What Can Local Transfer Entropy Tell Us about Phase-Amplitude Coupling in Electrophysiological Signals?

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).     

基于外光注入互耦合垂直腔面发射激光器的混沌随机特性研究

通过在互耦合垂直腔面发射激光器(VCSELs)系统中增加外光注入, 建立了一种基于偏振可调光反馈VCSEL驱动互耦合VCSELs混沌系统模型, 分析了增加外光驱动对互耦合激光器随机特性的影响. 以不可预测度作为随机特性的评价指标, 采用信息论中的排列熵作为相应量化工具, 对系统输出混沌信号的不可预测性进行定量分析.数值研究了光强度、时延、偏振旋转角度以及驱动激光器与耦合激光器间的频率失谐对输出信号随机特性的影响.结果表明: 外光注入能够增大互耦合VCSELs输出混沌信号的排列熵, 即外光注入能够有效提高耦合系统的随机特性; 驱动激光器可调偏振片偏转角度调节到45° 附近, 注入强度适中, 满足耦合强度大于驱动激光器自反馈强度条件, 系统输出信号的排列熵较大; 在耦合时延与驱动激光器反馈时延不相等的同时, 增加驱动激光器与耦合激光器频率失谐, 外光注入互耦合VCSELs的随机特性能够得到进一步提高.     

Learning alters theta amplitude, theta-gamma coupling and neuronal synchronization in inferotemporal cortex

Background

How oscillatory brain rhythms alone, or in combination, influence cortical information processing to support learning has yet to be fully established. Local field potential and multi-unit neuronal activity recordings were made from 64-electrode arrays in the inferotemporal cortex of conscious sheep during and after visual discrimination learning of face or object pairs. A neural network model has been developed to simulate and aid functional interpretation of learning-evoked changes.

Results

Following learning the amplitude of theta (4-8 Hz), but not gamma (30-70 Hz) oscillations was increased, as was the ratio of theta to gamma. Over 75% of electrodes showed significant coupling between theta phase and gamma amplitude (theta-nested gamma). The strength of this coupling was also increased following learning and this was not simply a consequence of increased theta amplitude. Actual discrimination performance was significantly correlated with theta and theta-gamma coupling changes. Neuronal activity was phase-locked with theta but learning had no effect on firing rates or the magnitude or latencies of visual evoked potentials during stimuli. The neural network model developed showed that a combination of fast and slow inhibitory interneurons could generate theta-nested gamma. By increasing N-methyl-D-aspartate receptor sensitivity in the model similar changes were produced as in inferotemporal cortex after learning. The model showed that these changes could potentiate the firing of downstream neurons by a temporal desynchronization of excitatory neuron output without increasing the firing frequencies of the latter. This desynchronization effect was confirmed in IT neuronal activity following learning and its magnitude was correlated with discrimination performance.

Conclusions

Face discrimination learning produces significant increases in both theta amplitude and the strength of theta-gamma coupling in the inferotemporal cortex which are correlated with behavioral performance. A network model which can reproduce these changes suggests that a key function of such learning-evoked alterations in theta and theta-nested gamma activity may be increased temporal desynchronization in neuronal firing leading to optimal timing of inputs to downstream neural networks potentiating their responses. In this way learning can produce potentiation in neural networks simply through altering the temporal pattern of their inputs.     

Measuring direction in the coupling of biological oscillators: a case study for electroreceptors of paddlefish

Recently developed methods for estimating directionality in the coupling between oscillators were tested on experimental time series data from electroreceptors of paddlefish, because each electroreceptor contains two distinct types of noisy oscillators. One type of oscillator is in the sensory epithelia, and another type is in the terminals of afferent neurons. Based on morphological organization and our previous work, we expected unidirectional coupling, whereby epithelial oscillations synaptically influence the spiking oscillators of afferent neurons. Using directionality analysis we confirmed unidirectional coupling of oscillators embedded in electroreceptors. We studied the performance of directionality algorithms for decreasing length of data. Also, we experimentally varied the strength of oscillator coupling, to test the effect of coupling strength on directionality algorithms.     

Synchronization in the BCS pairing dynamics as a critical phenomenon

Fermi gas with time-dependent pairing interaction hosts several different dynamical states. Coupling between the collective BCS pairing mode and individual Cooper pair states can make the latter either synchronize or dephase. We describe transition from phase-locked undamped oscillations to Landau-damped dephased oscillations in the collisionless, dissipationless regime as a function of coupling strength. In the dephased regime, we find a second transition at which the long-time asymptotic pairing amplitude vanishes. Using a combination of numerical and analytical methods we establish a continuous (type II) character of both transitions.     

