Stable In-phase Research Articles

A model of postural coordination dynamics

Prior research has shown that voluntary postural movement is characterized by stable in-phase and antiphase hip–ankle coordination modes. Prior modeling of coordination dynamics does not capture the stable fixed-points, phase transitions and hysteresis found in hip–ankle coordination. In this article a model was created to capture the dynamics of hip–ankle postural coordination. The present model follows the synergetic approach and uses two nonlinear oscillators to capture the dynamics of hip–ankle coordination. Terms for symmetry breaking and additive stochastic noise are included in the model. The model captures phase transitions from in-phase to antiphase coordination as movement frequency is scaled up and from antiphase to in-phase coordination as movement frequency is scaled down. The model also exhibits hysteresis, with phase transitions occurring at different movement frequencies as the control parameter is scaled up and down.

Synchronous motion of two vertically excited planar elastic pendula

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.

LLRF and timing system for the SCSS test accelerator at SPring-8

The 250MeV SCSS test accelerator as an extreme-ultra violet (EUV) laser source has been built at SPring-8. The accelerator comprises a 500kV thermionic gun, a velocity bunching system using multi-sub-harmonic bunchers (SHB) in an injector and a magnetic bunch compressor using a chicane of 4 bending magnets, a 5712MHz main accelerator to accelerate an electron beam up to 250MeV, and undulators to radiate the EUV laser. These bunch compression processes make short bunched electrons with a 300A peak current and a 300fs pulse width. The pulse width and peak current of an electron beam, which strongly affect the pulse width and intensity of the laser light, are mainly decided by the pulse compression ratio of the velocity bunching and the magnetic bunch compressing processes. The compression ratio is also determined due to an energy chirp along the beam bunch generated by an off-crest rf field at the SHB and cavities before the chicane. To constantly keep the beam pulse-width conducted by rf and timing signals, which are temporally controlled within subpicoseconds of the designed value, the low-level rf and timing system of the test accelerator has been developed. The system comprises a very low-noise and temporally stable reference signal source, in-phase and quadrature (IQ) modulators and demodulators, as well as VME type 12 bits analog-to-digital and digital-to-analog converter modules to manipulate an rf phase and amplitude by IQ functions for the cavity. We achieved that the SSB noise of the 5712MHz reference signal source was less than −120dBc/Hz at 1kHz offset from the reference frequency; the phase setting and detecting resolution of the IQ-modulators and demodulators were within +/−0.5° at 5712MHz. A master trigger VME module and a trigger delay VME module were also developed to activate the components of the test accelerator. The time jitter of the delay module was less than 0.7ps, sufficient for our present requirement. As a result, a beam energy variation of 0.06% was achieved and a time jitter of 46fs between the acceleration rf signal and the beam was realized.

Interpersonal dynamics and relative positioning to scoring target of performers in 1 vs. 1 sub-phases of team sports

In this study, we examined the effects of relative positioning of attacker–defender dyads to the basket on interpersonal coordination tendencies in basketball. To achieve this aim, four right-hand dominant basketball players performed in a 1 vs. 1 sub-phase, at nine different playing locations relative to the basket (from 0° to 180°, in 20° increments). Performers’ movement displacement trajectories were video-recorded and digitized in 162 trials. Results showed that interpersonal coordination tendencies changed according to the scaling of the relative position of performers to the basket. Stable in-phase modes of coordination were observed between performers’ longitudinal and lateral displacements (50.47% and 43.02%) on the left side of the court. On the right side of the court, a shift in the dominant mode of coordination was observed to a defender lead-lag of −30°, both for longitudinal and lateral displacements (30.51% and 32.65%). These results suggest how information about dribbler hand dominance and relative position to the basket may have constrained attacker–defender coordination tendencies in 1 vs. 1 sub-phases of basketball.

Spatiotemporal re-organization of large-scale neural assemblies underlies bimanual coordination

Bimanual coordination engages a distributed network of brain areas, the spatiotemporal organization of which has given rise to intense debates. Do bimanual movements require information processing in the same set of brain areas that are engaged by movements of the individual components (left and right hands)? Or is it necessary that other brain areas are recruited to help in the act of coordination? These two possibilities are often considered as mutually exclusive, with studies yielding support for one or the other depending on techniques and hypotheses. However, as yet there is no account of how the two views may work together dynamically. Using the method of Mode-Level Cognitive Subtraction (MLCS) on high density EEG recorded during unimanual and bimanual movements, we expose spatiotemporal reorganization of large-scale cortical networks during stable inphase and antiphase coordination and transitions between them. During execution of stable bimanual coordination patterns, neural dynamics were dominated by temporal modulation of unimanual networks. At instability and transition, there was evidence for recruitment of additional areas. Our study provides a framework to quantify large-scale network mechanisms underlying complex cognitive tasks often studied with macroscopic neurophysiological recordings.

