Slow Excitation Research Articles

Asymmetric neuromodulation in the respiratory network contributes to rhythm and pattern generation.

Like other brain circuits, the brainstem respiratory network is continually modulated by neurotransmitters that activate slow metabotropic receptors. In many cases, activation of these receptors only subtly modulates the respiratory motor pattern. However, activation of some receptor types evokes the arrest of the respiratory motor pattern as can occur following the activation of µ-opioid receptors. We propose that the varied effects of neuromodulation on the respiratory motor pattern depend on the pattern of neuromodulator receptor expression and their influence on the excitability of their post-synaptic targets. Because a comprehensive characterization of these cellular properties across the respiratory network remains challenging, we test our hypothesis by combining computational modelling with ensemble electrophysiologic recording in the pre-Bötzinger complex (pre-BötC) using high-density multi-electrode arrays (MEA). Our computational model encapsulates the hypothesis that neuromodulatory transmission is organized asymmetrically across the respiratory network to promote rhythm and pattern generation. To test this hypothesis, we increased the strength of neuromodulatory connections in the model and used selective agonists in situ while monitoring pre-BötC ensemble activities. The model predictions of increasing slow inhibition were consistent with experiments examining the effect of systemic administration of the 5HT1aR agonist 8-OH-DPAT. Similarly, the predicted effects of increasing slow excitation in the model were experimentally confirmed in pre-BötC ensemble activities before and after systemic administration of the µ-opioid receptor agonist fentanyl. We conclude that asymmetric neuromodulation can contribute to respiratory rhythm and pattern generation and accounts for its varied effects on breathing.

Full-wave simulations on helicon and parasitic excitation of slow waves near the edge plasma

Helicon waves are thought to be promising in various tokamaks, such as DIII-D, because they can penetrate reactor-grade high-density cores and drive the off-axis current with higher efficiency. In the frequency regime ∼ 476 MHz, both slow electrostatic and fast electromagnetic helicon waves can coexist in DIII-D. If the antenna parasitically excites the slow mode, these waves can propagate along the magnetic field line into the scrape-off layer (SOL). Although the importance of the misalignment of the Faraday screen and the electron density in the SOL on the excitation and propagation of slow modes is well known, the conditions for minimizing slow mode excitation have yet to be optimized. Using the Petra-M simulation code in the 2D domain, we analyze the effects of the misalignment of the antenna in the poloidal direction, the misalignment of the Faraday screen in the toroidal direction, and the density in front of the antenna on slow mode generation. Our results suggest that the misalignment of the Faraday screen is a critical factor in reducing the slow mode and that the misalignment angle should be below ∼ 5° to minimize the slow wave excitation. When the electron density is higher than 3.5×1018 m−3 in the SOL, the generation of the slow mode from the antenna is minimized and unaffected by the misalignment of the Faraday screen.

Bifurcations and mixed mode oscillations in a bi-stable plasma model with slow parametric excitation.

In this study, considering a bi-stable plasma model with slow parametric excitation, the bifurcation of periodic and chaotic responses as well as the resulting fast-slow motions is discussed analytically and numerically. For a nonautonomous fast sub-system, the generalized harmonic balancing method is utilized to obtain an averaged system. Bifurcation analysis about the averaged system shows that the critical manifolds form a S-shape structure. Meanwhile, supercritical and subcritical period doubling (PD) occurs on the upper branch simultaneously. As the frequency of the external excitation changes, bifurcation points on the limit cycle manifolds can present different relative locations. Moreover, an additional bi-stable structure induced by Cusp bifurcation emanates from the upper branch. On the other hand, the existence of a chaotic attractor and the corresponding boundary crisis phenomenon are verified using the Melnikov method and the basin of attraction. The structures of the numerical bifurcation diagram show good agreements with the analytical results. Considering two cases of low-frequency excitation, the corresponding fast-slow dynamics are discussed. It is found that, when the fast-slow flow passing the subcritical PD point, a low frequency with different magnitudes will lead to two patterns of bifurcation delay, i.e., the typical one and the excessive delay, which suppress the PD. As for the boundary crisis point, the slow passage effects show no distinct influence. Thus, three transition mechanisms based on two cases of the bifurcation structure are explained, including "fold of cycle-fold of cycle" type, "fold of cycle-delayed subcritical PD" type, and "fold of cycle-boundary crisis" type.

