Frequency Entrainment Research Articles

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle.

A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to time-dependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction δ of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and δ was varied over the range 0.1≤δ≤1. Reducing δ was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at δ=0.1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles.

Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

Commentary on Some Recent Theses Relevant to Combating Aging: August 2017.

Theses reviewed in this issue include "Engineering Cellular Input-Output for the Robust Control of Mammalian Cell-Based Therapies"; "Enzyme-Instructed Self-Assembly (EISA) Selectively Targets Cancer Cells"; "Exploration of helminth-derived immunoregulatory molecules as options for therapeutic intervention in allograft rejection and autoimmune disease"; "Expression of the Medial HOXA genes is indispensible for self-renewal in human hematopoietic stem cells"; "Gamma frequency entrainment attenuates amyloid load and modifies microglia"; and "Heterogeneous Distribution of Microvascular Blood Flow Contributes to Impaired Skeletal Muscle Oxygenation in Diabetes".

Can Rhythmic Sensory Stimulation Decrease Cognitive Decline in Alzheimer's Disease?: A Clinical Case Study

Background/Objectives: To present Rhythmic Sensory Stimulation (RSS) as a potential new treatment of Alzheimer’s disease (AD).Design: Longitudinal case study over a three year period.Setting: RSS was provided both in a long-term care/research facility and in-home.Participant: One 92 year old female with AD.Intervention: Treatments consisted of RSS resulting in gamma frequency entrainment, provided by two different treatment devices over three years.Measurements: Quantitative and qualitative measures were used including: MMSE, SLUMS, interviews, observation notes and a participant question sheet.Results: MMSE scores since diagnosis three years earlier, as well as cognition, clarity, and awareness were reported by the case’s husband to have remained unchanged.Conclusion: Although further research is warranted, this case suggests that RSS has potential to help maintain cognition in AD.

Nonlinear characterization of a Rossler system under periodic closed-loop control via time-frequency and bispectral analysis

This study has two primary objectives; they are to investigate the nonlinear interactions (or quadratic phase-coupling) in a chaotic Rossler system under periodic closed-loop control via wavelet bispectral analysis; and to further identify the component mechanisms of synchronization. It is observed that a fixed-gain, fixed-frequency controller produces quadratic phase-coupling and decoupling along lines of constant frequency and that are perpendicular to the diagonal of the bicoherence matrix. Further, it was also observed that for synchronization to occur, both frequency entrainment and quadratic phase-coupling must be present. It was found that forcing the Rossler system with a constant frequency did not reduce the amplitude of the resulting period-1 orbit at sufficiently high gains. For the controller with a fixed gain and time-varying error signal, it was found that the time varying forcing frequency (adjusted by an extremum seeking feedback loop) linearizes the Rossler system and in doing so, suppresses the phase coherence completely. The time-varying forcing frequency removes the conditions for frequency entrainment by providing broadband attenuation; the result is suppression without synchronization.

Overview of recent HL-2A experiments

Since the last Fusion Energy Conference, significant progress has been made in the following areas. The first high coupling efficiency low-hybrid current drive (LHCD) with a passive–active multi-junction (PAM) antenna was successfully demonstrated in the H-mode on the HL-2A tokamak. Double critical impurity gradients of electromagnetic turbulence were observed in H-mode plasmas. Various ELM mitigation techniques have been investigated, including supersonic molecular beam injection (SMBI), impurity seeding, resonant magnetic perturbation (RMP) and low-hybrid wave (LHW). The ion internal transport barrier was observed in neutral beam injection (NBI) heated plasmas. Neoclassical tearing modes (NTMs) driven by the transient perturbation of local electron temperature during non-local thermal transport events have been observed, and a new type of non-local transport triggered by the ion fishbone was found. A long-lasting runaway electron plateau was achieved after argon injection and the runaway current was successfully suppressed by SMBI. It was found that low-n Alfvénic ion temperature gradient (AITG) modes can be destabilized in ohmic plasmas, even with weak magnetic shear and low-pressure gradients. For the first time, the synchronization of geodesic acoustic mode (GAM) and magnetic fluctuations was observed in edge plasmas, revealing frequency entrainment and phase lock. The spatiotemporal features of zonal flows were also studied using multi-channel correlation Doppler reflectometers.

