Marcel den Nijs

Power-law scaling in the brain surface electric potential.

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.

Cortical activity during motor execution, motor imagery, and imagery-based online feedback

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.

Line Tensions, Correlation Lengths, and Critical Exponents in Lipid Membranes Near Critical Points

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.

QUANTUM MODEL FOR COMMENSURATE - INCOMMENSURATE TRANSITIONS

A one-dimensional quantum mechanical model with three states per site is considered. Its ground state shows several commensurate-incommensurate transitions analogous to ones previously studied in two-dimensional statistical mechanics. Using duality arguments, several relations between the phase transition lines can be stated precisely. Further data about the phase diagram can be derived numerically by using strong coupling expansions, including an expansion for the q-dependent mass gap. A fermion analysis is employed to develop exact properties of the incommensurate or floating phase. One new feature is the existence of a Lifshitz point where the critical exponents α, β and γ take the value of the three-state Potts model while the mass gap exponent, ν, equals one, characteristic of the Ising model.

Observation of surface roughening on Ni(115)

We present evidence that the equilibrium topography of the Ni(115) surface in the temperature range 100 K<T<1000 K is that expected above its roughening temperature. This conclusion is based on a detailed line shape analysis of the specular diffraction peak at anti‐Bragg angles as a function of temperature. The experimental results are combined with a generic phase diagram for stepped (11m) surfaces of face centered cubic (fcc) metals and is estimated that the roughening temperature of Ni(115) is below 50 K, that of Ni(113) approximately 200±50 K, and that of Ni(001) well above 420 K.

Dynamic Modulation of Local Population Activity by Rhythm Phase in Human Occipital Cortex During a Visual Search Task

Brain rhythms are more than just passive phenomena in visual cortex. For the first time, we show that the physiology underlying brain rhythms actively suppresses and releases cortical areas on a second-to-second basis during visual processing. Furthermore, their influence is specific at the scale of individual gyri. We quantified the interaction between broadband spectral change and brain rhythms on a second-to-second basis in electrocorticographic (ECoG) measurement of brain surface potentials in five human subjects during a visual search task. Comparison of visual search epochs with a blank screen baseline revealed changes in the raw potential, the amplitude of rhythmic activity, and in the decoupled broadband spectral amplitude. We present new methods to characterize the intensity and preferred phase of coupling between broadband power and band-limited rhythms, and to estimate the magnitude of rhythm-to-broadband modulation on a trial-by-trial basis. These tools revealed numerous coupling motifs between the phase of low-frequency (δ, θ, α, β, and γ band) rhythms and the amplitude of broadband spectral change. In the θ and β ranges, the coupling of phase to broadband change is dynamic during visual processing, decreasing in some occipital areas and increasing in others, in a gyrally specific pattern. Finally, we demonstrate that the rhythms interact with one another across frequency ranges, and across cortical sites.

Queuing transitions in the asymmetric simple exclusion process

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as deltarho approximately x(-nu) with nu=1/3, and x is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent nu=1/3 is universal and independent of the dynamic exponent of the underlying dynamic process. Fast bonds create only power-law shaped depletion queues, and with an exponent that could be equal to nu=2/3, but the numerical results yield consistently somewhat smaller values nu approximately 0.63(3). The implications of these results to faceting of growing interfaces and localization of directed polymers in random media, both in the presence of a columnar defect are pointed out as well.

Macroscopic car condensation in a parking garage

An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes macroscopically occupied. The total car density rho(o) and the exit probability alpha from the garage are the two control parameters. At the transition, the number of parked cars N(p) diverges in both cases, with the length of the road N(s), as N(p) approximately N(y(p))(s) with y(p)=1/2. Towards the transition, the number of parked cars vanishes as N(p) approximately epsilon(beta) with beta=1, epsilon=/alpha-alpha(*)/ or epsilon=|rho(*)(o)-rho(o)/ being the distance from the transition. The transition into the normal phase represents also the onset of transmission of information through the garage. This gives rise to unusual parked car autocorrelations and car density profiles near the garage, which depend strongly on the group velocity of the fluctuations along the road.

Brain surface electrode co-registration using MRI and x-ray

Electrocorticographic recording is now being used in a wide variety of experimental settings. We present a simple method which can be used to estimate electrode position with respect to brain gyral anatomy using a pre-implantation MRI and post-implantation coronal and sagittal x-rays. It is semi-automated, with the user manually rotating and scaling an x-ray to fit brain outline, identifying threshold values for brain surface rendering, and clicking on electrodes on an x-ray. Electrode positions can be rapidly identified and rendered in about 20 minutes from start to finish. This approach is useful when the MRI quality is poor, there is no quality CT, but one would like to understand the relationship between experimental result and brain anatomy.

Crossover Scaling Functions in One Dimensional Dynamic Growth Models.

The crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang (KPZ) type growth is studied for the body-centered solid-on-solid model. The time needed to reach the stationary state