Three-Dimensional Dynamic Modelling and Analysis of a Dual-Cable Winding Hoisting System

In this paper, a three-dimensional dynamic model of a dual-cable winding hoisting system is presented to simulate and analyze its coupled vibrations. The equations of motion of this system are derived based on a substructure method and Lagrange’s equations of the first kind, in which the longitudinal–torsional coupled mechanical characteristics of the hoisting cables are considered. Longitudinal and transverse natural frequencies of the system are obtained and studied, and its dynamic responses due to some assumed displacement excitations are calculated. Numerical results agree well with those from ADAMS simulation, and the results have shown that longitudinal and transverse resonances are inevitable, but the transverse resonance has little effect on the conveyance; Slow longitudinal excitations should be avoided, thus avoiding the first-order longitudinal resonance since the system longitudinal vibration is dominated by its first-order mode; the torque in the hoisting cable is mainly induced by its tension under longitudinal–torsional coupled mechanical characteristics of the cable, and a torque release device is suggested to protect the hoisting cable from torsion failure; Torsional and transverse vibrations of the conveyance are been well restricted by the guiding cables even when the guiding cable pre-tension is zero. The results of this paper can be used to improve the parameter design of the ultra-deep shaft hoisting systems.

Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations

This paper aims to report the fast–slow dynamics in the Rayleigh oscillator with two slow square wave excitations. Typically, a square wave excitation is a periodic excitation that has instantaneous alternation between maximum and minimum amplitude levels, which may trigger a transient response in the system. We show that, by introducing two square wave excitations with multiple frequencies, fast–slow oscillations with catastrophic jumps can be observed in the Rayleigh oscillator. Then, we explain the generation mechanisms of these fast–slow oscillations based on the fast–slow analysis, in which the two slow square wave excitations with different frequencies are transformed based on their frequency ratio, and subsequently treated as a single slow variable. Our study shows that square wave excitations play a crucial role in determining the fast–slow dynamics of the system. Under the control of square wave excitations, the equilibrium can exhibit rapid jumps in different levels, and the variation of amplitude of the limit cycle is not gradual, characterized by instantaneous increase and decrease. Such phenomenon can be referred to as the step-shaped sharp transition of attractor, which accounts for the generation of fast–slow oscillations. Furthermore, with the increase of the frequency ratios, the rectangular-pulse-shaped explosion can be created in the solutions branches of the fast subsystem, which thus leads to fast–slow oscillations with multiple catastrophic jumps. Based on this, the fast–slow oscillations of point–point type and fast–slow oscillations of cycle–cycle type are revealed.

Causal phase-dependent control of non-spatial attention in human prefrontal cortex

Non-spatial attention is a fundamental cognitive mechanism that allows organisms to orient the focus of conscious awareness towards sensory information that is relevant to a behavioural goal while shifting it away from irrelevant stimuli. It has been suggested that attention is regulated by the ongoing phase of slow excitability fluctuations of neural activity in the prefrontal cortex, a hypothesis that has been challenged with no consensus. Here we developed a behavioural and non-invasive stimulation paradigm aiming at modulating slow excitability fluctuations of the inferior frontal junction. Using this approach, we show that non-spatial attention can be selectively modulated as a function of the ongoing phase of exogenously modulated excitability states of this brain structure. These results demonstrate that non-spatial attention relies on ongoing prefrontal excitability states, which are probably regulated by slow oscillatory dynamics, that orchestrate goal-oriented behaviour.

