Time-scale Domain Research Articles

Wheeze type classification using non-dyadic wavelet transform based optimal energy ratio technique

Background and objectiveWheezes in pulmonary sounds are anomalies which are often associated with obstructive type of lung diseases. The previous works on wheeze-type classification focused mainly on using fixed time-frequency/scale resolution based on Fourier and wavelet transforms. The main contribution of the proposed method, in which the time-scale resolution can be tuned according to the signal of interest, is to discriminate monophonic and polyphonic wheezes with higher accuracy than previously suggested time and time-frequency/scale based methods. MethodsAn optimal Rational Dilation Wavelet Transform (RADWT) based peak energy ratio (PER) parameter selection method is proposed to discriminate wheeze types. Previously suggested Quartile Frequency Ratios, Mean Crossing Irregularity, Multiple Signal Classification, Mel-frequency Cepstrum and Dyadic Discrete Wavelet Transform approaches are also applied and the superiority of the proposed method is demonstrated in leave-one-out (LOO) and leave-one-subject-out (LOSO) cross validation schemes with support vector machine (SVM), k nearest neighbor (k-NN) and extreme learning machine (ELM) classifiers. ResultsThe results show that the proposed RADWT based method outperforms the state-of-the-art time, frequency, time-frequency and time-scale domain approaches for all classifiers in both LOO and LOSO cross validation settings. The highest accuracy values are obtained as 86% and 82.9% in LOO and LOSO respectively when the proposed PER features are fed into SVM. ConclusionsIt is concluded that time and frequency domain characteristics of wheezes are not steady and hence, tunable time-scale representations are more successful in discriminating polyphonic and monophonic wheezes when compared with conventional fixed resolution representations.

Partitioning Eddy-Covariance Methane Fluxes from a Shallow Lake into Diffusive and Ebullitive Fluxes

Methane ( $$\mathrm {CH}_{4}$$ ) is known to be emitted from lakes to the atmosphere via processes such as diffusion and ebullition (i.e., bubble emission). We developed a practical method for partitioning eddy-covariance $$\mathrm {CH}_{4}$$ fluxes from a shallow lake into diffusive and ebullitive fluxes using a wavelet analysis based on local scalar similarity between the $$\mathrm {CH}_{4}$$ concentration and other reference scalars, such as the air temperature or water vapour concentration, in the wavelet time-scale domain, with the hypothesis that similar and dissimilar fluctuation components are related to diffusive and ebullitive $$\mathrm {CH}_{4}$$ fluxes, respectively. Our method is applied to approximately two weeks of data obtained at a shallow mid-latitude lake. The partitioned diffusive flux has a physically sound relationship with wind speed, supporting the validity of the method. The ratio of the diffusive flux to the total flux is typically 0.11 with flow from an area of steady bubble emission, but otherwise 0.36. Further validation is required using a larger dataset and data from other lakes. The proposed method can be easily applied to historical data because it requires only 10-Hz data of $$\mathrm {CH}_{4}$$ concentration and other reference scalars, along with an empirical parameter.

A multi-resolution and multivariate analysis of the dynamic relationships between crude oil and petroleum-product prices

This paper proposes the use of a novel multivariate, dynamic approach – wavelet local multiple correlation (WLMC) (Fernández-Macho, 2018) – to analyse the relationship between oil time series in the time-scale domain. This approach is suitable for use with energy data of any kind that change over time and involve heterogeneous agents who make decisions across different time horizons and operate on different time scales. The study of the links between multivariate oil time series is of great importance in energy research, e.g., it is extremely important for petroleum industry refiners and investors to know the relationships and margins between output prices and crude oil costs. The estimation of wavelet correlations in a multivariate framework between such prices is a suitable way to analyse crude oil and petroleum products as a system. To exemplify the use of WLMC, we analyse the relationships between the prices of seven commodities: West Texas Intermediate crude oil and six distilled products (conventional gasoline, regular gasoline, heating oil, diesel fuel, kerosene and propane) from 10/06/2006 to 17/01/2017. The results reveal that the wavelet correlations are strong throughout the period studied and there is a strong decay in correlation values from 2013 to 2015. The most plausible explanation for this decay is overproduction of tight oil in the U.S. and a slowdown in global demand for oil. Furthermore, our results also reveal that heating oil, diesel and kerosene maximise the multiple correlation with respect to the other oil variables on different scales, indicating that these products are the most dependent variables in the crude-product/price system. WLMC offers new opportunities for applications in energy research and other fields.

