Wavelet Cross-correlation Analysis Research Articles

Higher-order turbulence statistics and multiscale characterization of morphodynamics in a riverbank section with an upstream mining pit

Channel dredging has become a common phenomenon across several fluvial systems. Pits dredged in the riverbank can influence the downstream turbulence and affect the bank slope and central channel morphodynamics. Erodible bed experiments were conducted in a laboratory flume having a riverbank cross section with three different bank slopes, i.e., 25°, 31°, and 40° with and without a mining pit. Flow over the bank slope and near the bank toe was most affected by the pit excavation at the channel upstream. Turbulence levels were amplified within the flow over the slope and near the bank toe. The logarithmic scaling range of higher-order fluctuations at the bank toe is greater for with pit case. The complex interaction of simultaneous processes like pit migration, sliding failure and bank erosion, and fluvial erosion was studied at multiple length scales and time scales. A wavelet cross correlation analysis was used to calculate the celerity of bedform migration at the bank toe along the flow. Statistical celerity of bedforms with smaller scales (up to 15 mm length scales) is significantly higher due to pit interaction. The study reveals that instream mining has notable effects on the inherent nature of higher-order turbulence statistics, especially near the bank slope and toe, as well as the multiscale morphological structures.

Correlation analysis of the temporal dynamics of subcutaneous blood perfusion and skin temperature in post-occlusion reactive hyperaemia test

The digital thermal monitoring approach examines dynamic finger temperature in response to post-occlusive reactive hyperaemia (PORH) test and is a cost-effective way to study microvessels’ regulatory functions. The degree of dependency between skin temperature and subcutaneous blood perfusion in the PORH test, however, remains an unsettled subject. The purpose of this study is to evaluate their correlations and explore the prospects of restoring subcutaneous blood perfusion using skin temperature readings. 10 volunteers participated the experimental study of PORH test, and subcutaneous blood perfusion and skin temperature images of hand were captured by laser speckle contrast imaging (LSCI) and infrared (IR) camera respectively. Wavelet cross-correlation (WCC) analysis of extracted LSCI and IR signals in the resting phase of PORH test revealed that as frequency increased within 0.005 ∼ 0.1 Hz, the modules of WCC reduced and phase shift increased. Based on phase shift characteristics, the distances of thermal wave propagation were estimated 0.9 mm ∼ 2.3 mm, which were basically consistent with the measurement depth of LSCI. We further demonstrated that when the frequency-dependent delay and attenuation were taken into account, the correlation of oscillations between LSCI and IR signals improved significantly. Finally, an algorithm was proposed to reconstruct IR signals, which could be used to improve the possibilities of restoring subcutaneous blood perfusion from skin temperature recordings in PORH tests. The prospective applications of this study include indirect measurement of subcutaneous blood perfusion and the assessment of microvessels’ regulatory functions through skin temperature oscillations.

Hydrating Capabilities of the Biopolymers Produced by the Marine Thermophilic Bacillus horneckiae SBP3 as Evaluated by ATR-FTIR Spectroscopy.

The surfactin-like lipopeptide (BS-SBP3) and the exopolysaccharide (EPS-SBP3) produced by the polyextremophilic Bacillus horneckiae SBP3 (DSM 103063) have been recently described as valuable biopolymers useful in biotechnological applications. To investigate the hydrating capabilities of BS-SBP3 and EPS-SBP3, here we evaluated (i) their wetting properties, measuring the contact angle; (ii) their moisture uptake abilities using the gravimetric method; and (iii) their hydrating states (from 0 to 160% w/w of water content) using ATR-FTIR spectroscopy. BS-SBP3 reduced the water contact angle on a hydrophobic surface from 81.7° to 51.3°, whereas the contact angle in the presence of EPS-SBP3 was 72.9°, indicating that BS-SBP3 improved the wettability of the hydrophobic surface. In the moisture uptake tests, EPS-SBP3 absorbed more water than BS-SBP3, increasing its weight from 10 mg to 30.1 mg after 36 h of 100% humidity exposure. Spectral distance and cross-correlation analyses were used to evaluate the molecular changes of the two biopolymers during the hydration process. As the water concentration increased, BS-SBP3 spectra changed in intensity in the two contributions of the OH-stretching band named “closed” and “open” (3247 and 3336 cm−1, respectively). Differently, the spectra of EPS-SBP3 exhibited a broader peak (3257 cm−1), which shifted at higher water concentrations. As evaluated by the spectral distance and the wavelet cross-correlation analysis, the OH-stretching bands of the BS-SBP3 and EPS-SBP3 changed as a function of water content, with two different sigmoidal trends having the inflection points at 80% and 48%, respectively, indicating peculiar water-properties of each biopolymer. As wetting agents, these biopolymers might replace industrially manufactured additives in agriculture and the food and cosmetic industries.

