Analyzing spatio-temporal patterns of genuine cross-correlations

In multivariate time series analysis, the equal-time cross-correlation is a classic and computationally efficient measure for quantifying linear interrelations between data channels. When the cross-correlation coefficient is estimated using a finite amount of data points, its non-random part may be strongly contaminated by a sizable random contribution, such that no reliable conclusion can be drawn about genuine mutual interdependencies. The random correlations are determined by the signals' frequency content and the amount of data points used. Here, we introduce adjusted correlation matrices that can be employed to disentangle random from non-random contributions to each matrix element independently of the signal frequencies. Extending our previous work these matrices allow analyzing spatial patterns of genuine cross-correlation in multivariate data regardless of confounding influences. The performance is illustrated by example of model systems with known interdependence patterns. Finally, we apply the methods to electroencephalographic (EEG) data with epileptic seizure activity.

Genuine cross-correlations: Which surrogate based measure reproduces analytical results best?

The analysis of short segments of noise-contaminated, multivariate real world data constitutes a challenge. In this paper we compare several techniques of analysis, which are supposed to correctly extract the amount of genuine cross-correlations from a multivariate data set. In order to test for the quality of their performance we derive time series from a linear test model, which allows the analytical derivation of genuine correlations. We compare the numerical estimates of the four measures with the analytical results for different correlation pattern. In the bivariate case all but one measure performs similarly well. However, in the multivariate case measures based on the eigenvalues of the equal-time cross-correlation matrix do not extract exclusively information about the amount of genuine correlations, but they rather reflect the spatial organization of the correlation pattern. This may lead to failures when interpreting the numerical results as illustrated by an application to three electroencephalographic recordings of three patients suffering from pharmacoresistent epilepsy.

Stochastic rank correlation: a robust merit function for 2D/3D registration of image data obtained at different energies

In this article, the authors evaluate a merit function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type merit functions with the flexibility of mutual-information-type merit functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman's rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another merit function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other merit functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.

Artificial oxygen fluxes measured by the eddy correlation method using stirring-sensitive oxygen microsensor and oxygen optodes in a flume experiment

In the last decade, the aquatic eddy correlation (EC) technique has proven to be a powerful approach for non-invasive measurements of oxygen fluxes across the sediment water interface. Fundamental to the EC approach is the correlation of turbulent velocity and oxygen concentration fluctuations measured with high frequencies in the same sampling volume. Oxygen concentrations are commonly measured with fast responding electrochemical microsensors. However, due to their own oxygen consumption, electrochemical microsensors are sensitive to changes of the diffusive boundary layer surrounding the probe and thus to changes in the ambient flow velocity. The so-called stirring sensitivity of microsensors constitutes an inherent correlation of flow velocity and oxygen sensing and thus an artificial flux which can confound the benthic flux determination. To assess the artificial flux we measured the correlation between the turbulent flow velocity and the signal of oxygen microsensors in a sealed annular flume without any oxygen sinks and sources. Experiments revealed significant correlations, even for sensors designed to have low stirring sensitivities of ~0.7%. The artificial fluxes depended on ambient flow conditions and, counter intuitively, increased at higher velocities because of the nonlinear contribution of turbulent velocity fluctuations. The measured artificial fluxes ranged from 2 - 70 mmol m**-2 d**-1 for weak and very strong turbulent flow, respectively. Further, the stirring sensitivity depended on the sensor orientation towards the flow. Optical microsensors (optodes) that should not exhibit a stirring sensitivity were tested in parallel and did not show any significant correlation between O2 signals and turbulent flow. In conclusion, EC data obtained with electrochemical sensors can be affected by artificial flux and we recommend using optical microsensors in future EC-studies. Flume experiments were conducted in February 2013 at the Institute for Environmental Sciences, University of Koblenz-Landau Landau. Experiments were performed in a closed oval-shaped acrylic glass flume with cross-sectional width of 4 cm and height of 10 cm and total length of 54 cm. The fluid flow was induced by a propeller driven by a motor and mean flow velocities of up to 20 cm s-1 were generated by applying voltages between 0 V and 4 V DC. The flume was completely sealed with an acrylic glass cover. Oxygen sensors were inserted through rubber seal fittings and allowed positioning the sensors with inclinations to the main flow direction of ~60°, ~95° and ~135°. A Clark type electrochemical O2 microsensor with a low stirring sensitivity (0.7%) was tested and a fast-responding needle-type O2 optode (PyroScience GmbH, Germany) was used as reference as optodes should not be stirring sensitive. Instantaneous three-dimensional flow velocities were measured at 7.4 Hz using stereoscopic particle image velocimetry (PIV). The velocity at the sensor tip was extracted. The correlation of the fluctuating O2 sensor signals and the fluctuating velocities was quantified with a cross-correlation analysis. A significant cross-correlation is equivalent to a significant artificial flux. For a total of 18 experiments the flow velocity was adjusted between 1.7 and 19.2 cm s**-1, and 3 different orientations of the electrochemical sensor were tested with inclination angles of ~60°, ~95° and ~135° with respect to the main flow direction. In experiments 16-18, wavelike flow was induced, whereas in all other experiments the motor was driven by constant voltages. In 7 experiments, O2 was additionally measured by optodes. Although performed simultaneously with the electrochemical sensor, optode measurements are listed as separate experiments (denoted by the attached 'op' in the filename), because the velocity time series was extracted at the optode tip, located at a different position in the flume.

