Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form from 80 to 500 Hz. This scaling index, , is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory “asynchronous,” scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent “synchronous” rhythm-based paradigm.

During active movement the electric potentials measured from the surface of the motor cortex exhibit consistent modulation, revealing two distinguishable processes in the power spectrum. At frequencies Ͻ40 Hz, narrow-band power decreases occur with movement over widely distributed cortical areas, while at higher frequencies there are spatially more focal power increases. These high-frequency changes have commonly been assumed to reflect synchronous rhythms, analogous to lower-frequency phenomena, but it has recently been proposed that they reflect a broad-band spectral change across the entire spectrum, which could be obscured by synchronous rhythms at low frequencies. In 10 human subjects performing a finger movement task, we demonstrate that a principal component type of decomposition can naively separate low-frequency narrow-band rhythms from an asynchronous, broad-spectral, change at all frequencies between 5 and 200 Hz. This broad-spectral change exhibited spatially discrete representation for individual fingers and reproduced the temporal movement trajectories of different individual fingers.

Membranes containing a wide variety of ternary mixtures of high chain-melting temperature lipids, low chain-melting temperature lipids, and cholesterol undergo lateral phase separation into coexisting liquid phases at a miscibility transition. When membranes are prepared from a ternary lipid mixture at a critical composition, they pass through a miscibility critical point at the transition temperature. Since the critical temperature is typically on the order of room temperature, membranes provide an unusual opportunity in which to perform a quantitative study of biophysical systems that exhibit critical phenomena in the two-dimensional Ising universality class. As a critical point is approached from either high or low temperature, the scale of fluctuations in lipid composition, set by the correlation length, diverges. In addition, as a critical point is approached from low temperature, the line tension between coexisting phases decreases to zero. Here we quantitatively evaluate the temperature dependence of line tension between liquid domains and of fluctuation correlation lengths in lipid membranes to extract a critical exponent, nu. We obtain nu = 1.2 +/- 0.2, consistent with the Ising model prediction nu = 1. We also evaluate the probability distributions of pixel intensities in fluorescence images of membranes. From the temperature dependence of these distributions above the critical temperature, we extract an independent critical exponent of beta = 0.124 +/- 0.03, which is consistent with the Ising prediction of beta = 1/8.

Imagery of motor movement plays an important role in learning of complex motor skills, from learning to serve in tennis to perfecting a pirouette in ballet. What and where are the neural substrates that underlie motor imagery-based learning? We measured electrocorticographic cortical surface potentials in eight human subjects during overt action and kinesthetic imagery of the same movement, focusing on power in “high frequency” (76–100 Hz) and “low frequency” (8–32 Hz) ranges. We quantitatively establish that the spatial distribution of local neuronal population activity during motor imagery mimics the spatial distribution of activity during actual motor movement. By comparing responses to electrocortical stimulation with imagery-induced cortical surface activity, we demonstrate the role of primary motor areas in movement imagery. The magnitude of imagery-induced cortical activity change was ∼25% of that associated with actual movement. However, when subjects learned to use this imagery to control a computer cursor in a simple feedback task, the imagery-induced activity change was significantly augmented, even exceeding that of overt movement.

No abstract