Inter‐annual and inter‐decadal variability modes of the Athens total cloud cover

The historical observations of the total cloud cover (TCC) index since 1900 from the National Observatory of Athens archives were used here, in order to investigate the inter‐annual variability of TCC. Multi‐spectral decomposition analysis was applied in order to resolve statistically significant modes of TCC variability out of the estimated stochastic variations. An increase of the Athens TCC (A‐TCC) was ascertained during the observational period (1900–2012). The observed A‐TCC variability was found to be composed by “a dominant nonlinear trend” that represents the centennial increment of the cloud cover, and “a small number of sub‐decadal oscillatory modes,” particularly in the winter series. Additionally, the evolutionary history of the A‐TCC variability involves a significant regime shift in about 1960 that was followed by an increase on the mean TCC level and an enhancement of the positive TCC trends apart from winter, in which the trend was faded out. The influence of global and hemispheric climatic variability patterns on the observed A‐TCC changes was explored in the timescale domain along with the impacts of the Mediterranean evaporation field. Results showed that the A‐TCC inter‐decadal variability is strongly coupled with the Atlantic Multidecadal Oscillation (AMO) and the Mediterranean evaporation during all seasons, except winter, in which the atmospheric dynamic drives decadal and sub‐decadal TCC variations, primarily modulated by the North Atlantic Oscillation (NAO). During the hot season, the AMO and the Mediterranean Sea thermodynamic processes become major regulators of the A‐TCC variability, particularly on the inter‐decadal scales, but the tropospheric North Atlantic activity still affects the A‐TCC through the summer NAO (SNAO) pattern. In this framework, different epochs were discerned in the relation of the A‐TCC with the Mediterranean evaporation field, which seem to be associated with the prevalence either of sea thermodynamic processes or of the atmospheric dynamics.

Wavelet-crosscorrelation-based interferometric redatuming in 4D seismic

Interferometric virtual source (VS) redatuming crosscorrelates downgoing waves with the corresponding upgoing waves to convert records from surface-source gathers to virtual gathers at the buried receiver locations. The assumption is that the VS records show the reduced effects of overburden complexity and therefore provide improved seismic repeatability and image quality. In practice, however, the repeatability and quality of the redatumed data can be degraded by one-sided illumination and inadequate preprocessing. In the presence of complex near-surface structure for land redatuming, the intricate shallow structure and highly variable weathering layers introduce surface multiples, ground-roll/scattering noise, and interference among different wave modes that additionally contaminates the down- and upgoing wavefields. To address these issues, we have developed a new interferometric redatuming method based on crosscorrelation in the wavelet domain. Specifically, by transforming time-offset data into the local time-scale (TS) and local TS-wavenumber domains, we have designed and applied filters on the amplitude of the cross spectra in each domain to suppress the aforementioned artifacts and noise, while maintaining accurate kinematic information by retaining the original phase spectra. The new procedure involves forward wavelet transform of the source records, crosscorrelating the wavelet coefficients, filtering in the corresponding domains, and then inverse wavelet transformation to produce the VS records. Components associated with scattering noise and ground roll can be effectively suppressed because our designed filters tackle their features accurately in the local TS and local TS-wavenumber domains, respectively. We tested the method on data from 13 time-lapse surveys that included a significant repeatability problem across a 17-month survey gap, and we compared the results with results from the conventional VS methods. Our VS method produced the best improvement in imaging and repeatability, a positive step forward for land seismic monitoring.

The influence of antecedent conditions on flood risk in sub-Saharan Africa

Abstract. Most flood early warning systems have predominantly focused on forecasting floods with lead times of hours or days. However, physical processes during longer timescales can also contribute to flood generation. In this study, we follow a pragmatic approach to analyse the hydro-meteorological pre-conditions of 501 historical damaging floods from 1980 to 2010 in sub-Saharan Africa. These are separated into (a) weather timescale (0–6 days) and (b) seasonal timescale conditions (up to 6 months) before the event. The 7-day precipitation preceding a flood event (PRE7) and the standardized precipitation evapotranspiration index (SPEI) are analysed for the two timescale domains, respectively. Results indicate that high PRE7 does not always generate floods by itself. Seasonal SPEIs, which are not directly correlated with PRE7, exhibit positive (wet) values prior to most flood events across different averaging times, indicating a relationship with flooding. This paper provides evidence that bringing together weather and seasonal conditions can lead to improved flood risk preparedness.