Spikes matter for phase-locked bursting in inhibitory neurons

We show that inhibitory networks composed of two endogenously bursting neurons can robustly display several coexistent phase-locked states in addition to stable antiphase and in-phase bursting. This work complements and enhances our recent result [Jalil, Belykh, and Shilnikov, Phys. Rev. E 81, 045201(R) (2010)] that fast reciprocal inhibition can synchronize bursting neurons due to spike interactions. We reveal the role of spikes in generating multiple phase-locked states and demonstrate that this multistability is generic by analyzing diverse models of bursting networks with various fast inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, and the Purkinje neuron model.

Delay- and Coupling-Induced Firing Patterns in Oscillatory Neural Loops

For a feedforward loop of oscillatory Hodgkin-Huxley neurons interacting via excitatory chemical synapses, we show that a great variety of spatiotemporal periodic firing patterns can be encoded by properly chosen communication delays and synaptic weights, which contributes to the concept of temporal coding by spikes. These patterns can be obtained by a modulation of the multiple coexisting stable in-phase synchronized states or traveling waves propagating along or against the direction of coupling. We derive explicit conditions for the network parameters allowing us to achieve a desired pattern. Interestingly, whereas the delays directly affect the time differences between spikes of interacting neurons, the synaptic weights control the phase differences. Our results show that already such a simple neural circuit may unfold an impressive spike coding capability.

Simultaneous spectrum and coherent combining by active phasing dual two-tone all-fiber MOPA chains

We present a new approach for simultaneous spectral and coherent combining in a master oscillator power amplifier (MOPA) configuration with active phasing. Spectrally combined single-frequency seed lasers are employed as a master oscillator for the all-fiber power amplifier chain, which provides robust performance suppressing of the stimulated Brillouin scattering effect, while coherent combining of spectrally combined amplifiers with active phase control provides stable in-phase combining, despite the strong phase fluctuation. In experiments, two spectrally combined seed MOPA chains are coherently combined with a total output power of 390 W. The power of the main lobe in the closed loop is two times of that value in the open loop, and visibility of more than 75% of the long-exposure interference pattern at the receiving plane is obtained.

Frequency-induced changes in interlimb interactions: Increasing manifestations of closed-loop control

In bimanual coordination, interactions between the limbs result in attraction to in-phase and antiphase coordination. Increasing movement frequency leads to decreasing stability of antiphase coordination, often resulting in a transition to the more stable in-phase pattern. It is unknown, however, how this frequency-induced loss of stability is engendered in terms of the interlimb interactions underwriting bimanual coordination. The present study was conducted to help resolve this issue. Using an established method (based on comparison of various unimanual and bimanual tasks involving both passive and active movements), three sources of interlimb interaction were dissociated: (1) integrated timing of feedforward signals, (2) afference-based correction of relative phase errors, and (3) phase entrainment by contralateral afference. Results indicated that phase entrainment strength remained unaffected by frequency and that the stabilizing effects of error correction and integrated timing decreased with increasing frequency. Their contributions, however, reflected an interesting interplay as frequency increased. For moderate frequencies coordinative stability was predominantly secured by integrated timing processes. However, at high frequencies, the stabilization of the antiphase pattern required combined contributions of both integrated timing and error correction. In sum, increasing frequency was found to induce a shift from predominantly open-loop control to more closed-loop control. The results may be accounted for by means of an internal forward model for sensorimotor integration in which the sensory signals are compared to values predicted on the basis of efference copies.

Gestural reorganization in Mandarin contracted syllables.