Feedback between surface and deep processes: Insight from time series analysis of sedimentary record

Sediment accumulation and subduction at continental margins are hypothesized to be crucial in the operation of Wilson cycle style plate tectonics on Earth. To test this hypothesis, we explore the interaction between continental sedimentation and plate tectonics by utilizing a 3.5 Gyr continent-scale sediment abundance record from the Macrostrat database. Wavelet analysis of a time series of sedimentary rock volume identified a supercontinent-like cycle of ∼500 Myr across the past 3.0 Gyr. Intriguingly, this long-term fluctuation in net sedimentation record that indicates continent-derived sediment flux into oceanic crust is in phase with the vigor of subduction activity (as characterized by zircon εHf and δ18O isotopes) through time. These agreements provide independent evidence for the hypothesis that the operation of Wilson cycle style plate tectonics was facilitated by sediment accumulation and subduction (lubrication) at continental margins. Moreover, wavelet cross-correlation analysis of sediment abundance and subduction flux suggests an increasingly efficient sediment cycling via subduction since ∼3.0 Ga, notably coinciding with transition periods of atmospheric oxygen levels at the beginning and end of the Proterozoic. The results suggest that the co-evolving surface process and plate tectonics that increased long-term net sequestration of organic carbon could have contributed to the initial rise of atmospheric oxygen at the beginning of the Proterozoic and the climb to sustained modern levels in the early Phanerozoic.

Cerebral cortex and autonomic nervous system responses during emotional memory processing.

Psychiatric symptoms are often accompanied by somatic symptoms induced by the activity of the autonomic nervous system (ANS). The aim of this study was to calculate the time lag between electroencephalography (EEG) and electrocardiography (ECG) responses, to clarify the changes in the relationship between the cerebral cortex (CC) and the sympathetic nervous system (SNS) during emotional recall processing. Twenty-two healthy young adults were examined. Their EEG and ECG data were simultaneously recorded during emotional audiovisual recall tasks using pleasant and unpleasant stimuli for 180 s, with three repetitions (Epochs 1 & 2 and Epoch 3). The EEG data were analyzed using a fast Fourier transform (FFT) to obtain a time series of relative power spectra, XE, in the theta 1, theta 2, alpha 1, alpha 2, alpha 3, beta 1, beta 2, and beta 3 bands. Time series of RR (inter-beat) intervals (time intervals between successive R waves) derived from the ECG spectral analysis using FFT was applied to the resampled time series of RR intervals over about 60 s to obtain a time series of power spectra for the ratio low frequency/high frequency (LH/HF), XC, which reflects the activity of the sympathetic nervous function. The time lag between XE and XC was calculated using wavelet-crosscorrelation analysis. The results demonstrated that the brain responded to unfamiliar emotionally pleasant stimuli in Epochs 1 & 2 earlier than the SNS, whereas the brain and SNS responded to unfamiliar unpleasant stimuli nearly simultaneously. The brain was activated rapidly in response to familiar unpleasant stimuli, although SNS responded more rapidly to familiar pleasant stimuli than the brain in Epoch 3. Our results quantitatively describe the relationship between the CC and the ANS during emotional recall.