Broken Rotor Bar Fault Detection and Classification Using Wavelet Packet Signature Analysis Based on Fourier Transform and Multi-Layer Perceptron Neural Network

As a result of increasing machines capabilities in modern manufacturing, machines run continuously for hours. Therefore, early fault detection is required to reduce the maintenance expenses and obviate high cost and unscheduled downtimes. Fault diagnosis systems that provide features extraction and patterns classification of the fault are able to detect and classify the failures in machines. The majority of the related works that reported a procedure for detection of rotor bar breakage so far have applied motor current signal analysis using discrete wavelet transform. In this paper, the most appropriate features are extracted from the coefficients of a wavelet packet transform after fast Fourier transform of current signal. The aim of this study is to develop an effective and sensitive method for fault detection under low load conditions. Through combining the strength of both time-scale and frequency domain analysis techniques, a unified wavelet packet signature analysis pinpoints the fault signature in the special fault-oriented frequency bands. The wavelet analysis combined with a feed-forward neural network classifier provides an intelligent methodology for the automatic diagnosis of the fault severity during runtime of the motor. The faults severity is considered as one, two, and three broken rotor bars. The results have confirmed that the proposed method is effective for diagnosing rotor bar breakage fault in an induction motor and classification of fault severity.

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets (IGWs), and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform (IGWT) maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW’s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the subband signal bandwidth can be regulated effectively by the transform’s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform’s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

Application of Cyclo-Nonstationary Indicators for Bearing Monitoring Under Varying Operating Conditions

Condition monitoring assesses the operational health of rotating machinery, in order to provide early and accurate warning of potential failures such that preventative maintenance actions may be taken. To achieve this target, manufacturers start taking on the responsibilities of engine condition monitoring, by embedding health-monitoring systems within each engine unit and prompting maintenance actions when necessary. Several types of condition monitoring are used including oil debris monitoring, temperature monitoring, and vibration monitoring. Among them, vibration monitoring is the most widely used technique. Machine vibro-acoustic signatures contain pivotal information about its state of health. The current work focuses on one part of the diagnosis stage of condition monitoring for engine bearing health monitoring as bearings are critical components in rotating machinery. A plethora of signal processing tools and methods applied at the time domain, the frequency domain, the time–frequency domain, and the time-scale domain have been presented in order to extract valuable information by proposing different diagnostic features. Among others, an emerging interest has been reported on modeling rotating machinery signals as cyclo-stationary, which is a particular class of nonstationary stochastic processes. The goal of this paper is to propose a novel approach for the analysis of cyclo-nonstationary signals based on the generalization of indicators of cyclo-stationarity (ICNS) in order to cover the speed-varying conditions. The effectiveness of the approach is evaluated on an acceleration signal captured on the casing of an aircraft engine gearbox, provided by SAFRAN.

Comparison of hemispheric asymmetry measurements for emotional recordings from controls

Four asymmetry measurements (conventional coherence function (CCF), cross wavelet correlation (CWC), phase lag index (PLI), and mean phase coherence (MPC)) have been compared to each other for the first time in order to recognize emotional states (pleasant (P), neutral (N), unpleasant (UP)) from controls in EEG sub-bands (delta (0–4 Hz), theta (4–8 Hz), alpha (8–16 Hz), beta (16–32 Hz), gamma (32–64 Hz)) mediated by affective pictures from the International Affective Picture Archiving System (IAPS). Eight emotional features, computed as hemispheric asymmetry between eight electrode pairs (Fp1 − Fp2, F7 − F8, F3 − F4, C3 − C4, T7 − T8, P7 − P8, P3 − P4, and O1 − O2), have been classified by using data mining methods. Results show that inter-hemispheric emotional functions are mostly mediated by gamma. The best classification is provided by a neural network classifier, while the best features are provided by CWC in time-scale domain due to non-stationary nature of electroencephalographic (EEG) series. The highest asymmetry levels are provided by pleasant pictures at mostly anterio-frontal (F3 − F4) and central (C3 − C4) electrode pairs in gamma. Inter-hemispheric asymmetry levels are changed by each emotional state at all lobes. In conclusion, we can state the followings: (1) Nonlinear and wavelet transform-based methods are more suitable for characterization of EEG; (2) The highest difference in hemispheric asymmetry was observed among emotional states in gamma; (3) Cortical emotional functions are not region-specific, since all lobes are effected by emotional stimuli at different levels; and (4) Pleasant stimuli can strongly mediate the brain in comparison to unpleasant and neutral stimuli.

