Time-dependent Coherence Research Articles

Real-world characterization of vestibular contributions during locomotion.

The vestibular system, which encodes our head movement in space, plays an important role in maintaining our balance as we navigate the environment. While in-laboratory research demonstrates that the vestibular system exerts a context-dependent influence on the control of balance during locomotion, differences in whole-body and head kinematics between indoor treadmill and real-world locomotion challenge the generalizability of these findings. Thus, the goal of this study was to characterize vestibular-evoked balance responses in the real world using a fully portable system. While experiencing stochastic electrical vestibular stimulation (0-20 Hz, amplitude peak ± 4.5 mA, root mean square 1.25 mA) and wearing inertial measurement units (IMUs) on the head, low back, and ankles, 10 participants walked outside at 52 steps/minute (∼0.4 m/s) and 78 steps/minute (∼0.8 m/s). We calculated time-dependent coherence (a measure of correlation in the frequency domain) between the applied stimulus and the mediolateral back, right ankle, and left ankle linear accelerations to infer the vestibular control of balance during locomotion. In all participants, we observed vestibular-evoked balance responses. These responses exhibited phasic modulation across the stride cycle, peaking during the middle of the single-leg stance in the back and during the stance phase for the ankles. Coherence decreased with increasing locomotor cadence and speed, as observed in both bootstrapped coherence differences (p < 0.01) and peak coherence (low back: 0.23 ± 0.07 vs. 0.16 ± 0.14, p = 0.021; right ankle: 0.38 ± 0.12 vs. 0.25 ± 0.10, p < 0.001; left ankle: 0.33 ± 0.09 vs. 0.21 ± 0.09, p < 0.001). These results replicate previous in-laboratory studies, thus providing further insight into the vestibular control of balance during naturalistic movements and validating the use of this portable system as a method to characterize real-world vestibular responses. This study will help support future work that seeks to better understand how the vestibular system contributes to balance in variable real-world environments.

Modelling and simulating thunderstorm/downburst winds using S-transform and discrete orthonormal S-transform

Fluctuating winds from intense thunderstorm/downburst are often modelled as the amplitude modulated evolutionary stochastic processes and simulated based on the spectral representation method. Aspects of the modelling and simulation include assessing time and frequency dependent power spectrum, and the identification of the amplitude and frequency modulations are not straightforward. The present study uses the S-transform and discrete orthonormal S-transform to evaluate the time-frequency power spectral density (TFPSD) functions and coherence functions of nonstationary winds. The results for a thunderstorm/downburst event indicate that the coherence is time-dependent. The use of the TFPSD functions and a newly developed simulation method to generate winds acted on single and multiple points with a time-dependent coherence is shown. A comparison of the mean of the TFPSD of the simulated winds to its corresponding target is used to validate the adequacy of the simulation models. The use of the simulated records to assess the record-to-record variability on the maximum responses of a nonlinear inelastic single-degree-of-freedom system is given.

Multivariate Locally Stationary Wavelet Analysis with the mvLSW R Package

This paper describes the R package mvLSW. The package contains a suite of tools for the analysis of multivariate locally stationary wavelet (LSW) time series. Key elements include: (i) the simulation of multivariate LSW time series for a given multivariate evolutionary wavelet spectrum (EWS); (ii) estimation of the time-dependent multivariate EWS for a given time series; (iii) estimation of the time-dependent coherence and partial coherence between time series channels; and, (iv) estimation of approximate confidence intervals for multivariate EWS estimates. A demonstration of the package is presented via both a simulated example and a case study with EuStockMarkets from the datasets package.

Generation of partially coherent beams with controllable time-dependent coherence

A straight effective method to produce partially coherent beams with controllable time-dependent coherence is demonstrated. We theoretically deduce that a time-dependent partially coherent beam can be generated by imposing dynamic random phase on a coherent laser beam. The degree of coherence of the beam is determined by an amplitude control parameter of the dynamic random phase. We experimentally corroborate that after a completely coherent laser beam reflected from a spatial light modulator, loaded with a particular dynamic random phase, this beam is transformed into a partially coherent beam with time-dependent coherence.

Exploring Dephasing of a Solid-State Quantum Emitter via Time- and Temperature-Dependent Hong-Ou-Mandel Experiments.

We probe the indistinguishability of photons emitted by a semiconductor quantum dot (QD) via time- and temperature-dependent two-photon interference (TPI) experiments. An increase in temporal separation between consecutive photon emission events reveals a decrease in TPI visibility on a nanosecond time scale, theoretically described by a non-Markovian noise process in agreement with fluctuating charge traps in the QD's vicinity. Phonon-induced pure dephasing results in a decrease in TPI visibility from (96±4)% at 10K to a vanishing visibility at 40K. In contrast to Michelson-type measurements, our experiments provide direct access to the time-dependent coherence of a quantum emitter on a nanosecond time scale.

