One Action System or Two? Evidence for Common Central Preparatory Mechanisms in Voluntary and Stimulus-Driven Actions

Human behavior is comprised of an interaction between intentionally driven actions and reactions to changes in the environment. Existing data are equivocal concerning the question of whether these two action systems are independent, involve different brain regions, or overlap. To address this question we investigated whether the degree to which the voluntary action system is activated at the time of stimulus onset predicts reaction times to external stimuli.Werecorded event-related potentials while participants prepared and executed left- or right-hand voluntary actions, which were occasionally interrupted by a stimulus requiring either a left- or right-hand response. In trials where participants successfully performed the stimulus-driven response, increased voluntary motor preparation was associated with faster responses on congruent trials (where participants were preparing a voluntary action with the same hand that was then required by the target stimulus), and slower responses on incongruent trials. This suggests that early hand-specific activity in medial frontal cortex for voluntary action trials can be used by the stimulus-driven system to speed responding. This finding questions the clear distinction between voluntary and stimulus-driven action systems. © 2011 the authors

Stochastic Ergodicity Breaking: a Random Walk Approach

The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann--Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure

Kelvin-Helmholtz Instability in a Weakly Ionized Medium

Ambient interstellar material may become entrained in outflows from massive stars as a result of shear flow instabilities. We study the linear theory of the Kelvin - Helmholtz instability, the simplest example of shear flow instability, in a partially ionized medium. We model the interaction as a two fluid system (charged and neutral) in a planar geometry. Our principal result is that for much of the relevant parameter space, neutrals and ions are sufficiently decoupled that the neutrals are unstable while the ions are held in place by the magnetic field. Thus, we predict that there should be a detectably narrower line profile in ionized species tracing the outflow compared with neutral species since ionized species are not participating in the turbulent interface with the ambient ISM. Since the magnetic field is frozen to the plasma, it is not tangled by the turbulence in the boundary layer.Comment: 21 pages, 4 figure

Universal fluctuations in the support of the random walk

A random walk starts from the origin of a d-dimensional lattice. The occupation number n(x,t) equals unity if after t steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sums M(t) of observables defined locally on the field of occupation numbers. Examples are the number S(t) of visited sites; the area E(t) of the (appropriately defined) surface of the set of visited sites; and, in dimension d=3, the Euler index of this surface. In d > 3, the averages (t) all increase linearly with t as t-->infinity. We show that in d=3, to leading order in an asymptotic expansion in t, the deviations from average Delta M(t)= M(t)-(t) are, up to a normalization, all identical to a single "universal" random variable. This result resembles an earlier one in dimension d=2; we show that this universality breaks down for d>3.Comment: 17 pages, LaTeX, 2 figures include

The twisted fourth moment of the Riemann zeta function

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length $T^{{1/11} - \epsilon}$Comment: 28 pages. v2: added reference

Analysis of a fully packed loop model arising in a magnetic Coulomb phase

The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fully-packed two-colour loop model in three dimensions. We present a detailed analysis of the statistics of these loops, which avoid themselves and other loops of the same colour, and contrast their behaviour to an analogous two-dimensional model. The properties of another extended degree of freedom are also addressed, flux lines of the emergent gauge field of the Coulomb phase, which appear as "Dirac strings" in spin ice. We mention implications of these results for related models, and experiments.Comment: 5 pages, 4 figure