A suite of global, cross-scale topographic variables for environmental and biodiversity modeling, links to files in GeoTIFF format

Topographic variation, the spatial variation in elevation and terrain features, underpins a myriad of patterns and processes in geography and ecology and is key to understanding the variation of life on the planet. The characterization of this variation is scale-dependent, i.e. it varies with the distance over which features are assessed and with the spatial grain (grid cell resolution) of analysis. A fully standardized and global multivariate product of different terrain features has the potential to support many large-scale basic research and analytical applications, however to date, such technique is unavailable. Here we used the digital elevation model products of global 250 m GMTED and near-global 90 m SRTM to derive a suite of topographic variables: elevation, slope, aspect, eastness, northness, roughness, terrain roughness index, topographic position index, vector ruggedness measure, profile and tangential curvature, and 10 geomorphological landform classes. We aggregated each variable to 1, 5, 10, 50 and 100 km spatial grains using several aggregation approaches (median, average, minimum, maximum, standard deviation, percent cover, count, majority, Shannon Index, entropy, uniformity). While a global cross-correlation underlines the high similarity of many variables, a more detailed view in four mountain regions reveals local differences, as well as scale variations in the aggregated variables at different spatial grains. All newly-developed variables are available for download at http://www.earthenv.org and can serve as a basis for standardized hydrological, environmental and biodiversity modeling at a global extent.

Green's function retrieval through cross-correlations in a two -dimensional complex reverberating medium

International audience

G7 Stock Markets: Who is The First to Defeat The DCCA Correlation?

Following the methodology of Ferreira and Dionísio (2016), the objective of this paper is to analyze the behavior stock markets in the G7 countries and find which of those countries is the first to reach levels of long-range correlations that are not significant. We carry out this analysis using detrended cross-correlation analysis and its correlation coefficient, to check for the existence of long-range dependence in time series. The existence of long-range dependence could be understood as a possibility of EMH violation. This analysis remains interesting because studies are not conclusive about the existence or not of long memory in stock return rates.

Selective activation of the rectus abdominis muscle during low-intensity and fatiguing tasks

In order to understand the potential selective activation of the rectus abdominis muscle, we conducted two experiments. In the first, subjects performed two controlled isometric exercises: the curl up (supine trunk raise) and the leg raise (supine bent leg raise) at low intensity (in which only a few motor units are recruited). In the second experiment, subjects performed the same exercises, but they were required to maintain a certain force level in order to induce fatigue. We recorded the electromyographic (EMG) activities of the lower and upper portions of the rectus abdominis muscle during the exercises and used spatial-temporal and frequency analyses to describe muscle activation patterns. At low-intensity contractions, the ratio between the EMG intensities of the upper and lower portions during the curl up exercise was significantly larger than during the leg raise exercise (p = 0.02). A cross-correlation analysis indicated that the signals of the abdominal portions were related to each other and this relation did not differ between the tasks (p = 0.12). In the fatiguing condition, fatigue for the upper portion was higher than for the lower portion during the curl up exercise (p = 0.008). We conclude that different exercises evoked, to a certain degree, individualized activation of each part of the rectus abdominis muscle, but different portions of the rectus abdominis muscle contributed to the same task, acting like a functional unit. These results corroborate the relevance of varying exercise to modify activation patterns of the rectus abdominis muscle.

Anticipation of pain enhances the nociceptive transmission and functional connectivity within pain network in rats

Background: Expectation is a very potent pain modulator in both humans and animals. There is evidence that pain transmission neurons are modulated by expectation preceding painful stimuli. Nonetheless, few studies have examined the influence of pain expectation on the pain-related neuronal activity and the functional connectivity within the central nociceptive network. Results: This study used a tone-laser conditioning paradigm to establish the pain expectation in rats, and simultaneously recorded the anterior cingulate cortex (ACC), the medial dorsal thalamus (MD), and the primary somatosensory cortex (SI) to investigate the effect of pain expectation on laser-induced neuronal responses. Cross-correlation and partial directed coherence analysis were used to determine the functional interactions within and between the recorded areas during nociceptive transmission. The results showed that under anticipation condition, the neuronal activity to the auditory cue was significantly increased in the ACC area, whereas those to actual noxious stimuli were enhanced in all the recorded areas. Furthermore, neuronal correlations within and between these areas were significantly increased under conditions of expectation compared to those under non-expectation conditions, indicating an enhanced synchronization of neural activity within the pain network. In addition, information flow from the medial (ACC and MD) to the lateral (SI cortex) pain pathway increased, suggesting that the emotion-related neural circuits may modulate the neuronal activity in the somatosensory pathway during nociceptive transmission. Conclusion: These results demonstrate that the nociceptive processing in both medial and lateral pain systems is modulated by the expectation of pain.

