used to summarize the Europe Brent Spot Price EBSP data dollars per barrel from May 1987 to July 2013 on daily and monthly base. This study is the first attempt in the literature for linguistic summarization of the EBSP time series with the aim to establish a decision support tool that can be used for generating linguistic propositions helping the estimation of future behaviors and fluctuations of oil price time series for oil-importer countries such as Turkey. Economic interpretations of generated linguistic propositions about the main features of EBSP trends duration, dynamics of change, and variability and a procurement strategy, indicating that Turkey could cut back on oil importation about $573.88 million between 1996 and 2012, are suggested from the perspective of Turkey.

Superstatistical fluctuations in time series of leverage returns

We analyze to what extent the emergence of fat-tailed q-Gaussian distributions of daily leverage returns of North American industrial companies that survive default and de-listing between 2006 and 2012 can be described by superstatistics. To this end, we compare mean values of the Tsallis entropic parameter q obtained by two independent methods: (i) direct fitting of q-Gaussians to distributions of leverage returns; and (ii) derived from shape parameters of Gamma distributions fitted to histograms of inverted realized variances of these returns. For a vast majority of companies, we observe the striking consistency of average values of q obtained by both methods. This finding supports the applicability of superstatistical hypothesis, which assumes that q-Gaussians result from the superposition of locally normal distributions with Gamma-distributed precision (inverted variance).

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

Fluctuation of rainfall time series in Malawi: An analysis of selected areas

Inter annual fluctuation of rainfall in Malawi was studied using a 31 year time series from selected rain gauge stations with the aim of analyzing the spatial and temporal characteristics of rainfall in Malawi. The study found strong inter-annual fluctuation of rainfall, with topography and location playing major roles in the annual rainfall distribution. The seasonal index and precipitation concentration index showed that rainfall is highly seasonal and highly concentrated with most stations receiving rainfall in three months, except for Nkhatabay which has seasonal rainfall. The intra annual rainfall distribution was highly variable in time and space. Cross correlations among the stations suggested two distinct zones, zone 1 composed of Karonga and Nkhatabay and zone 2 composed of Bolero, Kasungu, Salima, Dedza, Mangochi, Makoka and Ngabu. Spectral analysis of the rainfall time series revealed cycles at five to eight years, suggesting links with the El Nino Southern Oscillation and double the period of the Quasi Biennial Oscillation. Apart from the common cycles, the rainfall time series of the two zones showed periods of 13.64 and 10.06 years, respectively, which suggests links with the solar cycle. These cycles are consistent with those found in other southern Africa countries.

Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

The dynamical analysis of inter-trial fluctuations near goal equivalent manifolds.

Using the concept of task manifolds, a number of data analysis methods have been used to explain how redundancy influences the structure of variability observed during repeated motor performance. Here we describe investigations that integrate the task manifold perspective with the analysis of Inter-Trial task dynamics. Goal equivalent manifolds (GEMs), together with optimal control ideas, are used to formulate simple models that serve as experimentally testable hypotheses on how Inter-Trial fluctuations are generated and regulated. In an experimental context, these phenomenological models allow us to show how error-correcting control is spatiotemporally organized around a given GEM. To illustrate our approach, we apply it to study the variability observed in a virtual shuffleboard task. The geometric stability properties of the Inter-Trial dynamics near the GEM are extracted from fluctuation time series data. We find that subjects exhibit strong control of fluctuations in an eigendirection transverse to the GEM, whereas they only weakly control fluctuations in an eigendirection nearly, but not exactly, tangent to it. We demonstrate that our dynamical analysis is robust under coordinate transformations, and discuss how our results support a generalized interpretation of the minimum intervention principle that suggests the involvement of competing costs in addition to goal-level error minimization.