Strong coupling of nonlinear electronic and biological oscillators: reaching the "amplitude death" regime

Interaction between an electronic and a biological circuit has been investigated for a pair of electrically connected nonlinear oscillators, with a spontaneously oscillating olivary neuron as the single-cell biological element. By varying the coupling strength between the oscillators, we observe a range of behaviors predicted by model calculations, including a reversible low-energy dissipation "amplitude death" where the oscillations in the coupled system cease entirely.     

Observation of interference between two distinct autoionizing states in dissociative photoionization of H2

Dissociative photoionization (DPI) of randomly oriented H(2) molecules has been studied using linearly polarized synchrotron radiation at selected photon energies of 31, 33, and 35 eV. Large amplitude oscillations in the photoelectron asymmetry parameter β, as a function of electron energy, have been observed. The phase of these β oscillations are in excellent agreement with the results of recent close coupling calculations [Fernández and Martín, New J. Phys. 11, 043020 (2009)]. We show that the oscillations are the signature of interferences between the 1Q(1)?(1)Σ(u)(+) and 1Q(2)?(1)Π(u) doubly excited states decaying at different internuclear distances. The oscillations thus provide information about the classical paths followed by the nuclei. The presence of such oscillations is predicted to be a general phenomenon in DPI.     

Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators

Experimental observations of time-delay-induced amplitude death in two coupled nonlinear electronic circuits that are individually capable of exhibiting limit-cycle oscillations are described. The existence of multiply connected death islands in the parameter space of coupling strength and time delay for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds [Phys. Rev. Lett. 80, 5109 (1998); Physica (Amsterdam) 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay, and the onset of both in-phase and antiphase collective oscillations.     

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.     

Specific Emitter Identification Based on Visibility Graph Entropy

The specific emitter identification(SEI) technique determines the unique emitter of a given signal by using some external feature measurements of the signal. It has recently attracted a great deal of attention because many applications can benefit from it. This work addresses the SEI problem using two methods, namely, the normalized visibility graph entropy(NVGE) and the normalized horizontal visibility graph entropy(NHVGE)based on treating emitters as nonlinear dynamical systems. Firstly, the visibility graph(VG) and the horizontal visibility graph(HVG) are used to convert the instantaneous amplitude, phase and frequency of received signals into graphs. Then, based on the information captured by the VG and the HVG, the normalized Shannon entropy(NSE) calculated from the corresponding degree distributions are utilized as the rf fingerprint. Finally, four emitters from the same manufacturer are utilized to evaluate the performance of the two methods. Experimental results demonstrate that both the NHVGE-based method and NVGE-based method are quite effective and they perform much better than the method based on the normalized permutation entropy(NPE) in the case of a small amount of data. The NVGE-based method performs better than the NHVGE-based method since the VG can extract more information than the HVG does. Moreover, our methods do not distinguish between the transient signal and the steady-state signal, making it practical.     

Coupled chaotic oscillators and their relation to a central pattern generator for artificial quadrupeds

Animal locomotion employs different periodic patterns known as animal gaits. In 1993, Collins and Stewart recognized that gaits possessed certain symmetries and characterized the gaits of quadrupeds and bipeds using permutation symmetry groups, which impose constraints on the locomotion center called the central pattern generator (CPG) in the animal brain. They modeled the CPG by coupling four nonlinear oscillators and found that it was possible to reproduce all symmetries of the gaits by changing the coupling strength. Here we propose to extend this idea using coupled chaotic oscillators synchronized using the Pyragas method in order to characterize the CPG symmetries. We also evaluate the time series behavior when the foot is in contact with the ground: this has potential robotic applications.     

Amplitude death in systems of coupled oscillators with distributed-delay coupling

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.     

Measuring causality by directional symbolic mutual information approach

We propose a novel measure to assess causality through the comparison of symbolic mutual information between the future of one random quantity and the past of the other. This provides a new perspective different from the conventional conceptions. Based on this point of view, a new causality index is derived that uses the definition of directional symbolic mutual information. This measure presents properties different from the time delayed mutual information since the symbolization captures the dynamic features of the analyzed time series. In addition to characterizing the direction and the amplitude of the information flow, it can also detect coupling delays. This method has the property of robustness, conceptual simplicity, and fast computational speed.     

A drive-free vibratory gyroscope

Computational and analytical works have shown that certain coupling schemes can lead to significant enhancements in sensitivity, accuracy, and lower costs for a wide range of sensor devices whose output and performance depends directly on the ability of individual units to generate stable limit cycle oscillations. Vibratory gyroscopes are very good candidates for this new paradigm as their accuracy and sensitivity are directly dependent on the ability of a driving signal to produce and maintain oscillations with stable amplitude, phase, and frequency. To achieve higher accuracy, we show proof of concept of a novel scheme: a drive-free coupled gyroscope system in which the coupling alone can lead to self-regulated limit cycle oscillations in the drive- and sense-axes with stable constant amplitude and phase-locking.     