Historical analysis of interannual rainfall variability and trends in southeastern Brazil based on observational and remotely sensed data

The Brazilian Southeast is considered a humid region. It is also prone to landslides and floods, a result of significant increases in rainfall during spring and summer caused by the South Atlantic Convergence Zone (SACZ). Recently, however, the region has faced a striking rainfall shortage, raising serious concerns regarding water availability. The present work endeavored to explain the meteorological drought that has led to hydrological imbalance and water scarcity in the region. Hodrick-Prescott smoothing and wavelet transform techniques were applied to long-term hydrologic and sea surface temperature (SST)—based climate indices monthly time series data in an attempt to detect cycles and trends that could help explain rainfall patterns and define a framework for improving the predictability of extreme events in the region. Historical observational hydrologic datasets available include monthly precipitation amounts gauged since 1888 and 1940 and stream flow measured since the 1930s. The spatial representativeness of rain gauges was tested against gridded rainfall satellite estimates from 2000 to 2015. The analyses revealed variability in four time scale domains—infra-annual, interannual, quasi-decadal and inter-decadal or multi-decadal. The strongest oscillations periods revealed were: for precipitation—8 months, 2, 8 and 32 years; for Pacific SST in the Nino-3.4 region—6 months, 2, 8 and 35.6 years, for North Atlantic SST variability—6 months, 2, 8 and 32 years and for Pacific Decadal Oscillation (PDO) index—6.19 months, 2.04, 8.35 and 27.31 years. Other periodicities less prominent but still statistically significant were also highlighted.

Singular value conditions for stability of dynamic switched systems

In this paper, the stability of a certain class of time-varying systems evolving over nonuniformly spaced discrete domains is analyzed. Switched systems, used here in the context of dynamic equations over time scale domains, arise naturally in applications when a continuous time system is discretized via a sample-and-hold method with multiple sample rates. The stability of switched systems is typically deduced by appealing to certain interrelated properties of the subsystems (such as pairwise commutativity [24], simultaneous diagonalization [7], simultaneous triangularizability [8], or other Lie algebraic conditions [1]) which imply the existence of a common quadratic Lyapunov function. A novel approach is used here to determine the existence of quadratic Lyapunov functions which does not rely on how the subsystems interact with each other. This new method instead examines the role they each play in the aggregate system by way of singular value conditions. Results implying switched system stability and instability are developed under the two primary methods of examining such systems: how the system behaves during arbitrary switching and how it behaves under the influence of a particular switching signal. Several examples illuminating the results are provided throughout the text, as well as important insight discussing certain bounds on these results as they apply to stability theory in general.

Detection of epileptic seizure using Kraskov entropy applied on tunable-Q wavelet transform of EEG signals

Abstract The electroencephalogram (EEG) signals are basically electrophysiological signals that are normally used to access the condition of brain. Epilepsy is one of the brain's disorder. Automated diagnosis of epilepsy can be done by measuring and analyzing the nonlinear and non-stationary trends in EEG signals. This paper introduces a new diagnostic approach for analysis and classification of seizure and seizure-free EEG signals. In time-scale domain, the tunable-Q wavelet transform (TQWT) can reliably represent the sparsity in oscillatory signals. The proposed methodology begins with application of TQWT to efficiently characterize the non-stationary behavior and sparsity of EEG signals. TQWT decomposes the considered signals into a valuable set of band-limited signals termed as sub-bands for better feature extraction. Kraskov entropy is a nonlinear parameter to detect the presence of nonlinear trends in the signals. After decomposition, Kraskov entropy is computed from the specific sub-band as a decisive feature in order to discriminate seizure-free from the epileptic seizure EEG signals. Subsequently, obtained feature vectors are used for classifying the seizure and seizure-free EEG signals using the least square support vector machine (LS-SVM) classifier. While doing analysis, it has been observed that value of proposed Kraskov entropy based feature is significantly higher for seizure EEG signals as compared to that of seizure-free EEG signals. Furthermore, the experimental results of this work has demonstrated significant values of classification accuracy, sensitivity, specificity and Matthew's correlation coefficient. It is noteworthy that proposed framework uses single feature to diagnose the epilepsy accurately. Also the application of the proposed work on EEG data from the University of Bonn, Germany highlights the consistency and in some cases superiority of the proposed method over other popular methods.

