Zero Phase Lag Research Articles

Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve

Event Abstract Back to Event Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve Gamma oscillations (30-70 Hz) can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices in which gamma was induced by tetanus. Additionally, oscillations the gamma band can synchronize with nonzero phase lag between pairs of EEG electrodes. There are two mechanisms by which long range synchronization could occur: by locking to a common input or via reciprocal coupling. Here we address phase-locking that arises via bidirectional coupling of two limit cycle oscillators with a conduction delay. It is often implied that for two distal oscillators, phase lags equal to the conduction delay are expected, and how synchronization can take place over long distances in a stable manner is considered an open question. Here we assume that under conditions in which two local circuit generators of gamma oscillations arise separated by some distance, these circuits function as intrinsic nonlinear oscillators that are bidirectionally coupled with a conduction delay. Nothing is assumed regarding the oscillators other than that the phase response curve (PRC) can be measured using an input that approximates the one received from the other oscillator, and that the effect of the coupling is dissipated within one network period such that the coupling is effectively pulsatile. Here we derive existence and stability criteria based on the PRC for phase locking with delays of any length, and test them on oscillators with a wide variety of PRCs and varying levels of heterogeneity. The method is accurate for any shape PRC that we examined and therefore very general. For identical frequencies, identical coupling strength, and identical delays, synchrony emerges as a consequence of symmetry. We show that for both homogenous and heterogenous networks, in phase synchronization alternates with out of phase synchronization as the delay is increased, with regions of bistability in the intermediate values. In practice, the frequencies of the local circuits are unlikely to be identical; therefore, the cycle periods need to be altered via phase resetting in order to reach a common frequency. If the coupling is strong, as it must be in order for synchronization to occur rapidly, and the frequencies, conduction delays and PRCs of the oscillators are similar, then the input to each neuron will arrive at a similar phase, resulting in a small phase lag in the firing times. The stability of the phase locking depends upon the slope of the phase resetting curve at the phase at which the input is received in the phase locked mode. In other circuits, the conduction delays are asymmetric, in which case additional mechanisms may be required to achieve near zero phase lag. Having an explicit and general solution for the existence and stability of in phase locking with delay can provide insight into how such locking is achieved in the brain. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.139 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 02 Feb 2009; Published Online: 02 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Bistable Network Behavior of Layer I Interneurons in Auditory Cortex

GABAergic interneurons in many areas of the neocortex are mutually connected via chemical and electrical synapses. Previous computational studies have explored how these coupling parameters influence the firing patterns of interneuronal networks. These models have predicted that the stable states of such interneuronal networks will be either synchrony (near zero phase lag) or antisynchrony (phase lag near one-half of the interspike interval), depending on network connectivity and firing rates. In certain parameter regimens, the network can be bistable, settling into either stable state depending on the initial conditions. Here, we investigated how connectivity parameters influence spike patterns in paired recordings from layer I interneurons in brain slices from juvenile mice. Observed properties of chemical and electrical synapses were used to simulate connections between uncoupled cells via dynamic clamp. In uncoupled pairs, action potentials induced by constant depolarizing currents had randomly distributed phase differences between the two cells. When coupled with simulated chemical (inhibitory) synapses, however, these pairs exhibited a bimodal firing pattern, tending to fire either in synchrony or in antisynchrony. Combining electrical with chemical synapses, prolonging tau(Decay) of inhibitory connections, or increasing the firing rate of the network all resulted in enhanced stability of the synchronous state. Thus, electrical and inhibitory synaptic coupling constrain the relative timing of spikes in a two-cell network to, at most, two stable states, the stability and precision of which depend on the exact parameters of coupling.