Wavelet decomposition approach for understanding time-varying relationship of financial sector variables: a study of the indian stock market

In this paper, we study the effect of overall stock market sentiment in India on sectoral indices and on individual stock prices in terms of co-movement, dependence and volatility transmission along with the magnitude and persistence of the effects. The study uses wavelet decomposition framework for breaking down different financial time series into time-varying components. Quantile Regression, Wavelet Multiple Correlation and Cross-Correlation analysis, and Diebold-Yilmaz spillover analysis are then applied to investigate the nature of dependence, association, and spillover dynamics. For further focus, we have considered different time periods separately to identify the effect of market phases. Interesting results are obtained with respect to persistence of shocks, both across and within time periods. These have implications with respect to understanding market behavior and also perception of sectors and stocks. Keywords: Wavelet Decomposition, SENSEX, Quantile Regression, Wavelet Multiple Correlation, Wavelet Multiple Cross Correlation, Diebold-Yilmaz Spillover.

Temporally irregular electrical stimulation to the epileptogenic focus delays epileptogenesis in rats

BackgroundVariation in the temporal patterns of electrical pulses in stimulation trains has opened a new field of opportunity for the treatment of neurological disorders, such as pharmacoresistant temporal lobe epilepsy. Whether this novel type of stimulation affects epileptogenesis remains to be investigated. ObjectiveThe purpose of this study was to analyze the effects of temporally irregular deep brain stimulation on kindling-induced epileptogenesis in rats. MethodsTemporally irregular deep brain stimulation was delivered at different times with respect to the kindling stimulation. Behavioral and electrographic changes on kindling acquisition were compared with a control group and a temporally regular deep brain stimulation-treated group. The propagation of epileptiform activity was analyzed with wavelet cross-correlation analysis, and interictal epileptiform discharge ratios were obtained. ResultsTemporally irregular deep brain stimulation delivered in the epileptogenic focus during the interictal period shortened the daily afterdischarge duration, slowed the progression of seizure stages, diminished the generalized seizure duration and interfered with the propagation of epileptiform activity from the seizure onset zone to the ipsi- and contralateral motor cortex. We also found a negative correlation between seizure severity and interictal epileptiform discharges in rats stimulated with temporally irregular deep brain stimulation. ConclusionThese results provide evidence that temporally irregular deep brain stimulation interferes with the establishment of epilepsy by delaying epileptogenesis by almost twice as long in kindling animals. Thus, temporally irregular deep brain stimulation could be a preventive approach against epilepsy.

The Indian inflation–growth relationship revisited: robust evidence from time–frequency analysis

ABSTRACTThis article re-visits the inflation–growth nexus in India using the tools of wavelet, i.e. wavelet correlation, wavelet cross-correlation and scale by scale Granger causality test. Wavelet cross-correlation analysis shows that at the shortest scales inflation and economic growth were independent; at medium scales, there exists feedback effect; and at higher scales, only economic growth is leading to inflation. Furthermore, we find: (a) high and increasing dependence between inflation and economic growth, particularly after mid-2002; (b) high-frequency components of economic growth Granger-cause low-frequency component of CPI-based inflation and vice-versa, and at all scales economic growth Granger-cause inflation at scales of 4–6 and no evidence of causality was detected from WPI-based inflation to economic growth; (c) results indicate that there is no long-run causal link between inflation and economic growth. This study presents new insights for policymakers to sustain economic development by using inflation as an economic tool in India.

Synchrony in catchment stream colour levels is driven by both local and regional climate