Mobility of a Mononucleotide within a Lipid Matrix: A Neutron Scattering Study.

An essential question in studies on the origins of life is how nucleic acids were first synthesized and then incorporated into compartments about 4 billion years ago. A recent discovery is that guided polymerization within organizing matrices could promote a non-enzymatic condensation reaction allowing the formation of RNA-like polymers, followed by encapsulation in lipid membranes. Here, we used neutron scattering and deuterium labelling to investigate 5′-adenosine monophosphate (AMP) molecules captured in a multilamellar phospholipid matrix. The aim of the research was to determine and compare how mononucleotides are captured and differently organized within matrices and multilamellar phospholipid structures and to explore the role of water in organizing the system to determine at which level the system becomes sufficiently anhydrous to lock the AMP molecules into an organized structure and initiate ester bond synthesis. Elastic incoherent neutron scattering experiments were thus employed to investigate the changes of the dynamic properties of AMP induced by embedding the molecules within the lipid matrix. The influence of AMP addition to the lipid membrane organization was determined through diffraction measurement, which also helped us to define the best working Q range for dynamical data analysis with respect to specific hydration. The use of different complementary instruments allowed coverage of a wide time-scale domain, from ns to ps, of atomic mean square fluctuations, providing evidence of a well-defined dependence of the AMP dynamics on the hydration level.

An integrated alcoholic index using tunable-Q wavelet transform based features extracted from EEG signals for diagnosis of alcoholism

Alcoholism affects the structure and functioning of brain. Electroencephalogram (EEG) signals can depict the state of brain. The EEG signals are ensemble of various neuronal activity recorded from different scalp regions having different characteristics and very low magnitude in microvolts. These factors make human interpretation difficult and time consuming to analyze these signals. Moreover, these highly varying EEG signals are susceptible to inter/intra variability errors. So, a Computer-Aided Diagnosis (CAD) can be used to identify the alcoholic and normal subjects accurately. However, these EEG signals exhibit nonlinear and non-stationary properties. Therefore, it needs much effort in deciphering the diagnostic evidence from them using linear time and frequency-domain methods. The nonlinear parameters together with time-frequency/scale domain methods can help to detect tiny changes in these signals. The correntropy is nonlinear indicator which characterizes the dynamic behavior of EEG signals in time-scale domain. In this paper, we present a new way for diagnosis of alcoholism using Tunable-Q Wavelet Transform (TQWT) based features derived from EEG signals. The feature extraction is performed using TQWT based decomposition and extracted Centered Correntropy (CC) from the forth decomposed detail sub-band. The Principal Component Analysis (PCA) is used for feature reduction followed by Least Squares-Support Vector Machine (LS-SVM) for classifying normal and alcoholic EEG signals. In order to make sure reliable classification performance, 10-fold cross-validation scheme is adopted. Our proposed system is able to diagnose the alcoholic and normal EEG signals, with an average accuracy of 97.02%, sensitivity of 96.53%, specificity of 97.50% and Matthews correlation coefficient of 0.9494 for Q-factor (Q) varying between 3 and 8 using Radial Basis Function (RBF) kernel function. Also, we have established a novel Alcoholism Risk Index (ARI) using three clinically significant features to discriminate the given classes by means of a single number. This system can be used for automated diagnosis and monitoring of alcoholic subjects to evaluate the effect of treatment.

Optimal covariance estimation of discrete-time locally self-similar processes in time-scale and ambiguity domains

ABSTRACTThis paper investigates the optimal estimate of the covariance function in the sense of mean-square of errors, for the class of discrete-time locally self-similar processes. The covariance function is estimated in time-scale and ambiguity domains. Since the class of estimators is completely characterized in terms of kernels, the problem is reduced to finding the optimal kernel, which is obtained in time-scale domain. Also, the optimal kernel is computed for two classes of discrete-time locally self-similar and locally self-similar chirp processes. Furthermore, it is shown that the proposed method gives more accurate estimate than the ordinary methods for non stationary processes.

Characterization of Subdural Stimulation-Induced Afterdischarge Activity Using the Continuous Wavelet Transform.