Mesoscale electric fluctuations interacting with zonal flows, magnetic fluctuations and turbulence

New mesoscale electric fluctuations (MSEFs) are identified in the edge plasmas of the HL-2A tokamak using multiple Langmuir probe arrays. The MSEFs, resulting from the synchronization and having components of dominant geodesic acoustic mode (GAM) and m/n = 6/2 potential fluctuations, are found at the same frequency as that of the magnetic fluctuations of m/n = 6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n = 6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. The nonlinear coupling analyses show that the MSEFs couple to turbulence and low frequency zonal flows (LFZFs). This suggests that the MSEFs may contribute to the LFZF formation, reduction of turbulence level, and thus confinement regime transitions. The analysis of the envelope modulation demonstrates that both the MSEFs and the LFZFs modulate the turbulence while the MSEFs are modulated by the LFZFs.

Alpha-range visual and auditory stimulation reduces the perception of pain.

Alpha power is believed to have an inverse relationship with the perception of pain. Increasing alpha power through an external stimulus may, therefore, induce an analgesic effect. Here, we attempt to modulate the perception of a moderately painful acute laser stimulus by separately entraining three frequencies across the alpha band: 8, 10 and 12Hz. Participants were exposed to either visual or auditory stimulation at three frequencies in the alpha-band range and a control frequency. We collected verbal pain ratings of laser stimuli from participants following 10 minutes of flashing LED goggle stimulation and 10 minutes of binaural beat stimulation across the alpha range. Alterations in sleepiness, anxiety and negative mood were recorded following each auditory or visual alpha-rhythm stimulation session. A significant reduction in pain ratings was found after both the visual and the auditory stimulation across all three frequencies compared with the control condition. In the visual group, a significantly larger reduction was recorded following the 10-Hz stimulation than succeeding the 8- and 12-Hz conditions. This study suggests that a short presentation of auditory and visual stimuli, oscillating in the alpha range, have an analgesic effect on acute laser pain, with the largest effect following the 10-Hz visual stimulation. Pain reductions following stimulation in the alpha range are independent of sleepiness, anxiety, and negative moods. This study provides new behavioural evidence showing that visual and auditory entrainment of frequencies in the alpha-wave range can influence the perception of acute pain in humans.

Synchronization of Geodesic Acoustic Modes and Magnetic Fluctuations in Toroidal Plasmas.

The synchronization of geodesic acoustic modes (GAMs) and magnetic fluctuations is identified in the edge plasmas of the HL-2A tokamak. Mesoscale electric fluctuations (MSEFs) having components of a dominant GAM, and m/n=6/2 potential fluctuations are found at the same frequency as that of the magnetic fluctuations of m/n=6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n=6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. Such nonlinear synchronization may also contribute to low-frequency zonal flow formation, reduction of turbulence level, and thus confinement regime transitions.

Rod Driven Frequency Entrainment and Resonance Phenomena.

A controversy exists on photic driving in the human visual cortex evoked by intermittent photic stimulation. Frequency entrainment and resonance phenomena are reported for frequencies higher than 12 Hz in some studies while missing in others. We hypothesized that this might be due to different experimental conditions, since both high and low intensity light stimulation were used. However, most studies do not report radiometric measurements, which makes it impossible to categorize the stimulation according to photopic, mesopic, and scotopic vision. Low intensity light stimulation might lead to scotopic vision, where rod perception dominates. In this study, we investigated photic driving for rod-dominated visual input under scotopic conditions. Twelve healthy volunteers were stimulated with low intensity light flashes at 20 stimulation frequencies, leading to rod activation only. The frequencies were multiples of the individual alpha frequency (α) of each volunteer in the range from 0.40 to 2.30∗α. Three hundred and six-channel whole head magnetoencephalography recordings were analyzed in time, frequency, and spatiotemporal domains with the Topographic Matching Pursuit algorithm. We found resonance phenomena and frequency entrainment for stimulations at or close to the individual alpha frequency (0.90–1.10∗α) and half of the alpha frequency (0.40–0.55∗α). No signs of resonance and frequency entrainment phenomena were revealed around 2.00∗α. Instead, on-responses at the beginning and off-responses at the end of each stimulation train were observed for the first time in a photic driving experiment at frequencies of 1.30–2.30∗α, indicating that the flicker fusion threshold was reached. All results, the resonance and entrainment as well as the fusion effects, provide evidence for rod-dominated photic driving in the visual cortex.

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators.

We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.

