Interoscillator Coupling Research Articles

Kinematic control of walking.

The planar law of inter-segmental co-ordination we described may emerge from the coupling of neural oscillators between each other and with limb mechanical oscillators. Muscle contraction intervenes at variable times to re-excite the intrinsic oscillations of the system when energy is lost. The hypothesis that a law of coordinative control results from a minimal active tuning of the passive inertial and viscoelastic coupling among limb segments is congruent with the idea that movement has evolved according to minimum energy criteria (1, 8). It is known that multi-segment motion of mammals locomotion is controlled by a network of coupled oscillators (CPGs, see 18, 33, 37). Flexible combination of unit oscillators gives rise to different forms of locomotion. Inter-oscillator coupling can be modified by changing the synaptic strength (or polarity) of the relative spinal connections. As a result, unit oscillators can be coupled in phase, out of phase, or with a variable phase, giving rise to different behaviors, such as speed increments or reversal of gait direction (from forward to backward). Supra-spinal centers may drive or modulate functional sets of coordinating interneurons to generate different walking modes (or gaits). Although it is often assumed that CPGs control patterns of muscle activity, an equally plausible hypothesis is that they control patterns of limb segment motion instead (22). According to this kinematic view, each unit oscillator would directly control a limb segment, alternately generating forward and backward oscillations of the segment. Inter-segmental coordination would be achieved by coupling unit oscillators with a variable phase. Inter-segmental kinematic phase plays the role of global control variable previously postulated for the network of central oscillators. In fact, inter-segmental phase shifts systematically with increasing speed both in man (4) and cat (38). Because this phase-shift is correlated with the net mechanical power output over a gait cycle (3, 4), phase control could be used for limiting the overall energy expenditure with increasing speed (22). Adaptation to different walking conditions, such as changes in body posture, body weight unloading and backward walk, also involves inter-segmental phase tuning, as does the maturation of limb kinematics in toddlers.

Density matrix negativity for two oscillators in an Agarwal bath.

A system of two harmonic oscillators is placed in an Agarwal bath. The resulting quantum master equations are studied with the help of quantum characteristic functions. The density matrix positivity is investigated in view of the recent interest in searching for a sound quantum dissipation theory. An analytical criterion is derived for density matrix negativity for two uncoupled oscillators. It is found that, for an initial two-oscillator squeezed state with a real squeezing parameter s, density matrix negativity occurs for two uncoupled oscillators at temperatures lower than Planck's over 2 pi omega/(k(B) ln coth/s/) with omega the oscillator frequency and k(B) the Boltzmann factor. As a by-product an analytical expression is also obtained for determining the quantum separability of two uncoupled oscillators. The effects of interoscillator coupling on density matrix negativity are discussed.

Analysis and modeling of the locomotor central pattern generator as a network of coupled oscillators.

The primary functions of spinal locomotor central pattern generators (CPGs) are to provide oscillatory motor commands to individual joints or segments and to control the precise timing of those commands across all joints or segments for efficient, coordinated locomotor behavior. Our ability to understand the neuronal mechanisms underlying intersegmental coordination has been hampered by the complexity of propriospinal interconnectivity and the paucity of quantitative data on the magnitude and timing of those connections. Theoretical approaches have therefore been employed to discover general rules by which CPG-like oscillator systems must be constructed to produce appropriate coordinated locomotor behavior; the locomotor CPG is represented as a network of oscillators, where each oscillator generates local motor output and interoscillator coupling provides intersegmental coordination. Mathematical analysis of such coupled oscillator systems has provided a number of experimentally testable predictions regarding the link between coupling and coordination. Application of these network-level predictions to the results of electrophysiological experiments has required data analysis methods that can relate the behavior of the in vitro spinal cord to the variables employed by the mathematical model. Hence, our most recent work has focused on developing analytic tools for quantifying the changes in locomotor output that result form experimental manipulations of the propriospinal system in terms of frequency, intersegmental phase, and intersegmental correlation. Results of recent experiments can now be used to put further constraints on the allowable kinds of intersegmental coupling provided by mathematical modeling of the system.

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.

Interoscillator coupling effects on the OH stretching band of liquid water

We have studied the OH stretch spectrum in water to explore the effects of interoscillator coupling. Both H2O, which may have significant intra and intermolecular coupling, and dilute HOD in D2O, which is isotopically decoupled, were studied over a broad range of temperature from −33 °C to 160 °C. By adding a small amount of a calibration dopant, we obtained quantitative spectra. We found interoscillator coupling plays a large role at all temperatures. At high temperature, intramolecular coupling contributes to a downshift in the peak position for H2O as compared to HOD. Intermolecular coupling, however, still has some influence at high temperature. At low temperature, the large excess intensity below 3200 cm−1 in H2O compared to HOD we find is due to an enhanced Raman cross section due to intermolecularly coupled in-phase OH stretch oscillations. We define a degree of delocalization for coupling as the idealized number of perfectly in-phase oscillators that could cause the enhanced scattering and find N≂2 for liquid H2O at −33 °C. An exact isosbestic crossing is not found and this can be understood given the changing line shape that the intermolecular coupling can induce. All the properties of the spectrum approach those found in amorphous solid water or ice near the supercooled water anomalous temperature, Ts≂−45 °C.

A comparison of circatidal rhythmicity and entrainment by hydrostatic pressure cycles in the rock goby, Gobius paganellus L. and the shanny, Lipophrys pholis (L.)

The intertidal teleosts Gobius paganellus and Lipophrys pholis show endogenous circatidal activity rhythms when recorded in constant conditions. Under these conditions, the rhythm of L. pholis is the more precise which may indicate stronger coupling between underlying circalunadian oscillators in this species. In G. pagunellus the inter‐oscillator coupling may be weaker and this could enable a more subtle interpretation of tidal fluctuations than in L. pholis. The oscillators may, however, be fundamentally different in the two species; circalunadian in G. paganellus and circatidal in L. pholis.When exposed to hydrostatic pressure cycles of tidal frequency both species responded pre‐ dominantly to increasing pressure, which suggests that in the wild they are likely to be most active on the rising tide. Hydrostatic pressure cycles are confirmed as a zeitgeber for both species by the successful entrainment of some individuals. The lack of entrainment of others impIies that additional zeitgebers are required for complete entrainment.

Local mode assignments for the CD-stretching overtone spectra of deuterated methyl iodide and deuterated methyl cyanide: effects of increased interoscillator coupling on local mode states of C3v symmetry

The overtone spectra of CD3I and CD3CN are measured at room temperature in the liquid phase in the regions of CD-stretching local mode overtones corresponding to ΔvCD = 2–5. The spectra are analyzed in terms of a harmonically coupled local mode model. The local mode parameters ω, ωx, and γ′v, the interoscillator coupling between the methyl CD bonds, are determined. A comparison of the spectra of the CH3Z molecules (Z = Cl, Br, I, CN) to the spectra of CD3I and CD3CN reveals the spectral effects of increased interoscillator coupling between the CD bonds.

Molecular motions in liquid HSiCl 3 and DSiCl 3 by Raman and IR spectroscopy

The parallel v 1, band of pure liquid HSiCl 3 and DSiCl 3 and some of their isotopically diluted solutions are analyzed by Raman and IR spectroscopy. The relaxation times τ v τ 1R and τt 2R are deduced from the correlation functions G v, G 1R and G 2R. It appears that the tumbling motion is identical for HSiCl 3 and DSiCl 3 and no interoscillator coupling occurs.