We address the problem of characterization of afterdischarges (ADs) that often arise in patients with intractable focal epilepsy who, as part of their evaluation, undergo cortical electrical stimulation: A standard diagnostic and evaluation procedure before respective surgery. A total of 1333 channels of data recorded in 17 trials of seven patients whose EEG showed ADs (on a total of 156 channels) during cortical stimulation were examined in the time-scale domain using a complex Morlet scalogram. We found excellent characterization of the AD channels based on the distribution functions of the sum of the wavelet coefficients in the two lowest scales corresponding to the frequency range [20, 80] Hz, i.e., the β and γ ranges of EEG. We suggest that the transient Morlet wavelet and the scale domain activity function of the EEG in the two lowest scales (as defined in this paper) could serve as a very useful decision aid in the identification of ADs during and after cortical electrical stimulation. In patients undergoing cortical electrical stimulation, AD waveforms can cause misleading test results by altering the ongoing electroencephalogram (EEG), and can become unwanted seizures. Any process to suppress the ADs rests on a reliable method to distinguish them from normal EEG channels, a task that is usually performed by visual inspection, and that is complicated by the fact that ADs have multiple distinct morphologies. The single feature of the EEG in our study resulted in average probability of detection of 0.99 with an average false alarm probability of 0.04. It is likely that the addition of one or two more features to our decision aid could improve sensitivity and selectivity to near perfection.

Convergence of Clock Processes and Aging in Metropolis Dynamics of a Truncated REM

We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law distribution function, almost surely in the random environment and in the full range of time scales and temperatures for which such a result can be expected to hold. This establishes that the dynamics ages in the same way as Bouchaud’s REM-like trap model, thus extending the universality class of the latter model. The proof relies on a clock process convergence result of a new type where the number of summands is itself a clock process. This reflects the fact that the exploration process of Metropolis dynamics is itself an aging process, governed by its own clock. Both clock processes are shown to converge to stable subordinators below certain critical lines in their time-scale and temperature domains, almost surely in the random environment.

Cognitive tasks during walking affect cerebral blood flow signal features in middle cerebral arteries and their correlation to gait characteristics.

Gait is a complex process involving both cognitive and sensory ability and is strongly impacted by the environment. In this paper, we propose to study of the impact of a cognitive task during gait on the cerebral blood flow velocity, the blood flow signal features and the correlation of gait and blood flow features through a dual task methodology. Both cerebral blood flow velocity and gait characteristics of eleven participants with no history of brain or gait conditions were recorded using transcranial Doppler on mid-cerebral artery while on a treadmill. The cognitive task was induced by a backward counting starting from 10,000 with decrement of 7. Central blood flow velocity raw and envelope features were extracted in both time, frequency and time-scale domain; information-theoretic metrics were also extracted and statistical significances were inspected. A similar feature extraction was performed on the stride interval signal. Statistical differences between the cognitive and baseline trials, between the left and right mid-cerebral arteries signals and the impact of the antropometric variables where studied using linear mixed models. No statistical differences were found between the left and right mid-cerebral arteries flows or the baseline and cognitive state gait features, while statistical differences for specific features were measured between cognitive and baseline states. These statistical differences found between the baseline and cognitive states show that cognitive process has an impact on the cerebral activity during walking. The state was found to have an impact on the correlation between the gait and blood flow features.

Simulation of yearly rainfall time series at microscale resolution with actual properties: Intermittency, scale invariance, and rainfall distribution

Rainfall is a physical phenomenon resulting from the combination of numerous physical processes involving a wide range of scales, from microphysical processes to the general circulation of the atmosphere. Moreover, unlike other geophysical variables such as water vapor concentration, rainfall is characterized by a relaxation behavior that leads to an alternation of wet and dry periods. It follows that rainfall is a complex process which is highly variable both in time and space. Precipitation is thus characterized by the following features: rain/no-rain intermittency, multiple scaling regimes, and extreme events. All these properties are difficult to model simultaneously, especially when a large time and/or space scale domain is required. The aim of this paper is to develop a simulator capable of generating high-resolution rain-rate time series (15 s), the main statistical properties of which are close to an observed rain-rate time series. We also attempt to develop a model having consistent properties even when the fine-resolution-simulated time series are aggregated to a coarser resolution. In order to break the simulation problem down into subcomponents, the authors have focused their attention on several key properties of rainfall. The simulator is based on a sequential approach in which, first, the simulation of rain/no-rain durations permits the retrieval of fractal properties of the rain support. Then, the generation of rain rates through the use of a multifractal, Fractionally Integrated Flux (FIF), model enables the restitution of the rainfall's multifractal properties. This second step includes a denormalization process that was added in order to generate realistic rain-rate distributions.