Abstract. Streams draining upland catchments carry large quantities of carbon from terrestrial stocks to downstream freshwater and marine ecosystems. Here it either enters long-term storage in sediments or enters the atmosphere as gaseous carbon through a combination of biotic and abiotic processes. There are, however, increasing concerns over the long-term stability of terrestrial carbon stores in blanket peatland catchments as a result of anthropogenic pressures and climate change. We analysed sub-annual and inter-annual changes in river water colour (a reliable proxy measurement of dissolved organic carbon; DOC) using 6 years of weekly data, from 2011 to 2016. This time-series dataset was gathered from three contiguous river sub-catchments, the Black, the Glenamong and the Srahrevagh, in a blanket peatland catchment system in western Ireland, and it was used to identify the drivers that best explained observed temporal change in river colour. The data were also used to estimate annual DOC loads from each catchment. General additive mixed modelling was used to identify the principle environmental drivers of water colour in the rivers, while wavelet cross-correlation analysis was used to identify common frequencies in correlations. At 130 mg Pt Co L−1, the mean colour levels in the Srahrevagh (the sub-catchment with lowest rainfall and higher forest cover) were almost 50 % higher than those from the Black and Glenamong, at 95 and 84 mg Pt Co L−1 respectively. The decomposition of the colour datasets revealed similar multi-annual, annual and event-based (random component) trends, illustrating that environmental drivers operated synchronously at each of these temporal scales. For both the Black and its nested Srahrevagh catchment, three variables (soil temperature, soil moisture deficit, SMD, and the weekly North Atlantic Oscillation, NAO) combined to explain 54 % and 58 % of the deviance in colour respectively. In the Glenamong, which had steeper topography and a higher percentage of peat intersected by streams, soil temperature, the log of stream discharge and the NAO explained 66 % of the colour concentrations. Cross-wavelet time-series analysis between river colour and each environmental driver revealed a significant high common power relationship at an annual time step. Each relationship however, varied in phase, further highlighting the complexity of the mechanisms driving river colour in the sub-catchments. The estimated mean annual DOC loads for the Black and Glenamong rivers to Lough Feeagh were similar at 15.0 and 14.7 t C km−2 yr−1 respectively. The important role of past and current precipitation and, in particular, temperature emphasises the vulnerability of blanket peatland carbon stores to projected climate change and highlights the interaction of local and regional climate in controlling aquatic carbon export. Our results show that water colour (and hence DOC) concentrations can vary considerably between neighbouring catchments and also that regional-scale climatic drivers control the trends in intra- and inter-annual flux of DOC through the system. The combination of locally determined concentrations and regionally controlled fluxes produces aquatic DOC loads that vary over both the annual cycle and over multiple years.

A Physical–Mathematical Approach to Climate Change Effects through Stochastic Resonance

The aim of this work is to study the effects induced by climate changes in the framework of the stochastic resonance approach. First, a wavelet cross-correlation analysis on Earth temperature data concerning the last 5,500,000 years is performed; this analysis confirms a correlation between the planet’s temperature and the 100,000, 41,000, and 23,000-year periods of the Milankovitch orbital cycles. Then, the stochastic resonance model is invoked. Specific attention is given to the study of the impact of the registered global temperature increase within the stochastic model. Further, a numerical simulation has been performed, based on: (1) A double-well potential, (2) an external periodic modulation, corresponding to the orbit eccentricity cycle, and (3) an increased value of the global Earth temperature. The effect of temperature increase represents one of the novelties introduced in the present study and is determined by downshifting the interaction potential used within the stochastic resonance model. The numeric simulation results show that, for simulated increasing values of the global temperature, the double-well system triggers changes, while at higher temperatures (as in the case of the absence of a global temperature increase although with a different threshold) the system goes into a chaotic regime. The wavelet analysis allows characterization of the stochastic resonance condition through the evaluation of the signal-to-noise ratio. On the basis of the obtained findings, we hypothesize that the global temperature increase can suppress, on a large time scale corresponding to glacial cycles, the external periodic modulation effects and, hence, the glacial cycles.

Visualization of Correlation and Time-lag between the Sites of the Brain for EEG using Wavelet-crosscorrelation Analysis According to Differences in Duration of Epileptiform Discharges

Visualization of Correlation and Time-lag between the Sites of the Brain for EEG using Wavelet-crosscorrelation Analysis According to Differences in Duration of Epileptiform Discharges

Evolution of IOD-ENSO relationship at multiple time scales

Both El Nino-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) are important indicators of the potential impact of climate at the global scale. The IOD-ENSO relationship at different timescales is temporally non-uniform, which is important to understand in order to evaluate its socioeconomic impacts. Here, we developed and applied a wavelet cross-correlation analysis approach for investigating the evolution of the IOD-ENSO relationship over a 150-year period. We found that the IOD-ENSO relationship was statistically significant at the dominant timescales of 1.5, 3, and 24 year, with the correlation degree varying with time. The hysteresis effect between IOD and ENSO and the evolution of their relationship obviously differ at the three dominant timescales. The positive (negative) IOD and El Nino (La Nina) events were mainly determined by the variability of IOD and ENSO at the timescale < 3 year. Strong positive IOD events in the September-October-November period would more likely be related to El Nino events 2 months later and La Nina events 14 months later, but negative IOD events would rarely co-occur with El Nino or La Nina events. The result achieved in this study can serve as a useful guide for the long-term forecast of IOD and ENSO.