Patient Adaptive Neurofeedback for ADHD Therapy

An EEG-Based audiovisual stimulation system was tested on a group of 32 ADHD patients. The efficacy was compared in a pre- and post analysis over a treatment period of 3 month with a control group and a group of patients with an EEGbased neurofeedback therapy. The number of impulsivity errors in a stop-signal paradigm at several distinct times during and after the therapy was used as a quality marker. The main feature of this method uses real-time-EEG data derived parameters for a controlled manipulation of EEG patterns with persistently strong audio-visual stimuli. It is based upon a direct feedback of changes in short-term coherences in the context of central nervous stimulus processing to control the stimulating frequency. The real-time EEG processing is done on the basis of time-dependent coherence analysis of the theta and beta band.

Extracting phase-dependent human vestibular reflexes during locomotion using both time and frequency correlation approaches

Daily activities, such as walking, may require dynamic modulation of vestibular input onto motoneurons. This dynamic modulation is difficult to identify in humans due to limitations in the delivery and analysis of current vestibular probes, such as galvanic vestibular stimulation. Stochastic vestibular stimulation, however, provides an alternative method to extract human vestibular reflexes. Here, we used time-dependent coherence and time-dependent cross-correlation, coupled with stochastic vestibular stimulation, to investigate the phase dependency of human vestibular reflexes during locomotion. We found that phase-dependent activity from the medial gastrocnemius muscles is correlated with the vestibular signals over the 2- to 20-Hz bandwidth during the stance phase of locomotion. Vestibular-gastrocnemius coherence and time-dependent cross-correlations reached maximums at 21 ± 4 and 23 ± 8% of the step cycle following heel contact and before the period of maximal electromyographic activity (38 ± 5%). These results demonstrate 1) the effectiveness of these techniques in extracting the phase-dependent modulation of vestibulomuscular coupling during a cyclic task; 2) that vestibulomuscular coupling is phasically modulated during locomotion; and 3) that the period of strongest vestibulomuscular coupling does not correspond to the period of maximal electromyographic activity in the gastrocnemius. Therefore, we have shown that stochastic vestibular stimulation, coupled with time-frequency decomposition, provides an effective tool to assess the contribution of vestibular ex-afference to the muscular control during locomotion.

Measurement of coherence dynamics based on coherent anti-Stokes Raman scattering

Nanosecond time-resolved evolution of coherence between two nondegenerate ground levels has been investigated in Rb atomic vapor. Using STIRAP and fractional STIRAP, a time-dependent coherence is prepared and indirectly monitored by the generated coherent Raman scattering signal proportional to the coherence. The experimental data fit very well with numerical simulations. This technique have potential applications in nonlinear process based on atomic coherence.

Filtering noise for synchronised activity in multi-trial electrophysiology data using Wiener and Kalman filters

Novel approaches to effectively reduce noise in data recorded from multi-trial physiology experiments have been investigated using two-dimensional filtering methods, adaptive Wiener filtering and reduced update Kalman filtering. Test data based on signal and noise model consisting of different conditions of signal components mixed with noise have been considered with filtering effects evaluated using analysis of frequency coherence and of time-dependent coherence. Various situations that may affect the filtering results have been explored and reveal that Wiener and Kalman filtering can considerably improve the coherence values between two channels of multi-trial data and suppress uncorrelated components. We have extended our approach to experimental data: multi-electrode array (MEA) local field potential (LFPs) recordings from the inferotemporal cortex of sheep and LFP vs. electromyogram (LFP-EMG) recording data during resting tremor in Parkinson’s disease patients. Finally general procedures for implementation of these filtering techniques are described.

Molecular quantum-dot cellular automata: From molecular structure to circuit dynamics

We establish a method for exploring the dynamics of molecular quantum-dot cellular automata (QCA) devices by hierarchically combining the techniques of quantum chemistry with the nonequilibrium time-dependent coherence vector formalism. Single QCA molecules are characterized using ab initio quantum chemistry methods. We show how to construct a simple model Hamiltonian for each QCA cell based on parameters extracted from the ab initio calculation. The model Hamiltonian captures well the relevant switching behavior and can then be used to calculate the time-dependent coherence vector, including thermal and nonequilibrium behavior. This enables us to explore dynamic behavior and power dissipation for various QCA devices and circuits.

Study of coherence by speckle interferometry

A simple method for studying the time-dependent coherence of laser radiation by speckle interferometry is proposed and tested by experiment.

Detecting time-dependent coherence between non-stationary electrophysiological signals—A combined statistical and time–frequency approach

Various time–frequency methods have been used to study time-varying properties of non-stationary neurophysiological signals. In the present study, a time–frequency coherence estimate using continuous wavelet transform (CWT) together with its confidence intervals are proposed to evaluate the correlation between two non-stationary processes. The approach is based on averaging over repeat trials. A systematic comparison between approaches using CWT and short-time Fourier transform (STFT) is carried out. Simulated data are generated to test the performance of these methods when estimating time–frequency based coherence. In contrast to some recent studies, we find that CWT based coherence estimates do not supersede STFT based estimates. We suggest that a combination of STFT and CWT would be most suitable for analysing non-stationary neural data. Tests are presented to investigate the time and frequency discrimination capabilities of the two approaches. The methods are applied to two experimental data sets: electroencephalogram (EEG) and surface electromyogram (EMG) during wrist movements in a healthy subject, and local field potential (LFP) and surface EMG recordings during resting tremor in a Parkinsonian patient. Supporting software is available at http://www.dcs.warwick.ac.ukffeng/software/COD and http://www.neurospec.org.