Estimation of the vocal tract transfer function with application to glottal wave analysis

A new method for determining the vocal tract transfer function for voiced speech is proposed. The method exploits the frequency domain characteristics of voiced speech and the concepts of minimum-phase systems. The short-time spectrum of voiced speech contains information about the glottal source and vocal tract filter components. In voiced speech there is usually a small frequency gap between the glottal source peak frequency response and the first formant of the vocal tract. The inherent inability of linear prediction parametric modelling in discriminating between closely spaced frequency components can make accurate modelling/estimation of the first formant (in the presence of a close and elevated peak due to the glottal flow) in voiced speech very difficult. A fixed pre-emphasis (single-pole, high-pass filter), commonly used in existing inverse filtering methods to reduce the influence of the glottal source, is not guaranteed to give the desired result across a range of voice types e.g. breathy, pressed and modal. The proposed method overcomes this problem by suppressing the glottal wave contribution using a dynamic, multi-pole, zero-phase lag high-pass filter, prior to analysis. In addition to minimising the influence of the glottal source, an expanded analysis region is provided in the form of a pseudo-closed phase. The technique also takes into cognizance the time varying nature of the vocal tract filter by determining, adaptively, an optimum vocal tract filter function using the properties of minimum phase systems. The performance of the new method is evaluated using synthesized and real speech. The results show that, under certain conditions, the method estimates the vocal tract formants and bandwidths more accurately than an existing closed phase inverse filtering technique.

Sensorless control of interior permanent-magnet machine drives with zero-phase lag position estimation

This paper presents an improved method to estimate rotor motion states for an interior permanent-magnet machine drive. This approach is based on the estimation of a saliency-based electromotive force (EMF) in the stationary reference frame using a state filter. The spatial information obtained from the estimated saliency-based EMF is used in an observer to estimate the motor motion states. By using the commanded torque as a feedforward input to the observer, the motion state estimation has zero-phase lag, providing a very-high-bandwidth estimate.

A Study on the Dynamic Characteristics of an ER Fluid Controlled Displacement Transmitter with Two Output Units

In this paper, a novel array-type dynamic displacement output transmitter utilizing the tunable viscoelastic property of the electrorheological fluid as a control valve mechanism is studied. The characteristics of this ER valve are modeled theoretically and its major design parameters are identified thereafter. In addition, by applying electric field upon the concentric electrodes of the ER valve, the controllability of the output displacement due to the change in the stiffness and damping properties of the ER fluid is investigated experimentally. It is found that the cross-talk between two output units is insignificant in this design setup and therefore, two units can be operated independently. Finally, the transient responses of the output fluid chamber under the pulse-type controlled electric field with different duty time and phase are measured. It is concluded that under the sinusoidal excitation of the displacement amplitude, the output chamber can have minimal response as the controlled electric field is at its highest permissible magnitude and zero phase lag.

A Field Theory of Consciousness

This article summarizes a variety of current as well as previous research in support of a new theory of consciousness. Evidence has been steadily accumulating that information about a stimulus complex is distributed to many neuronal populations dispersed throughout the brain and is represented by the departure from randomness of the temporal pattern of neural discharges within these large ensembles. Zero phase lag synchronization occurs between discharges of neurons in different brain regions and is enhanced by presentation of stimuli. This evidence further suggests that spatiotemporal patterns of coherence, which have been identified by spatial principal component analysis, may encode a multidimensional representation of a present or past event. How such distributed information is integrated into a holistic percept constitutes the binding problem. How a percept defined by a spatial distribution of nonrandomness can be subjectively experienced constitutes the problem of consciousness. Explanations based on a discrete connectionistic network cannot be reconciled with the relevant facts. Evidence is presented herein of invariant features of brain electrical activity found to change reversibly with loss and return of consciousness in a study of 176 patients anesthetized during surgical procedures. A review of relevant research areas, as well as the anesthesia data, leads to a postulation that consciousness is a property of quantumlike processes, within a brain field resonating within a core of structures, which may be the neural substrate of consciousness. This core includes regions of the prefrontal cortex, the frontal cortex, the pre- and paracentral cortex, thalamus, limbic system, and basal ganglia.

