Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium

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

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

The Three Founders of Botany: Rare Works from Special Collections

The Special Collections Department has many wonderful herbals in its rare book collection. In 2012, the department received Hieronymus Bock’s New Kreuter Buch. This completed former Department Head Tanya Zanish-Belcher’s dream of having an herbal written by each of the three founders of botany. The department decided to highlight these three herbals through an exhibit. The exhibit was on display from May 3 through October 15, 2013.https://lib.dr.iastate.edu/speccoll_exhibits/1002/thumbnail.jp

Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.Comment: 15 pages, 9 figures, submited to PR

Sandpiles with height restrictions

We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of particles per site), cannot exceed two. This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded. Two toppling rules are considered: in one, the particles are redistributed independently, while the other involves some cooperativity. We study the fixed-energy system (no input or loss of particles) using cluster approximations and extensive simulations, and find that it exhibits a continuous phase transition to an absorbing state at a critical value zeta_c of the particle density. The critical exponents agree with those of the unrestricted Manna sandpile.Comment: 10 pages, 14 figure

Nonuniversality in the pair contact process with diffusion

We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2 grows logarithmically with the system size. The anomalous behavior of m is traced to a violation of scaling in the order parameter probability density, which in turn reflects the presence of two distinct sectors, one purely diffusive, the other reactive, within the active phase. Studies restricted to the reactive sector yield precise estimates for exponents beta and nu_perp, and confirm finite size scaling of the order parameter. In the course of our study we determine, for the first time, the universal value m_c = 1.334 associated with the parity-conserving universality class in one dimension.Comment: 9 pages, 5 figure

Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.Comment: 4 pages, 2 figures, final versio

A solvable non-conservative model of Self-Organized Criticality

We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)] that a lack of conservation in the microscopic dynamics of an SOC-model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Broeker and Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)] and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.Comment: 4 pages in RevTeX format (2 Figures) submitted to PR

Emergent spatial correlations in stochastically evolving populations

We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a truncation approximation and supported by computer simulations, reveal emergent strategies of survival for minority agents based on selection of patterns. Minority agents exhibit defensive clustering and cooperative behavior close to phase transitions.Comment: 11 pages, 4 figures, Adobe PDF forma