Low Frequency Cortico-Muscular Coherence During Voluntary Rapid Movements of the Wrist Joint

Rapid voluntary point-to-point wrist tracking movements are generated by the co-operative action of a large number of wrist muscles activated in a stereotypic pattern. This pattern is composed of a two burst sequence occurring in synergist and antagonist muscles. The time course and duration of these bursts are relatively fixed but the burst magnitude in any one muscle varies in relation to the direction of movement and the preferred directional tuning characteristic of the muscle. This creates a highly adaptive method for generating fast movements to different positions in space. In this study we have examined the extent to which this adaptive burst behaviour can be associated with activity changes occurring in the contralateral motor cortex. Time dependent coherence estimates were obtained from simultaneous recordings of the electroencephalogram (EEG) made from the contralateral sensorimotor cortex and the electromyogram (EMG) from various wrist flexor and extensor muscles during fast point-to-point wrist tracking movements. Using the onset of movement as a trigger, event related coherence estimates reveal the presence of short lasting periods of low frequency (<12 Hz) coherence during the execution of fast wrist movements. The onset and duration of the periods of low frequency coherence vary with direction of movement and the temporal burst profile of a particular muscle's EMG activity. It is therefore likely that a significant low frequency activation of the motor cortex plays a part in the generation of the EMG burst patterns that underpin rapid point-to-point movements of the human wrist.

Geometrical aspects of aging and rejuvenation in the Ising spin glass: A numerical study

We present a comprehensive study of non-equilibrium phenomena in the low temperature phase of the Edwards-Anderson Gaussian spin glass in 3 and 4 spatial dimensions. Many effects can be understood in terms of a time dependent coherence length, $\ell_T$, such that length scales smaller that $\ell_T$ are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependence of $\ell_T$ is found to be compatible with critical power-law dynamical scaling for small times/high temperatures, crossing over to an activated logarithmic growth for longer times/lower temperatures, in agreement with recent experimental results. The activated regime is governed by a `barrier exponent' psi which we estimate to be psi ~ 1.0 and psi ~ 2.3 in 3 and 4 dimensions, respectively. We observe for the first time the rejuvenation and memory effects in the four dimensional sample, which, we argue, is unrelated to `temperature chaos'. Our discussion in terms of length scales allows us to address several experimentally relevant issues, such as super-aging versus sub-aging effects, the role of a finite cooling rate, or the so-called Kovacs effect.

Simultaneous phase control of Li2 wave packets in two electronic states

State-selective phase control of rotational Li2 wave packets, prepared simultaneously in the E(1∑g+) electronic state by one photon absorption and the A(1∑u+) electronic state by resonant impulsive stimulated Raman scattering, is demonstrated. Following the initial population of a rovibrational launch state on the A electronic potential energy curve with a cw laser, a single sub-picosecond wave packet preparation pulse centered near 800 nm simultaneously creates a two-state rotational wave packet in the E state (νE=18, JE=23 and 25) and a three-state rotational wave packet in the A state (νA=15, JA=22, 24, and 26). A temporally delayed 800 nm probe pulse subsequently ionizes both electronic components of the wave packet to allow measurement of the time-dependent coherence in these two electronic states. Via phase manipulation of resonant transition frequencies contained within the preparation pulse, the phases of the E(18,25) and A(15,26) quantum states are either varied concurrently or individually controlled, whereas the phases of the other rovibronic states of the wave packet are in all cases held essentially constant. This phase manipulation is shown to be more complex than a simple additive effect involving the phases applied to the resonant frequencies. These experimental results are compared with the predictions of second order time-dependent perturbation theory. Although systematic discrepancies exist, most likely due to an additional phase introduced during the two-photon probe process, once these differences are accounted for, good agreement is found between experiment and perturbation theory.

Time-Resolved Speckle Analysis: A New Approach to Coherence and Dephasing of Optical Excitations in Solids

A new method to measure the time-dependent coherence of both homogeneously and inhomogeneously broadened optical excitations in solids is presented. The coherence degree of resonantly excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). This method determines the decays of intensity and coherence separately, thus distinguishing lifetime from pure dephasing. The secondary emission of excitons in semiconductor quantum wells is investigated. Here the combination of static disorder and inelastic scattering leads to a partially coherent emission. The temperature dependence is well explained by phonon scattering.

Vertical spatial coherence model for a transient signal forward-scattered from the sea surface

The treatment of acoustic energy forward scattered from the sea surface, which is modeled as a random communications scatter channel, is the basis for developing an expression for the time-dependent coherence function across a vertical receiving array. The derivation of this model uses linear filter theory applied to the Fresnel-corrected Kirchhoff approximation in obtaining an equation for the covariance function for the forward-scattered problem. The resulting formulation is used to study the dependence of the covariance on experimental and environmental factors. The modeled coherence functions are then formed for various geometrical and environmental parameters and compared to experimental data.