“Syllable contraction” is a type of spontaneous pronunciation in Chinese that reduces a sequence of syllables to a lesser number [Cheng (1985)]. The present study examines the phenomenon under the framework of articulatory phonology, in which speech is composed of gestures whose timing is controlled by a system of planning oscillators [Goldstein et al. (2006)]. The experiment tests the hypothesis that Mandarin contracted syllables result from a transition from anti-phase to the more stable in-phase coordination between vowel gestures of successive syllables. Such phase shifts have been implicated in sound changes in other languages [e.g., Parrell (2009)]. If such shifts occur, vowels in contracted words should exhibit coproduction of (lexically) sequential vowels. This is tested by comparing disyllabic function words, which are more likely to be contracted [Tseng (2001)], to non-function words. Results show that F2 is lower when the vowel in contracted disyllabic words is followed by a front vowel lexically and higher when the vowel in contracted words is followed by a front vowel lexically. The absence of such effects where the vowels do not differ in backness confirms that the effect is a result of coproduction. These results thus support the gestural organization hypothesis for Mandarin contraction.

Premature infant swallowing: Patterns of tongue-soft palate coordination based upon videofluoroscopy

Coordination between movements of individual tongue points, and between soft palate elevation and tongue movements, were examined in 12 prematurely born infants referred from hospital NICUs for videofluoroscopic swallow study (VFSS) due to poor oral feeding and suspicion of aspiration. Detailed post-evaluation kinematic analysis was conducted by digitizing images of a lateral view of digitally superimposed points on the tongue and soft palate. The primary measure of coordination was continuous relative phase of the time series created by movements of points on the tongue and soft palate over successive frames. Three points on the tongue (anterior, medial, and posterior) were organized around a stable in-phase pattern, with a phase lag that implied an anterior to posterior direction of motion. Coordination between a tongue point and a point on the soft palate during lowering and elevation was close to anti-phase at initiation of the pharyngeal swallow. These findings suggest that anti-phase coordination between tongue and soft palate may reflect the process by which the tongue is timed to pump liquid by moving it into an enclosed space, compressing it, and allowing it to leave by a specific route through the pharynx.

Relationship between flood/drought disasters and ENSO from 1857 to 2003 in the Taihu Lake basin, China

In this paper, the relationship between flood/drought change in the Taihu Lake basin (TLB) and ENSO is investigated based on reconstructed flood/drought rank series (FD) and NINO-3.4 SST (DJF) data from 1857 to 2003. With the aid of empirical mode decomposition (EMD) method, the paper reveals that FD series and ENSO both contain strong inter-annual, decadal, multi-decadal and centennial signals, and have quite similar periodicities. The EMD method also obtains a monotonic trend for both series: the trend of FD series is upward, which suggests that flood trend is significant, and the trend of NINO-3.4 SST is also upward showing an increase of El Nino events. Continuous wavelet transform obtains similar oscillations for FD and NINO-3.4 SST series with those of EMD method. The results of cross wavelet and wavelet coherence suggest that there was stable in-phase relation between FD and NINO-3.4 SST from 1857 to 1950s, while this in-phase relation is not clear during recent decades. This conclusion is also verified by χ 2 test. These findings indicate weakening linkage between ENSO and flood/drought disasters in the TLB, which must be taken into account in the prediction of flood and drought disasters in the study area.

Coordination of complex bimanual multijoint movements under increasing cycling frequencies: The prevalence of mirror-image and translational symmetry

The present study examined the principles underlying inter and intralimb coordination constraints during performance of bimanual elbow–wrist movements at different cycling frequencies (from 0.75 Hz to 2.50 Hz). Participants performed eight coordination tasks that consisted of a combination of in-phase (IN) and/or anti-phase (AN) coordination modes between both elbows and wrists (interlimb), with isodirectional (Iso) or non-isodirectional (NonI) coordination modes within each limb (intralimb). As expected, the principle of muscle homology (in-phase coordination), giving rise to mirror symmetrical movements with respect to the mid-sagittal plane, had a powerful influence on the quality of global coordinative behavior both between and within limbs. When this principle was violated (i.e., when the anti-phase mode was introduced in one or both joint pairs), the non-isodirectional intralimb mode exhibited a (de)stabilizing role in coordination, which became more pronounced at higher cycling frequencies. However, pattern loss with increasing cycling frequency resulted not only in convergence toward the more stable in-phase patterns with the elbows and wrists but also to the anti-phase patterns (which were associated with directional compatibility of within-limb motions). Moreover, participants generally preserved their initial mode of coordination (either in-phase or anti-phase) in the proximal joints (i.e., elbows) while shifting from anti-phase to in-phase (or vice versa) with their distal joint pair (i.e., wrists). Taken together, these findings reflect the impact of two immanent types of symmetry in bimanual coordination: mirror-image and translational symmetry.