P3-3-1. Features of the correlation between the sites of EEG based on the difference in duration of epileptiform discharges

To investigate differences in the duration of epileptiform discharges, wavelet-crosscorrelation analysis was performed to identify correlations and time-lags between sites of the brain. Electroencephalography recordings were categorized into two time spans according to the duration of the epileptiform discharge: short run, 2–3 s; and long run, ⩾3 s. Both runs were subcategorized into before, during, and after epileptiform discharge groups. The EEG was divided into 2-s segments. In all patients, wavelet-crosscorrelation coefficients (WCC) and time-lag (LAG) at 6 Hz were calculated between all electrodes, and between all electrodes and the temporal region electrodes for each segment. In both runs, comparison of all electrodes revealed that the highest correlation occurred during epileptiform discharge. In both runs, comparison of the temporal region electrodes revealed that similar WCC and LAG values occurred before and during epileptiform discharge. In addition, the results of the long run indicated that similar WCC and LAG values occurred after epileptiform discharge, which suggest that the temporal region of the brain remains in a state of preparation for a seizure in cases of long runs, even after epileptiform discharge.

P3-3-2. Resemblance of the connectivity in the brain of patients suffering from epilepsy with small-world networks

The brain network between healthy individuals and patients suffering from epileptiform discharges was compared to investigate whether or not the brain network of patients with epileptiform discharges resembles a small world network. The EEG (19 channels) of the healthy subjects and patients were recorded during a state of relaxation. Segments of 2 s during the eyes closed were analyzed in the healthy individuals’ EEG. In the patients’ EEG, segments of two seconds were analyzed during epileptiform discharge. Wavelet-crosscorrelation analysis was used to obtain wavelet-crosscorrelation coefficients (WCC). WCC was calculated in the alpha bandwidth (non-discharge), and the theta band (discharge). Three network parameters were calculated: the shortest path length, the global efficiency, and the clustering coefficient. The results in the theta band showed that the shortest path length during discharge in the patients was significantly lower than non-discharge and healthy individuals. Both the clustering coefficient and global efficiency in the patients during discharge were significantly higher than non-discharge and healthy subjects. No significant results were found in the alpha band. These results suggest that the network in the brain of patients during a discharge could be more resembling to a small world network.

A Detection Method for Friction Vibration Based on Harmonic Wavelet Packet Transform and Cross-Correlation Analysis

Running-in wear experiments were conducted on a spherical-on-disk tester. The vibration signals collected in the experiments were detected by a combination of harmonic wavelet packet transform (HWPT) and cross-correlation analysis (CCA) methods. Experimental results show that the friction vibration signals detected in tangential and normal directions have the characteristics of no time delay and strong correlation. Their root-mean-square (RMS) values gradually reduce and enter a steady-state of fluctuation with the experiments time, which are consistent with the variation of friction coefficient and reflect the change of wear states from the running-in wear to the stable wear. Therefore, the detection of friction vibration can be realized by a combination of HWPT and CCA methods.

Thermal restraint on PEG-EG mixtures by FTIR investigations and wavelet cross-correlation analysis

The aim of the present work is to investigate the thermal response of PolyEthylene Glycol 1000 (PEG1000) and of its mixtures with the monomer Ethylene Glycol (EG). On purpose Attenuated Total Reflectance Infra-Red (ATR-IR) spectra were collected, in the spectral range spanning from 400 cm−1 to 4000 cm−1, on PEG1000 and on its mixtures with EG, as a function of concentration and temperature, through positive thermal scans, i.e. by increasing temperature. It will be shown that ATR-IR technique reveals a powerful tool for the characterization of the thermal response in polymeric systems. The registered spectra have been analyzed both on the whole investigated spectral range, as well as, separately, on the restricted intramolecular OH stretching vibrational contribution region. In the first case the displacement of the spectral features from the spectrum at the lowest temperature, taken as reference spectrum, shows a lower dependence for the mixture. As far as the intramolecular OH vibrational contribution is concerned, besides a conventional analysis in terms of band components, three different data analysis procedures have been applied, i.e. the characterization of the temperature dependence of the intramolecular OH stretching center frequency, of the spectral distance and of the wavelet cross correlation coefficient. The three applied data analysis approaches indicates that the addition of a small amount of pure EG to PEG1000 significantly influences the OH vibrational properties of the PEG1000 polymeric matrix. The three different methods furnish a unique coherent interpretative picture which supports the validity of the applied approaches. Furthermore, the analyses show the presence of a higher thermal restraint for the PEG + EG mixture which confirms that, within the three-dimensional networks of hydrogen bonded EG-PEG1000 mixtures, a key role is played by EG in determining an increase of the hydrogen bond network density.