Pathological neurons generate ripples at the UP-DOWN transition disrupting information transfer.

To confirm and investigate why pathological high-frequency oscillations (pHFOs), including ripples (80-200 Hz) and fast ripples (200-600 Hz), are generated during the UP-DOWN transition of the slow wave and if information transmission mediated by ripple temporal coupling is disrupted in the seizure-onset zone (SOZ). We isolated 217 total units from 175.95 intracranial electroencephalography (iEEG) contact-hours of synchronized macro- and microelectrode recordings from 6 patients. Sleep slow oscillation (.1-2 Hz) epochs were identified in the iEEG recording. iEEG HFOs that occurred superimposed on the slow wave were transformed to phasors and adjusted by the phase of maximum firing in nearby units (i.e., maximum UP). We tested whether, in the SOZ, HFOs and associated action potentials (APs) occur more often at the UP-DOWN transition. We also examined ripple temporal correlations using cross-correlograms. At the group level in the SOZ, HFO and HFO-associated AP probability was highest during the UP-DOWN transition of slow wave excitability (p < < .001). In the non-SOZ, HFO and HFO-associated AP was highest during the DOWN-UP transition (p < < .001). At the unit level in the SOZ, 15.6% and 20% of units exhibited more robust firing during ripples (Cohen's d = .11-.83) and fast ripples (d = .36-.90) at the UP-DOWN transition (p < .05 f.d.r. corrected), respectively. By comparison, also in the SOZ, 6.6% (d = .14-.30) and 8.5% (d = .33-.41) of units had significantly less firing during ripples and fast ripples at the UP-DOWN transition, respectively. Additional data shows that ripple and fast ripple temporal correlations, involving global slow waves, between the hippocampus, entorhinal cortex, and parahippocampal gyrus were reduced by >50% in the SOZ compared to the non-SOZ (N = 3). The UP-DOWN transition of slow wave excitability facilitates the activation of pathological neurons to generate pHFOs. Ripple temporal correlations across brain regions may be important in memory consolidation and are disrupted in the SOZ, perhaps by pHFO generation.

On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings

Multiple timescale effects can be reflected bursting oscillations in many classical nonlinear oscillators. In this work, we are concerned about the bursting oscillations induced by two timescale effects in the damped Helmholtz-Rayleigh-Duffing oscillator (written as DHRDO for short) excited by slow-changing parametrical and external forcings. By using trigonometric function variation and authenticating the slow excitations as a slowly varying state variable, the time-varying DHRDO can be rewritten as a new time-invariant system. Then, the critical conditions of some typical bifurcations are presented by bifurcation theory. With the help of bifurcation analyses, six bursting patterns, i.e., ‘Hopf/Hopf-Hopf/Hopf’ bursting, ‘fold/Homoclinic-Hopf/Hopf’ bursting, ‘fold/Homoclinic/Hopf’ bursting, ‘Hopf/fold/Homoclinic/Hopf’ bursting, ‘Hopf/Homoclinic/Homoclinic/Hopf’ bursting and ‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’ bursting, are explored by the slow/fast decomposition method and the other techniques. Our findings provide different forms of the excited state oscillation modes as well as the bursting patterns. In addition, we use the numerical simulation to prove the correctness of the theoretical analyses.

Sliding bursting oscillations related to transcritical bifurcation delay in an excited vector field with frequency switching

The purpose of this paper is to report sliding bursting dynamics related to transcritical bifurcation delay, a common route to bursting dynamics. As an example, a simple nonlinear oscillator with a slow parametric excitation is considered, in which bursting oscillations resulted from transcritical bifurcation delay can be observed. Typically, such oscillations exhibit prolonged rest phases, characterized by the oscillations that moves along the unstable origin of the system. We show that interesting dynamical characteristics can be observed in the bursting oscillations if the excitation frequency switches between two different values. In particular, additional rest phases, i.e., the newly created non-zero sliding behaviors, characterized by that the trajectory slides along the frequency switching threshold for some time, can be exhibited in the presence of frequency switching. This forms the so-called sliding bursting oscillations. Then, we investigate the dynamical mechanisms of these oscillations and explore their transitions in relation to the variation of frequency switching threshold. As a result, several different patterns of sliding bursting oscillations are obtained. In particular, we find that sliding bursting oscillations may diverge to infinity for some threshold windows, and this can be understood by the analysis of attracting basins.