Short duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the anti-phase pattern.

Mutually inhibitory pacemaker neurons with duty cycle close to 50% operate as a half-center oscillator (anti-phase coordination, i.e., 180 degrees out of phase), even in the presence of weak to modest gap junctional coupling. For electrical coupling strength above a critical value synchronization occurs. But, as shown here with modeling studies, the effects of electrical coupling depend critically on a cell's duty cycle. Instead of oscillating either in-phase or anti-phase, model cells with short duty cycle express additional rhythmic patterns, and different transitions between them, depending on electrical coupling strength. For weak or no electrical coupling, cells do not oscillate in anti-phase but instead exhibit almost in-phase activity. Strengthening this weak coupling leads to stable anti-phase activity. With yet stronger electrical coupling stable inphase (synchrony) emerges but it coexists with the anti-phase pattern. Thus the network shows bistability for an intermediate range of coupling strength. For sufficiently strong electrical coupling synchrony is the network's only attracting rhythmic state. Our results, numerical and analytical (phase plane analysis), are based on a minimal but biophysically motivated pacemaker model for the slowly oscillating envelope of bursting neurons. However, illustrations for an Hodgkin-Huxley model suggest that some of our results for short duty cycle may extend to patterning of repetitive spikes. In particular, electrical coupling of intermediate strength may promote anti-phase activity and provide bistability of anti-phase and in-phase spiking.

Transitions between dynamical states of differing stability in the human brain

What mechanisms underlie the flexible formation, adaptation, synchronization, and dissolution of large-scale neural assemblies from the 10(10) densely interconnected, continuously active neurons of the human brain? Nonlinear dynamics provides a unifying perspective on self-organization. It shows that the emergence of patterns in open, nonequilibrium systems is governed by their stability in response to small disturbances and predicts macroscopic transitions between patterns of differing stability. Here, we directly demonstrate that such transitions can be elicited in the human brain by interference at the neural level. As a probe, we used a classic motor coordination paradigm exhibiting well described movement states of differing stability. Functional neuroimaging identified premotor (PMA) and supplementary motor (SMA) cortices as having neural activity linked to the degree of behavioral instability. These regions then were transiently disturbed with graded transcranial magnetic stimulation, which caused sustained and macroscopic behavioral transitions from the less stable out-of-phase to the stable in-phase movement, whereas the stable pattern could not be affected. Moreover, the strength of the disturbance needed (a measure of neural stability) was linked to the degree of behavioral stability, demonstrating the applicability of nonlinear system theory as a powerful predictor of the dynamical repertoire of the human brain.

Phase locking dynamics in 2D Josephson junction arrays with external load

Phase locking in a basic two-dimensional hybrid Josephson junction array consisting of two rows and four columns shunted by an external load is investigated, exploiting an approximation combining the ideas of harmonic balance with that of the slowly varying phase procedure. Using small ring inductances, the junction voltages within the same row oscillate nearly in-phase unless the external magnetic flux in the loops is near a multiple of a quarter of the flux quantum. Without external load we have found a stable antiphase regime where both rows carry out uniform interferometer oscillations. A stable in-phase regime, favored in an optimized radiation source, can be reached by means of an external inductive shunt for small external fields only.

A dynamical model for mirror movements

In an experiment involving the unimanual performance of rhythmic movements about the elbow joint, mirror movements (MM) (i.e., unintended, associated movements) were observed in the arm not instructed to move. The amplitude of these movements was small relative to that of the intended movements (in the order of 0.5 to 5%). Complex patterns of relative phasing were observed between the intended movements and the MM that were characterized by the presence of higher harmonics in the oscillating units. The patterns in question depended on the frequency of the intended movements, which was varied from 0.5 to 3 Hz. At low frequencies, cases of both in- and anti-phase coordination were observed amidst various other instances of phase locking. MM were smaller in the anti-phase than in the in-phase coordination. At higher frequencies, the occurrence of in-phase coordination was most common while instances of anti-phase coordination were absent. To account for these properties, a dynamical model for the coordination between large-amplitude intended movements and small-amplitude MM was derived in the form of a model of nonlinearly coupled nonlinear oscillators with unequal amplitudes. The derived model was shown to correspond well with many quantitative and qualitative features of the observed dynamics of MM, including frequency locking, stable in-phase and anti-phase coordination, coordination-dependency of mirror movement amplitudes, and the presence of higher harmonics. The implications of the obtained experimental and analytical results and numerical parameter optimizations for the study of MM were discussed.