ウェーブレット相互相関解析を用いたてんかん性異常波を含む脳波の帯域別領域別部位間関連性

ウェーブレット相互相関解析を用いたてんかん性異常波を含む脳波の帯域別領域別部位間関連性

Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach

The West Texas Intermediate (WTI) spot price shows high volatility and in 2014 and 2015 when quoted prices declined sharply, long-term prices in future markets were less volatile. These prices are different and diverge depending on how they process fundamental and transitory factors. US tight oil production has been a major innovation with significant macroeconomic effects. In this paper we use WTI spot prices and long-term futures prices, the latter calculated as the expected value with a stochastic model calibrated with the futures quotes of each sample day. These long-term prices are the long-term equilibrium value under risk neutral measurement. In order to analyze potential time-scale relationships between spots and future, we perform a wavelet cross-correlation analysis using a novel wavelet graphical tool recently proposed. To check the direction of the causality, we apply non-linear causality tests to raw data and log returns as well as to the wavelet transform of the spot and futures prices. Our results show that in the spot and futures markets for the period 24 February 2006–2 April 2016 there is a bi-directional causality effect for most time scales (from intra-week to biannual). This suggests that spot and futures prices react simultaneously to new information.

Ethylene Glycol - Polyethylene Glycol (EG-PEG) Mixtures: Infrared Spectra Wavelet Cross-Correlation Analysis.

Infrared spectra were collected on mixtures of ethylene glycol (EG) and polyethylene glycol 600 (PEG600) as a function of weight fraction from pure EG to pure PEG600. In this paper, it will be shown that while the OH vibrational contribution drastically reduces its center frequency from 3450 cm-1 to 3300 cm-1 in the weight fraction range 0-25%, the displacement of the mixture spectral features of the mixtures from ideal behavior, i.e., in the absence of interaction, shows the presence of a non-ideal mixing process. Furthermore, wavelet cross-correlation analysis of the registered pairs of spectra and of the intramolecular O-H stretching contributions reveals how the addition of a small amount of pure EG to PEG600 dramatically influences the structural properties of the polymeric matrix, owing to an increase the intermolecular connectivity. In particular, the wavelet cross-correlation parameters, evaluated between each pair of the registered data as a function of weight fraction, in a linear-logarithmic plot, reveals an inflection point for a weight fraction of about 25% of EG, which confirms that, within the three-dimensional networks of hydrogen-bonded EG-PEG600 molecules, a key role is played by EG in determining an increase in the hydrogen-bond network density.

Investigation of cosmic ray penetration with wavelet cross-correlation analysis

Aims. We use Fermi and Planck data to calculate the cross correlation between gamma ray signal and gas distribution in different scales in giant molecular clouds (GMC). Then we investigate the cosmic rays (CRs) penetration in GMCs with these informations. Methods.We use the wavelet technique to decompose both the gamma ray and dust opacity maps in different scales, then we calculate the wavelet cross correlation functions in these scales. We also define wavelet response as an analog to the impulsive response in Fourier transform and calculate that in different scales down to Fermi angular resolution. Results. The gamma ray maps above 2 GeV show strong correlation with the dust opacity maps, the correlation coefficient is larger than 0.9 above a scale of 0.4 degree.The derived wavelet response is uniform in different scales. Conclusions. We argue that the CR above 10 GeV can penetrate the giant molecular cloud freely and the CRs distributions in the same energy range are uniform down to parsec scale.