Unravelling the fluorescence kinetics of light-harvesting proteins with simulated measurements

The plant light-harvesting pigment-protein complex LHCII is the major antenna sub-unit of PSII and is generally (though not universally) accepted to play a role in photoprotective energy dissipation under high light conditions, a process known Non-Photochemical Quenching (NPQ). The underlying mechanisms of energy trapping and dissipation within LHCII are still debated. Various models have been proposed for the underlying molecular detail of NPQ, but they are often based on different interpretations of very similar transient absorption measurements of isolated complexes. Here we present a simulated measurement of the fluorescence decay kinetics of quenched LHCII aggregates to determine whether this relatively simple measurement can discriminate between different potential NPQ mechanisms. We simulate not just the underlying physics (excitation, energy migration, quenching and singlet-singlet annihilation) but also the signal detection and typical experimental data analysis. Comparing this to a selection of published fluorescence decay kinetics we find that: (1) Different proposed quenching mechanisms produce noticeably different fluorescence kinetics even at low (annihilation free) excitation density, though the degree of difference is dependent on pulse width. (2) Measured decay kinetics are consistent with most LHCII trimers becoming relatively slow excitation quenchers. A small sub-population of very fast quenchers produces kinetics which do not resemble any observed measurement. (3) It is necessary to consider at least two distinct quenching mechanisms in order to accurately reproduce experimental kinetics, supporting the idea that NPQ is not a simple binary switch.

Effect of short-term plasticity on working memory

The way in which persistent firing activity and synaptic plasticity are orchestrated to underlie working memory in recurrent neural networks is not fully understood. Here, we build a continuous attractor network of pyramidal cells and interneurons to simulate an oculomotor delayed response task. Both short-term facilitation (STF) and short-term depression (STD) manifest at synapses between pyramidal cells. The efficacy of individual synapses depends on the time constants of STF and STD as well as the presynaptic firing rate. Self-sustained firing activity (i.e., a bump attractor) during the delay period encodes the cue position. The bump attractor becomes more robust against random drifts and distractions with enhancing STF or reducing STD. Keeping STF and STD at appropriate levels is crucial for optimizing network performance. Our results suggest that, besides slow recurrent excitation and strong global inhibition, short-term plasticity plays a prominent role in facilitating mnemonic behavior.

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations.

In this paper, we consider novel bursting energy harvesting under combined external and parametrical slow excitations, and a harvester is realized by employing an externally and parametrically excited post-buckled beam. Based on the method of fast-slow dynamics analysis, multiple-frequency oscillation, with two slow commensurate excitation frequencies, is used to observe complex bursting patterns, the behaviors of the bursting response are presented, and some novel one-parameter bifurcation patterns are observed. Furthermore, the bursting harvesting performances of the single and the two slow commensurate excitation frequencies are compared, and it was found that the two slow commensurate excitation frequencies can be used to improve the harvesting voltage.