Bifurcational Mechanism of Multistability Formation and Frequency Entrainment in a van der Pol Oscillator with an Additional Oscillatory Circuit

In this paper, the bifurcational mechanism of frequency entrainment in a van der Pol oscillator coupled with an additional oscillatory circuit is studied. It is shown that bistability observed in the system is based on two bifurcations: a supercritical Andronov–Hopf bifurcation and a sub-critical Neimark–Sacker bifurcation. The attracting basin boundaries are determined by stable and unstable invariant manifolds of a saddle two-dimensional torus.

A Unifying Organ Model of Pancreatic Insulin Secretion.

The secretion of insulin by the pancreas has been the object of much attention over the past several decades. Insulin is known to be secreted by pancreatic β-cells in response to hyperglycemia: its blood concentrations however exhibit both high-frequency (period approx. 10 minutes) and low-frequency oscillations (period approx. 1.5 hours). Furthermore, characteristic insulin secretory response to challenge maneuvers have been described, such as frequency entrainment upon sinusoidal glycemic stimulation; substantial insulin peaks following minimal glucose administration; progressively strengthened insulin secretion response after repeated administration of the same amount of glucose; insulin and glucose characteristic curves after Intra-Venous administration of glucose boli in healthy and pre-diabetic subjects as well as in Type 2 Diabetes Mellitus. Previous modeling of β-cell physiology has been mainly directed to the intracellular chain of events giving rise to single-cell or cell-cluster hormone release oscillations, but the large size, long period and complex morphology of the diverse responses to whole-body glucose stimuli has not yet been coherently explained. Starting with the seminal work of Grodsky it was hypothesized that the population of pancreatic β-cells, possibly functionally aggregated in islets of Langerhans, could be viewed as a set of independent, similar, but not identical controllers (firing units) with distributed functional parameters. The present work shows how a single model based on a population of independent islet controllers can reproduce very closely a diverse array of actually observed experimental results, with the same set of working parameters. The model’s success in reproducing a diverse array of experiments implies that, in order to understand the macroscopic behaviour of the endocrine pancreas in regulating glycemia, there is no need to hypothesize intrapancreatic pacemakers, influences between different islets of Langerhans, glycolitic-induced oscillations or β-cell sensitivity to the rate of change of glycemia.

Periodically-forced density wave oscillations in boiling flow at low forcing frequencies: Nonlinear dynamics and control issues

In this paper, we investigate the effect of a periodic perturbation of total pressure drop on density wave oscillations (DWOs) in a boiling channel (BC). The focus is on the nonlinear dynamics and control of the DWO at low forcing frequencies ff+ for a range of inlet subcooling number Nsub. At a relatively high Nsub, the system exhibits frequency entrainment. Relying on the harmonic balance applied to the linearized model for DWOs, semi-analytical solutions can successfully explain the numerically-detected harmonic entrainment. The effect of ff+ and Nsub on the periodically-perturbed DWOs has been studied. We also propose a nonlinear model predictive controller (NMPC) to control the periodically-forced DWOs. The performance of NMPC was found to be improving on increasing Nsub and on decreasing ff+ in 0≤ff+<2fn+ (fn+ is natural frequency), except the regions of entrainment. Both the numerical simulations and the semi-analytical solutions consistently predict the control effort that also varies with ff+ and Nsub.

Fidelity of frequency and phase entrainment of circuit-level spike activity during DBS.

High-frequency stimulation is known to entrain spike activity downstream and upstream of several clinical deep brain stimulation (DBS) targets, including the cerebellar-receiving area of thalamus (VPLo), subthalamic nucleus (STN), and globus pallidus (GP). Less understood are the fidelity of entrainment to each stimulus pulse, whether entrainment patterns are stationary over time, and how responses differ among DBS targets. In this study, three rhesus macaques were implanted with a single DBS lead in VPLo, STN, or GP. Single-unit spike activity was recorded in the resting state in motor cortex during VPLo DBS, in GP during STN DBS, and in STN and pallidal-receiving area of motor thalamus (VLo) during GP DBS. VPLo DBS induced time-locked spike activity in 25% (n = 15/61) of motor cortex cells, with entrained cells following 7.5 ± 7.4% of delivered pulses. STN DBS entrained spike activity in 26% (n = 8/27) of GP cells, which yielded time-locked spike activity for 8.7 ± 8.4% of stimulus pulses. GP DBS entrained 67% (n = 14/21) of STN cells and 32% (n = 19/59) of VLo cells, which showed a higher fraction of pulses effectively inhibiting spike activity (82.0 ± 9.6% and 86.1 ± 16.6%, respectively). Latency of phase-locked spike activity increased over time in motor cortex (58%, VPLo DBS) and to a lesser extent in GP (25%, STN DBS). In contrast, the initial inhibitory phase observed in VLo and STN during GP DBS remained stable following stimulation onset. Together, these data suggest that circuit-level entrainment is low-pass filtered during high-frequency stimulation, most notably for glutamatergic pathways. Moreover, phase entrainment is not stationary or consistent at the circuit level for all DBS targets.