Internal vibrations of a vector soliton in the coupled nonlinear Schrödinger equations

Static and dynamic properties of a two-component soliton are studied via the variational approximation (VA), consideration of the radiation spectrum, and direct numerical simulations. The VA, based on a Gaussian Ansatz, proves to be (as compared to the direct simulations) fairly accurate in some respects and inaccurate in others---in particular, the predictions for the widths of the stationary states are about a sixth part greater than the actual widths. We formulate an empirically modified version of the variational approximation: at the end of the analysis, the Gaussian is replaced by sech with properly rescaled widths. This hybrid VA yields extremely accurate predictions for the stationary states. The error in the width prediction is \ensuremath{\lesssim}1%, and simulations demonstrate minuscule radiation losses. The VA model predicts three eigenmodes of the soliton's internal vibrations, all of which are observed numerically. Oscillation of the separation between the two components is found to be the most persistent mode, and in-phase oscillation of the two widths is the next most persistent one; in contrast, the out-of-phase width oscillations are unstable, quickly rearranging themselves into the stable in-phase mode. These features are easily explained by comparing the corresponding vibrational eigenfrequencies to the spectral gaps which isolate oscillations localized at the soliton from delocalized radiation modes. For vector solitons with energy nearly equally divided between the components, the analysis reveals a remarkable feature: saturation of the separation oscillations, with the radiative decay virtually ceasing at a finite level of the mode's amplitude. The relatively stable in-phase width-oscillation mode decays indefinitely, but according to a very slow power law rather than exponentially. Lastly, for large-amplitude vibrations, the VA models predict dynamical chaos, but, due to the quick decay of the large oscillations, direct simulations show no chaos.

Age-related differences in the integration of sensory information during the execution of a bimanual coordination task.

Young (n = 7) and elderly (n = 7) subjects performed bimanual coordination patterns in the transverse plane according to the in-phase or antiphase mode. Sensory information was manipulated through visual (with or without vision of the limbs) and proprioceptive input (with or without vibratory stimuli on one limb). Movement patterns with vibrations showed higher deviations from the intended relative phase than did those without vibrations. This finding suggests that the proprioceptive information induced by the vibrations and the movement interfered, leading to a disruption of the coordination patterns. In addition, as compared with the elderly, the young subjects performed more stable movements under normal circumstances but were more strongly affected by vibratory stimuli during the performance of in-phase movements. During antiphase movements, both age groups experienced a decrease of pattern stability. Furthermore, the absence or presence of visual feedback influenced the performance of the young subjects more than that of the elderly. The presence of vision led to stable in-phase movements, whereas a decrease of pattern stability was observed for antiphase movements. In general, these results demonstrate that manipulation of feedback sources affects young subjects more than elderly ones, and this can be related to a reduced sensory sensitivity as a function of aging.

Spontaneous transitions and symmetry: Pattern dynamics in human four-limb coordination

Transitions between the coordinative patterns of rhythmically moving human arms and legs were studied to test the predictions of a four-component model (Schöner, Jiang and Kelso, 1990). Based upon results from previous two-component experiments (Kelso and Jeka, 1992), three assumptions were made about the four-limb system: (1) all limb pairs produce stable in-phase and anti-phase patterns; (2) the coupling between homologous limbs (i.e., right and left arms or right and left legs) is appreciably stronger than the coupling between nonhomologous limbs (i.e., arm and leg); and (3) right-left symmetry. An analysis of a four-component model (Jeka, Kelso and Kiemel, 1993) led to the prediction of four attracting invariant circles, each with two stable patterns in the state space of four-limb dynamics. In an experiment to test this prediction, subjects were required to cycle all four limbs in one of the eight patterns to the beat of an auditory metronome whose frequency was systematically increased. All subjects demonstrated spontaneous transitions corresponding to pathways along the invariant circles. Pre-transition relative phase variability increased with required frequency up to the transition, suggesting that loss of pattern stability induced the observed transitions. Thus, despite a large number of potential transitions, differential coupling between limb pairs and symmetry of the pattern dynamics restricts the behavior of the human four-limb system to a limited area of its state space.