Optimal Frequency and Amplitude of Vertical Viewpoint Oscillation for Improving Vection Strength and Reducing Neural Constrains on Gait

Inducing self-motion illusions referred as vection are critical for improving the sensation of walking in virtual environments (VE). Adding viewpoint oscillations to a constant forward velocity in VE is effective for improving vection strength under static conditions. However, the effects of oscillation frequency and amplitude on vection strength under treadmill walking conditions are still unclear. Besides, due to the visuomotor entrainment mechanism, these visual oscillations would affect gait patterns and be detrimental for achieving natural walking if not properly designed. This study was aimed at determining the optimal frequency and amplitude of vertical viewpoint oscillations for improving vection strength and reducing gait constraints. Seven subjects walked on a treadmill while watching a visual scene. The visual scene presented a constant forward velocity equal to the treadmill velocity with different vertical viewpoint oscillations added. Five oscillation patterns with different combinations of frequency and amplitude were tested. Subjects gave verbal ratings of vection strength. The mediolateral (M-L) center of pressure (CoP) complexity was calculated to indicate gait constraints. After the experiment, subjects were asked to give the best and the worst oscillation pattern based on their walking experience. The oscillation frequency and amplitude had strong positive correlations with vection strength. The M-L CoP complexity was reduced under oscillations with low frequency. The medium oscillation amplitude had greater M-L CoP complexity than the small and large amplitude. Besides, subjects preferred those oscillation patterns with large gait complexity. We suggested that the oscillation amplitude with largest M-L CoP complexity should first be chosen to reduce gait constraints. Then, increasing the oscillation frequency to improve vection strength until individual preference or the boundary of motion sickness. These findings provide important guidelines to promote the sensation of natural walking in VE.     

Measuring causality by taking the directional symbolic mutual information approach

We propose a novel measure to assess causality through the comparison of symbolic mutual information between the future of one random quantity and the past of the other.This provides a new perspective that is different from the conventional conceptions.Based on this point of view,a new causality index is derived that uses the definition of directional symbolic mutual information.This measure presents properties that are different from the time delayed mutual information since the symbolization captures the dynamic features of the analyzed time series.In addition to characterizing the direction and the amplitude of the information flow,it can also detect coupling delays.This method has the property of robustness,conceptual simplicity,and fast computational speed.     

Control of giant breathing motion in c60 with temporally shaped laser pulses

Femtosecond laser pulses tailored with closed-loop, optimal control feedback were used to excite oscillations in C60 with large amplitude by coherent heating of nuclear motion. A characteristic pulse sequence results in significant enhancement of C2 evaporation, a typical energy loss channel of vibrationally hot C60. The separation between subsequent pulses in combination with complementary two-color pump-probe data and time-dependent density functional theory calculations give direct information on the multielectron excitation via the t(1g) resonance followed by efficient coupling to the radial symmetric a(g)(1) breathing mode.     

链式互耦合半导体激光器的实时混沌同步

通过在互耦合外腔半导体激光器之间增加中继激光器,建立了一种链式互耦合半导体激光器混沌同步系统模型.理论分析了系统的实时混沌同步条件,数值研究了注入电流、互耦合条件、反馈条件等对系统实时混沌同步品质的影响,揭示了同步质量在反馈强度和互耦合强度二维参数空间的分布规律.结果表明:注入电流较大时,满足互耦合强度和反馈强度相同,互耦合延时和反馈延时相等,系统中所有激光器之间可同时实现稳定高品质实时混沌同步;中心激光器和边激光器之间的稳定实时混沌同步分布在在互耦合强度和反馈强度较小的区域以及互耦合强度和反馈强度相近的区域;边激光器之间由于同时接收到中心激光器实施的相同注入,能够较容易的实现稳定高品质的实时混沌同步.该系统可进一步扩展成为实现远距离的双向实时混沌同步或阵列激光器系统的实时混沌同步.     

Delay signatures in the chaotic intensity output of a quantum dot laser with optical feedback

Delay identification from the chaotic intensity output of a quantum dot laser with optical feedback is done using numerical and information theoretic techniques. Four quantifiers, namely autocorrelation function, delayed mutual information, permutation entropy and permutation statistical complexity, are employed in delay estimation. A detailed comparison of these quantifiers with different feedback rates and delay is undertaken. Permutation entropy and permutation statistical complexity are calculated with different dimensions of symbolic reconstruction to obtain the best results.     

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions.Jansen's neural mass model(NMM) was initially proposed to study the origin of alpha oscillations.Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods.In this study,we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM.First,the sigmoid nonlinear function in the NMM is approximated by its describing function,allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part.Second,by conducting a theoretical analysis,we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and,furthermore,accurately determine its amplitude and frequency.The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations.Furthermore,strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.