Asymmetric dynamics and critical behavior in the Bak-Sneppen model

We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak-Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All non-symmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetry-based universality classes for extremal dynamics.Comment: 14 pages, 8 figures, 1 tabl

Orbital transfer vehicle concept definition and system analysis study, 1985. Volume 2: OTV concept definition and evaluation. Book 2: OTV concept definition

This portion of the Orbit Transfer Vehicle (OTV) Concept Definition and System Analysis Study, Volume 2, Book 2, summarizes the flight vehicle concept selection process and results. It presents an overview of OTV mission and system design requirements and describes the family of OTV recommended, the reasons for this recommendation, and the associated Phase C/D Program

Series expansion for a stochastic sandpile

Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory [R. Dickman and R. Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to O(t^{16}). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.Comment: Extended series and improved analysi

ADAR-mediated RNA editing suppresses sleep by acting as a brake on glutamatergic synaptic plasticity.

It has been postulated that synaptic potentiation during waking is offset by a homoeostatic reduction in net synaptic strength during sleep. However, molecular mechanisms to support such a process are lacking. Here we demonstrate that deficiencies in the RNA-editing gene Adar increase sleep due to synaptic dysfunction in glutamatergic neurons in Drosophila. Specifically, the vesicular glutamate transporter is upregulated, leading to over-activation of NMDA receptors, and the reserve pool of glutamatergic synaptic vesicles is selectively expanded in Adar mutants. Collectively these changes lead to sustained neurotransmitter release under conditions that would otherwise result in synaptic depression. We propose that a shift in the balance from synaptic depression towards synaptic potentiation in sleep-promoting neurons underlies the increased sleep pressure of Adar-deficient animals. Our findings provide a plausible molecular mechanism linking sleep and synaptic plasticity

Absorbing-state phase transitions: exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for the pair contact process

Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

Asymptotic behavior of the order parameter in a stochastic sandpile

We derive the first four terms in a series for the order paramater (the stationary activity density rho) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported. We reorganize the pertubation theory for the model, recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J. Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties. Since the process has a strictly conserved particle density p, the Fourier mode N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a random variable. Isolating this mode, we obtain a new effective action leading to an expansion for rho in the parameter kappa = 1/(1+4p). This requires enumeration and numerical evaluation of more than 200 000 diagrams, for which task we develop a computational algorithm. Predictions derived from this series are in good accord with simulation results. We also discuss the nature of correlation functions and one-site reduced densities in the small-kappa (large-p) limit.Comment: 18 pages, 5 figure

Absorbing-state phase transitions with extremal dynamics

Extremal dynamics represents a path to self-organized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a phase transition to an absorbing state, we define an ``extremal absorbing" process, providing the link to the associated extremal (nonabsorbing) process. Stationary properties of the latter correspond to those at the absorbing-state phase transition in the former. Studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible. In the case of the Bak-Sneppen (BS) model, the absorbing version is closely related to the "$f$-avalanche" introduced by Paczuski, Maslov and Bak [Phys. Rev. E {\bf 53}, 414 (1996)], or, in spreading simulations to the "BS branching process" also studied by these authors. The corresponding nonextremal process belongs to the directed percolation universality class. We revisit the absorbing BS model, obtaining refined estimates for the threshold and critical exponents in one dimension. We also study an extremal version of the usual contact process, using mean-field theory and simulation. The extremal condition slows the spread of activity and modifies the critical behavior radically, defining an ``extremal directed percolation" universality class of absorbing-state phase transitions. Asymmetric updating is a relevant perturbation for this class, even though it is irrelevant for the corresponding nonextremal class.Comment: 24 pages, 11 figure

Detection thresholds of macaque otolith afferents

The vestibular system is our sixth sense and is important for spatial perception functions, yet the sensory detection and discrimination properties of vestibular neurons remain relatively unexplored. Here we have used signal detection theory to measure detection thresholds of otolith afferents using 1 Hz linear accelerations delivered along three cardinal axes. Direction detection thresholds were measured by comparing mean firing rates centered on response peak and trough (full-cycle thresholds) or by comparing peak/trough firing rates with spontaneous activity (half-cycle thresholds). Thresholds were similar for utricular and saccular afferents, as well as for lateral, fore/aft, and vertical motion directions. When computed along the preferred direction, full-cycle direction detection thresholds were 7.54 and 3.01 cm/s(2) for regular and irregular firing otolith afferents, respectively. Half-cycle thresholds were approximately double, with excitatory thresholds being half as large as inhibitory thresholds. The variability in threshold among afferents was directly related to neuronal gain and did not depend on spike count variance. The exact threshold values depended on both the time window used for spike count analysis and the filtering method used to calculate mean firing rate, although differences between regular and irregular afferent thresholds were independent of analysis parameters. The fact that minimum thresholds measured in macaque otolith afferents are of the same order of magnitude as human behavioral thresholds suggests that the vestibular periphery might determine the limit on our ability to detect or discriminate small differences in head movement, with little noise added during downstream processing

Diffusive epidemic process: theory and simulation

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B -> A and A + B -> 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly, or at the same rate as B particles.Comment: 19 pages, 5 figure