Multichannel modulation of depolarizing and repolarizing ion currents increases the positive rate‐dependent action potential prolongation

Prolongation of the action potential duration (APD) could prevent reentrant arrhythmias if prolongation occurs at the fast excitation rates of tachycardia with minimal prolongation at slow excitation rates (i.e., if prolongation is positive rate-dependent). APD prolongation by current anti-arrhythmic agents is either reverse (larger APD prolongation at slow rates than at fast rates) or neutral (similar APD prolongation at slow and fast rates), which may not result in an effective anti-arrhythmic action. In this report we show that, in computer models of the human ventricular action potential, the combined modulation of both depolarizing and repolarizing ion currents results in a stronger positive rate-dependent APD prolongation than modulation of repolarizing potassium currents. A robust positive rate-dependent APD prolongation correlates with an acceleration of phase 2 repolarization and a deceleration of phase 3 repolarization, which leads to a triangulation of the action potential. A positive rate-dependent APD prolongation decreases the repolarization reserve with respect to control, which can be managed by interventions that prolong APD at fast excitation rates and shorten APD at slow excitation rates. For both computer models of the action potential, ICaL and IK1 are the most important ion currents to achieve a positive rate-dependent APD prolongation. In conclusion, multichannel modulation of depolarizing and repolarizing ion currents, with ion channel activators and blockers, results in a robust APD prolongation at fast excitation rates, which should be anti-arrhythmic, while minimizing APD prolongation at slow heart rates, which should reduce pro-arrhythmic risks.

Laser–Plasma Wake Velocity Control by Multi-Mode Beatwave Excitation in a Channel

The phase velocity of a laser-driven wakefield can be efficiently controlled in a plasma channel. A beatwave of two long laser pulses is used. The frequency difference between these two laser pulses equals the local plasma frequency, so that the slow resonant excitation of the plasma wave is possible. Because the driver energy is spread over many plasma periods, the interference pattern can run with an arbitrary velocity along the channel and generate the wakefield with the same phase velocity. This velocity is defined by the channel radius and the structure of laser transverse modes excited in the channel. The wake velocity can be matched exactly to the witness velocity. This can be the vacuum speed of light for ultra-relativistic witnesses, or subluminal velocities for low-energy, weakly relativistic witnesses such as muons.

Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam harvester under fast–slow excitation

Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam harvester under fast–slow excitation

Sufficient conditions and criteria for the pulse-shaped explosion related to equilibria in a class of nonlinear systems

The pulse-shaped explosion (PSE) is a novel sharp transition behavior which can give rise to bursting oscillations. Exploring a general theory applied to PSE is an important problem in the research of PSE. In this paper, we propose a two-dimensional ordinary differential equation (ODE), which can represent a class of dynamical systems with multiple-frequency slow excitations, and contribute to the theoretical understanding of the generation of PSE. Based on the fast–slow analysis, we firstly transform the ODE with multiple-frequency slow excitations into the one with a single slow variable, and thus we can obtain the fast subsystem, based on which the sufficient conditions for the existence of PSE related to equilibria are given. Then, we analyze the sufficient conditions for PSE by considering the behavior of the equilibrium theoretically. Besides, the criteria of different PSE patterns related to equilibria are developed to investigate different manifestations of PSE. Finally, the validity of the theoretical analysis is showed by numerical results of several concrete examples satisfying the class of ODE given in this paper. Our results provide the sufficient conditions and criteria for PSE involved in the proposed ODE family, and facilitate one to generate any desired dynamical systems exhibiting PSE within the framework of the suggested equation form.

Study on the Solidification Mechanism of Cr in Ettringite and Friedel’s Salt

The solidification of heavy metal Cr has always been a challenge in the treatment of Cr-containing wastes, due to its high mobility in alkaline environments. In addition, the solidification mechanism of Cr has not been fully investigated. In this study, blast furnace slag (BFS)-based cementitious materials were used as binders for the immobilization of heavy metal Cr to investigate the solidification mechanism of Cr in different hydration products. From XRD, FTIR, XPS, and XANES analyses, it could be seen that SO42− in ettringite was replaced by Cr in the form of CrO42−, making SO42− re-dissolve in the liquid phase. The SO42− in the solution would compete with CrO42− ions, leading to the direct influence of SO42− content on the solidification efficiency of Cr. In ettringite, Cr mainly existed in the form of Cr6+, accounting for more than 84% however, Cr was solidified in Friedel’s salt under two coexisting valence states (Cr6+ and Cr3+). This resulted not only from the slow excitation rate of the BFS in the cementitious system that did not contain sulfate, but also from the existence of a certain amount of reducing substances in the BFS, such as Fe2+ and S2−, which could reduce some of Cr6+ to Cr3+. In Friedel’s salt, the residual Cr6+ replaced Cl− in the form of CrO42−, whereas the Cr3+ replaced Al3+. The binding energies of Cr 2p3/1 and Cr 2p3/2 decreased with the addition of Cr, indicating that the coordination numbers of Cr3+ and Cr6+ increased, and that the binding energies of Cr3+ and Cr6+ decreased after entering the structure of Friedel’s salt.