Abrupt intensification of ENSO forced by deglacial ice-sheet retreat in CCSM3

The influence of ice-sheet retreat on the El Nino–Southern Oscillation (ENSO) variability is studied using a transient simulation in NCAR-CCSM3 forced only by variations in continental ice sheets during the last deglaciation. The most striking feature is an abrupt strengthening of ENSO (by ~25 %) at 14 thousand years before present (ka BP) in response to a significant retreat (an equivalent ~25 m sea-level rise) of the Laurentide ice sheet (LIS). This abrupt intensification of ENSO is caused mainly by a sudden weakening of the equatorial annual cycle through the nonlinear mechanism of frequency entrainment, rather than an increase in the coupled ocean–atmosphere instability. The weakened annual cycle corresponds to a reduced north–south cross-equatorial annual mean SST contrast in the eastern Pacific. This reduced interhemispheric SST gradient—significant cooling north of the equator—is forced predominantly by an anomalous easterly from an abrupt polarward shift of the jet stream in the Northern Hemisphere, which extends to the northeastern tropical Pacific Ocean surface and is reinforced by the wind-evaporation-SST feedback then propagates equatorward; it could also be contributed by a fast sea-ice expansion and a consequent cooling in the North Pacific and North Atlantic that is induced by the retreat of the LIS.

Synchronization in oscillator networks with time delay and limited non-homogeneous coupling strength

Motivated by the needs of multi-agent systems in the presence of sensing and communication which is delayed, intermittent, and asynchronous, we present a Kuramoto-type model as the delay inherent in such systems is taken into account. First, we have investigated a condition on maximum delay for the frequency entrainment of non-identical Kuramoto oscillators with heterogeneous delays and a constant coupling gain. Our next mission is to investigate the model of delayed coupled Kuramoto oscillators, which are characterized by non-identical natural frequencies and non-homogeneous coupling strength. We assume that the difference between the coupling gains is less than a certain limited value \(M\), and on the basis of Lyapunov stability theorem, we present a strictly positive lower bound for \(M\) to achieve a consensus on the derivatives of the phases. This consensus property is even more surprising because the phases themselves do not necessarily reach a consensus. We apply our results to these oscillators and show that synchronization is guaranteed for appropriate initial conditions.

Development of Expanded Periodical Input Control for Periodic Motion with Multiple Frequency Components

&lt;div class=""abs_img""&gt;&lt;img src=""[disp_template_path]/JRM/abst-image/00260006/03.png"" width=""300"" /&gt;Frequency entrainment by EPIC&lt;/div&gt; The semi-active assist mechanism proposed as a soft, flexible power assist device consists of an elastomer and actuator. Assist force is controlled by the actuator. in previous study, skill assist using periodical input control (PIC) had a motion-correction effect in motion for a single frequency. However, there is a problem by energy control in periodical input control for motion with multiple frequency components. In this study, we propose expanded PIC for motion with multiple frequency components. We verified the effect of skillassist considering multiple frequency components of human motion. &lt;/span&gt;

Synchronized renal blood flow dynamics mapped with wavelet analysis of laser speckle flowmetry data.

Full-field laser speckle microscopy provides real-time imaging of superficial blood flow rate. Here we apply continuous wavelet transform to time series of speckle-estimated blood flow from each pixel of the images to map synchronous patterns in instantaneous frequency and phase on the surface of rat kidneys. The regulatory mechanism in the renal microcirculation generates oscillations in arterial blood flow at several characteristic frequencies. Our approach to laser speckle image processing allows detection of frequency and phase entrainments, visualization of their patterns, and estimation of the extent of synchronization in renal cortex dynamics.

Quantum synchronization of two Van der Pol oscillators

Synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime is studied. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. The differences to the behavior of one quantum Van der Pol oscillator subject to an external drive are discussed. Moreover, a possible experimental realization of two coupled quantum Van der Pol oscillators in an optomechanical setting is described.