A self calibration method using a soft clustering procedure for eye movement recordings

A nearly automatic method for calibrating eye movement records has been developed. This very robust method is based on a soft clustering algorithm which allows exploration of the whole range of eye movement records for reliable calibration. In contrast to many other methods which carry out the calibration on several discrete points, this method is suitable for continuous determination of the transfer function of the eye movement transducer. Moreover it simultaneously uses the combined properties of vestibulo-ocular reflex, neck-to-eye reflex and smooth pursuit system to reach approximately a unity gain and zero phase lag (in subjects with no severe vestibular disorders or ocumomotor palsy). In addition, this method does not rely heavily on the degree of attention of the subject. The method is particularly suited for the calibration of non linear or noisy transducers like Electro Oculography (EOG). Calibration is performed within a few seconds. So when necessary in clinical applications it is possible to repeat calibrations frequently.

Modelling the perceptual segregation of double vowels with a network of neural oscillators

The ability of listeners to identify two simultaneously presented vowels can be introducing a difference in fundamental frequency (F0) between the vowels. We propose an explanation for this phenomenon in the form of a computational model of concurrent sound segregation, which is motivated by neurophysiological evidence of oscillatory firing activity in the auditory cortex and thalamus. More specifically, the model represents the perceptual grouping of auditory frequency channels as synchronised (phase-locked zero phase lag) oscillations in a neural network. Computer simulations on a vowel set used in psychophysical studies confirm that the model qualitatively matches the performance of human listeners; vowel identification performance increases with increasing difference in F0. Additionally, the model is able to replicate other findings relating to the perception of harmonic complexes in which one component is mistuned.

Coherency and connectivity in oscillating neural networks: linear partialization analysis.

This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works.

Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo.

1. We have shown previously, with experimental and computer models, how a '40 Hz' (gamma) oscillation can arise in networks of hippocampal interneurones, involving mutual GABAA-mediated synaptic inhibition and a source of tonic excitatory input. Here, we explore implications of this model for some hippocampal network phenomena in the rat in vitro and in vivo. 2. A model network was constructed of 1024 CA3 pyramidal cells and 256 interneurones. AMPA (alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid), NMDA (N-methyl-D-aspartate), GABAA and GABAB receptors were simulated on pyramidal cells and on interneurones. 3. In both model and experiment, the frequency of network oscillations, in the gamma range, depended upon three parameters: GABAA conductance and decay time constant in interneurone-->interneurone connections, and the driving current to the interneurones. 4. The model of gamma rhythm predicts an average zero phase lag between firing of pyramidal cells and interneurones, as observed in the rat hippocampus in vivo. The model also reproduces a gamma rhythm whose frequency changes with time, at theta frequency (about 5 Hz). This occurs when there is 5 Hz modulation of a tonic signal to chandelier and basket cells. 5. Synchronized bursts can be produced in the model by several means, including partial blockade of GABAA receptors or of AMPA receptors on interneurones, or by augmenting AMPA-mediated EPSCs. In all of these cases, the burst can be followed by a 'tail' of transiently occurring gamma waves, a phenomenon observed in the hippocampus in vivo following sharp waves. This tail occurs in the model because of delayed excitation of the interneurones by the synchronized burst. A tail of gamma activity was found after synchronized epileptiform bursts both in the hippocampal slice (CA3 region) and in vivo. 6. Our data suggest that gamma-frequency EEG activity arises in the hippocampus when pools of interneurones receive a tonic or slowly varying excitation. The frequency of the oscillation depends upon the strength of this excitation and on the parameters regulating the inhibitory coupling between the interneurones. The interneurone network output is then imposed upon pyramidal neurones in the form of rhythmic synchronized IPSPs.

Modeling and canceling tremor in human-machine interfaces

Zero-phase modeling and canceling of tremor can improve precision in human-machine control applications. Past methods of tremor suppression have been hindered by feedback delays due to phase lag and by the inability to track tremor frequency over time. The weighted-frequency Fourier linear combiner (WFLC) is an adaptive noise canceller that precisely models tremor with zero phase lag. This article briefly presents the WFLC algorithm and describes its application to computer input filtering, clinical tremor quantification, and active tremor canceling for microsurgery.