Fossil groups in the Millennium simulation Their environment and its evolution

Context. Fossil systems are defined to be X- ray bright galaxy groups ( or clusters) with a two- magnitude difference between their two brightest galaxies within half the projected virial radius, and represent an interesting extreme of the population of galaxy agglomerations. However, the physical conditions and processes leading to their formation are still poorly constrained. Aims. We compare the outskirts of fossil systems with that of normal groups to understand whether environmental conditions play a significant role in their formation. We study the groups of galaxies in both, numerical simulations and observations. Methods. We use a variety of statistical tools including the spatial cross- correlation function and the local density parameter Delta(5) to probe differences in the density and structure of the environments of "" normal"" and "" fossil"" systems in the Millennium simulation. Results. We find that the number density of galaxies surrounding fossil systems evolves from greater than that observed around normal systems at z = 0.69, to lower than the normal systems by z = 0. Both fossil and normal systems exhibit an increment in their otherwise radially declining local density measure (Delta(5)) at distances of order 2.5 r(vir) from the system centre. We show that this increment is more noticeable for fossil systems than normal systems and demonstrate that this difference is linked to the earlier formation epoch of fossil groups. Despite the importance of the assembly time, we show that the environment is different for fossil and non- fossil systems with similar masses and formation times along their evolution. We also confirm that the physical characteristics identified in the Millennium simulation can also be detected in SDSS observations. Conclusions. Our results confirm the commonly held belief that fossil systems assembled earlier than normal systems but also show that the surroundings of fossil groups could be responsible for the formation of their large magnitude gap.

Void fraction measurement and signal analysis from multiple-electrode impedance sensors

Void fraction sensors are important instruments not only for monitoring two-phase flow, but for furnishing an important parameter for obtaining flow map pattern and two-phase flow heat transfer coefficient as well. This work presents the experimental results obtained with the analysis of two axially spaced multiple-electrode impedance sensors tested in an upward air-water two-phase flow in a vertical tube for void fraction measurements. An electronic circuit was developed for signal generation and post-treatment of each sensor signal. By phase shifting the electrodes supplying the signal, it was possible to establish a rotating electric field sweeping across the test section. The fundamental principle of using a multiple-electrode configuration is based on reducing signal sensitivity to the non-uniform cross-section void fraction distribution problem. Static calibration curves were obtained for both sensors, and dynamic signal analyses for bubbly, slug, and turbulent churn flows were carried out. Flow parameters such as Taylor bubble velocity and length were obtained by using cross-correlation techniques. As an application of the void fraction tested, vertical flow pattern identification could be established by using the probability density function technique for void fractions ranging from 0% to nearly 70%.

Turbulent Time and Length Scale Measurements in High-Velocity Open Channel Flows

In high-velocity open channel flows, the measurements of air-water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air-water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8 E+5 to 7.1 E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air-water depth Y90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95 to 0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

Fast Structure-Based Assignment of 15N HSQC Spectra of Selectively 15N-Labeled Paramagnetic Proteins

A novel strategy for fast NMR resonance assignment of N-15 HSQC spectra of proteins is presented. It requires the structure coordinates of the protein, a paramagnetic center, and one or more residue-selectively N-15-labeled samples. Comparison of sensitive undecoupled N-15 HSQC spectra recorded of paramagnetic and diamagnetic samples yields data for every cross-peak on pseudocontact shift, paramagnetic relaxation enhancement, cross-correlation between Curie-spin and dipole-dipole relaxation, and residual dipolar coupling. Comparison of these four different paramagnetic quantities with predictions from the three-dimensional structure simultaneously yields the resonance assignment and the anisotropy of the susceptibility tensor of the paramagnetic center. The method is demonstrated with the 30 kDa complex between the N-terminal domain of the epsilon subunit and the theta subunit of Escherichia Coll DNA polymerase III. The program PLATYPUS was developed to perform the assignment, provide a measure of reliability of the assignment, and determine the susceptibility tensor anisotropy.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Turbulence Characterisation of High-Velocity Free-Surface Flows

In high-velocity free-surface flows, air is continuously being trapped and released through the free-surface. Such high-velocity highly-aerated flows cannot be studied numerically because of the large number of relevant equations and parameters. Herein an advanced signal processing of traditional single- and dual-tip conductivity probes provides some new information on the air-water turbulent time and length scales. The technique is applied to turbulent open channel flows in a large-size facility. The auto- and cross-correlation analyses yield some characterisation of the large eddies advecting the bubbles. The transverse integral turbulent length and time scales are related to the step height: i.e., Lxy/h ~ 0.02 to 0.2, and T.sqrt(g/h) ~ 0.004 to 0.04. The results are irrespective of the Reynolds numbers. The present findings emphasise that turbulent dissipation by large-scale vortices is a significant process in the intermediate zone between the spray and bubbly flow regions (0.3 < C < 0.7). Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. The results are significant because they provide a picture general enough to be used to characterise the air-water flow field in prototype spillways.