Coupling the neural and physical dynamics in rhythmic movements

A pair of coupled oscillators simulating a central pattern generator (CPG) interacting with a pendular limb were numerically integrated. The CPG was represented as a van der Pol oscillator and the pendular limb was modeled as a linearized, hybrid spring-pendulum system. The CPG oscillator drove the pendular limb while the pendular limb modulated the frequency of the CPG. Three results were observed. First, sensory feedback influenced the oscillation frequency of the coupled system. The oscillation frequency was lower in the absence of sensory feedback. Moreover, if the muscle gain was decreased, thereby decreasing the oscillation amplitude of the pendular limb and indirectly lowering the effect of sensory feedback, the oscillation frequency decreased monotonically. This is consistent with experimental data (Williamson and Roberts 1986). Second, the CPG output usually led the angular displacement of the pendular limb by a phase of 90° regardless of the length of the limb. Third, the frequency of the coupled system tuned itself to the resonant frequency of the pendular limb. Also, the frequency of the coupled system was highly resistant to changes in the endogenous frequency of the CPG. The results of these simulations support the view that motor behavior emerges from the interaction of the neural dynamics of the nervous system and the physical dynamics of the periphery

Bubble formation and growth - Study of the boundary conditions at a liquid-vapor interface through irreversible thermodynamics Quarterly progress report, Mar. - May 1966

Nonequilibrium effect on vapor bubble growth determined in study of boundary conditions at liquid-vapor interfac

The Second Law and Cosmology

I use cosmology examples to illustrate that the second law of thermodynamics is not old and tired, but alive and kicking, continuing to stimulate interesting research on really big puzzles. The question "Why is the entropy so low?" (despite the second law) suggests that our observable universe is merely a small and rather uniform patch in a vastly larger space stretched out by cosmological inflation. The question "Why is the entropy so high" (compared to the complexity required to describe many candidate "theories of everything") independently suggests that physical reality is much larger than the part we can observe.Comment: Transcript of talk at the MIT Keenan Symposium; video available at http://mitworld.mit.edu/video/513, including slides and animation

Emergence of Thermodynamics from Darwinian Dynamics

Darwinian dynamics is manifestly stochastic and nonconservative, but has a profound connection to conservative dynamics in physics. In the present paper the main ideas and logical steps leading to thermodynamics from Darwinian dynamics are discussed in a quantitative manner. A synthesis between nonequilibrum dynamics and conservative dynamics is outlined.Comment: latex, 8 page

Exploiting Multiple Sensory Modalities in Brain-Machine Interfaces

Recent improvements in cortically-controlled brain-machine interfaces (BMIs) have raised hopes that such technologies may improve the quality of life of severely motor-disabled patients. However, current generation BMIs do not perform up to their potential due to the neglect of the full range of sensory feedback in their strategies for training and control. Here we confirm that neurons in the primary motor cortex (MI) encode sensory information and demonstrate a significant heterogeneity in their responses with respect to the type of sensory modality available to the subject about a reaching task. We further show using mutual information and directional tuning analyses that the presence of multi-sensory feedback (i.e. vision and proprioception) during replay of movements evokes neural responses in MI that are almost indistinguishable from those responses measured during overt movement. Finally, we suggest how these playback-evoked responses may be used to improve BMI performance

Temporal Evolution of Both Premotor and Motor Cortical Tuning Properties Reflect Changes in Limb Biomechanics

A prevailing theory in the cortical control of limb movement posits that premotor cortex initiates a high-level motor plan that is transformed by the primary motor cortex (MI) into a low-level motor command to be executed. This theory implies that the premotor cortex is shielded from the motor periphery and therefore its activity should not represent the low-level features of movement. Contrary to this theory, we show that both dorsal (PMd) and ventral premotor (PMv) cortices exhibit population-level tuning properties that reflect the biomechanical properties of the periphery similar to those observed in M1. We recorded single-unit activity from M1, PMd, and PMv and characterized their tuning properties while six rhesus macaques performed a reaching task in the horizontal plane. Each area exhibited a bimodal distribution of preferred directions during execution consistent with the known biomechanical anisotropies of the muscles and limb segments. Moreover, these distributions varied in orientation or shape from planning to execution. A network model shows that such population dynamics are linked to a change in biomechanics of the limb as the monkey begins to move, specifically to the state-dependent properties of muscles. We suggest that, like M1, neural populations in PMd and PMv are more directly linked with the motor periphery than previously thought

Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation with Maximal Entropy Production and Other Nonunitary Processes

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.Comment: To appear in Reports on Mathematical Physics. Presented at the The Jubilee 40th Symposium on Mathematical Physics, "Geometry & Quanta", Torun, Poland, June 25-28, 200

Improving Brain–Machine Interface Performance by Decoding Intended Future Movements

Objective. A brain–machine interface (BMI) records neural signals in real time from a subject\u27s brain, interprets them as motor commands, and reroutes them to a device such as a robotic arm, so as to restore lost motor function. Our objective here is to improve BMI performance by minimizing the deleterious effects of delay in the BMI control loop. We mitigate the effects of delay by decoding the subject\u27s intended movements a short time lead in the future. Approach. We use the decoded, intended future movements of the subject as the control signal that drives the movement of our BMI. This should allow the user\u27s intended trajectory to be implemented more quickly by the BMI, reducing the amount of delay in the system. In our experiment, a monkey (Macaca mulatta) uses a future prediction BMI to control a simulated arm to hit targets on a screen. Main Results. Results from experiments with BMIs possessing different system delays (100, 200 and 300 ms) show that the monkey can make significantly straighter, faster and smoother movements when the decoder predicts the user\u27s future intent. We also characterize how BMI performance changes as a function of delay, and explore offline how the accuracy of future prediction decoders varies at different time leads. Significance. This study is the first to characterize the effects of control delays in a BMI and to show that decoding the user\u27s future intent can compensate for the negative effect of control delay on BMI performance

Bubble formation and growth - Study of the boundary conditions at a liquid-vapor interface through irreversible thermodynamics Quarterly progress report, Jun. - Aug. 1966

Steady state mercury evaporation experiment to measure transport coefficient in liquid-vapor interface boundary condition stud