Small perturbation of excitation frequency leads to complex fast–slow dynamics

Fast–slow oscillations are frequently encountered in dynamical systems with slow excitations. The excitation frequencies are often disturbed by various factors. However, the effects of excitation frequency perturbation on fast–slow oscillations are rarely reported. Here the Duffing system is taken as an example, in which typical fast–slow oscillations can be observed. The present paper aims to report the effects of a small perturbation of excitation frequency on the fast–slow oscillations. Typically, complex fast–slow dynamics can be observed if a small perturbation of excitation frequency is introduced. The generation of complex fast–slow oscillations is revealed by using the frequency conversion fast–slow analysis. This study shows that a small perturbation of excitation frequency may complicate the vector field of the fast subsystem, which thus leads to complex bifurcation behaviors and finally gives rise to complex fast–slow oscillations. In particular, the smaller the excitation frequency perturbation, the more complex are the fast–slow oscillations.

Positive rate-dependent action potential prolongation by modulating potassium ion channels.

Pharmacological agents that prolong action potential duration (APD) to a larger extent at slow rates than at the fast excitation rates typical of ventricular tachycardia exhibit reverse rate dependence. Reverse rate dependence has been linked to the lack of efficacy of class III agents at preventing arrhythmias because the doses required to have an antiarrhythmic effect at fast rates may have pro‐arrhythmic effects at slow rates due to an excessive APD prolongation. In this report, we show that, in computer models of the ventricular action potential, APD prolongation by accelerating phase 2 repolarization (by increasing IKs) and decelerating phase 3 repolarization (by blocking IKr and IK1) results in a robust positive rate dependence (i.e., larger APD prolongation at fast rates than at slow rates). In contrast, APD prolongation by blocking a specific potassium channel type results in reverse rate dependence or a moderate positive rate dependence. Interventions that result in a strong positive rate dependence tend to decrease the repolarization reserve because they require substantial IK1 block. However, limiting IK1 block to ~50% results in a strong positive rate dependence with moderate decrease in repolarization reserve. In conclusion, the use of a combination of IKs activators and IKr and IK1 blockers could result in APD prolongation that potentially maximizes antiarrhythmic effects (by maximizing APD prolongation at fast excitation rates) and minimizes pro‐arrhythmic effects (by minimizing APD prolongation at slow excitation rates).

Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation

The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order systems. The pitchfork bifurcation, Hopf bifurcation and limit cycle bifurcation are discussed in detail, and it was found that Hopf bifurcation only happens while the fractional order is bigger than 1. On the other hand, the influence of the amplitude of parametric excitation on cluster oscillation models is discussed. The results show that amplitude regulates cluster oscillation models with different bifurcation types. The point–point cluster oscillation only relates to pitchfork bifurcation. The point–cycle cluster oscillation includes pitchfork bifurcation and Hopf bifurcation. The point–cycle–cycle cluster oscillation involves three kinds of bifurcation, i.e., the pitchfork bifurcation, Hopf bifurcation and limit cycle bifurcation. The larger the amplitude, the more bifurcation types are involved. The research results of cluster oscillation and its generation mechanism will provide valuable theoretical basis for mechanical manufacturing and engineering practice.