Statistical approach to the analysis of olive long-term pollen season trends in southern Spain

Analysis of long-term airborne pollen counts makes it possible not only to chart pollen-season trends but also to track changing patterns in flowering phenology. Changes in higher plant response over a long interval are considered among the most valuable bioindicators of climate change impact. Phenological-trend models can also provide information regarding crop production and pollen–allergen emission. The interest of this information makes essential the election of the statistical analysis for time series study.We analysed trends and variations in the olive flowering season over a 30-year period (1982–2011) in southern Europe (Córdoba, Spain), focussing on: annual Pollen Index (PI); Pollen Season Start (PSS), Peak Date (PD), Pollen Season End (PSE) and Pollen Season Duration (PSD). Apart from the traditional Linear Regression analysis, a Seasonal-Trend Decomposition procedure based on Loess (STL) and an ARIMA model were performed.Linear regression results indicated a trend toward delayed PSE and earlier PSS and PD, probably influenced by the rise in temperature. These changes are provoking longer flowering periods in the study area.The use of the STL technique provided a clearer picture of phenological behaviour. Data decomposition on pollination dynamics enabled the trend toward an alternate bearing cycle to be distinguished from the influence of other stochastic fluctuations. Results pointed to show a rising trend in pollen production.With a view toward forecasting future phenological trends, ARIMA models were constructed to predict PSD, PSS and PI until 2016. Projections displayed a better goodness of fit than those derived from linear regression.Findings suggest that olive reproductive cycle is changing considerably over the last 30years due to climate change. Further conclusions are that STL improves the effectiveness of traditional linear regression in trend analysis, and ARIMA models can provide reliable trend projections for future years taking into account the internal fluctuations in time series.

Learning to Reproduce Fluctuating Time Series by Inferring Their Time-Dependent Stochastic Properties: Application in Robot Learning Via Tutoring

This study proposes a novel type of dynamic neural network model that can learn to extract stochastic or fluctuating structures hidden in time series data. The network learns to predict not only the mean of the next input state, but also its time-dependent variance. The training method is based on maximum likelihood estimation by using the gradient descent method and the likelihood function is expressed as a function of the estimated variance. Regarding the model evaluation, we present numerical experiments in which training data were generated in different ways utilizing Gaussian noise. Our analysis showed that the network can predict the time-dependent variance and the mean and it can also reproduce the target stochastic sequence data by utilizing the estimated variance. Furthermore, it was shown that a humanoid robot using the proposed network can learn to reproduce latent stochastic structures hidden in fluctuating tutoring trajectories. This learning scheme is essential for the acquisition of sensory-guided skilled behavior.

Superstatistical Fluctuations in Time Series of Leverage Returns

Fat tails of q-Gaussian distributions of daily log-leverage-returns of 520 North American industrial firms reported by Katz and Tian (2013) imply a significantly higher credit risk at short time-horizons and/or large initial distances to the default barrier than forecasted by traditional structural models. Superstatistics can explain the origin of this behavior and allows for a straightforward generalization of conventional models of default. Here, we verify manifestation of these distributions with Kolmogorov-Smirnov test and analyze to what extent emergence of q-Gaussians can be described by superstatistics. To this end, we compare mean values of the Tsallis entropic parameter q obtained by two independent methods: i) direct fitting of q-Gaussians to distributions of log-leverage-returns and ii) derived from shape parameters of Gamma distributions fitted to histograms of inversed realized variances of these returns. For a vast majority of companies, we observe the striking consistency of the average values of q, converging to 1.47, obtained by both methods. This finding supports the applicability of superstatistical hypothesis, which assumes that q-Gaussians result from locally normal fluctuations with Gamma-distributed precision. Notably, for a small group of firms (~8%) having distributions with divergent second moment, the mean values of q derived by both methods are very different. It is likely that in this group of issuers, fluctuations of daily log-leverage-returns are so violent that the superstatistical model assumptions are not applicable. These findings are important for practical implementations of credit risk valuations and pricing of credit securities.

Analysis of long-term fluctuations in stream flow time series: An application to Litani River, Lebanon

Litani River is the largest river in Lebanon and has been affected by several physical and anthropogenic factors that influenced its flow dynamics. By means of the Singular Spectrum Analysis (SSA), the time dynamics of the stream flow of seven sites along the course of Litani River was investigated, extracting for each site the long-term trend. A clear decreasing trend characterizes all the long-term trends of the stream flow. Furthermore, several peaks were identified, consistent with the rainfall rate and snow cover variability.